Math III Review [578574]
Math III Review [578574] | |
|Student | |
|Class | |
|Date | |
|Read the following and answer the questions below: |
|The Ferris Wheel |
| |
|The Ferris Wheel |
|“School’s out!” Ryan shouted gleefully to his older sister, Claire, as he barged through the front door of his house and slung his backpack |
|on the floor. They attended the local high school, where Ryan had been a freshman and Claire a junior. Summer vacation had finally begun. |
|Ryan and Claire had even more reason to celebrate because the family vacation their parents had planned to Chicago, Illinois, was now only |
|two days away. Claire had wanted to visit Chicago ever since her friend Marco returned from a visit there; she still remembers how he ranted|
|and raved about all there was to see and do in the “Windy City.” |
|Ryan and Claire had been doing research online about the numerous sights to see and all the exciting things they should do on their visit. |
|Claire was very interested in seeing the downtown area with its prominent buildings and skyscrapers, many having been designed by important |
|architects. But both Ryan and Claire were most excited about finally getting to go to Navy Pier, an amusement park located on Lake Michigan |
|that includes a musical carousel, indoor mall, great food, and the famous Ferris wheel. |
|[pic] |
|“Hey, Ryan, did you know that the Navy Pier Ferris wheel is 150 feet high?” Claire said in amazement. “According to this information, that’s|
|as tall as a 13-story building.” |
|“You aren’t going to ride the Ferris wheel. You will be too frightened once you see how high it really is,” Ryan teased. |
|“Oh, be quiet, Ryan! I won’t be too scared, especially since we will all be together—that is, as long as you promise not to rock the |
|carriage when we get to the top. This website says that it has 40 carriages, or gondolas, that you sit in, and each one will seat up to 6 |
|people. Therefore, we will all definitely be able to fit in one.” |
|Claire went on to read that during the 7-minute ride, she would be able to see most of downtown. In fact, from the top of the Ferris wheel, |
|on a clear day, one could see 50 miles in all directions. |
|“Look! It says you can see the entire downtown area when you get to the top.” |
|“That’s great, Claire. But the only sight I want to see is my eating a Chicago-style hot dog with fries and a funnel cake.” Ryan laughed at |
|his joke, but Claire was too busy studying the website to even look away and roll her eyes at his absurd comment, which would have been her |
|normal reaction. |
|Claire loved to learn about how things were built, all the way from the inception of the idea drafted on paper to the actual building of the|
|structure, which is why she planned to study architecture in college. She found the subject fascinating and read as much as she could about |
|the Ferris wheel, wanting to know when, why, and how it came about. |
|Claire discovered that the Ferris wheel was invented by George Washington Ferris back in the 1890s. The first Ferris wheel was 25 stories |
|high and was made entirely of steel. It had a diameter of 250 feet and was supported by 2 towers, each 140 feet high. There were 36 enclosed|
|carriages that could hold slightly more than 1,400 passengers at any given time. The ride itself lasted for 10 minutes, circling 2 full |
|revolutions around; the first revolution was slower than the second so that passengers could be loaded into the carriages. |
| [pic] |
|It debuted at the World’s Columbian Exposition, which is more commonly known as the 1893 Chicago World’s Fair. George Ferris wanted the |
|attendees of the fair to marvel at his innovative invention and forget about the Eiffel Tower, which had been revealed four years earlier at|
|the Paris International Exposition. Though the wheel was popular at first, it soon lost its superstar appeal and was dismantled and |
|eventually sold as scrap metal. |
|Claire looked up from her computer. She was more excited than ever, knowing that soon she would experience all of the sites she had read |
|about. There was only one thing left to do: pack. |
| |
|1. |Read “The Ferris Wheel” and answer the question. |
| | |
| |Claire and Ryan’s carriage on the Navy Pier Ferris wheel travels 205 feet counterclockwise from the loading point before they can get a |
| |clear view of the city. How many radians, rounded to the nearest hundredth, does the carriage rotate to reach this point? |
| |/files/assess_files/a43bce28-0af2-4b4d-bdd2-2ea5b5a1b99b/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
|2. |Read “The Ferris Wheel” and answer the question. |
| | |
| |Explain how the unit circle in the coordinate plane relates to the rotation of the Navy Pier Ferris wheel. How does this comparison |
| |enable the extension of trigonometric functions to all real numbers? |
| |/files/assess_files/d78059eb-9df5-49a0-8e88-d98e0a5401b7/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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[pic]
|3. |What is the simplified form of the expression [pic] |
| |/files/assess_files/77fbc320-8cb5-4cb9-8b08-4b06546e242a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|4. |If [pic] what is the value of [pic] |
| |/files/assess_files/1d7b69f6-8b31-4da5-90f4-58a2735bc89e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|5. |Which expression is equivalent to (3x2 – 5x + 4) + (2x2 – 7)? |
| | |
| |A. |
| |5x2 – 5x – 3 |
| | |
| | |
| |B. |
| |5x2 – 5x – 11 |
| | |
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| |C. |
| |6x2 – 5x – 3 |
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| |D. |
| |5x4 – 5x – 3 |
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|6. |Which expression is equivalent to [pic] |
| |/files/assess_files/0afd9c50-762a-4c2b-a0df-3319446bff34/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| | [pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|7. |What are the zeros of the polynomial function [pic] |
| |/files/assess_files/54b906c9-7ac1-4268-ae44-88309dc1931b/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|8. |Which function has a remainder of 3 when divided by [pic] |
| |/files/assess_files/6e35fa42-fdf9-4ef9-ad88-5f618a2e97ca/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|9. |Which polynomial has exactly 2 positive x-intercepts? |
| |/files/assess_files/cb016a52-9850-4958-846b-64057a25f42c/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|10. |Which graph best represents the function [pic] |
| | |
| |/files/assess_files/dae58c63-798e-47b3-82e8-24fe37f00dca/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|11. |Let the function [pic] What are all the x-intercepts for the graph of [pic] |
| |/files/assess_files/3f9dff62-95fa-44c3-b179-b6390a8b4262/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|12. |A polynomial [pic]can be expressed so that [pic] What is the value of a? |
| |/files/assess_files/003ab456-9dbf-4162-a4e7-87da318171f4/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|13. |Part A: |
| |Prove the identity for the cube of a binomial: |
| |[pic] |
| |Part B: |
| |Explain the change in the formula when the binomial indicates addition rather than subtraction. |
| |/files/assess_files/a20b82cf-8d5d-40f1-9ba8-0cfbc1eed846/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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|14. |For this task, assume that a and b are both positive and a is greater than b. |
| |Part A. Use the diagram below to prove the polynomial identity ,[pic] when a is the length of the largest, outer square, and b is the |
| |length of the white square. Justify your reasoning. |
| | |
| |[pic] |
| | |
| |Part B. Draw a diagram that can be used to prove the polynomial identity [pic]Use the diagram to prove the polynomial identity and |
| |justify your reasoning. |
| | |
| |Part C. Use polynomial division to prove the polynomial identity [pic]Explain why polynomial division can be used to prove this |
| |polynomial identity. Can the same method be used to prove the polynomial identity [pic]Explain why or why not. |
| | |
| |Part D. There is also a geometric way of proving the difference of cubes polynomial identity. Use the three-dimensional figures below |
| |to construct an argument as to why [pic]for [pic]and [pic] |
| | |
| |[pic] |
| | |
| |Part E. Draw the figures that can help prove [pic]for [pic]and [pic]Use the figures to construct an argument as to why [pic]for the |
| |given values of a and b. |
| | |
| |Part F. Could a similar geometric method be used to prove [pic]Explain why or why not. |
| |/files/assess_files/b9251d14-4977-4d64-836f-797b389bab59/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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|15. |Which polynomial identity can be proved using the polynomial division given below? |
| | |
| |[pic] |
| |/files/assess_files/0cf2e88c-8dec-4d26-a79a-b916e47bd590/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|16. |The distributive property is used to prove which of the given identities shown below are true? |
| | |
| | [pic] |
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| | [pic] |
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| | [pic] |
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| |/files/assess_files/dd9aeeea-763c-4dc6-b63b-fde8d0818d8e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |I and II only |
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| |B. |
| |I and III only |
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| |C. |
| |II and III only |
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| |D. |
| |I, II, and III |
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|17. |Which of these expressions is equivalent to [pic] |
| |/files/assess_files/c4bf90fd-0708-4189-bdbf-c954eb409cb1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|18. |Given: [pic] If [pic] what is the value of [pic] |
| |/files/assess_files/8fd604ec-e1b9-4797-9c1e-232d8e1635e8/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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|19. |A computer repairman charges $50 to come to a home or office, plus $30 per hour of work. During one week, he visits 12 homes or |
| |offices earning $1,800. How many hours did the repairman work? |
| | |
| |A. |
| |22 hours |
| | |
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| |B. |
| |40 hours |
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| |C. |
| |42 hours |
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| |D. |
| |58 hours |
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|20. |A high school is hosting a basketball tournament. Their goal is to raise at least $1,500.00. Students can buy tickets for $3.00 and |
| |non-students for $5.00. The seating capacity for the gym is 400 people. Which could represent the number of each type of ticket sold |
| |to meet the high school’s goal and not exceed the capacity of the gym? |
| | |
| |A. |
| |100 student, 200 non-student |
| | |
| | |
| |B. |
| |125 student, 175 non-student |
| | |
| | |
| |C. |
| |150 student, 350 non-student |
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| |D. |
| |170 student, 229 non-student |
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|21. |Alma invests $300 in an account that compounds interest annually. After 2 years, the balance of the account is $329.49. To the nearest|
| |tenth of a percent, what is the rate of interest on the account? |
| |/files/assess_files/a61e4316-498a-4c2e-8164-f7e941b74a43/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |6.9% |
| | |
| | |
| |B. |
| |5.4% |
| | |
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| |C. |
| |4.8% |
| | |
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| |D. |
| |4.4% |
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|22. |Trevor is making two types of bracelets. |
| |Each Type P bracelet needs 12 inches of leather and 3 inches of string. |
| |Each Type Q bracelet needs 4 inches of leather and 18 inches of string. |
| |Trevor has 5 yards of leather and 6 yards of string. |
| |x equals the number of Type P bracelets Trevor makes. |
| |y equals the number of Type Q bracelets Trevor makes. |
| |Which system of equations models the constraints on the number of bracelets Trevor can make? |
| | |
| |A. |
| |12x + 4y ≤ 180 |
| |3x + 18y ≤ 216 |
| |x ≥ 0 |
| |y ≥ 0 |
| | |
| | |
| |B. |
| |12x + 3y ≤ 180 |
| |4x + 18y ≤ 216 |
| |x ≥ 0 |
| |y ≥ 0 |
| | |
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| |C. |
| |12x + 4y ≤ 5 |
| |3x + 18y ≤ 6 |
| |x ≥ 0 |
| |y ≥ 0 |
| | |
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| |D. |
| |12x + 3y ≤ 5 |
| |4x + 18y ≤ 6 |
| |x ≥ 0 |
| |y ≥ 0 |
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|23. |The escape velocity, v, with which a body should be projected so that it overcomes the gravitational pull of the Earth is given as |
| |[pic]where g is the acceleration due to gravity on the Earth and R is the radius of the Earth. |
| | |
| |Part A. Find the formula that can be used to calculate the acceleration due to gravity on the Earth, given the escape velocity and the|
| |radius of the Earth. |
| | |
| |Part B. Find the formula that can be used to calculate the radius of the Earth, given the acceleration due to gravity and the escape |
| |velocity. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/bcda67c8-2b79-4384-82ea-4e1648647e3a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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|24. |The sum of three consecutive integers is 51. What is the value of the largest integer? |
| | |
| |A. |
| |16 |
| | |
| | |
| |B. |
| |17 |
| | |
| | |
| |C. |
| |18 |
| | |
| | |
| |D. |
| |19 |
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|25. |Jacob stated that he solved the equation [pic]using the addition and multiplication property of equality. Which statement is true? |
| |/files/assess_files/4b0ed0c1-f9b6-491e-9485-903793b4a703/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Jacob added [pic]to both sides and multiplied both sides by [pic] |
| | |
| | |
| |B. |
| |Jacob added [pic]to both sides and multiplied both sides by [pic] |
| | |
| | |
| |C. |
| |Jacob added [pic]to both sides and multiplied both sides by [pic] |
| | |
| | |
| |D. |
| |Jacob added [pic]to both sides and multiplied both sides by [pic] |
| | |
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|26. |The equation [pic]can be used to convert temperature from degrees Fahrenheit [pic]to degrees Celsius [pic]Which of these could be the|
| |first step in solving the equation for [pic] |
| |/files/assess_files/e5dce407-b258-4193-b67a-28f6ed98f7c7/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|27. |Which value is a solution to the equation [pic] |
| |/files/assess_files/61a31ae6-4ccc-4d31-824d-4102e410632e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
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| |B. |
| |[pic] |
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| |C. |
| |[pic] |
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| |D. |
| |[pic] |
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|28. |Consider this equation. |
| | |
| |[pic] |
| |Part A. Solve the equation for x, showing all steps and both resulting values of x. |
| | |
| |Part B. Do both values of x represent solutions to the equation? Explain your answer. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/61df0de5-0f40-4356-bbba-297dea1ff2e5/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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|29. |For what value of p is the expression [pic] equivalent to the expression [pic] |
| |/files/assess_files/4f611d4c-2c05-48ce-ba7b-7d14dcfb478f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| | [pic] |
| | |
| | |
| |B. |
| | [pic] |
| | |
| | |
| |C. |
| | [pic] |
| | |
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| |D. |
| | [pic] |
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|30. |Write and solve the equations for the situations listed below. Choose the most efficient method to solve each equation and show your |
| |work. |
| | |
| |Part A. A drawing room is in the shape of a square and has an area of 144 square feet. Write an equation to determine the side, s, of |
| |the room length. |
| | |
| |Part B. There is a table with a width of 3 feet less than its length and an area of 10 square feet. Write and solve an equation to |
| |determine the length and width of the table. |
| | |
| |Part C. A sofa has a length that is 3 feet more than twice its width. If the sofa occupies an area of 18 square feet, write and solve |
| |an equation to determine the approximate dimensions of the sofa. |
| | |
| |Part D. A rectangular plot of land is to be fenced in using 100 feet of fencing. If you want the maximum area to be fenced in, |
| |what would be the dimensions of the plot of land that is fenced? |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/d5010294-5d9e-40e0-8f30-85dc07004eca/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
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|31. |Susan has a vegetable garden on a rectangular piece of property. Last year, she divided her garden into three square sections: |
| |In the south section, she planted beans. |
| |In the middle section, she planted carrots. |
| |In the north section, she planted cabbage. |
| |This year, Susan makes two changes to her garden: |
| |First, she uses some of the area of the cabbage section for a tool shed. She builds the tool shed along the north end of the property.|
| |The tool shed goes all the way across the north end of the property and measures 2 yards from front to back. After subtracting the |
| |area taken up by the tool shed, the area of Susan's three vegetable plots is 133 square yards. |
| |Second, she decides to surround her garden with a fence to keep the vegetables safe from animals. She will need to fence all four |
| |sides of the garden. The tool shed will be outside of the fence. |
| |Part A. Draw a picture to represent Susan's vegetable garden, the fence, and the tool shed. Label each part of the picture. |
| |Part B. Write an expression for the area that Susan will use this year to plant vegetables, in terms of x, the length of the short |
| |edge of her property. Set that expression equal to 133. |
| |Part C. Solve the equation from Part B using two methods: |
| |Use the method of completing the square to change the equation into the form [pic]where p and q are real numbers. Solve for x. Show |
| |your work. |
| |Use the quadratic formula. Solve for x. Show your work. |
| |What is the length of the short side of the garden? |
| |Part D. Determine how many yards of fencing Susan will need. |
| |/files/assess_files/abc5a32f-bb3b-4d5c-af7d-0801885b8af0/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|32. |If quadratic equation [pic]is rewritten in the form of [pic]what are the values of p and q? |
| |/files/assess_files/606a9c9c-ac36-4f33-a2e0-c5343863a6c1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|33. |Which choice is an ordered pair that, for every real number k, represents a point that lies on the graph of 30x – 5y = 10? |
| | |
| |A. |
| |(k + 2, 6k + 10) |
| | |
| | |
| |B. |
| |(k + 4, 6k + 20) |
| | |
| | |
| |C. |
| |(3k, 18k + 2) |
| | |
| | |
| |D. |
| |(5k, 30k + 2) |
| | |
| | |
| | |
|34. |If a point [pic]is on the graph of the equation [pic]and also on the graph of [pic]what is the value of b? |
| |/files/assess_files/6b102119-68dd-44b0-8e51-69f9c394c026/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|35. |Who Will Catch Up When? |
| | |
| |Three friends are packing gift boxes to be handed out at the high school dance. Each box has ten sections to be filled. They |
| |each pack the boxes at different rates. |
| | |
| |Part A. The tables below show Kelsey’s and Andrew’s progress. The variable t stands for the time that has passed since their starting |
| |time at 10:00 a.m. [pic] Andrew had already packed 4 boxes the day before. |
| | |
| |Fill in the tables, assuming that each person packs the boxes at a constant rate. |
| | |
| |[pic] |
| | |
| |Part B. Let the number of boxes Kelsey packs be represented by k(t) and the number Andrew packs by a(t). Using the information from |
| |the tables, write the functions for k(t) and a(t). Interpret each function in terms of the context it represents. |
| | |
| |Kelsey: |
| | |
| |Andrew: |
| | |
| |In terms of k(t) and a(t), what equation can be solved to find the time at which both Kelsey and Andrew have packed the same number of|
| |boxes? Explain. |
| |Part C. Graph and label the functions k(t) and a(t) on the same coordinate grid below. |
| | |
| |[pic] |
| | |
| |What is the solution of the equation that was written in part B that could be used to find the time at which Kelsey and Andrew have |
| |packed the same number of boxes? Explain how you can find the solution on the graph and then verify your answer by solving the |
| |equation algebraically. |
| | |
| |Part D. The third friend, James, starts out packing the boxes very quickly but then slows down. His approximate progress can be |
| |modeled by the square root equation below, where t stands for the time that has passed since their starting time at 10:00 a.m. |
| | |
| |[pic] |
| | |
| |Fill in the table to show James’s progress. Round the values to the nearest 0.1 box. |
| |[pic] |
| | |
| | |
| |Part E. Sketch a graph of the function j(t) on the coordinate grid above, where k(t) and a(t) are already graphed. |
| |Write the equation that could be used to find the time at which Kelsey and James have packed the same number of boxes. Approximate the|
| |solution or solutions to this equation using the graph. |
| |Write the equation that could be used to find the time at which Andrew and James have packed the same number of boxes. Approximate the|
| |solution or solutions to this equation using the graph. |
| |/files/assess_files/2c03f496-e56c-40bf-a036-f3239c64c802/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|36. |If f(x) = 5(2)x and g(x) = –2x + 46, for what positive value of x does f(x) = g(x)? |
| | |
| |A. |
| |3 |
| | |
| | |
| |B. |
| |5 |
| | |
| | |
| |C. |
| |40 |
| | |
| | |
| |D. |
| |46 |
| | |
| | |
| | |
|37. |Two functions are shown below. |
| |f(x) = 2x + 2 |
| |g(x) = –2x + 6 |
| | |
| |For what value of x does f(x) = g(x)? |
| | |
| |A. |
| |1 |
| | |
| | |
| |B. |
| |2 |
| | |
| | |
| |C. |
| |4 |
| | |
| | |
| |D. |
| |6 |
| | |
| | |
| | |
|38. |What is the maximum number of intersections an exponential function can have with a linear function? |
| | |
| |A. |
| |0 |
| | |
| | |
| |B. |
| |1 |
| | |
| | |
| |C. |
| |2 |
| | |
| | |
| |D. |
| |3 |
| | |
| | |
| | |
|39. |Let [pic]Find all real values of x such that [pic] |
| |/files/assess_files/f5a8abd3-784e-429a-a737-d380010fac6c/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|40. |Which expression is equivalent to [pic]where k is an even number? |
| |/files/assess_files/f7fd2ee0-1adf-401b-9feb-a09639f95c16/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|41. |The expression for the amount of money earned on a savings account compounded quarterly is given by the expression [pic]where |
| |[pic]represents the principal and [pic]is the time in years since the principal was invested. Which expression is the equivalent form |
| |of the given expression and shows the amount earned when the interest is compounded half-yearly? |
| |/files/assess_files/fa9a7def-071e-40af-b469-21314ee2ac64/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|42. |Jesse and Shaun are comparing investment products to see who has the better investment rate for their money. |
| |The interest on the money Jesse invested in Product X is compounded annually. The value of the investment after n years can be found |
| |using the formula [pic] where [pic] is the intial amount of money invested. |
| |The interest on the money Shaun invested in Product Y is compounded monthly. The value of the investment after m months can be found |
| |using the formula [pic] where [pic] is the intial amount of money invested. |
| |Part A. Rewrite Jesse's formula to find the approximate equivalent monthly interest rate. Show your work. |
| |Part B. Which product offers the best return on an investment? Use the interest rates to justify your answer. |
| |/files/assess_files/1417ab43-7cfa-4bce-8dab-92cec9d3f07e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|43. |An athlete is training to run a marathon. She plans to run 2 miles the first week. She increases the distance by 8% each |
| |week. Which function models how far she will run in the nth week? |
| |/files/assess_files/66e08ced-a2ca-4c95-ba22-372e254ac258/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|44. |Cindy invested $2,800. The function V(t) = 2,800(1.025)t models the value of Cindy’s investment after y months. The function |
| |S(t) = 10t models the amount of money that Cindy has saved in a safe at her house after t months. Which function C(t) models the |
| |combined value of the investment and money in the safe? |
| | |
| |A. |
| |C(t) =2,810(1.025)t |
| | |
| | |
| |B. |
| |C(t) = 2,800(1.025)11t |
| | |
| | |
| |C. |
| |C(t) =(2,800 + 10t)(1.025)t |
| | |
| | |
| |D. |
| |C(t) =2,800(1.025)t + 10t |
| | |
| | |
| | |
|45. |A plane is at a height of 30,000 feet above the ground when it begins to descend at a rate of 1,500 feet per minute. If [pic] and |
| |[pic]write a recursive formula that can be used to determine the height of the plane above the ground after n number of minutes. |
| |/files/assess_files/a6fa714b-b374-4756-806f-972671af4dcf/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|46. |The ingredients for a particular kind of European chocolates cost $12 per box. The foil wrappers cost $0.05 per piece of chocolate. |
| |The box has x pieces of chocolates in it. Which function represents the total cost per piece of chocolate? |
| |/files/assess_files/d0e45a42-920f-456a-9de2-2dc59a661c25/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|47. |Which recursive formula models the sequence shown below? |
| |–3, 1, 5, 9, . . . |
| | |
| |A. |
| |NEXT = NOW + 4 |
| | |
| | |
| |B. |
| |NEXT = NOW – 4 |
| | |
| | |
| |C. |
| |NEXT = 4 • NOW |
| | |
| | |
| |D. |
| |NEXT = 4 • NOW + 7 |
| | |
| | |
| | |
|48. |At the beginning of the school year, Jason’s dad gave him $50 to put into his lunch account. Jason spends $2 each day on his lunch. |
| |Which recursive formula models the amount of money that Jason has in his account? |
| | |
| |A. |
| |NEXT = NOW + 2 |
| | |
| | |
| |B. |
| |NEXT = NOW – 2 |
| | |
| | |
| |C. |
| |NEXT = 50 – 2 • NOW |
| | |
| | |
| |D. |
| |NEXT = 52 – 2 • NOW |
| | |
| | |
| | |
|49. |If [pic]and [pic] which equation represents the explicit formula for the sequence? |
| |/files/assess_files/15174b9d-4d12-4375-8764-241ec0a30eec/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|50. |The first term of an arithmetic sequence is 3. The nth term of the sequence is found by using the formula [pic]Which other formula |
| |could be used to find the nth term? |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|51. |Which transformation occurs to the graph of f(x) = x to produce the graph of g(x) = x + 2? |
| | |
| |A. |
| |down 2 units |
| | |
| | |
| |B. |
| |up 2 units |
| | |
| | |
| |C. |
| |left 2 units |
| | |
| | |
| |D. |
| |right 2 units |
| | |
| | |
| | |
|52. |If the graph of [pic] is translated 2 units right and 4 units down, which of these functions describes the transformed graph? |
| |/files/assess_files/9a7100e0-fd58-4daa-910b-57660ed7773a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|53. |The function f(x) = 6x was replaced with f(x) + k resulting in the function shown in the table below. |
| |x |
| |y |
| | |
| |0 |
| |10 |
| | |
| |1 |
| |15 |
| | |
| |2 |
| |45 |
| | |
| |3 |
| |225 |
| | |
| | |
| |What is the value of k? |
| | |
| |A. |
| |7 |
| | |
| | |
| |B. |
| |8 |
| | |
| | |
| |C. |
| |9 |
| | |
| | |
| |D. |
| |10 |
| | |
| | |
| | |
|54. |The function f(x) = x – 2 was translated down 6 units, resulting in the function g(x). Which function represents g(x)? |
| | |
| |A. |
| |g(x) = 6x – 2 |
| | |
| | |
| |B. |
| |g(x) = 2x – 8 |
| | |
| | |
| |C. |
| |g(x) = x – 8 |
| | |
| | |
| |D. |
| |g(x) = x + 4 |
| | |
| | |
| | |
|55. |A function [pic]is defined as [pic]where [pic] |
| | |
| |Part A. Write a function [pic]that represents the inverse of the function [pic] |
| | |
| |Part B. How do the domain and range of [pic] compare with the domain and range of the inverse function [pic] |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/68958dda-80e4-448a-8ec6-f990ee7bc08d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|56. |The table below shows the attempts made by four students to find the inverse of the function [pic] |
| | |
| |[pic] |
| | |
| |Which student correctly found the inverse of the function? |
| |/files/assess_files/46793a49-ef5b-447e-b39a-37e2c6e23650/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Daniel |
| | |
| | |
| |B. |
| |Jean |
| | |
| | |
| |C. |
| |Scott |
| | |
| | |
| |D. |
| |Sophia |
| | |
| | |
| | |
|57. |The function h(t) = 200 – 16t represents the height of a ball dropped from 200 feet. How far had the ball traveled after falling for |
| |11 seconds? |
| | |
| |A. |
| |16 feet |
| | |
| | |
| |B. |
| |24 feet |
| | |
| | |
| |C. |
| |176 feet |
| | |
| | |
| |D. |
| |200 feet |
| | |
| | |
| | |
|58. |The function f(t)=12,000(1.075)t models the value of an investment t years from now. What is the meaning of the value of f(5)? |
| | |
| |A. |
| |the value of the investment 5 years ago |
| | |
| | |
| |B. |
| |the value of the investment in 5 years |
| | |
| | |
| |C. |
| |the initial value of the investment |
| | |
| | |
| |D. |
| |the interest rate the investment earns |
| | |
| | |
| | |
|59. |The table below shows the cost for a toy company to produce different amounts of toys. |
| | Toys Produced |
| | Cost |
| | |
| | 1,000 |
| | $122,000 |
| | |
| | 3,000 |
| | $26,000 |
| | |
| | 5,000 |
| | $10,000 |
| | |
| | 7,000 |
| | $74,000 |
| | |
| | |
| |Assuming a quadratic relationship, about how many toys should the company produce to minimize costs? |
| | |
| |A. |
| |1,000 |
| | |
| | |
| |B. |
| |4,000 |
| | |
| | |
| |C. |
| |5,000 |
| | |
| | |
| |D. |
| |6,000 |
| | |
| | |
| | |
|60. |The table below shows the distance Chris is located from his school at different times. |
| | |
| | Time |
| | (minutes) |
| | Distance |
| | (miles) |
| | |
| | 0 |
| | 20 |
| | |
| | 3 |
| | 18 |
| | |
| | 6 |
| | 16 |
| | |
| | 9 |
| | 14 |
| | |
| | 12 |
| | 12 |
| | |
| | 15 |
| | 10 |
| | |
| | |
| |Assuming a linear relationship, how long will it take Chris to get to school? |
| | |
| |A. |
| |20 minutes |
| | |
| | |
| |B. |
| |24 minutes |
| | |
| | |
| |C. |
| |27 minutes |
| | |
| | |
| |D. |
| |30 minutes |
| | |
| | |
| | |
|61. |Jimmy threw a baseball in the air from the roof of his house. The path followed by the baseball can be modeled by the function |
| |[pic]where t represents the time in seconds after the ball was thrown and [pic] represents its height, in feet, from the ground. |
| | |
| |Part A. How high is the roof from the ground? How many seconds did it take for the ball to hit the ground after it was thrown off the |
| |roof? |
| | |
| |Part B. Jimmy wanted to throw the ball at a maximum height of 120 feet. Did Jimmy's baseball reach this height after it was thrown? |
| |Explain your answer. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/b6307745-b9ba-451d-8985-ac79361db1e1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|62. |Which function has the following features? |
| |symmetry over the y-axis |
| |increasing for all [pic] |
| |y-intercept of 0 |
| |/files/assess_files/dcdef885-4834-4326-8a02-406ba7f4ff69/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|63. |Part A. Emma’s cell phone plan charges $0.20 for each text message. The function [pic]represents the cost of the total number of text |
| |messages Emma sends and receives. If x represents the total number of messages, what is the domain of the function [pic] |
| | |
| |Part B. How will the domain of the function [pic]change if Emma puts a limit of $25 on her monthly texting bill? |
| | |
| |Part C. The dollar amount of Emma’s prepaid call balance decreases by r for each second of a call. The call balance left is modeled by|
| |the function [pic]where b is the initial balance in dollars and s is the number of seconds. What is the domain of the function [pic] |
| | |
| |Part D. Emma changes her call plan from prepaid to pay-as-you-go. The function [pic]represents the total bill she pays after a month, |
| |where A is the fixed monthly fees and [pic]is the amount in dollars charged for each second of calls she made. What is the reasonable |
| |domain of the function [pic]in terms of the given context? |
| |/files/assess_files/aababb6f-1400-41f5-bd46-7fe4d8e1d191/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|64. |The table below shows the population of a state during different years. |
| | Year (x) |
| | Population (y) |
| | |
| | 2004 |
| | 8,500,000 |
| | |
| | 2006 |
| | 8,900,000 |
| | |
| | 2007 |
| | 9,000,000 |
| | |
| | 2008 |
| | 9,200,000 |
| | |
| | 2010 |
| | 9,500,000 |
| | |
| | |
| |What is the approximaterelative domain of the line of best fit for the data? |
| | |
| |A. |
| |x > 0 |
| | |
| | |
| |B. |
| |x > 1650 |
| | |
| | |
| |C. |
| |x > 1952 |
| | |
| | |
| |D. |
| |x > 2004 |
| | |
| | |
| | |
|65. |Function [pic]has a minimum value of [pic]and a maximum value of 8. Which graph most likely represents function [pic] |
| |/files/assess_files/f7b43a07-1fa0-4fa1-850f-efa2a950e907/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|66. |Which graph represents the function [pic] |
| |/files/assess_files/b67b37b9-88f6-4bc3-a9dc-4b6c50a8d53e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|67. |Which is the graph of 3x – 2y = 4? |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|68. |Graphing |
| |Part A. Consider the functions [pic] and [pic] What are the domain and range of each function? |
| | |
| |Part B. What are the x-intercepts and y-intercepts (if any) on [pic]On [pic] |
| | |
| |Part C. Where are the functions increasing or decreasing? |
| | |
| |Part D. What are the maximum points (if any) on [pic]and [pic] |
| | |
| | |
| |Part E. Sketch graphs of the functions [pic]and [pic] |
| | |
| |[pic] [pic] |
| | |
| |Part F. How are the graphs of the two functions in part A related? How do you see these relationships in the equations? |
| | |
| |Part G. Sketch graphs of the functions [pic]and [pic] Explain how you determined the coordinates of key points. |
| | |
| |[pic] [pic] [pic] |
| | |
| |Part H. How are the graphs of the three functions in part G related? How do you see these relationships in the equations? |
| |/files/assess_files/6b562523-ee29-4abf-b019-59d8e2e6fa95/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|69. |The height in feet, [pic] a kangaroo reaches [pic]seconds after it has jumped in the air is modeled by the quadratic function |
| |[pic]Which equation shows the correctly factored version of the function and the number of seconds it takes for the kangaroo to return|
| |to the ground? |
| |/files/assess_files/c741d23a-ab57-447e-9c59-8ae7ffd0791f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic]8 seconds |
| | |
| | |
| |B. |
| |[pic]1.5 seconds |
| | |
| | |
| |C. |
| |[pic]8 seconds |
| | |
| | |
| |D. |
| |[pic]1.5 seconds |
| | |
| | |
| | |
|70. |The function f(x) = 19,000(0.89)x models the value of a boat x years after its purchase. Which statement correctly describes the value|
| |of the boat? |
| | |
| |A. |
| |The value is decreasing by 11% per year. |
| | |
| | |
| |B. |
| |The value is decreasing by 89% per year. |
| | |
| | |
| |C. |
| |The value is increasing by 11% per year. |
| | |
| | |
| |D. |
| |The value is increasing by 89% per year. |
| | |
| | |
| | |
|71. |Genevieve deposited $400 into her bank account. The equation [pic] can be used to calculate the value of her money after t years. What|
| |is the annual interest rate she is earning on her deposit? |
| |/files/assess_files/200ddc68-bca2-42da-afa9-b927e68d59e9/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| | 0.07% |
| | |
| | |
| |B. |
| | 1.07% |
| | |
| | |
| |C. |
| | 7% |
| | |
| | |
| |D. |
| |107% |
| | |
| | |
| | |
|72. |The function f(x) = 2,500(0.97)x models the value of an investment after x months. Which statement is true about the value of the |
| |investment? |
| | |
| |A. |
| |The value of the investment increases by 3% each month. |
| | |
| | |
| |B. |
| |The value of the investment decreases by 3% each month. |
| | |
| | |
| |C. |
| |The value of the investment increases by 97% each month. |
| | |
| | |
| |D. |
| |The value of the investment decreases by 97% each month. |
| | |
| | |
| | |
|73. |Joseph compared the function f(x) = 3x2 + 2x – 1 to the quadratic function that fits the values shown in the table below. |
| | x |
| | g(x) |
| | |
| |0 |
| |–1 |
| | |
| |1 |
| |8 |
| | |
| |2 |
| |23 |
| | |
| |3 |
| |44 |
| | |
| |4 |
| |71 |
| | |
| | |
| |Which statement is true about the two functions? |
| | |
| |A. |
| |The functions have the same y-intercepts. |
| | |
| | |
| |B. |
| |The functions have the same x-intercepts. |
| | |
| | |
| |C. |
| |The functions have the same vertex. |
| | |
| | |
| |D. |
| |The functions have the same axis of symmetry. |
| | |
| | |
| | |
|74. |Austin and Janda threw grappling hooks into the air. The function [pic]gives the height, in feet, of Austin’s hook x seconds after he |
| |threw it. The graph below shows the height, in feet, of Janda’s hook x seconds after she threw it. |
| | |
| |[pic] |
| | |
| |If both of them threw the grappling hooks at the same time, which of these statements is true? |
| |/files/assess_files/6394e985-bdd0-4196-b9a2-a19c5f6fc564/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Austin’s hook hit the ground first. |
| | |
| | |
| |B. |
| |Austin’s hook reached its maximum height first. |
| | |
| | |
| |C. |
| |Austin’s hook reached a greater maximum height. |
| | |
| | |
| |D. |
| |Austin threw the hook from a greater initial height. |
| | |
| | |
| | |
|75. |Two functions are shown below. |
| |f(x) = 1.02x + 100 |
| |g(x) = 50(1.02)x |
| | |
| |What is the smallest positive integer in which the value of g(x) exceeds the value of f(x)? |
| | |
| |A. |
| |60 |
| | |
| | |
| |B. |
| |59 |
| | |
| | |
| |C. |
| |55 |
| | |
| | |
| |D. |
| |50 |
| | |
| | |
| | |
|76. |Ronald invests $1000 at a simple interest rate of 10% for 4 years. His best friend Rudy invests the same amount of money, but earns |
| |10% interest compounded annually for 4 years. |
| |Part A |
| |Create a table to show the amount of Rudy's investment after each year. Calculate the amount of Ronald's investment after 4 years. |
| |Part B |
| |Based on the amounts they made, which friend made the better investment? Explain. |
| |/files/assess_files/1bfb8546-48fd-4b2e-94af-7f03f254647c/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|77. |Clara’s and Michelle’s parents started saving for college in 1998. |
| |Clara’s college fund can be modeled by the function f(x) = 500x + 2,500, where x is the number of years since 1998. |
| |Michelle’s college fund can be modeled by the function g(x) = 2,500(1.1)x, where x is the number of years since 1998. |
| |About what year will Michelle’s college fund first exceed Clara’s college fund? |
| | |
| |A. |
| |2013 |
| | |
| | |
| |B. |
| |2015 |
| | |
| | |
| |C. |
| |2017 |
| | |
| | |
| |D. |
| |2019 |
| | |
| | |
| | |
|78. |Which table shows the function that increases at the fastest rate? |
| |/files/assess_files/ac29a5e7-2659-4e6f-aa00-e7e0af2ddd9f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|79. |For what value of x is it true that [pic] |
| |/files/assess_files/ed6470ff-61a2-416a-a0f2-ccb54ff083f1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|80. |The bacteria in a certain Petri dish grow at a rate modeled by [pic]where [pic] represents the number of bacteria in the dish and t |
| |represents the time in minutes since the introduction of the bacteria. Which equation can be used to determine how many minutes will |
| |pass before there are 68 bacteria in the dish, if the dish started with a single bacterium? |
| |/files/assess_files/45b79e8b-b68c-49e2-be50-33d4ed9979ee/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic]minutes |
| | |
| | |
| |B. |
| |[pic]minutes |
| | |
| | |
| |C. |
| |[pic]minutes |
| | |
| | |
| |D. |
| |[pic]minutes |
| | |
| | |
| | |
|81. |What is the solution to the equation [pic] |
| |/files/assess_files/9d003f18-f80a-4d34-aa4f-639583dd185f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|82. |What is the solution to the equation [pic] |
| |/files/assess_files/6c8bbd8b-65be-477e-b1c4-aa3c98822034/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|83. |Circle P, shown below, has a radius of 1 unit. |
| | |
| |[pic] |
| | |
| |Which of these equations correctly identifies the relationship between angle QPR, in radians, and the length, a, of arc QR? |
| |/files/assess_files/85f3b81a-8d24-4610-af9d-8ece5f351ee1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|84. |Let [pic] and [pic] be two values such that [pic][pic][pic]but [pic] |
| | |
| |Express [pic]in terms of [pic]. |
| | |
| |/files/assess_files/8af4ed90-5157-4816-8f3c-1234f0a29b40/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|85. |In the right triangle pictured below, the measure of angle A, in radians, is [pic]The side adjacent to angle A measures 6 cm and the |
| |side opposite measures 5 cm. |
| |[pic] |
| |Which of the following values is closest to [pic] |
| |/files/assess_files/58f23906-a934-4257-ab34-f83256a9ca5b/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|86. |Toni claims that the cosine of [pic] is equal to the cosine of [pic]. |
| |Which equation could be used to justify Toni's claim? |
| | |
| |/files/assess_files/45d4f13d-d4fb-4228-ae71-12c5594a83a2/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic]for any integer k |
| | |
| | |
| |D. |
| | [pic] for any integer k |
| | |
| | |
| | |
|87. |Which function best represents a sine curve that repeats every 12 units and has a maximum of 42 and a minimum of 4? |
| |/files/assess_files/c96f4e22-b7eb-4bb0-9309-414753bf65cb/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|88. |George’s height above the ground as he rides a Ferris wheel ranges from 4 meters to 30 meters. If it takes 200 seconds to complete one|
| |revolution, which sine function represents his height, [pic][pic]from the ground as a function of time, [pic] |
| |/files/assess_files/e854032f-d88d-4b5a-b1c0-8fafbae9bfbb/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic][pic] |
| | |
| | |
| |B. |
| |[pic][pic] |
| | |
| | |
| |C. |
| |[pic][pic] |
| | |
| | |
| |D. |
| |[pic][pic] |
| | |
| | |
| | |
|89. |A Ferris wheel with a diameter of 40 feet completes 2 revolutions in one minute. The center of the wheel is 30 feet above the ground. |
| |If a person taking a ride starts at the lowest point, which trigonometric function can be used to model the rider’s height h(t) above |
| |the ground after t seconds? (Consider the height of the rider negligible). |
| |/files/assess_files/e021c663-1cbc-4416-9106-a23d3016fdd8/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|90. |Nan draws the swinging end of a pendulum 10 centimeters to the left of its rest position and releases it to swing. She wants to model |
| |the horizontal displacement of the pendulum, d, as a function of time, t, where [pic]at the point of release. Which function family is|
| |best for Nan to use and why? |
| |/files/assess_files/c034481d-b85c-427a-be7f-9e5d0d14d8da/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic], because [pic] |
| | |
| | |
| |B. |
| |[pic], because [pic]is an extremum |
| | |
| | |
| |C. |
| |[pic], because [pic] |
| | |
| | |
| |D. |
| |[pic], because [pic]is an extremum |
| | |
| | |
| | |
|91. |What is the value of [pic]if [pic]and [pic]Write your answer in simplest form. |
| |/files/assess_files/068dd808-d66b-4f2a-824f-914ef0ab93ef/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|92. |Point P is a point on the unit circle. |
| |[pic] |
| | |
| |Part A. Use the Pythagorean theorem and the diagram above to prove the trigonometric identity [pic] |
| | |
| |Part B. If [pic] use the identity to find [pic] |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/611ad65e-db41-4317-9865-ca5f656660ef/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|93. |Based on the diagram below, how can the Pythagorean identity [pic] be shown? |
| | |
| |[pic] |
| |/files/assess_files/5a1f2201-52a4-468b-bf23-4736191844b9/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|94. |Let p represent a point on the unit circle, in the second quadrant. The line including p and the origin has a slope of -2. What is the|
| |x-value of p? |
| |/files/assess_files/b268a6cb-5082-4a7e-a975-12ffc3dc6401/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| | [pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|95. |Similarity in Circles |
| |Geometric similarity is an extremely useful concept. Similar figures are alike except for their size; their corresponding angles are |
| |congruent, and their corresponding parts are proportional. On the coordinate plane, one figure can be mapped to the other by a series |
| |of transformations. |
| | |
| |Part A. Consider these two equilateral triangles. Are they similar? How do you know? Write a proportion showing the relationship of |
| |their sides. |
| | |
| |[pic] |
| | |
| |Part B. Are any two squares similar? Tell how you know. |
| | |
| |Remember that the measure of each angle of a regular polygon is [pic]where n is the number of sides. Can you make a general statement |
| |about the similarity of two regular polygons (n-gons) with the same number of sides? Explain your answer. |
| | |
| |Part C. As the number of sides of a regular polygon increases, what figure does it begin to look like? |
| | |
| |[pic] [pic] [pic] [pic] [pic] [pic] [pic] |
| | |
| |What is a reasonable conclusion about the similarity of figures of this kind of different sizes? |
| | |
| |Part D. Consider these two circles on the coordinate plane. What is the radius of circle A? Of circle B? Write the ratio. Write the |
| |ratios for the diameters and circumferences of the two circles. Are the circles proportional? |
| | |
| |[pic] |
| | |
| | |
| |[pic] |
| | |
| | |
| |Part E. You can also prove that two figures are similar by showing that a series of transformations will map one figure to the other. |
| |What is the equation for circle A? |
| | |
| |Part F. What series of transformations will map circle A to circle B? Write the equation for circle B. Are these two circles similar? |
| | |
| |Part G. Any two circles can be centered at the origin through translations. If both circles are centered at the origin, what one |
| |transformation will map one to the other, proving their similarity? If the equation of one circle is [pic]and the radius of the other |
| |circle is f times the radius of the first, what is the equation of the second circle? |
| | |
| |What is the equation of the second circle if the center is NOT [pic]In either case, no matter what the size or position of the |
| |circles, are all circles similar? |
| |/files/assess_files/68fe0888-c4e3-431b-9f9b-0f00c7f776d3/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|96. |Which statement best explains why all circles are similar? |
| |/files/assess_files/5df69686-3da1-466d-ae10-8efa43cc77df/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |All circles have exactly one center point. |
| | |
| | |
| |B. |
| |The diameter of all circles is twice the length of the radius. |
| | |
| | |
| |C. |
| |All circles can be mapped onto any other circle using only translations. |
| | |
| | |
| |D. |
| |All circles can be mapped onto any other circle using a translation and dilation. |
| | |
| | |
| | |
|97. |Which property of quadrilaterals inscribed in a circle can be used to find the value of x in the figure below? |
| | |
| |[pic] |
| |/files/assess_files/e80efcf3-a568-4956-87d5-a46998d49385/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |The difference between an opposite pair of angles is 180°. |
| | |
| | |
| |B. |
| |The difference between an opposite pair of angles is 0°. |
| | |
| | |
| |C. |
| |The sum of an opposite pair of angles is 180°. |
| | |
| | |
| |D. |
| |The sum of an opposite pair of angles is 360°. |
| | |
| | |
| | |
|98. |In the figure given below, [pic]is a diameter of the circle with center O. |
| | |
| |[pic] |
| | |
| |If [pic]what is [pic] |
| |/files/assess_files/e42de44b-cd2a-408d-9904-7109345ebe3f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |60° |
| | |
| | |
| |B. |
| |70° |
| | |
| | |
| |C. |
| |80° |
| | |
| | |
| |D. |
| |110° |
| | |
| | |
| | |
|99. |In the figure below, [pic]are radii of the circle with center O. |
| |[pic] |
| | |
| |Given that [pic]what is [pic] |
| |/files/assess_files/20c75473-c1e9-4c8f-9121-8b9189ab4c49/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |20° |
| | |
| | |
| |B. |
| |35° |
| | |
| | |
| |C. |
| |40° |
| | |
| | |
| |D. |
| |80° |
| | |
| | |
| | |
|100. |In the figure shown below, [pic]and [pic]are radii of the circle with center [pic]If [pic] what is [pic] |
| | |
| |[pic] |
| |/files/assess_files/23d8912c-dbb2-4420-892c-6a0d9f47172a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |56° |
| | |
| | |
| |B. |
| |62° |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |124° |
| | |
| | |
| | |
|101. |Points A, B, C, and D lie on circle E as shown in the figure below. |
| | |
| |[pic] |
| |Which statement must be true about the figure? |
| |/files/assess_files/0d2f12db-c61f-4950-9234-31ba602357cb/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|102. |The figure shown below is a circle. |
| | |
| |[pic] |
| | |
| |Which statement must be true? |
| |/files/assess_files/9d89b00a-94a7-4711-bb63-e5beed3c24a4/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|103. |Amy is designing a piece of jewelry to sell in her craft store. She begins with the triangular piece of silver, as shown below. |
| | |
| |[pic] |
| | |
| |Part A. Amy wants to add a circular piece of gold that will be inscribed inside the triangular piece of silver. Use a compass and |
| |straightedge to show how she can add the circular piece to the triangle above. Explain the steps you used to perform the |
| |construction. |
| | |
| |Part B. She needs to know the radius of the inscribed circle so that she can calculate the circumference and area of the circular |
| |gold piece she needs to make for the jewelry. Given that the silver triangle is a right triangle with side lengths a, b, and c, find|
| |the equation Amy can use to determine the radius of the circle, r. Explain your answer and draw a diagram or use your construction |
| |in part A to support your reasoning. |
| | |
| |Part C. Amy then decides to inscribe another similar silver triangle inside a circular piece of copper so that each vertex of the |
| |triangle touches the edge of the copper circle. Use a compass and straightedge to construct her design below. Explain the steps you |
| |used to perform the construction. |
| | |
| |[pic] |
| | |
| |Part D. A couple of months ago, Amy designed a piece of jewelry with a gold quadrilateral inscribed on a circular piece of silver. |
| |She found the sketch of her design in her desk drawer, as shown below. |
| | |
| |[pic] |
| | |
| |Now Amy wants to produce an identical piece of jewelry but needs to know the exact angle measures for the gold quadrilateral. What |
| |geometric property about quadrilaterals can Amy use to find the measures of the angles of her jewelry design? Use a paragraph proof |
| |to justify your response. |
| | |
| |Part E. What are the measures of the three missing angles in Amy’s sketch of the piece of jewelry in part D? Explain how you know. |
| |/files/assess_files/f38810e5-a0b4-41e3-8752-0f341bc52e95/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|104. |Quadrilateral [pic]is inscribed in circle E. Angle [pic]is a central angle, and angle [pic] is an inscribed angle. |
| | |
| |[pic] |
| | |
| |Which statement about the angles in this figure must be true? |
| |/files/assess_files/8f8ce4dd-178a-47a9-a2f4-ec56f616db57/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|105. |In the given image, [pic]and the angles are measured in radians. Which of these must be true? |
| | |
| |[pic] |
| |/files/assess_files/f941cd23-3203-4f6d-8d88-140f7087043e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|106. |Part A |
| |Using the circle below, set up a proportion to determine the length, m, of arc HI. Use [pic]for the central angle of a complete |
| |circle and [pic]for the circumference of the circle where r is the radius. Solve for m. |
| |[pic] |
| | |
| |Part B |
| |The circle below has a central angle which measures 2.1 radians and a diameter of 3 inches. Find the length, in inches, of arc HJ. |
| |[pic] |
| |/files/assess_files/92bec440-776c-4eac-94df-f74331c73d97/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|107. |In circle C below, [pic]is measured in radians. |
| | |
| |[pic] |
| | |
| |Which expression can be used to find the area of the shaded sector? |
| |/files/assess_files/791ecae4-7fd4-4f74-accf-28df88080857/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|108. |Ashley is studying circle O, shown below. |
| |[pic] |
| | |
| |She wrote the steps below. |
| | |
| |[pic] |
| | |
| |What did Ashley derive? |
| |/files/assess_files/93613958-b4bd-44ce-a4aa-11b2a8d881e3/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |that all circles are similar |
| | |
| | |
| |B. |
| |the formula for arc length |
| | |
| | |
| |C. |
| |the formula for the area of a sector of a circle |
| | |
| | |
| |D. |
| |that a central angle has the same measure as the arc it subtends |
| | |
| | |
| | |
|109. |Which of these correctly defines a ray? |
| |/files/assess_files/247f1b00-e7f0-4774-8f93-9592363c2d4f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |a part of a line with exactly two end points |
| | |
| | |
| |B. |
| |a straight path that extends endlessly in both directions |
| | |
| | |
| |C. |
| |a circular path such that every point on the path is equidistant from its center |
| | |
| | |
| |D. |
| |a part of a line that begins at a particular point and extends endlessly in one direction |
| | |
| | |
| | |
|110. |The distance between points A and P is the same as the distance between points B and P. If P does not lie on a line joining the |
| |points A and B, which of these conclusions are true? |
| | |
| | I. All the points on [pic]will be equidistant from point P. |
| | |
| | II. The angles [pic]and [pic]are congruent. |
| | |
| | III. [pic] and [pic] form [pic] |
| | |
| | IV. [pic] and [pic] form arc APB. |
| |/files/assess_files/e4084220-1d0c-4e5b-a71d-ae3087bba8dc/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |I and III |
| | |
| | |
| |B. |
| |II and IV |
| | |
| | |
| |C. |
| |II and III |
| | |
| | |
| |D. |
| |I and IV |
| | |
| | |
| | |
|111. |What is a definition of a line that is parallel to [pic] |
| | |
| |A. |
| |a coplanar line that bisects [pic] |
| | |
| | |
| |B. |
| |a coplanar line that does not intersect [pic] |
| | |
| | |
| |C. |
| |a coplanar line that intersects [pic]at a right angle |
| | |
| | |
| |D. |
| |a coplanar line that intersects [pic]but not at a right angle |
| | |
| | |
| | |
|112. |Chris draws an image of two lines that lie in the same plane and are equidistant at all points. Which of these describes the image |
| |drawn by Chris? |
| |/files/assess_files/cc27fbd3-2275-4ecc-a976-a42988207b41/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |an angle |
| | |
| | |
| |B. |
| |parallel lines |
| | |
| | |
| |C. |
| |intersecting lines |
| | |
| | |
| |D. |
| |perpendicular lines |
| | |
| | |
| | |
|113. |A proof of the Alternate Interior Angles Theorem, using parallel lines a and b with transversal m, is shown below. |
| | |
| | [pic] |
| |Which property is used in step 4? |
| |/files/assess_files/1b6e17be-6c5e-43d0-8103-e3d0680f984d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |reflexive property |
| | |
| | |
| |B. |
| |transitive property |
| | |
| | |
| |C. |
| |associative property |
| | |
| | |
| |D. |
| |commutative property |
| | |
| | |
| | |
|114. |Two parallel lines are cut by a transversal x and a transversal y so that x and y intersect at point Q as shown. |
| |[pic] |
| |Wong constructs the following argument: |
| | |
| |Angle a is [missing reason 1] and therefore congruent to one angle in the triangle formed by lines m, x, and y. |
| | |
| |Angles b and c are [missing reason 2] and therefore congruent to two other angles in the triangle. |
| | |
| |The sum of the three angles in a triangle is 180 degrees. Therefore [pic]. |
| |What are the missing reasons in Wong’s argument? |
| |/files/assess_files/c41b9722-dd10-41f4-ae70-1f9fbb53c18b/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Reason 1: an alternating exterior angle with one angle in the triangle |
| |Reason 2: vertical angles with the other two angles in the triangle |
| | |
| | |
| |B. |
| |Reason 1: an alternating exterior angle with one angle in the triangle |
| |Reason 2: complementary angles with the other two angles in the triangle |
| | |
| | |
| |C. |
| |Reason 1: a corresponding angle with one angle in the triangle |
| |Reason 2: vertical angles with the other two angles in the triangle |
| | |
| | |
| |D. |
| |Reason 1: a corresponding angle with one angle in the triangle |
| |Reason 2: complementary angles with the other two angles in the triangle |
| | |
| | |
| | |
|115. |John draws [pic]with [pic]as the perpendicular bisector of [pic]such that [pic]and [pic]are congruent to each other. |
| | |
| | [pic] |
| | |
| |Which statement can John use this figure to prove? |
| |/files/assess_files/dff709e8-2193-4f23-b4f5-939809b22285/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Every isosceles triangle is a right triangle. |
| | |
| | |
| |B. |
| |The base angles of any triangle are congruent. |
| | |
| | |
| |C. |
| |The points on the perpendicular bisector of a side of a triangle are equidistant from all of the vertices of the triangle. |
| | |
| | |
| |D. |
| |The points on the perpendicular bisector of a side of a triangle are equidistant from the vertices of the side it bisects. |
| | |
| | |
| | |
|116. |Part A. In the figure below, [pic]Based on facts about corresponding angles and vertical angles, write a paragraph proof to show |
| |that the measures of angles 1 and 8 are equal. |
| |[pic] |
| | |
| |Part B. If it had not already been determined that [pic] in this figure, would the information that [pic] be enough to verify that p|
| |is in fact parallel to q? Justify your answer using relevant theorems about lines and angles. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/81c5ddce-5015-48d7-bfe3-0975dd97fe7a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|117. |John writes the proof below to show that the sum of the angles in a triangle is equal to 180º. |
| | |
| | [pic] |
| | |
| |Which of these reasons would John NOT need to use in his proof? |
| |/files/assess_files/f2d291a3-71dc-4faf-bf69-f52ef7616504/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |The sum of the angles on one side of a straight line is 180º. |
| | |
| | |
| |B. |
| |If a statement about a is true and [pic]the statement formed by replacing a with b is also true. |
| | |
| | |
| |C. |
| |When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. |
| | |
| | |
| |D. |
| |When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent. |
| | |
| | |
| | |
|118. |In triangle [pic][pic]and [pic]Which of these can be proved using the triangle sum theorem? |
| |/files/assess_files/bf3b635a-0f68-488d-b5ce-c82f70781eea/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|119. |In isosceles triangle [pic]Roshni’s teacher asked different students to draw different segments in triangle [pic]Roshni drew a |
| |median from vertex R to point T on side [pic]as shown below. |
| | |
| |[pic] |
| |The teacher asked the students to trade papers with a partner and identify which type of segment their partner had |
| |drawn. Roshni’s partner, Jose, looked at her drawing and told her he thought that she had drawn an altitude. |
| | |
| |Part A. Is [pic] an altitude, median, neither, or both? Explain using a paragraph proof. |
| | |
| |Part B. Is [pic] a perpendicular bisector of [pic]Explain using the definition of perpendicular bisector and your answer to part A. |
| | |
| |Part C. Does [pic]bisect [pic]Explain using a two-column proof as shown below. |
| | |
| |[pic] |
| | |
| |Part D. If Roshni draws a median from [pic]to S, is the median also an altitude? Why or why not? How does this compare to the result|
| |in part A? |
| | |
| | |
| | |
| | Use words, numbers, and/or pictures to show your work. |
| | |
| |/files/assess_files/e44cc23b-0868-4d42-8f95-7a50c351295f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|120. |In [pic] |
| | |
| |[pic] |
| | |
| |Given the information above, which statement can be proved to be true? |
| |/files/assess_files/5424ebeb-0a7f-4537-a3e1-36c81c493b8e/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Triangle [pic]is isosceles. |
| | |
| | |
| |B. |
| |[pic]is perpendicular to [pic] |
| | |
| | |
| |C. |
| |The length of [pic]is half the length of [pic] |
| | |
| | |
| |D. |
| |Triangle [pic] is congruent to triangle [pic] |
| | |
| | |
| | |
|121. |A proof of the base angle theorem is shown. |
| | |
| |[pic] |
| | |
| |Which statements correctly complete the proof? |
| |/files/assess_files/6a8a1691-7638-4576-aa02-826afcc384a6/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|122. |The statements of a two-column proof are listed below. |
| | |
| |[pic] |
| | |
| |What should the corresponding reasons be? |
| |/files/assess_files/90959dda-ac93-40da-bdc1-115f9490fa11/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |1. Given; 2. Definition of congruency; 3. Definition of congruency; 4. SAS theorem; 5. CPCTC |
| | |
| | |
| |B. |
| |1. Given; 2. Definition of congruency; 3. Reflexive property; 4. Hypotenuse-leg theorem; 5. CPCTC |
| | |
| | |
| |C. |
| |1. Given; 2. Definition of perpendicular lines; 3. Definition of congruency; 4. SAS theorem; 5. CPCTC |
| | |
| | |
| |D. |
| |1. Given; 2. Definition of perpendicular lines; 3. Reflexive property; 4. Hypotenuse-leg theorem; 5. CPCTC |
| | |
| | |
| | |
|123. |Properties of Parallelograms |
| | |
| |In this task, you will be proving and comparing properties of certain types of parallelograms. |
| | |
| |Figure [pic]below is a parallelogram. Extending the sides and drawing other lines in the parallelogram can be helpful when proving |
| |the properties of parallelograms. |
| | |
| |[pic] |
| | |
| |Part A. Mark all the angles in the figure that are congruent to [pic]Choose three pairs of these angles and explain how you know |
| |they are congruent. |
| | |
| |[pic] |
| | |
| |Part B. [pic]are both perpendicular to [pic]Based on properties of parallelograms, how do you know [pic]How do you know [pic] |
| | |
| |Part C. Use the facts from parts A and B in a paragraph proof to prove that the opposite sides of parallelogram [pic]are congruent. |
| | |
| |Part D. In the figure below, parallelogram [pic]has diagonals that intersect at point E. Use the properties of triangles and |
| |parallel lines in the two-column proof template below to show that the diagonals of the parallelogram bisect each other. |
| | |
| |[pic] |
| | |
| |Part E. Figure [pic] is a parallelogram with diagonals [pic]intersecting at point Z. If [pic]what can be determined about |
| |parallelogram [pic]Use a paragraph proof to explain your answer. Add labels and/or marks to the figure below to support your proof. |
| | |
| |[pic] |
| | |
| |Part F. Use the two-column proof template and rhombus [pic] shown below to prove that the diagonals of a rhombus bisect its angles. |
| | |
| |[pic] |
| | |
| |Part G. Compare the properties of parallelograms. Fill in the chart to show whether a property is always, sometimes, or never |
| |true for each type of parallelogram listed. |
| | |
| |[pic] |
| |/files/assess_files/29d63ec8-84ff-4462-900b-a91853fbb08f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|124. |The figure below shows the parallelogram ABCD with segments AC and BD as diagonals. |
| | |
| |[pic] |
| | |
| |Which of these correctly proves that the diagonals of a parallelogram bisect each other? |
| |/files/assess_files/9f02334a-67eb-491f-bccf-6b07c9072256/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|125. |Consider the quadrilateral with vertices [pic][pic] |
| |Part A. |
| |One way to prove that the quadrilateral is a parallelogram is to show that the diagonals bisect each other. Explain two other different |
| |methods that can be used to prove that the quadrilateral is a parallelogram. |
| |Part B. |
| |Explain how Part A illustrates the claim that the diagonals of a parallelogram bisect each other. |
| |/files/assess_files/b34aef25-f9a5-44b7-a3db-ff0efe8200a3/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|126. |Quadrilateral MATH includes the points M(2,-4) and A(5,-2). |
| |Part A: Find coordinates for T and H such that quadrilateral MATH is a rectangle. |
| |Part B: Prove that the resulting quadrilateral is a rectangle. |
| |/files/assess_files/35b2be84-6239-4781-9f4e-3778dc2cb018/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|127. |An architect is designing a new city park. She draws a scale model that includes plans for different park features. |
| | |
| |Part A. The architect includes a triangular playground in her design of the park. In her scale model, the playground is in the shape of |
| |an isosceles triangle with a 112° angle and two legs that measure 1.5 inches. Use a protractor and a ruler to create the scale model of |
| |the playground. Explain the steps you used to complete the construction. |
| | |
| |Part B. A sprinkler will be placed in one area of the park. The region to be watered by the sprinkler is shown below. |
| | |
| |[pic] |
| | |
| |Use a compass and a straightedge to bisect the angle of the region the sprinkler will water. Explain the steps you used to complete the |
| |construction. |
| | |
| |Part C. The architect’s plans for the park include a brick wall with a flower garden in front of it, as shown by the diagram below. |
| | |
| |[pic] |
| | |
| |The flower garden will be divided into two equal halves with different types of flowers planted in each half. What geometric |
| |construction can be used to divide the garden into two equal halves? Perform the construction on the diagram above and explain the steps|
| |you used to complete the construction. |
| | |
| |Part D. A walking trail is planned to form a straight path between the parking lot and the athletic fields at the opposite end of |
| |the park, as shown below. |
| | |
| |[pic] |
| | |
| |The architect wants to design a bicycle route that goes through point X and is parallel to the walking trail. Construct and label the |
| |bicycle route on the diagram above. Explain the steps you used to complete the construction. |
| | |
| |Part E. The architect wants to make another path for joggers. The new path will intersect the walking trail and bicycle route and run |
| |perpendicular to both. Use the diagram in part D to construct the jogging path. Explain the steps you used to complete the construction.|
| | |
| |/files/assess_files/fae3eeef-e87d-4f89-87d0-469c391226f9/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|128. |Line m and point P are shown in the diagram. |
| | |
| |[pic] |
| | |
| |Which method would not be used to construct a line through point P that is parallel to line m? |
| | |
| | |
| |A. |
| |Draw a transversal through point P intersecting line m. Construct a pair of congruent corresponding angles. |
| | |
| | |
| |B. |
| |Draw a transversal through point P intersecting line m. Construct a pair of congruent alternate interior angles. |
| | |
| | |
| |C. |
| |Construct a line l through point P that is perpendicular to line m. Construct a line, k, through point P that is parallel to line l. |
| | |
| | |
| |D. |
| |Construct a line l through point P that is perpendicular to line m. Construct a line, k, through point P that is perpendicular to line |
| |l. |
| | |
| | |
| | |
|129. |The figure below shows [pic] |
| | |
| |[pic] |
| | |
| |Part A. Construct [pic]the same length as [pic]using a compass and a straightedge. Explain how you know the line segments are the same |
| |length. |
| | |
| |Part B. Use a compass and straightedge to construct the perpendicular bisector of [pic]Explain how you know the line segment you |
| |constructed is a perpendicular bisector. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/fb13e74d-d258-43f3-8213-b96cd5e391ff/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|130. |Amanda is constructing a line parallel to the line segment [pic]through point P. So far, she has taken the steps shown below. |
| | |
| |[pic] |
| | |
| |The first arc is the same distance from G as the second is from P. |
| | |
| |Part A. What further steps does she need to take to complete the construction? |
| | |
| |Part B. Sketch an example of what the completed construction would look like. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/eda75666-fe5c-4e75-82f0-4b79a4ffc320/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|131. |April wants to construct quadrilateral [pic] congruent to the quadrilateral shown below using only a compass and a straightedge. |
| | |
| |[pic] |
| | |
| |Part A. Her first step is to copy the base of the quadrilateral. Draw and explain the steps April should use to construct |
| |[pic] congruent to [pic] |
| | |
| |Part B. Next, April needs to copy [pic]Draw and explain the steps she should use to construct an angle congruent to [pic] along |
| |[pic] with the vertex at point [pic] |
| | |
| |Part C. What are the next two steps that April needs to perform in order to successfully continue her construction? Draw and explain the|
| |steps she needs to take. |
| | |
| |Part D. Complete April’s construction of quadrilateral [pic]Draw and explain the steps she needs to take to finish her copied figure. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/448af0b2-925d-425b-a146-fa0dc71a6a24/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|132. |Correct Constructions |
| | |
| |Rajon is using a compass and a straightedge, along with his knowledge of the characteristics of lines, angles, and triangles, to draw |
| |figures according to certain specifications. |
| | |
| |Part A. First, he has to draw the perpendicular bisector of segment [pic]He starts by opening the compass so that the opening is greater|
| |than half the length of the segment. He puts the point of the compass on one end of the segment and draws an arc, as shown. What are the|
| |next steps to drawing the bisector? |
| | |
| |[pic] |
| | |
| |Part B. Use the tools to complete the drawing. Label the points where the arcs intersect [pic]and [pic]and label the midpoint of |
| |[pic]point [pic] |
| | |
| |Part C. Construct triangles [pic]and [pic]and use them to explain how you know that the segment you have made is a bisector of [pic] |
| | |
| |Part D. Now, Rajon will draw a line parallel to line [pic]that passes through point [pic]shown below. Explain how he can use a compass |
| |and a straightedge to achieve this. |
| | |
| |[pic] |
| | |
| |Part E. Draw the required line and explain how you know it is parallel to the original line. Label points as necessary. |
| | |
| |Part F. Finally, Rajon will bisect the angle below. Explain how he can use a compass and a straightedge to bisect the angle. |
| | |
| |[pic] |
| | |
| |Part G. Explain how you know that the two angles formed by the bisector are congruent. |
| |/files/assess_files/43b6823b-a5f1-47b6-ae27-d083aa692d59/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|133. |The equation shown below represents a circle. Which statement describes the key features of the circle that can be determined from the |
| |equation? |
| |[pic] |
| |/files/assess_files/25b65a23-0c7a-4815-b235-90c555d1ca3c/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |The circle has a center at [pic]and radius of 2 units. |
| | |
| | |
| |B. |
| |The circle has a center at [pic]and radius of 2 units. |
| | |
| | |
| |C. |
| |The circle has a center at [pic]and radius of 4 units. |
| | |
| | |
| |D. |
| |The circle has a center at [pic]and radius of 4 units. |
| | |
| | |
| | |
|134. |What is the equation of the circle that has a center at [pic] and a radius of 4 units? |
| |/files/assess_files/7217ee40-b2ee-49dd-9c8d-dee76f535c7a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|135. |What is the center and the radius of a circle given by the equation [pic] |
| |/files/assess_files/03e7ec23-d8d3-431a-a78d-2db26e95d50a/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|136. |In the standard xy-coordinate plane, the horizontal line [pic]intersects the circle |
| |[pic] |
| |at two points, [pic]and [pic] |
| |Part A: Complete the square to determine the standard form of the equation of the circle: |
| | [pic] |
| |Part B: Find a value for [pic]such that the distance from [pic]to [pic]is 10. Show your work or explain your reasoning. |
| |/files/assess_files/98a899c4-523b-40f8-91d6-2d2707211a36/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|137. |A circle with a radius of 3 units has its center at the origin. Which equation gives any point [pic]on the circle? |
| |/files/assess_files/4eef49f3-f517-4826-aebe-d2ad0cc6ae27/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|138. |A circle with its diameter is shown on the coordinate grid below. |
| | |
| |[pic] |
| | |
| |Which equation represents the circle given above? |
| |/files/assess_files/c91c2657-702a-474a-90b5-e6f271108c00/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|139. |Given that a certain parabola has a focus at [pic]and a directrix at [pic]answer the following questions. |
| | |
| |Part A. What are the coordinates of the vertex of the parabola? Show your work. |
| | |
| |Part B. Does the parabola open up, down, left, or right? Explain your answer using the locations of the focus and vertex. |
| | |
| |Part C. Derive the equation that represents this parabola. Show your work and explain your steps. |
| | |
| |Part D. Sketch a graph of this parabola on the coordinate plane below. Label the vertex of the parabola as well as the focus and |
| |directrix. |
| | |
| | [pic] |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/2d5609a8-98f1-42f5-bead-afc9b16afc9c/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|140. |What is the vertex of a parabola with focus [pic]and directrix [pic] |
| |/files/assess_files/13d79f4a-7254-4324-afe6-1f676271d86d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|141. |What is the equation of a parabola with a focus of [pic] and a directrix that goes through a point that is ten units directly above the |
| |focus? |
| |/files/assess_files/d475e8dd-2d90-4dd5-ba70-1c2b7e646133/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|142. |What is the equation of a parabola with a focus of [pic]and a directrix of [pic] |
| |/files/assess_files/2132f03f-50a6-4a83-a7ee-4214dd7f5402/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|143. |Katie is using graph paper to sketch a design for a flat wooden bench that will have a rectangular seat. The front and side views that |
| |Katie sketched are shown below. |
| | |
| |[pic] |
| | |
| |If Katie uses a scale on the graph paper in which each box represents a 6-inch by 6-inch square, what are the dimensions of the seat of |
| |the bench Katie is designing? |
| |/files/assess_files/92ba0bca-8938-448c-95d0-2fb73907d6d0/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |2 feet long by 2.5 feet deep |
| | |
| | |
| |B. |
| |5 feet long by 2 feet deep |
| | |
| | |
| |C. |
| |5.5 feet long by 2.5 feet deep |
| | |
| | |
| |D. |
| |10 feet long by 5 feet deep |
| | |
| | |
| | |
|144. |Pet Fence |
| | |
| |Dana is planning to build an enclosure in her yard so that her dogs can play in a secure area. She is planning to use fencing that comes|
| |in rigid 6-foot-long sections. She cannot bend the individual sections, but she can join them at any angle to form different polygons. |
| |Dana has enough money to buy 24 sections of fencing, including one with a gate. Dana plans to use all 24 sections of fencing when |
| |building the enclosure for her dogs. |
| | |
| |Part A. Dana first considers making a rectangular enclosure. In the table below, list all possible ways Dana could use the fencing to |
| |make an enclosure that has an area of at least 900 square feet. What is the greatest rectangular area Dana could enclose with the 24 |
| |sections of fencing? Explain your answer. |
| | |
| | [pic] |
| | |
| |Part B. Dana decides to sketch models of the rectangular enclosures. She uses tick-marks to show each section of fencing on the models, |
| |and she labels what will be the actual length and width of the enclosures. If [pic] represents two pieces of fencing placed next to each|
| |other, use a ruler or graph paper to sketch models of all of the possible enclosures that have an area of at least 1,000 square feet. |
| |Label the models with what will be the actual lengths and widths of the enclosures. How does the area of each enclosure, in square feet,|
| |relate to the area of each enclosure in fence section by fence section? Use the models you drew to help explain your answer. |
| | |
| |Part C. Dana is also considering making the enclosure in the shape of a regular hexagon. Use a ruler or graph paper to sketch a model of|
| |a regular hexagon with tick-marks to show how many fence sections would be needed for each side. Include the length of each side, in |
| |feet. Then, divide the hexagon into sections so that you can compute its area in square feet. Show how you chose to divide the |
| |hexagon and show your work for computing the area. When appropriate, leave side lengths in radical form. For your final answer, round |
| |the area to the nearest square foot. |
| | |
| |Part D. Dana’s sister suggested she make the enclosure in the shape of a regular octagon. Use a ruler or graph paper to sketch a model |
| |of a regular octagon with tick-marks to show how many fence sections would be needed for each side. Include the length of each side, in |
| |feet. Then, divide the octagon into sections so that you can compute its area in square feet, and sketch your divisions on your model. |
| |Show your work and label the lengths you used in your calculations. When appropriate, leave side lengths in radical form. For your final|
| |answer, round the area to the nearest square foot. |
| | |
| |Part E. If Dana uses all 24 pieces of fencing as the sides of the enclosure, how could Dana construct the enclosure in order to maximize|
| |the area? Describe the configuration and explain your answer. |
| |/files/assess_files/336e171e-905e-469f-b018-b119b33ee812/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|145. |Build a Corner Cupboard |
| | |
| | |
| |You are taking an interest in carpentry and want to design a corner cupboard for books and knickknacks. A corner cupboard, or cabinet, |
| |is shaped like a triangular prism and fits into the corner of a room. You use geometric methods to work out the specifications for the |
| |cabinet. |
| |[pic] |
| | |
| |Part A. Given the space you have available, you are thinking that the cabinet should come out 18 inches (in.) from the corner along each|
| |wall. How wide will it be across the front? Show your work, and give your answer to the nearest inch. |
| | |
| |Part B. The back corner of the cabinet measures [pic]What is the measure of the two other angles of the cabinet? |
| | |
| |How deep will the cabinet be, from the back corner to the center front of the cabinet? Show your work, and give your answer to the |
| |nearest inch. |
| | |
| |Part C. You would like the cabinet to be 6 feet tall. At the bottom, there will be 1 shelf enclosed by doors that are 2 feet high. There|
| |will be an open shelf at the level of the top of the doors, 3 other evenly spaced shelves, and then the top of the cabinet. You will |
| |have to buy extra wood to allow for waste when you cut it, but what is the minimum amount of wood you need for the sides, shelves, and |
| |top excluding the doors? Show your work, and give your answer to the nearest square foot. |
| | |
| |Part D. What is the area of each shelf in square inches? What is the total volume of the cabinet in cubic feet? Give your answer to the |
| |nearest cubic foot. Show your work. |
| | |
| |Part E. With triangular shelves, not all of the area is always usable space. You have a set of books you want to put on one of the |
| |shelves, with bookends at either end. Each book is 9 in. high, 6 in. wide, and [pic]in. thick. If you put the books in a row across the |
| |shelf, with the spine of each book at the edge of the shelf, what is the maximum number of books you can put in the row? Draw a sketch, |
| |show your work, and explain your answer. |
| | |
| |Part F. You are thinking about making a small 3-in. rail for the top shelf, as shown in darker gray below. |
| | |
| |[pic] |
| | |
| |Show how you could cut a piece of wood like the one below to make the rail with the least waste possible. Label lengths and angles. What|
| |is the minimum length of wood that you would need? |
| |[pic] |
| |/files/assess_files/807de584-7cde-4774-961c-8f94b89bef69/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|146. |Sandy is designing cartons to hold cans of beans. The cartons are in the shape of a rectangular prism, and the cans are cylinders |
| |measuring 6.858 centimeters (cm) in diameter and 10.16 cm tall. The carton must be able to hold 30 cans on one layer and have a length |
| |no greater than 50 cm. |
| |Due to restrictions on the machine that creates the cartons, Sandy first completes her calculations and then rounds her results up to |
| |the next 0.25 cm. |
| | |
| |Part A |
| |Determine the dimensions for the base of the carton that would best accommodate 30 cans with the least amount of space left over. Show |
| |and explain your work. |
| | |
| |Part B |
| |Using the dimensions found for part A, determine the amount of area NOT covered by the cans on the base level. Show your work. Round |
| |your answer to the nearest hundredth. |
| |Part C |
| |The material for the cans weighs 0.0055 ounces per square centimeter. How many ounces does each can weigh? Round your answer to the |
| |nearest hundredth. |
| |/files/assess_files/48417206-825a-4392-bc43-7ee10531856b/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|147. |[pic]is obtained by dilating [pic]by a factor of 2, then translating it 5 units to the left. If [pic]which statement must be correct? |
| |/files/assess_files/8145725a-7a9b-4f59-bc8d-28c708bbc9f6/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Since translation preserves side lengths, the corresponding side [pic] |
| | |
| | |
| |B. |
| |Since translation preserves side lengths, the corresponding side [pic] |
| | |
| | |
| |C. |
| |Since dilation results in proportional side lengths, the corresponding side [pic] |
| | |
| | |
| |D. |
| |Since dilation results in proportional side lengths, the corresponding side [pic] |
| | |
| | |
| | |
|148. |Triangles [pic] and [pic] shown below, are similar. |
| |[pic] |
| |Which series of transformations best takes [pic]to [pic] |
| |/files/assess_files/8231ded2-09fd-431b-9e3d-49eedbc12d02/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |reflection over the y-axis, dilation by a factor of 0.75, and rotation about point F by 90° counter-clockwise |
| | |
| | |
| |B. |
| |reflection over the y-axis, dilation by a factor of 0.5, and rotation about point F by 45° counter-clockwise |
| | |
| | |
| |C. |
| |translation 16 units to the right, dilation by a factor of 0.75, and rotation about point F by 90° counter-clockwise |
| | |
| | |
| |D. |
| |translation 16 units to the right, dilation by a factor of 0.5, and rotation about point F by 45° counter-clockwise |
| | |
| | |
| | |
|149. |Given: [pic] |
| | |
| |Which of the following statements cannot be proven true or false for all cases? |
| |/files/assess_files/bec597e0-8614-4cef-9cff-6ba48c0a78cb/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|150. |In the diagram below, [pic] and the dimensions are in meters. |
| | |
| |[pic] |
| |What is the length of [pic] |
| | |
| |/files/assess_files/ebff1602-dec3-4256-b7cf-82f43b0cd46d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |34.4 meters |
| | |
| | |
| |B. |
| |40 meters |
| | |
| | |
| |C. |
| |43.2 meters |
| | |
| | |
| |D. |
| |45 meters |
| | |
| | |
| | |
|151. |Use the given image to answer part A and part B. |
| |[pic] |
| | |
| |Part A. What transformation(s) does [pic] undergo to produce [pic]Be as specific as possible. |
| | |
| |Part B. What is true about the corresponding angles of these triangles? Is this true for all triangles of this type? Explain. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/429a65d0-0b60-4efb-b7ab-2261e74282fa/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|152. |In the figure below, [pic]is the result of a dilation of [pic] with point B as the center of dilation. |
| |[pic] |
| |Which statement best uses this information to explain why the AA criterion can be used to prove [pic] |
| | |
| |/files/assess_files/5bc70507-51a9-4e56-bf2e-49f1358110cd/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |A dilation takes a line not passing through the center of dilation to a parallel line, so [pic]Because they are corresponding angles on |
| |parallel lines, [pic] and [pic] |
| | |
| | |
| |B. |
| |A dilation takes a line not passing through the center of dilation to a parallel line, so [pic]Because they are corresponding angles on |
| |parallel lines, [pic] and [pic] |
| | |
| | |
| |C. |
| |By the reflexive property, [pic] A dilation results in line segments that are proportional in the scale factor of the dilation. |
| |Therefore, [pic] |
| | |
| | |
| |D. |
| |By the reflexive property, [pic] A dilation results in line segments that are proportional in the scale factor of the dilation. |
| |Therefore, [pic] |
| | |
| | |
| | |
|153. |Ms. Morales showed her geometry students the figure below and told them that [pic] She asked them to use this information to prove that |
| |[pic]divides [pic]and [pic] proportionally. |
| |[pic] |
| | |
| |Hannah used the midpoint formula to show that [pic] and [pic] |
| |Jaden used the slope formula to prove that [pic]and [pic]have equal slopes. |
| |Omar used the distance formula to show that [pic] |
| | |
| |Which student or students used a formula that will help them prove the relationship? |
| |/files/assess_files/cdcd803a-05d4-4dc4-8691-e72b1ec07979/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Jaden only |
| | |
| | |
| |B. |
| |Omar only |
| | |
| | |
| |C. |
| |Hannah and Omar only |
| | |
| | |
| |D. |
| |Hannah, Jaden, and Omar |
| | |
| | |
| | |
|154. |In the given [pic] |
| | |
| |[pic] |
| | |
| |What is the value of x? |
| |/files/assess_files/0086fc02-8217-4ab6-8c49-051a667080d2/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |12 in. |
| | |
| | |
| |B. |
| |16 in. |
| | |
| | |
| |C. |
| |20 in. |
| | |
| | |
| |D. |
| |30 in. |
| | |
| | |
| | |
|155. |Which expression is equivalent to the expression [pic] |
| |/files/assess_files/b396bb6c-c713-4fff-852a-c1d7332e20d1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|156. |Which number is equivalent to the complex number [pic] |
| |/files/assess_files/f5fc9c45-34dc-4787-89a9-44c3be4738f4/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|157. |Use the expression [pic]to answer the questions below. |
| | |
| |Part A. If [pic]and [pic]what will be the real and imaginary part of the above expression? |
| | |
| |Part B. If [pic]and [pic]write the above expression in simplest complex form. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/f3b406f6-cdbf-47f6-968b-d4a5445cc378/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|158. |Which of these correctly defines the complex number i? |
| |/files/assess_files/17085c74-5c62-4c42-b136-e9b0ca9c9ec4/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|159. |Which expression is equivalent to [pic] |
| |/files/assess_files/52f5e9d2-6d97-426f-82c2-a0f7ead2dfa7/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|160. |Which expression is equivalent to [pic] |
| |/files/assess_files/4a7e05e9-3639-4309-9bd2-9c9da18caf19/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|161. |Use [pic]to answer the following questions. |
| |What is [pic]Give answer in [pic]form. |
| |Define [pic] in [pic] form such that [pic]is a real number. |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/c809b679-6576-4d6e-8b48-9ddafb748223/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|162. |What is the value of [pic] |
| |/files/assess_files/e211ed1d-00a4-4428-87db-35a1f54be11c/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|163. |What are the solutions of the equation [pic] |
| |/files/assess_files/76bc3088-4b9c-4be7-bc16-b213338ce124/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|164. |Which equation has [pic]as two of its solutions? |
| |/files/assess_files/bed0bb13-77d8-4df5-a6a3-6c071d6cc0c7/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|165. |Which of these are the solutions of the equation [pic] |
| |/files/assess_files/8b242392-d2f3-412e-a6e1-d79c714f0b3f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|166. |Which shows a solution of [pic] |
| |/files/assess_files/ad416d87-0fad-403a-a1b4-a05ebf9389b8/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|167. |The equation [pic]can be used to determine the kinetic energy of an object, where m is the mass, in kilograms, and v is the velocity, in|
| |meters per second. What are the units of kinetic energy? |
| |/files/assess_files/37350cec-1266-4413-9fb9-40a81f734ca7/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|168. |A recipe for cookies needs 6 tablespoons of butter per batch. Logan is making 6 batches of cookies for a bake sale. How much butter will|
| |Logan need? (Note: 4 tablespoons = [pic]cup) |
| | |
| |A. |
| |2 cups plus 4 tablespoons |
| | |
| | |
| |B. |
| |2 cups plus 8 tablespoons |
| | |
| | |
| |C. |
| |9 tablespoons |
| | |
| | |
| |D. |
| |36 cups |
| | |
| | |
| | |
|169. |John leaves his house for the local community center. He walks a distance of 3 miles from his house in 45 minutes before stopping at a |
| |store to pick up a bottle of water. From there, he walks to the community center, which is 5 miles away from the store, in 1 hour. What |
| |is John’s approximate average speed, in miles per minute, for the entire time he is walking? |
| |/files/assess_files/844b8e7c-8b76-42c7-8db9-260e2582dea1/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |0.067 |
| | |
| | |
| |B. |
| |0.076 |
| | |
| | |
| |C. |
| |0.083 |
| | |
| | |
| |D. |
| |0.150 |
| | |
| | |
| | |
|170. |Paul is a carpenter. He designs doors that are different sizes and shapes. His prices are dependent on the size of the door he designs. |
| | |
| |Part A. Paul wants to advertise his prices on a flyer. If he measures the dimensions of the door in feet to calculate the surface area, |
| |what units should he use to represent the cost? |
| | |
| |Part B. A customer calls and asks Paul what his prices would be if he measured the door in yards instead of feet. The equation |
| |[pic] describes the cost, c, Paul charges per unit of area, a, when measuring the dimensions of the door in feet. Write an equation to |
| |show the cost if Paul wee to measure the dimensions of the door in yards. |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/63daadec-eab8-4eae-a211-137510d7cd1f/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|171. |Which expression results in an irrational number when simplified? |
| |/files/assess_files/68845b07-3954-4f36-b946-3a40ea571207/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|172. |Is the expression shown below rational? |
| |[pic] |
| |/files/assess_files/8e8a0ff3-4fb3-45f0-a075-d949c2d7f68d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |Yes, because the sum of two irrational numbers is rational |
| | |
| | |
| |B. |
| |No, because the sum of two irrational numbers is irrational |
| | |
| | |
| |C. |
| |Yes, because the sum of a rational number and an irrational number is rational |
| | |
| | |
| |D. |
| |No, because the sum of a rational number and an irrational number is irrational |
| | |
| | |
| | |
|173. |The host of a television news program wants to predict the voters' preferred candidate in the upcoming election. Which of the following |
| |sampling processes would be the least subject to bias? |
| | |
| |A. |
| |The host sets up a booth at the local shopping mall and asks shoppers to participate in a survey. |
| | |
| | |
| |B. |
| |The host asks viewers to call in, text, or visit the show's website to participate in the survey. |
| | |
| | |
| |C. |
| |The host requires each of the show's employees to have four of their neighbors participate in the survey. |
| | |
| | |
| |D. |
| |The host acquires a list of all citizens who voted in the last election and selects every 100th voter on the list to participate in the |
| |survey. |
| | |
| | |
| | |
|174. |As senior class president, Grace wants to help the cafeteria provide more lunch items that the students like to eat. She designs a |
| |survey that assesses the favorite foods of students. After school one day, on her way to catch her bus, Grace administers the survey to |
| |50 students waiting at the bus loop where buses meet to take students home. |
| |Part A |
| |Will the results of this survey represent a random sample, a convenience sample, or a self-selected sample? Explain why. |
| |Part B |
| |Which sampling method would be the best method in this situation? Explain why. |
| |/files/assess_files/75a012c6-800b-4c1b-9cf2-54dd30053335/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|175. |Which characteristic in a statistical study is necessary in order for conclusions to be drawn regarding the whole population, based on |
| |the sample population? |
| |/files/assess_files/c40f54df-5559-48dd-906a-a72b3b86c559/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |The sample must be randomly selected. |
| | |
| | |
| |B. |
| |The sample must not be randomly selected. |
| | |
| | |
| |C. |
| |The population size must meet a minimum number requirement, based on the sample size. |
| | |
| | |
| |D. |
| |The population size must meet a maximum number requirement, based on the sample size. |
| | |
| | |
| | |
|176. |A teacher assigned students to determine the number of red cars in the student parking lot. |
| |Student 1 looked at all the cars in the student parking lot and recorded the number of red cars. |
| |Student 2 looked at the first 10 cars entering the student parking lot, counted the number of them that were red, and calculated the |
| |percent. The student multiplied this percent times the number of parking spaces in the parking lot to estimate the total number of red |
| |cars. |
| |Compare the methods used by the two students. Include the words random, sample, and population in your comparison. |
| |/files/assess_files/873f80d7-aaea-4223-aeac-5ae8da26a087/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|177. |An excerpt from a voting report is shown below. Use the information in the table to answer the questions below. |
| | |
| |[pic] |
| |Part A. The report lists a number and a percentage for each of the categories. Why should we take into consideration the |
| |voting percentages instead of simply looking at the number of people who vote within each category? |
| | |
| |Part B. Suppose a politician claims that more young citizens ages 18 to 24 vote than older citizens ages 75 and older. Do the data |
| |support this claim? Why or why not? |
| | |
| |Part C. Overall, what are some trends that you see in the type of people who vote? Who votes most frequently? Who votes less frequently?|
| | |
| |Use words, numbers, and/or pictures to show your work. |
| | |
| |/files/assess_files/df975d9e-81ae-458a-bab0-754287e2fcf6/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|178. |A sports-and-exercise shop sampled its customer base one weekend and asked 35 customers their age: |
| |24, 24, 24, 24, 24, 24, |
| |25, 25, |
| |26, 26, 26, 26, 26, 26, 26, 26, |
| |27, 27, 27, |
| |28, 28, 28, 28, 28, |
| |29, 29, |
| |30, 30, |
| |31, |
| |33, 33, 33, |
| |36, |
| |45, |
| |46 |
| |Which interval estimate of the population mean has a margin of error of 1.7 ? |
| |/files/assess_files/89b31b29-7715-4755-aa6c-dfe0db23d5dd/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |[pic] |
| | |
| | |
| |B. |
| |[pic] |
| | |
| | |
| |C. |
| |[pic] |
| | |
| | |
| |D. |
| |[pic] |
| | |
| | |
| | |
|179. |James wants to find out whether polyurethane swimsuits help swimmers swim faster. To investigate, he chose seven volunteers from his |
| |swim team to participate in an experiment. On two consecutive Sundays, he had each volunteer swim 50 meters. On one Sunday, each swimmer|
| |wore a polyurethane swimsuit, and on the other Sunday, each swimmer wore an ordinary swimsuit. The times he recorded are listed below. |
| | |
| |[pic] |
| | |
| |He then ran a simulation using a computer program to figure out what differences in means could be expected to occur simply due to |
| |random chance. Which statement best explains what James can conclude based on the results of the simulation? |
| |/files/assess_files/8eb5092a-c5c5-4ef1-a69e-0ba31ca79eae/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |James can conclude that polyurethane swimsuits help swimmers swim faster if the mean difference of the simulation is close to the |
| |experimental mean difference. |
| | |
| | |
| |B. |
| |James can conclude that polyurethane swimsuits help swimmers swim faster if the mean difference of the simulation is less than the |
| |experimental mean difference. |
| | |
| | |
| |C. |
| |James can conclude that polyurethane swimsuits help swimmers swim faster if the mean difference of the simulation is greater than the |
| |experimental mean difference. |
| | |
| | |
| |D. |
| |James can conclude that polyurethane swimsuits do not help swimmers swim faster if the mean difference is equal to the experimental mean|
| |difference. |
| | |
| | |
| | |
|180. |A survey was conducted where 150 high school students were asked the average amount of time they spent doing household chores in one |
| |week. The data collected resulted in a mean time of 180.5 minutes with a standard deviation of 5.5 minutes. Which of these represents a |
| |95% confidence interval for the mean weekly hours spent doing household chores of all high school students? |
| |/files/assess_files/ae1a306b-1e20-427b-9431-179be160e3fe/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |171.5–189.5 |
| | |
| | |
| |B. |
| |175–186 |
| | |
| | |
| |C. |
| |178.25–182.75 |
| | |
| | |
| |D. |
| |179.62–181.38 |
| | |
| | |
| | |
|181. |In a college math class, 500 students took a final exam. The final exam results showed students had an average score of 65.3% with a |
| |standard deviation of 5.2%. The scores on the final exam followed a normal distribution curve with population percentages as shown |
| |below. |
| |[pic] |
| |How many students scored above 54.9% but below 70.5%? |
| |/files/assess_files/99bb1f61-723d-42cc-a765-92eba0d8aa26/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |78 |
| | |
| | |
| |B. |
| |82 |
| | |
| | |
| |C. |
| |341 |
| | |
| | |
| |D. |
| |409 |
| | |
| | |
| | |
|182. |A factory manufactures light bulbs and then packs them in boxes to be shipped to its customers. Before each shipment, boxes are randomly|
| |chosen and the bulbs inside are inspected. The number of bulbs found to be defective in each box can be normally distributed. The mean |
| |number of defective bulbs in each box is 12 with a standard deviation of 2. |
| |[pic] |
| | |
| |Use the normal curve shown above to answer the questions. Let [pic] represent the mean and [pic] represent the standard deviation. |
| | |
| |Part A. If any one box among the sample of inspected boxes chosen has a total of 9 defective bulbs, what percentage of the sample boxes |
| |will have more defective bulbs than this box? Explain what this means in terms of the given context. |
| |Part B. If there are 60 boxes that contain between 12 and 15 defective bulbs, how many total boxes were inspected? |
| | |
| |Use words, numbers, and/or pictures to show your work. |
| |/files/assess_files/a61713d1-3253-4d58-820b-1051319d7efa/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| | |
| | |
|183. |A book editor was proofreading a draft of a novel. She found that the number of errors on each page of the book was normally |
| |distributed, with the mean number of errors on a page as 8 and a standard deviation of 1. If 82 pages had between 7 and 9 errors, what |
| |was the approximate total number of pages in the book? |
| |[pic] |
| |/files/assess_files/c194ba85-b07d-4ffd-a0a1-16549a0fbf0d/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |56 pages |
| | |
| | |
| |B. |
| |68 pages |
| | |
| | |
| |C. |
| |120 pages |
| | |
| | |
| |D. |
| |202 pages |
| | |
| | |
| | |
|184. |The distributions below represent the batting averages of the players on two baseball teams, A and B. |
| |[pic] |
| | |
| |Which of these is true based on the graph? |
| | |
| |I. The mean batting average for team A is less than the mean batting average for team B. |
| |II. The standard deviation for team A is less than the standard deviation for team B. |
| |/files/assess_files/ebec6b02-b35a-4022-95b7-9f893d184203/formula_sheets/FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| |FL-IBTP_Math_Reference_Sheet_Grade_9-12.pdf |
| | |
| |A. |
| |I only |
| | |
| | |
| |B. |
| |II only |
| | |
| | |
| |C. |
| |both I and II |
| | |
| | |
| |D. |
| |neither I nor II |
| | |
| | |
| | |
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