Percents Study Guide



Applying Proportionality 1

[pic]

A recipe that makes 1 1/2 dozen cookies requires 3/4 cup of sugar. Shanika wants to make 6 dozen cookies. How many cups of sugar will she need?

A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches, what is the actual distance between the cities?

Applying Proportionality 2

1) Mrs. Jackson bought 8 pounds of potatoes for $3.92. Which of the following represents the same price per pound?

10 pounds of potatoes for $4.70

25 pounds of potatoes for $11.25

5 pounds of potatoes for $2.45

20 pounds of potatoes for $9.60

2) 3)

[pic] [pic]

4) What scale factor was used to dilate ABC to A'B'C'?

[pic]

5) Which triangle is similar to !XYZ?

[pic]

A. [pic] C. [pic]

B. [pic] D. [pic]

Equations and Algebraic Reasoning

1) Solve: 3x – 11 = 9

2) Write the rule that describes the relationship between the term and its position n in the sequence below?

|Position |1 |2 |3 |4 |5 |n |

|Value |3 |5 |7 |9 | | |

3) Simplify 2(x + 5) + 12

4) The cost of renting a car is given by the formula C = 50n + 0.15d, where C is the cost in dollars, n is the number of days’ rental, and d is the distance driven in miles. How much would it cost to rent a car for a 15-day trip, and drive 475 miles each day?

5) What is the rule that describes the relationship between a term and its position n in the sequence?

[pic]

6) In the sequence 3, 12, 21, 30, 39, 48,... what is the value of the 8th term?

7) What is the distributive Property?

8) Write a sequence that follows the rule 3n-4, where n is the position of the term in the sequence?

9) Solve: [pic]

10) Solve: 5x + 16 = 28

Exponents, Square Roots and Scientific Notation

Exercise 1: Write each product in its abbreviated form and indicate its meaning.

1) 7 · 7 · 7 = __________ 2) 10 · 10 · 10 · 10 · 10 = _________

Exercise 2: Find the value of the following:

3) -4³ = __________________ 4) 12³ = _____________ 5) -8º = _________________

Exercise 3: What is the square root of the following:

6) The square root of 2025 is __________ 7) √29 = __________________

8) √0.0625 = ___________ 9) √95 = ____________________

Exercise 4: Estimate the square root of the following:

10) √34 = _________ 11) √160 = ____________

Exercise 5: Write each multiplication expression using exponents.

12) (8 ∙ 8) (8 ∙8) = ____________ 13) (x ∙ x) (x ∙ x) (x ∙ x) = ___________

14) (-12)(-12)(-12) = _____________ 15) (0.5)(0.5)(0.5)(0.5) = _____________

Exercise 6: Modeling square roots

16) Which model represents [pic]?

a.[pic] b.[pic] c.[pic] d.[pic]

Exercise 7: Write each power as a multiplication expression.

17) M³ = _____________ 18) 14² = _____________ 19) (-2)º = _______________

Exercise 8: Order of Operation

20) (3 · 3 – 3)² ÷ 3 + 3 ____________ 21) (8 – 2) · (8 – 1)² ÷ 3 ____________________

Exercise 9: Evaluate expressions

22) Evaluate m³ + n² for m = 3 and n = 5.

Exercise 10: Change to Standard Form

23) 5.3 x 10³ = ____________________ 24) 2.987 x 10² = ________________

Exercise 11: Change to Scientific Notation

25) 0.000067 = ___________ 26) 59800000 = ___________________

PERCENTS

1. Dale and his dad are shopping for a new computer. They find one that was originally marked $1,250. It is now on sale for 15% off, and Dale can get an additional 10% student discount off the reduced price. What will be the total cost, to the nearest cent, after a 7.5% sales tax is added onto the final selling price of the computer.

2. Mr. Marshall wants to purchase a shirt for work that originally costs $88.50. The store is offering a 30% discount off the original price. How much will Mr. Marshall pay for the shirt if a 6% sales tax is added? (Round to the nearest cent)

3. Miss Hannah’s second grade class was surveyed about their favorite season of the year. Of the students surveyed, [pic] preferred autumn, 61% preferred summer, 0.12 preferred winter, and 0.07 preferred spring. Which season do most students like the best? the least?

4. Sean goes to a music store and buys 2 CDs that cost $14.99 each. If there is a 5% sales tax, about how much will he spent in all?

5. A school district had about 1,450 students total last year. This year, the number of students increased by 9%. About how many students are in this district now?

6. Supposed a $30,000 carpenter salary is increased by 5% each year. What is the policeman's salary after 5 years?

7. Claire has been waiting for automobile prices to drop. She notices that in the last 3 months the price of the car she wants has gone down from $12,000 to $11,100. What is the percent of change in the price of the car?

8. Supposed you only have $100 dollars to spend on dinner.

Allowing 8% tax, and a 28% tip, how much can you order?

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