Manatee School for the Arts



Name______________________Date: ______________________Math 7, period _____FSA Review PacketSeventh Grade FSA Review PacketProportionsRulesExamples_____________ 1. A recipe uses 4 cups of flour to make 12 cookies. If you want 60 cookies, how much flour will you need?2. I took a random sample of 100 students and 42 buy lunch. How many students out of the 600 at school will buy lunch?Set up a proportion consistently.Cross multiply.Divide by the number with the variable.Word Problems1. Find the constant rate of change for the table below.Number of StudentsCost230460690Using the table, divide column y by column x.Constant Rate of 1. I drove 120 miles in 2 ? hours. What was my average speed?2. A sprinter runs 200 m. in 27 seconds. What is the average running rate?Divide the distance by the time.Use the A b/c key on the calculator for fractions.RateItems24Cost2040Divide the dependent row by the independent row to find the constant of proportionality.k = constant of proportionality. Put that in the equation y = kx.The number times k = cost.Constant ofa. Find the constant of proportionality.b. Use the constant of proportionality to write an equation in y = mx form.c. How much would 6 items cost?ProportionalityPractice for Proportions1. I made punch with 3 parts ginger ale to 2 parts Hi-C. I need 20 oz. of punch. How much Hi-C do I need?2. I ran 13 miles in 2 ? hours. What was my average speed?3a. What is the constant rate of change for the table below?MinutesNumber of Pages Read106020120301803b. Use the constant rate of change to write an equation in y = mx form.3c. How many pages would you read in 60 minutes?GeometryRulesExamples_____________ 1. If you wrap lace around a circle with a radius of 10 m., how much lace do you need?2. Find the radius of a circle with a circumference of 9π ft.Multiply the radius by 2 and then by the pi key on the calculator.Round to the nearest tenth.If being asked for the radius, the number in front of pi is the diameter. Divide by 2 to get the radius.Circumferenceof a CircleThe diameter of a pizza is 12 inches. What is the area of the pizza?Divide the diameter by 2.Multiply the resulting radius by itself, then by the pi key on the calculator.Round to the nearest tenth.Area of a Circle Practice for Geometry1. Find the circumference of a circle with a radius of 20 m.2. Find the area of a circle with a diameter of 10 m.3. Find the radius of a circle with a circumference of 15π m. ProbabilityRulesExamples_____________ 1. There are 3 red marbles, 4 blue marbles, and 6 green marbles. Find the probability you choose a red marble.2.Flavor# of StudentsVanilla10Chocolate15Strawberry5Find the probability of chocolate being the favorite flavor of a student.Find the total.Put the favorable outcomes over the total. Simple ProbabilityWhat is the probability of tossing two coins and having both land on heads?Find the probability of each event and multiply them together.IndependentProbabilityName two dependent events.Dependent Events do effect each other.DependentProbabilityIf you roll a die 40 times, how many times would you expect it to come up odd?Find the probability of the event.Multiply it by the number of times the event is occurring. OutcomesHow many outcomes are possible if you choose a letter from the word MATH and a letter from the word FINAL?Find the number of outcomes from each event and multiply them together. Counting PrinciplePractice for Probability1. What’s the probability of picking a dime if you have 3 dimes, 4 pennies, and 5 quarters?2. What is the probability a student will choose math as their favorite subject if you have conducted a survey and found 6 like SS, 10 like science and 15 like math?3. What’s the probability of tossing a pair of dice and having both come up even?4. Name two dependent events.5. You roll a die 60 times. How many should come up the number 1?6. How many outcomes are possible if you chose one letter from the word FUN and another letter from the word NOT.AlgebraRulesExamples_____________ 1. Simplify: 2(-3x – 4).2. Solve: 2(x + 1) = -14Multiply the number outside the parentheses by both terms inside the parentheses. If it is an equation, subtract the number from both sides of the equation.Divide by the number next to the variable on both sides of the equation. Distribution1. -15x + 6 + 6x – 32. (-4x + 6) – (8x – 10)Find like terms.Add or subtract the like terms by adding/subtracting the coefficients and keeping the variables.In cases of (), line them up. Remember to subtract all terms. Simplifying Expressions1. What is the last step in solving -3x + 2 < 10?2. Solve and graph 4x < 20When solving inequalities, the final step is to divide by the number with the variable and reverse the inequality sign if that number is negative.Otherwise, simply divide by the number with the variable.When graphing, <,> are open circles and <, > are closed.Shade in the appropriate direction. Inequalities1. Solve: 3x – 9 = 152. Solve: 6 + 4m = -26Add the number by itself to both sides of the equation.Divide by the number with the variable on both sides of the equation. Two-StepEquationsTimeDistance11502300How far would you go in 10 minutes?3450Divide the numbers in the two columns to determine the coefficient.Multiply that number by the given number of minutes. PatternsPractice for Algebra1. Simplify: 2(-4x – 3)2. Simplify: -4x + 9 + 8x - 23. Simplify: (-4x + 5) – (3x – 10)4. Which operation would be last when solving the inequality -5x + 9 < -65. Solve: 5x – 10 = 256. Solve: 3(x + 2) = 90 7. Solve and graph: 9x < 72.8. If the pattern continues, how far will it be in 10 minutes?Time (min.)Distance (ft.)120240360Algebra continuedRulesExamples_____________ 1. Solve: 2(x – 1) + 4x = 46Multiply the number outside the parentheses by both terms inside the parentheses. Combine like terms.Add the number to both sides of the equation.Divide by the number next to the variable on both sides of the equation. Distribution/CombiningLike Terms Equation1. Solve: 12x – 9 = 9x + 15Do the inverse of +/- to the smaller variable on both sides of the equation.Add the constant to both sides of the equation.Divide by the number with the variable on both sides of the equation. Variables onBoth Sides of the Equal Sign Equation Write and solve an equation for the following: A granola bar costs $2 and candy is $.50 each. You have $5. How many pieces of candy can you get?Create a two-step equation with a solution of 5. Prove your solution is correct.Write an equation as: cost=price of 1 item +cost of other itemxSubtract the constant on both sides of the equation. Divide by the coefficient on both sides of the equation.The solution of an equation is the value that makes the equation true. In other words, what is x?Writing/Solving TwoStep EquationsPractice for Algebra continued Solve: 8x – 4 = 12x + 12 Solve: 7(x – 2) + 3x = 463. Write and solve an equation for the following: A flower shop charges $3 per rose plus a $5 delivery fee. You spent $59 on roses. How many roses did you order?Percents1. 81% of all ticket sales were to adults. If there were 500 tickets sold, how many were to adults?2. Last year, there were 200 students in 6th grade. This year, there is 150% of that number. How many 6th graders are there this year?RulesExamples_____________ Change the percent to a decimal by moving the decimal point 2 places left.Multiply the decimal by the number. Percent of aNumberShirts are $40. They are on sale for 10% off. What is the sale price? Change the percent to a decimal by moving the decimal point 2 places left.Multiply the decimal by the price.Subtract your answer from the original price. DiscountInterest = principal ? rate ? timeFirst change the percent to a decimal by moving the decimal point 2 places left. How much interest would there be on a $1000 loan at 6.25% for 10 years?InterestSubtract the numbers. Divide by the ORIGINAL number.Multiply by 100.If the numbers went up, it is an increase.If the numbers went down, it is a decrease. Last year, there were 25 students in a class. This year, there is 30. What is the percent of change? Is it an increase or decrease? Percent of Change A $40 item is marked up 50%. What is the selling price of the item?Change the percent to a decimal by moving the decimal point 2 spaces left.Multiply the decimal by the cost.Add the product to the cost. MarkupPractice for Percents1. There were 400 students in attendance. 51% are boys. How many are boys?2. A $30 watch is discounted 15%. What is the sale price?3. You invested $5000 for 20 years at 7.25%. How much interest did you earn?4. A $50 watch was marked up to $60. What is the markup rate? Is it an increase or decrease?5. You bought an item for $25 on Ebay and plan on marking it up 65%. What price will you sell your item for to the nearest dollar?Rational NumbersRulesExamples_____________ Give an example of the commutative property.Give an example of the distributive property.When you switch terms, you are using the commutative property.When you multiply the term outside the parentheses by all terms inside the parentheses, you are using the distributive property. PropertiesIt was -15 degrees at 10 AM. By 2 PM, the temperature was 30 degrees. How much did the temperature rise?To find the distance between two integers, subtract the numbers, and take the absolute value of the answer. DistanceEvaluate if x = 9 and y = 4: xy ÷ 2Substitute the number for the variable. Multiply. If the signs are the same, the answer is positive. If the signs are different, the answer is negative.Divide. If the signs are the same, the answer is positive. If the signs are different, the answer is negative.EvaluatingFind the product of (-1/9)(-1/2).If the signs are the same, multiply and make the answer positive.Product means multiply. For fractions, multiply the numerators, multiply the denominators, and simplify.Multiplying1. What is the decimal 31/45?2. What is 1/3 as a decimal?Divide numerator ÷ denominator in calculator.Repeating decimals repeat.Put the repeating sign over the numbers that repeat. Fractions toDecimalsPut in order from least to greatest:62.5%, .0625, 5/9Change all numbers to a decimal.Move the decimal point on a percent 2 places left.For fractions, divide numerator ÷ denominator on the calculator.Place in order.If one digit is repeating, it is larger than the same number not repeating. Ordering RationalNumbersYou start at a distance above sea level of 50 feet. You hike down 40 feet, up 5 feet, down 30 feet, and up 20 feet. Where do you end your hike?Create an expression where you are adding all of the numbers.Use your calculator to complete the problem. Writing/SolvingRational #ProblemsPractice for Rational Numbers1. What property is demonstrated by 6 + -6 = 0?2. You started hiking at 31.3 feet below sea level. At the end of your hike, you were at 56.2 feet above sea level. How many feet did you climb? 3. If x = 3 and y = -1, what is the value of xy ÷ -3?4. What is the product of (-2/7)(-5/6)?5. What is the decimal equivalent of 23/45?6. Put the following numbers in order from least to greatest:12.5%, .125, 1/67. Change 1/6 to a decimal.8. You have a bank account balance of $305. You withdraw $40, deposit $25, withdraw $60 and deposit $10. What is your account balance at the end of the month?StatisticsRulesExamples_____________ 345186094615Compare the populations:Check the middle line-it’s the median.Subtract the ends of the boxes. The larger difference has the greater variation. Comparing PopulationsFind the median: 93, 45, 45, 100, 38.Put the numbers in order from least to greatest.Cross off one from each end. The middle number is the median. MedianFind the mode: 93, 45, 45, 100, 38.The number that occurs the most is the mode. Mode Find the mean: 93, 45, 45, 100, 38.Add all the numbers.Divide by the number of numbers. Mean Find the range: 93, 45, 45, 100, 38.Highest number – lowest number RangeWhat’s a biased sample for finding out the most popular instrument at a school?Biased samples ask people of a certain population the question regarding their own population. BiasedSamplePractice for Statistics1. Find the mean, median, range, and mode using the following data:1, 2, 3, 3, 4, 5, 6, 7, 8.2. What would be a biased sample if you wanted to know the most popular sport?3. Compare the populations. ................
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