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1 FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward are more relevant to the content of the PERT mathematics assessment.

2 Florida State College Review for PERT Mathematics Part MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question. Evaluate ( + )( ) 9 Find the area of the shaded area.. cm cm 9 square centimeters 9 square centimeters square centimeters square centimeters Find the average..,,, cm Solve.. For five mathematics tests your scores were,,,,. What was your average score? 9 Choose a strategy and solve.. Your car gets about 0 miles per gallon. You are planning to drive to see your friends who live about 90 miles away. How many gallons of gas will you need to purchase to make the trip to see your friends and to return home? State your answer to the nearest gallon? about 0 gallons about gallons about gallons about gallons 9. In 99 your house cost $,00. In 000 your house was valued at $0,0. How much did the value of your home increase? $9,0 $0,0 No increase, it was a decrease $, 0 0. While shopping you note the average price for a CD is $ including ta. You have $ in your pocket. About how many CDs can you buy? 9

3 Florida State College Review for PERT Mathematics Part. In 000 you weighed pounds. In 00 you weighed pounds, and in 00 you weighed pounds. How many pounds did you lose from 000 to 00? pounds No weight loss, you gained weight pounds pounds Solve.. Write this epression in words. + = Write the improper fraction as a mied number.. Solve for n. n The sum of and is The difference between and is The product of and is The quotient of and is Identify a fraction or mied number that represents the shaded part of the figure.. n Simplify the fraction Write the number as an improper fraction. Between the pair of numbers, place the correct sign: <, =, or >. 0. < > = < > =

4 Florida State College Review for PERT Mathematics Part Solve the problem below. Write your answer in simplest form.. Of a family s $0 weekly income, $ usually goes toward groceries. What fraction of the family s weekly income is usually spent on groceries? You need a piece of fabric yard long. Which of these is the smallest piece of fabric that would work? yard yard yard Subtract and simplify. Add and simplify

5 Florida State College Review for PERT Mathematics Part Solve the problem below and write your answer in simplest form. 9. A carpenter had a board long. He cut off. How long was the remaining board? 0. Brian was training to run a marathon. During the three-day period before the race he decided that he would train for a total of hours. If he trained for hours on the first day and 9 0 hours on the second day, how many hours would he need to train on the third day? Multiply and reduce to lowest terms Divide and reduce answers to lowest terms Solve the problem. None of these. Mary needs to save $0 for a computer. It was used and the sales man told her he would sell it to her for off the marked price. What is the price of the computer be after the mark down? $0 $0 None of these $0

6 Florida State College Review for PERT Mathematics Part 9. A bag of chips is ounces. A serving size is ounce. How many servings are in the bag of chips? servings 9 servings Write the decimal as a fraction or mied number in lowest terms Write the number in decimal notation.. five and hundredths Write the decimal number in words... one hundred sity-two and thirty-five tenths one hundred sity and two hundred thirty-five thousandths one hundred sity-two and thirty-five hundredths one hundred sity-two and thirty-five thousandths Write the number in decimal notation.. A strand of hair is twenty two thousandths of an inch thick. 0. inches 0.0 inches 0.00 inches inches Identify the place value of the in the decimal number below... Tenths Hundredths Thousandths Ten-thousandths Choose the answer with the correct sign between the pair of numbers < > = <.. >.. =. Put the numbers below in order from the smallest to the largest...,.0,. 0.,.0,.0.0,.0,..0,.,.0.,.0,.0 Round the numbers below as indicated. 9. Round 9.9 to the nearest whole number Round.9 to the nearest tenth.... Round to the indicated place.. The stock marked fell by.% last month. Round this to the nearest tenth of a percent..%.% %.%. The median income last year in this state was $,,. Round this to the nearest thousand dollars. $, $, 0.00 $,000 $,000

7 Florida State College Review for PERT Mathematics Part Write the ratio as a fraction in simplest form.. to In each of the problems below change the percent to an equivalent fraction or mied number.. % 00. %. 0 % Solve each percent problem below.. Find 0% of Find.% of Find 0% of $00. $ $0 $00 $ Find % of $,000. $ $000 $0 $00 Find the percent of increase or decrease in the problem below.. A surfer purchased a new surf board for $. The board was originally $0. What was the percent of change? % 0% % 0%. A crafter wants to make 0% profit on the items he makes. If the cost of materials is $.0, what should the items sell for to make a 0% profit? $. $.00 $. $.0 Find the mean of the set of numbers.. Your test scores are, 9,, 0,, and 9. Round your answer to the nearest whole number if necessary. 9 Use the tables to solve the following problems.. Dog Weight (pounds) Husky 9 St. Bernard Cocker Spaniel Yorkie. About how many times heavier is the largest dog when compared with the smallest dog?

8 Florida State College Review for PERT Mathematics Part Change the given quantity to the indicated unit.. 0 min = hours in = ft The following table is used to determine the minimum payment on a credit card bill. Find the square root of each of the problems below Find the perimeter of the figure below. 0. Balance $0- $.0-0 $ Min. Full $ 0% of Payment Balance balance $000.0 up $00 + % of balance greater than $000 ft ft ft What is the minimum payment if you owe $00? $00 $ $ $0 ft ft ft 9 ft ft. D. D. D. B. A. D. C. C 9. B 0. B. A. A.D. B. A. B.A. D 9. C 0. B. A. B. A. B. B. C. A. D 9. C 0. D. A.A. B. D. A. B. B. A 9. A 0. B. D. D. B. B. C. A. B. B 9. C 0. A. A. B. C. B. C. A. B. B 9. B 0. D. A. C. C. B. A. C. C. A 9. B 0. C. B. A A.B.C. D.D. D 9. C 0. A

9 Florida State College Review for PERT Mathematics Part Pre Algebra Practice. What is the perimeter of a rectangle that has a length of 9 cm and a width of cm? sq. cm cm 0 cm 0 sq. cm. What is the area of a square that has a side length of centimeters? cm sq. cm 0 sq. cm 0 cm. What is the area of a triangle that has a base of 9 inches and a height of 0 inches? in sq in 90 in 90 sq in. Use order of operations to simplify: (0 - ) 0. Use order of operations to simplify: ( ) Use order of operations to simplify: [ ( )]. Simplify: 9 ( ). Simplify: Simplify: y + y y + y y y + y + y + y + y + y 0. Simplify: Simplify: (0.)(.z).z 0. z.z. + z. Evaluate the following epression for = and y = : + y -. Evaluate the following epression for = and y = : ( y)( + y). Evaluate the following epression for = 0. and y =.: (y ) A

10 Florida State College Review for PERT Mathematics Part. Solve for : 0 = = 0 = 0. Solve for : + = + = = = =. Solve for : ( ) = ( ) = = = =. Solve for y: y = 0 9 y = y = y = 9 9. Solve for z: z = z y z = z = z = 0 0. Solve for z:. = 0.0z +. z = 0.9 z = 9 z = 0.0 z = 9. Solve for : =. =. =. = 0.. The formula for the perimeter of a rectangle is: P = L + W Solve for W when P = and L =. W =. W = W =. W =. Best Buy is selling a television for $0.00. Sales ta in Duval County is %. Using P as the amount I will have to pay for the television (including sales ta),write an algebraic equation that describes this transaction. P = (0.0)(0) P = P = 0 + (0.0)(0) P = 0(0.9). Jeremy put $0 into his savings account, which pays % per year simple interest and left it there for years. Using A as the total amount that will be in the bank at the end of the years, write an algebraic equation that describes this transaction. A = 0 + 0(0.0)() A = 0(0.0)() A = 0 0(0.0)() A = 0 + (0.0)(). Keisha is investing her money in an IR Initially she will be putting in $. Using C as the additional amount invested each month, translate this problem into an algebraic epression that will show how much Keisha invested for the entire year. + C C C + C 9

11 Florida State College Review for PERT Mathematics Part. Multiply and simplify where possible: ( ) 9. Multiply and simplify where possible: (y + z ) y + z y + z y + z + y + z. Multiply and simplify where possible: y( y z) y y z y y z y y z y z 9. Multiply and simplify where possible: ( )( + ) Multiply and simplify where possible: z + z + z z + z. Simplify: ( ) + ( + ) Simplify: (z z + ) (z z + ) z z + z + z z z z + z. Simplify:(z + ) +(z ) (z + z 9) z + z + z + z + z + z z + z 0. Multiply and simplify where possible: ( z )( z ) z z z z 9. C. B. B. D. D. C. D. C 9. B 0. A.B. D. A. B. B. A. C. C 9. D 0. D. D. A. C.A. D.D. B. A 9. B 0. D. A. C. B. B 0

12 Florida State College Review for PERT Mathematics Part Section Sample Problems. Simplify: a a a a a. Simplify: 0. Find using the greatest common factor. a b ab a b ab ab ab. Factor y. y( y) ( y)( y ) ( y)( y ) not factorable. Factor the trinomial a a ( a )( a ) ( a )( a ) ( a )( a ) ( a )( a ). Simplify: y y y y y y. Simplify: ( y 0 ) y 0 0. Find the and y intercepts and the slope of the given line: y. (, 0), ( 0, ), (, ), (, ), 0 0 (, ), (, ), 0 0 (, 0), ( 0, ), 9. To graph y you would begin at the y intercept which is: Solve for :. Solve for : a by c a by c c by a c by c by a a. Solve for : 0,,,,. Solve for :

13 Florida State College Review for PERT Mathematics Part Solutions Section Sample Problems:. D. B. D. C. A. A. A. A 9. B 0. C. C. B. C Simplify each problem Sample Problems Using Radicals a a a.. n n a a a b... k k.. r r h.. 0a.. n.. 0a ab 0a... k.. r 0hr Sample problems using factoring If necessary find the greatest common factor and then factor completely.. cd c d 0c d. y y. 9. m n. c c. b b. cd ( d c c d). ( y )( y ). ( )( ). ( m n)( m n ). ( c )( c ). ( b )( b )

14 Florida State College Review for PERT Mathematics Part Sample problems simplifying rational epressions Factor and reduce each epression to lowest terms.. 0 bc. t y y. b t y y. a a a a c. b. t. y y. a a. yz z. t 9 t y t t. a a a. y Sample problems multiplying and dividing rational epressions 9. d df a.. f a a a Sample problems adding and subtracting rational epressions. ab a. m m m. h 9h 0 h 0h. y y y y y. y y d d d d d. b ab. m m m h. h h

15 Florida State College Review for PERT Mathematics Part. y y y y. d d d 0 d Sample problems graphing linear equations. Give the slope and y intercept of the line determined by the equation y =.. Give the slope and y intercept of the graph for the equation. y. Give the and y intercepts for the line determined by the equation - + y =. Graph the equation y = + use an,y coordinate grid.. Graph the equation y use an,y coordinate grid.. Graph the equation y = use an,y coordinate grid.. Slope and y intercept. Slope and y intercept. intercept. Solve for when y = 0 and you get. Y intercept Solve for y when = 0 and you get.. To graph y = +, begin at the y intercept then count the slope which would be down units and right one unit because all whole numbers have a denominator of. Place a point here and connect with the y intercept.. To graph y, begin at the y intercept then count the slope which would be down units and right units. Place a point here and connect with the y intercept.. Use the intercepts to graph this equation. The intercept is and the y intercept is. Connect the intercepts with a line Sample problems solving quadratic equations Sample problems involving only a squared variable term... ( )... 9,..

16 Florida State College Review for PERT Mathematics Part Sample problems that can be solved by factoring: = or =. = or =. = or = Sample problems that can be solved using the quadratic formula. Write your answers in set notation {-9, -}.{0., -.}. {,}

17 Florida State College Review for PERT Mathematics Part Practice for Intermediate Algebra.Solve for :. Solve the system of equations: a b a b. Simplify: y 0y y 9 y ( y ) y y y y y y y ( y ) y y y y (, ) (, ) (, ) (, ). Solve the system of equations: y y. Add and simplify: ( ) 9 ( ) (, ) (, ) (, ) (, ). Solve the system of equations: y 9 9y (, ) (, ) (, ) (, ). Simplify: 9. Simplify: ( )( ) ( )( ) ( ) 9. Simplify: 9 0 ( ) ( )( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )( )

18 Florida State College Review for PERT Mathematics Part 0. Solve: 9. If f ( ), find f ( ).. If f ( ), find if f ( ) 9. Given f ( ), find f ( a ) a a a a a a a a. Simplify (put in rationalized form):. Simplify (put in rationalized form):. Write a linear equation in standard form that goes through the points (, ) and (, 9 ) : y y y y. Write a linear equation in slopeintercept form that is perpendicular to y and crosses (, ). y y y y. a. b. a. d. c. b. a. d 9. c 0. a. b. b. b. a. c. c. a

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