# Virginia Placement Test Practice Questions and Answers

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1 Virginia Placement Test Practice Questions and Answers

3 Practice Problems for UNIT 1 Operations with Positive Fractions 1. If you have four quarters, three dimes, two nickels, and two pennies, what fraction of the whole coin collection is in dimes?. Write as an improper fraction.. Write 9 5 as a mixed number. 4. Express 55using exponents. 5. Find the prime factorization of 180. Express your answer in exponential form. 6. Write 4 90 in simplest form. 7. Write the ratio of 14 days to weeks in simplest form. 8. Write the ratio of 4 teachers to 14 students in simplest form. 9. Write the rate of 400 miles in 8 hours in simplest form. 10. Find the LCM for8,1, and Find the LCD for 1, 1, and Enter the correct symbol (,,). 1. Add or subtract. 14. Add or subtract. 15. Add or subtract. 16. Add or subtract. 17. Add or subtract. 18. Add or subtract ? 4 15 Page 1

5 4. Your car uses 15 gallons of gasoline on a 10 mile trip. Find your car s miles per gallon. 5. The nurse s orders are to give the child tablespoons of medicine per day in 4 equally divided doses. How much medicine is to be given at each dose? 6. To maintain financial aid, a student must pass at least of their attempted credits each semester. If you are taking 16 credits this semester, how many credits must you pass? Practice Problems for UNIT Operations with Positive Decimals and Percents 1. Write twenty one and fifty six thousandths as a number.. Identify the place value of the digit 7 in the number Add Multiply 0.5 and Divide 5.7 by Simplify Round 0.47 to the nearest hundredth. 8. Estimate by first rounding each number to the nearest whole number. Give your estimate as a whole number. 9. Estimate.49 x by first rounding each number to the nearest whole number. Give your estimate as a whole number. 10. The square below contains 100 smaller squares, and 5 of them are shaded. What percent of the whole is shaded? 11. Write 5/8 as a percent. 1. Convert /16 to a decimal. 1. Convert 0.8 to a fraction 14. Write 0% as a fraction in simplest form. 15. Write 1.5% as a decimal. 16. Order the list of fractions and decimals from smallest to largest. 5/6, 0.658, 7/10, is what percent of 150? 18. Mrs. Toner s fifth grade class increased from 16 students last year to 0 students this year. What percent increase is this? 19. At the local paper mill, the number of industrial accidents decreased from 15 accidents last month to just 9 accidents this month. Find the percent decrease. 0. A laptop computer is priced at \$650. If the sales tax is 5%, find the total cost of the computer, including sales tax. 1. Scott Samuels had pharmaceutical sales of \$4,500 last month. If his commission rate is 9%, find the amount of his commission. Page

6 . Bill and Sue Maples borrowed \$8,000 for years at a simple interest rate of 18% per year. How much interest will they pay?. In the pie chart below, what percent of the Johnson s weekly expenses are spent on clothing? Johnson Family Weekly Expenses Clothing \$100 Groceries \$150 Utilities \$15 Transportation \$75 Entertainment \$50 4. The pie chart below shows sales by quarter for Smith Plumbing. If the total sales for the year are \$60,000, calculate the sales for the rd Quarter. Yearly Sales for Smith Plumbing 4th Qtr 9% rd Qtr 10% nd Qtr % 1st Qtr 58% Page 4

7 5. Using the bar graph below, determine how many Juniors are taking a math class if there are a total of 450 Juniors at the high school. Students Taking a Math Class Percent Freshman Sophomores Juniors Seniors 6. Using the line graph below, which month shows the greatest increase in sales for G Mart? Monthly Sales for G Mart Millions J F M A M J J A S O N D Month 7. Convert 7 feet to inches. 8. Convert 4 ounces to pounds. 9. Convert 1.8 meters to centimeters. 0. Convert.6 kilograms to grams. 1. Convert 750 milliliters to liters.. Using the conversion table, convert 5 quarts to liters.. Using the conversion table, convert 10 centimeters to inches. 4. Convert ½ hours to minutes. 5. Convert 68 degrees Fahrenheit to Celsius, using the formula. 6. Convert 15 degrees Celsius to Fahrenheit, using the formula. 7. Jason is serving a 10 kilogram turkey to 8 people. How many grams of meat is he allowing for each person? Round to the nearest whole gram. 8. Dan orders supplies for the science labs. Each of the 4 stations in the chemistry lab needs feet of rubber tubing. If rubber tubing sells for \$8.75 per yard, how much will it cost to equip all the stations? Page 5

8 Practice Problems for UNIT Algebra Basics 1. Find the absolute value:. Find the absolute value: 18. Write in exponential form: Write in exponential form: Evaluate: 6. Evaluate: 4 7. Evaluate: Perform the indicated operations and simplify: 6 + ( 10) 9. Perform the indicated operations and simplify: 10. Perform the indicated operations and simplify: 7(.1) 11. Perform the indicated operations and simplify: 7 ( 9) 1. Perform the indicated operations and simplify: Perform the indicated operations and simplify: 5 + ( 10) ( 4) Perform the indicated operations and simplify: 8 4 ( ) 15. Perform the indicated operations and simplify: + 4 (10 ) Write as a decimal number: Write in scientific notation:,061,000, Write in standard notation: 9. X Identify the property of real numbers that is being illustrated a. n + 5 = 5 + n b. x + ( y + z ) = ( x + y ) + z c. a ( b + c ) = ab + ac d. b + -b = 0 e. a + 0 = a f. a 1 = a g. a 1 = 1 a 0. Combine like terms: 19n + 0b 9b + 4n 1. Simplify completely: 5 + (x 1). Evaluate when x is 5: x + x 1. In the formula A = h (B + b), find A when h = 10, B =0, and b = Solve: n + 7 = 16 Page 6

9 5. Solve: + x = 6. Solve: 8x = 7 7. Solve:.4 + t = To obtain her bachelor s degree in nursing, Judy must complete 10 credit hours of instruction. If she has completed 60% of her requirement, how many credits did Judy complete? 9. A factory manufacturing low voltage relays found 4 defective relays in a lot of 80 relays. At this rate, how many defective relays can be expected in a lot of 740 relays? 0. The population of Lewisburg was 10,80. It decreased by 0 each year for 5 consecutive years. What was the population after 5 years? 1. The baggage compartment of a bus is a rectangle prism. The dimensions of the baggage compartment are 8 ft by 4 ft by 6 ft. What is the volume of the compartment? What is the perimeter of the floor? What is the area of the floor? 8 ft Volume Perimeter of floor Area of floor 4 ft floor 6 ft Practice Problems for UNIT 4 First Degree Equations and Inequalities in One Variable 1. Solve the equation x 9.. Solve the equation 5x 40.. Solve the equation 5 x + 7 4for x. 4. x Solve the equation for x. Round your answer to two decimal places Solve the equation y 6 9 for y. 6. Solve the equation 5 + 7t t for t. 7. Solve the equation ( x+ ) 9 x 7 for x. 8. Solve the equation 7y4 5y y and identify the solution as finite, the empty set, or all real numbers. 9. Solve the equation S A D for A. 10. Solve the equation D rt for t. 11. Solve the equation Pl w for w. 1. Solve 15 5t 55, if possible. 1. Solve.5x State the solution using inequality notation. 14. Solve the inequality 5( x) ( x 9). State the solution using inequality notation. 15. Solve the inequality 5. 8 t State the solution using interval notation. Page 7

10 16. Write the solution using interval notation. 17. Solve the inequality x. 18. A company pays its sales representatives 5 cents per mile if they use their personal cars. A sales representative submitted a bill to be reimbursed for \$ for driving. How many miles did the sales representative drive? 19. If an object traveled 0 miles at a rate of 5 miles per hour, how long (in hours) did it take to travel this distance? 0. A hardware store is having a 0% off sale. If an item has a list price of \$14.40, what is the item's sale price? 1. Tickets for a college baseball game are \$9 for lower level seats and \$5 for upper level seats. For a particular game, 850 lower level seats were sold. The total revenue from the ticket sales was \$9650. How many upper level seats were sold?. The bill for repairing a car was \$45. The cost for parts was \$160. The cost for labor was \$7 per hour. How many hours did the repair work take? Practice Problems for UNIT 5 Linear Equations, Inequalities, and Systems of Equations in Two Variables 1. Determine the coordinates of the point labeled 7. Determine which of the ordered pairs is a solution of the equation. x5 y+ 100 a) (,4) b) (0, ) c) ( 5,10) d) (4, 5). Graph the linear equation by completing the table. x y x+ 1 Page 8

11 4. Evaluate f () x x 1at x Estimate the x and y intercepts of the graph. 6. Graph the linear equation by plotting the x and y intercepts. x+ 4 y Sketch the graph of the equation y x + and label three points on the graph. 8. Graph. y 4 9. Graph. x 10. Sketch the graph of the linear inequality. 11. Find the slope (if possible) of the line passing through the points (4, 7) and (5, 10) Find the slope of the graph of the equation y x Find the slope of the graph of the equation by converting to slope intercept form. 5x8 y Find the slope of the given line. 15. Find the slope of 8, if possible 16. Find the slope of, if possible 17. Write the equation of the line that passes through the point Write the equation in slope intercept form. 4 0, 9 and has slope 9 m. 7 Page 9

12 18. Write the equation of the line that passes through the point (5, 5) and has slope m 5. Write the equation in slope intercept form. 19. Write an equation of the line that passes through the points ( 1, 10) and ( 5, ). Write the equation in slope intercept form. 0. Write an equation of a line passing through the points ( 5, 7) and ( 5, ). 1. Write an equation of a line passing through the points (1, ) and (14, ).. Write an equation of the line through the point (4, ) that is parallel to the line 5 x+ 6 y.. Write an equation of the line through the point (5, ) that is perpendicular to the line x+ 7y Determine whether 4,6, 7, 4, 4,5, 1, 1, or equations below. 5,8 is a solution of the system of 4 x+7y 0 x+9 y x y 5. Sketch the graphs of the equations and approximate any solutions of the system of x y linear equations. 6. If possible, solve the system below by elimination using substitution. x y 9 x+ y 7. If possible, solve the system below by elimination using addition. a b 7 4 a+b 8 8. Identify the system of linear equations as consistent and independent, consistent and dependent, or inconsistent. 4 x 4y 4 x y 6 9. Given 6 evaluate each of the following: 5,,, 0, Given the graph of below, evaluate 6, 0,, 1 Page 10

13 1. Given the graph of below, find such that 4. A hot air balloon at 100 feet descends at a rate of 85 feet per minute. Let y represent the height of the balloon and let x represent the number of minutes the balloon descends. Write an equation that relates the height of the hot air balloon to the number of minutes it descends.. You invest a total of \$5800 in two investments earning.5% and 5.5% simple interest. Your goal is to have a total annual interest income of \$8. Write a system of linear equations that represents this situation where x represents the amount invested in the.5% fund and y represents the amount invested in the 5.5% fund. Solve this system to determine the smallest amount that you can invest at 5.5% in order to meet your objective. Practice Problems for UNIT 6 Exponents, Factoring, and Polynomial Equations 8 1. Simplify the expression 7 x x uv. Simplify the expression. Assume that neither u nor v is zero uv s t 6. Simplify the expression 4. Find the value of Rewrite the expression. 5w using only positive exponents. Assume that z is not zero. 4z 9 8 Use the rules of exponents to simplify the expression x y 4 using only positive 6. exponents. Assume that neither x nor y is Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. a b 6 4 ab 8. Perform the indicated operations. Write each answer in scientific notation and then without exponents.. a). b) b Page 11

14 9. Is the polynomial below a monomial, binomial, trinomial, or none of these? 8x 4x 10. Find the sum 17x 5x 5 y y Multiply 1. Perform the division. 10z z z z 1. Find the sum 9x46x Find the difference x x 15. Multiply 5 x+ 69 x + 7 and simplify Find the difference x x x x 5 9. Perform the indicated operations and simplify. 5 x x 7 5 x 4 x Find the difference x x x x x 19. Multiply x 4x5x 7 and simplify. 0. Find the greatest common factor of gh, Factor the polynomialxy15x y 1x y.. Factor the polynomial by grouping, if possible. 9 8 gh, and. Factor the trinomial, if possible. z +14 z Factor the trinomial, if possible. m 7 m Factor the given polynomial z +0 z +7 completely. 6. Factor the trinomial, if possible. 0 g 6 g 1 7. Factor the difference of two squares: 5x 81y 8 gh, 4 y + y +8 y Factor the polynomial, if possible. 7 m +64n 9. Factor the polynomial below, if possible. z Solve the equation x 76x by factoring. 1. Solve the equation below by factoring. a +8 a+9 1. Solve the equation below by factoring. x 17 x +7x 0. An object is thrown upward from a height of 19 feet with an initial velocity of 64 feet per second. The height h (in feet) of the object after t seconds is modeled by the equation h t t How long will it take for the object to reach the ground? Page 1

15 4. The revenue R from the sale of x cameras is given by R 55 x x. The cost C of producing x cameras is given by C x. How many cameras must be produced and sold in order to break even? Practice Problems for UNIT 7 Rational Expressions and Equations 1. Identify all the values of x what make this expression undefined.. Identify all the values of x what make this expression undefined.. Rewrite this expression without negative exponents. 4. Simplify. 5. Given and, evaluate. 6. Perform the indicated operations and simplify Identify the Least Common Denominator of the two rational expressions Perform the indicated operations and simplify Perform the indicated operations and simplify Perform the indicated operations and simplify Perform the indicated operations and simplify Page 1

16 1. Perform the indicated operations and simplify. 1. Simplify. 14. Simplify. 15. Divide: 16. Use long division to find the quotient and express the remainder (if any) as a fraction Solve The current in the Red Cedar River is 6 mph. A canoe can travel 7 miles downstream in the same time that it takes to travel miles upstream when paddled at the same rate. Set up (but do not solve) a rational equation that could be used to find the rate the canoe is paddled, using x as this rate. 19. A loaded moving truck is traveling 0 mph faster than a freight train. In the time it takes the train to travel 15 miles, the truck travels 5 miles. Find the speed of the truck. 0. To estimate the number of fish in a lake, a park ranger catches 0 fish, tags them, and returns them to the lake. Later, 7 fish are caught, and it is found that 0 of them are tagged. Estimate the number of fish in the lake. 1. Source of Heat A will melt a pound of ice in hours and Source of Heat B will melt a pound of ice in 5 hours. How long will it take to melt a pound of ice if both sources are used at the same time? Practice Problems for UNIT 8 Rational Exponents and Radicals 1. Rewrite the following using radical notation. Simplify, if possible Rewrite the following using radical notation. Simplify, if possible Rewrite the following using radical notation. Simplify, if possible. 9x 5 Page 14

17 4. Use the calculator to approximate the radical 8 to three decimal places. 5. Fill in the blanks. The square root of 7 is between the consecutive integers and since 7 is between and. 6. Use the calculator to approximate the radical 10 to three decimal places. 7. Use the properties of exponents to simplify each expression. a Write answers with positive exponents. 8 a 8. Use the properties of exponents to simplify each expression Write answers with positive exponents. x y 9. Simplify. Assume that all variables represent any real numbers (positive or negative) Simplify. Assume that all variables represent any real numbers (positive or negative). 16x 11. Simplify. Assume that all variables represent any real numbers (positive or negative) m p 1. Simplify. Assume that all variables represent any real numbers (positive or negative). 5 56x 1. Simplify. Assume that all variables represent any real numbers (positive or negative) Simplify. Assume that all variables represent any real numbers (positive or negative) Simplify. Assume that all variables represent any real numbers (positive or negative) Which of the following are like radicals? Circle your answers. 7, 5, 8, 50, Perform the indicated operation. Simplify if possible x Perform the indicated operation. Simplify if possible. 7x Perform the indicated operation. Simplify if possible. 6x 0. Perform the indicated operation. Simplify if possible Rationalize the denominator. 14 8x Page 15

18 . Rationalize the denominator.. Rationalize the denominator. 4. Solve. 4 x Solve. x x 4 6. What is the mathematical symbol for 1? 7. Which of the following represent imaginary numbers? 9, 7i, 5, 1, 1 4, 64, i 8. Simplify each of the following using the imaginary unit. 7, 5, 88, 50, 1 9. Simplify using the imaginary unit. 0. A wire is needed to support a vertical pole 18 feet high. The cable is to be anchored 8 feet from the base of the pole. How much cable is needed? Approximate the answer to three decimal places. 1. Find the missing side. Give the exact answer as a simplified radical x. Find the distance between the points (9, 4) and ( 9, 10). Give the exact answer as a simplified radical. Practice Problems for UNIT 9 Functions, Quadratic Equations, and Parabolas 1. Of the following relations, circle those that represent functions: (a) (b) (c) 1,1, 1, (d) 1,1,,1 (e) Page 16

19 . Of the following relations, circle those that represent functions: a. b. c. d. e.. State the domain of the function defined by the set of ordered pairs. {(,), ( 1,0), (4,5), (7, 8)} 4. State the range of the function defined by the set of ordered pairs. {(,), ( 1,0), (4,5), (7, 8)} 5. State the domain and range of the function defined by the graph. 6. State the domain of the function 1 7. State the domain of the function 8. Given evaluate For the function 1 evaluate. 10. For the function 4evaluate. 11. Find the roots of Find the roots of Find the roots of 10. Page 17

20 14. Find the roots of Find the roots of Describe the roots of a quadratic function by matching the following where 4 is the discriminant of the quadratic formula: (a) 0and is not a perfect square (b) is a perfect square (c) 0 (d) 0 (I.) The quadratic has no real roots. (II.) The vertex of the graph of the quadratic function is on the x axis. (III.) The quadratic can be factored. (IV.) The quadratic has two distinct irrational roots. 17. Write 66in vertex form and indicate the coordinates of the vertex. 18. Write 41in vertex form and indicate the coordinates of the vertex. 19. Identify the vertex of 1 17 by using the formula method. For questions 0 through 6 you are given Does the graph representing this equation open upward or downward? How do you know? 1. Determine the vertex of the parabola by putting the equation in vertex form.. Determine the axis of symmetry of the parabola.. Determine the intercepts of the parabola. 4. Determine the intercept of the parabola. 5. Determine the points on the parabola when 1 and when On the grid given, make a sketch of the parabola. Be sure to indicate the vertex, axis of symmetry, intercepts, and y intercept. Label the graph appropriately. Page 18

21 7. A rectangular shaped vegetable garden next to a barn is to be fenced on three sides with 10 total feet of fencing. Find the dimensions of the garden that will maximize the area. 8. If the revenue function for a market gardener growing a crop of tomatoes is given by 50 where is the number of bushels grown, what is the maximum revenue possible? How many bushels are sold to yield this maximum revenue? 9. A flare is fired directly upward into the air from a boat that is experiencing engine problems. The height of the flare (in feet) above the water, t seconds after being fired is given by the model If the flare is designed to explode when it reaches its highest point, at what height will this occur? How many seconds after the flare is fired does it explode? 0. Can a function have two y intercepts? Explain your answer. 1. Is it possible for the range of a quadratic function to equal all real numbers? Explain your answer. Page 19

22 Answers to Practice Questions for UNIT 1 Operations with Positive Fractions inches \$ > pounds. \$. A. \$840 B. \$ mpg tablespoon Page 0

23 Answers to Practice Questions for UNIT Operations with Positive Decimals and Percents %. Hundredths % % , 7 10, 0.75, % 18. 5% 0. \$ \$,85. \$,880. 0% 4. \$6, November in lbs cm 0.,600 g L. 4.7L..94 in min 5. 0 o C o F g 8. \$140 Page 1

24 Answers to Practice Questions for UNIT Algebra Basics A= n= x= a. Commutative b. Associative c. Distributive d. Additive Inverse e. Additive Identity f. Multiplicative Identity g. Multiplicative Inverse 0. n + 1b 1. + x 6. x=9 7. t= credits V=19 ft P=8 ft A=48ft Answers to Practice Questions for UNIT 4 First Degree Equations and Inequalities in One Variable 1. x=11. x=8. x=7 4. x= y= 9 6. t= The empty set 9. A=S+D 10. t= D r P l 11. w 1. 8, x , 16. [ 4, 5) 17. x miles hours 0. \$ upper seats. 5 hours Page

25 Answers to Practice Questions for UNIT 5 Linear Equations, Inequalities, and Systems of Equations in Two Variables 1. (, ). b) (0, ). x Y= x x int: (1,0) y int: (0, ) 6. x int: ( 8, 0) y int: (0, 4) 8. y=4 (horizontal line, slope = 0) 7. (0, ) (, 4) (6, 6) (any three points on the line would be correct answers will vary) 9. x= (vertical line with undefined slope) (0, ) (,4) (6,6) Page

26 10. y x 4. (7, 4) is the only solution 5. (,0) 11. m= 1. 1 m m m =1 15. m is undefined 16. m = y= 5x y = x 1 0. x = 5 1. y = y x 6 6. (, 1) x =, y = 1 7. (, ) a =, b = 8. Consistent and Independent 9. f(5)=9, f( )= 1, f(/)= 4, f(0)= 6, f(6.)= f( 6)= 4, f(0)=, f( )=0, f(1)= 1. x=, that is f() = 4. y=100 85x..05x +.055y = 8; x + y = 5800; y=\$4000. Page 4

27 Answers to Practice Questions for UNIT 6 Exponents, Factoring, and Polynomial Equations x 17. 0x 1x v 5 1 s t x x 11x 4 4 5x 0x 8x 8x 1 7 g h wz x y 7. b 7a A) ; (4y )( y 7). (z+6)(z+8) 4. (m 15)(m + 8) 5. (z+9)(z+1) 6. prime B) ; Binomial (m 4 n)(9m 1mn 16 n ) ( z 5)( z 5z 5) 10. x y 5z z x 14. x 0. x=0, 8 1. a = 4. x=0, 9, 8. t=6 sec 4. 9 or 11 cameras x 89x 4 x 14x x Answers to Practice Questions for UNIT 7 Rational Expressions and Equations Page 5

28 1. x= 7 4. v=, b ac w 1 7. (x )(x+) x 0 ( x)( x) x= 6, mph hours Answers to Practice Questions for UNIT 8 Rational Exponents and Radicals , 9, 64, Page x , 5, 50

29 , 7,, 8. 6, 5, 1, 5, ft Answers to Practice Questions for UNIT 9 Functions, Quadratic Equations, and Parabolas 1. b,d 16. a. IV. a, b, d.,1,4,7 4. {y y=, 0, 5, 8} 5. D: [ 1, ] R: [ 5, 4] 6. [1, ) 7.,, , (1, ), ( 1, 15) 6. Graph b. II and III c. II and III d.i 17. ; (, ) ;1, (, 1) 0. Up, since a>0 1. (, 1).. (4, 0), (, 0) 4. (0, 8) Page 7

30 x = Axis of symmetry y intercept (0,8) x intercept (,0) x intercept (4,0) Vertex (, 1) 7. The width is =60 feet and the length is 0 feet 8. 5 bushels must be sold to yield the maximum revenue of \$ The flare will reach its highest point of 149 feet at t = sec. 0. A function cannot have two y intercepts since no x coordinate can have more than one y coordinate for a function. 1. The range for a quadratic function can never equal all real numbers. Every quadratic function has either a maximum value (if a < 0) or a minimum value (if a > 0) So the range can never be, Page 8

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