ASU Mathematics Placement Test Sample Problems June, 000. Evaluate (.5)(0.06). Evaluate (.06) (0.08). Evaluate ( ) 5. Evaluate [ 8 + ( 9) ] 5. Evaluate 7 + ( ) 6. Evaluate ( 8) 7. Evaluate 5 ( 8. Evaluate ) ( 8 ) ( ) 6 9. Evaluate 8 5 0. Evaluate..009 +.5. Evaluate ( ). Evaluate 5 [ ]. Evaluate the expression when x = and y = x xy + y. Evaluate the expression x when x = 5. Evaluate the expression when x = x 6 + x 6. Multiply and simplify ( v) 7. Multiply and simplify x(x ) (x + )(x ) 8. Simplify [ (x + ) ] 5x x x x + + 9x x + 9 9. Add and simplify + x + x 0. Simplify ( xyz). Simplify (a b) (ab ). Rewrite x without negative exponents. Simplify (xy ). Simplify 75 5. Simplify x 6. Simplify 6x (x ) x(x ) 6 7. Multiply and simplify 8. Divide and simplify x + x x + x + x x 8x + 7 x + x x 6x + 9 x ( ) t 9. Simplify + t ( ) t t 6 0. Rationalize the denominator and simplify. Rationalize the denominator and simplify. Divide and simplify y 9x 6 7xy x x. Simplify 9 6. Simplify 8x yz xy z 5. Divide x 9x x 8 8 t
6. Simplify x 5x x 9 7. Multiply and simplify u u 8 8. Simplify a + b 5a b 9. Simplify t [ t ( 5 t + t ) ] 0. Simplify 5xy x(x y). Multiply and simplify u( u u ). Simplify x [x (x + 7) ]. Simplify x x. Simplify 8 5. Multiply and simplify ( ) 6. Simplify 9x y 7. Multiply and simplify ( x )( x + ) 8. Add (7 x x ) + (y + ) 9. Subtract and simplify x x x + 50. Subtract (7 x x ) (x + ) ( ) 6 x 5. Simplify x 5. Multiply and simplify (x + )(x x + ) 5. Multiply and simplify [ (x y)] 5. Rationalize the denominator and simplify 55. Solve (x 5)(x + ) = 0 56. Solve x = 6 57. Solve the inequality x 5 58. Solve for y when y [y + (y )] = 0 59. Solve the system of equations x + y = x y = 9 60. Solve (x + )(x ) = 8 6. Solve the inequality > x > 6. Solve 6. Solve t = 6. Solve x + = x x + x + = 7 x + x 6 65. Solve x x 6 = 0 66. Solve for l when P = w + l 67. Solve 9x x = 0 68. Solve (x ) = x + 69. Solve + 0.5x = 5 70. Solve the system of equations x + y = 5 x y = 5 7. Solve for x when x + x = 7. Solve x 0 =
7. Solve x + 5 7. Solve (x + ) = 7 75. Solve x = x x + = 5 76. Solve the system x 5y = x + y = 5 77. Solve 7 x = 78. Solve x x 79. Solve x = 80. Solve x + = 5 8. Solve 6x x = 5 8. Solve the system of equations x + y = 5x + y = 8. Solve x 5x = 0 8. Solve x = 85. Solve x = x 86. Twelve is % of what number? 87. 90 is what percent of 50? 88. A candy store wishes to package a box of light and dark chocolates. The light chocolates cost $ per pound and the dark chocolates cost $5 per pound. If one pound of light chocolates is used, how many pounds of dark chocolates are needed to produce a mixture worth $.75 per pound? 89. How muchmustbe invested in an accountthatearns 6% simple interest in order to have $0, 000 in this account year from now? 90. A shirt that lists for $8 is advertised at 0% off. Find the selling price. 9. Atotalof$ 0, 000 is invested into two funds paying 7 % and 9% simple interest. The combined annual income for the two funds is $89. Determine how much is invested at each rate. 9. A company has 0 employees. If the number of employees is increased by 0%, how many employees will the company have? 9. Find the total amount paid for a washing machine if the downpayment of $75 is made plus 7 monthly payments of $50 each. 9. Two people travel to separate cities in the same amountoftime. The firstpersontravels 0 milesat an average speed that is two miles per hour slower than the second person. The second person travels 7 miles. What is the average speed of the slower car? 95. Find a number such that 7 added to twice this number is 76. 96. The sum of three consecutive integers is 7. Find these integers. 97. A man s shirt, advertised for sale at 0% off the original price, is now selling for $5. Find the original price of the shirt. 98. The length of a rectangle is three inches more than twice its width. The area of the rectangle is 7 square inches. Find the dimensions of the rectangle. 99. The product of two consecutive positive integers is 7. Find these numbers. 00. The sum of two numbers is 7. The second number is four less than four times the first number. Find the numbers. 0. Determine the slope of the line passing through the points (, ) and(, 5). (a) (b) 8 8 (d) 5 0. Find the slope of the line given by the equation 8x y = 7. (a) (b) 7 (d) 0
0. Using the slope, determine whether the graph of the line that is given by the equation x y+ = 0 rises, falls, is horizontal, or is vertical. (a) Rises (b) Falls Horizontal (d) Vertical (e) None 0. Find an equation for the line passing through the points (, ) and ( 6, ). (a) x + y = 7 (b) y + = 0 x + y + = 0 (d) x + y + 6 = 0 (e) None 05. Determine the slope of a line parallel to the line given by x y + 8 = 0. (a) (b) 8 8 (d) 5 06. Find the y-intercept of the graph of the equation 6x + 8y = (a) (,0) (b) 8 (0, 8 ) (d) ( 6, 8) 07. Determine the graph of the equation x y = (a) (b) (d) 08. Sketch the half-plane determined by the inequality x y > (a) (b) (d) 09. Find an equation for the horizontal line passing through the (, ). (a) y + = 0 (b) x = 0 y = 0 (d) x + = 0 0. Find an equation for the line passing through the point (, ) with the slope m = (a) y = x (b) x y = x y = 5 (d) x y = 5. Find an equation for the line passing through the point (, 6) and perpendicular to the line y = 0 (a) x 6y = 0 (b) x = y + 6 = 0 (d) y = 6. Evaluate 6 + (a) 7 (b) (d) 7. Simplify (a b ) (a b) (a) a8 b 5 a 9 b 7 (b) a8 b (d) a9 b 5
. Simplify x 5 x 7 (a) 6x 5 6x 5 (b) 0 (d) 6x 5. Solve the inequality 5x 7 (a) x 5 (b) x 5 x < 5 (d) x 9 5 6. Multiply (x ) (a) x x (b) x + x (d) x x + 7. Solve 5x = x (a) x = 0 (b) x = 0, 5 x = 0, 5 (d) No real solutions 8. Write without negative exponents xy (a) x y (b) xy xy (d) xy 9. Find the slope of the line going through (, ) and (, ) (a) 0 (b) undefined 7 (d) 7 0. Simplify 8 (a) 9 (b) (d),. Solve x x + = (a) ± (b) ± ± (d) ±. Evaluate the expression a a + 5 given that a = (a) (b) 0 5 (d) 9. A man has coins in dimes and nickles. His total is $.55. How many nickles does he have? (a) 0 (b) (d) Cannot be solved. Solve x + x = (a) ± 5 (b) ± 5 No real solution (d) ± 5 5. Simplify a/ a 5/ a / (a) a / (b) a 7/ (d) a 9/ a 7/ 5