COLLEGE ALGEBRA PREREQUISITE REVIEW NAME: CLASS: DUAL ENROLLMENT MAC 1105 DUE DATE: 08/23/10

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1 COLLEGE ALGEBRA PREREQUISITE REVIEW NAME: CLASS: DUAL ENROLLMENT MAC 1105 DUE DATE: 08/2/10 Evaluate the algebraic expression for the given value or values of the variable(s). 1) x2-2(x - y); x = 6 and y = 2 1) 2) y - 7x ; x = -1 and y = 5 2) 6x + xy Solve. ) The winning times (in seconds) in a speed-skating event for men can be represented by the formula T = x, where x represents the year, with x = 0 corresponding to (For example in 1992, x would be = 72.) According to the formula, what was the winning time in 1965? Round to the nearest hundredth. ) 4) It is estimated that y, the number of items of a particular commodity (in millions) sold in the United States in year x, where x represents the number of years since 1990, is given by the formula y = 1.66x That is, x = 0 represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold in 1995? 4) Find the intersection of the two sets. 5) {2, 7, 4, 9} {4, 11, 2} 5) Find the union of the two sets. 6) {2, } {2, 4, 8} 6) List all numbers from the given set B that are members of the given Real Number subset. 7) B = {20, 5, -9, 0, 0.4, 4} Integers 7) 1

2 8) B = {18, 7, -14, 0, 0.7, 4} Natural numbers 8) 9) B = {8, 8, -4, 0, 6, 4, 0.6, 0.72} Irrational numbers 9) 7 10) B = {17, 6, -2, 0, 7, 25, 0.6, 0.92} Rational numbers 10) 8 11) B = {10, 8, 0, 5, 16, -0.8, 0.2, -} Real numbers 11) 6 Rewrite the expression without absolute value bars. 12) ) 1) 12 + (-1) 1) 14) ) Simplify the algebraic expression. 15) (11z + 12) - (z - 8) 15) 16) -(2x - 5) - 4x ) Write the algebraic expression without parentheses. 17) 1 (4x) + [(2x) + (-2x)] 17) 4 18) - (5z - 7w + 4y) 18) Simplify the exponential expression. 19) x6 x 19) 2

3 20) (-9x4)(-7x7) 20) 21) (-x4y)(-4x6y2) 21) 22) x 1y1 x10y7 22) 2) -18x 8y8z8 2x4y5z7 2) 24) -15x 9y1 5x4y4 24) 25) x7y0 25) 26) 4x-4y5 26) 27) 12x 4y9 6xy-7 27) 28) x 4y-2 z-9 28) 29) (x7) -4 29) 0) (x-4)- 0) 1) (x-y6)-1 1) 2) (x-1y7z-5) -2 2)

4 ) -22x10y8 11x15y- ) 4) 4x2y2 z4 4 4) 5) 8x-4y-z 2xy-z- - 5) 6) 2-8x-2y 2-5x-5y6 6) Use the product rule to simplify the expression. 7) 24 7) 8) 20 8) Solve the problem. 9) The formula v = 2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on a curved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at an exit ramp as 810 feet. What is the maximum safe speed? 9) 40) The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9 x where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 6 months of age and a child 25 months of age? 40) Use the quotient rule to simplify the expression. 41) ) 4

5 42) ) 4) 45x 5x 4) 44) 120x4 6x 44) Add or subtract terms whenever possible. 45) ) 46) 6x - 150x x 46) Rationalize the denominator ) 15 47) 48) ) 49) ) 50) ) 5

6 Evaluate the radical expressions or indicate that the root is not a real number. 51) ) Simplify the radical expression. 52) ) Add or subtract terms whenever possible. 5) y 24x - 192xy 5) Evaluate the expression without using a calculator. 54) 274/ 54) Simplify using properties of exponents. 55) (4x2/)(9x1/4) 55) 56) (25x4y6) 1/2 56) Solve the problem. 57) The algebraic expression 0.07d/2 describes the duration of a storm, in hours, whose diameter is d miles. Use a calculator to determine the duration of a storm with a diameter of 15 miles. Round to the nearest hundredth. 57) Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 58) 6x x2 58) 59) 2x - 7 x 59) 60) x2 + x4 - x + 60) Perform the indicated operations. Write the resulting polynomial in standard form. 61) (4x4-8x - 7x2 + 8) - (9x4 + 4x - 2x2 + 9) 61) 62) (4x5-4x4-6x - 2) + (6x5-4x4 + 2x + 5) 62) 6

7 6) (4x2 + 4x + 7) + (2x2 + 8x + 4) - (5x + 2) 6) Find the product. 64) (x + 8)(2x2 + 9x + 6) 64) 65) (9x - 1)(x2-6x + 1) 65) 66) (5x2 + 9)(x2 + 5) 66) 67) (2x + )(x2 + ) 67) Solve the problem. 68) Write a polynomial in standard form that represents the volume of the open box. 68) x 11-12x 7-12x 7

8 69) Write a polynomial in standard form that represents the area of the shaded region. 69) x + 7 x + x + 2 x + 1 Find the product. 70) (2x + 4) 70) Perform the indicated operations. 71) (9x4y2 + 11xy + 12y) - (x4y2 + 5xy + 10y + 7x) 71) 72) (11x4y2-10x2y2 + 6xy) + (2x4y2-5x2y2 + 9xy) 72) 7) (12x4y2-5x2y2 + 4xy) + (x4y2-11x2y2 + 7xy) 7) Find the product. 74) (x2y2-6) 2 74) 75) (2xy2 - y)(2xy2 + y) 75) 8

9 Factor out the greatest common factor. 76) x(x + 1) + 4(x +1) 76) 77) x(x - 4) + 5(x - 4) 77) 78) x2(x - ) - (x - ) 78) Factor by grouping. Assume any variable exponents represent whole numbers. 79) x - 4x2 - x ) 80) x - 6x2 + 7x ) Factor the trinomial, or state that the trinomial is prime. 81) x2 + 4x ) 82) 5x2 + 7x ) 8) 10x2 + 7x ) 84) 5x2-22xy - 48y2 84) 85) 12x2 + 25xy + 12y2 85) Factor the difference of two squares. 86) 4x2-49y2 86) 9

10 87) (81x4-16) 87) Factor the perfect square trinomial. 88) 81x2-18x ) Factor completely, or state that the polynomial is prime. 89) 10x - 250x 89) Solve the problem. 90) Write an expression for the area of the shaded region and express it in factored form. 90) 9 y 9 y 91) Write an expression for the area of the shaded region and express it in factored form. 91) 10

11 92) Find the formula for the volume of the region outside the smaller rectangular solid and inside the larger rectangular solid. Express the volume in factored form. 92) a b b 8a a Find all numbers that must be excluded from the domain of the rational expression. 4 9) x - 7 9) 94) x - 2 x ) 95) x - 4 x2-2x ) 96) x + 4 x2-1x ) Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. x + 97) 97) 15x2 + 21x

12 x2 + 7x ) x2 + 11x ) 99) 7x 2 - x + 20 x ) Multiply or divide as indicated. 100) x + 1 x - x2 + x 6x -54x ) 101) x 2 + 1x + 42 x2 + x - 42 x2-49 x2 - x ) 102) x2 + 9x + 20 x2 + 11x + 0 x2 + 10x + 24 x2 + 8x ) 10) x 2-12x + 20 x2-15x + 6 x2-11x + 24 x2-8x ) 12

13 104) (y - 10) 2 11y ) 105) (x + 7) 2 x - 7 x x ) 106) x2 + 6x + 9 x2 + 11x + 24 x2 + x x2 + 1x ) 107) 5x 2 + 7x - 24 x - 9 x2 - x 25x2-64 x + 9 5x 107) Add or subtract as indicated. 108) 2x + 4 6x x + 9 4x ) 1

14 109) x 2-7x x x ) 110) x x2-2x x - 6 x2-2x ) 111) 9x + 14 x2 + 11x x + 5 x2 + 11x ) 112) 7 x + 8 x ) 11) 7 x x 11) 114) x + 5 x2-6x x + 1 x2-7x ) 14

15 115) x x x x ) Solve the problem. 116) Express the perimeter of the rectangle as a single rational expression. 116) 8 x x Simplify the complex rational expression. x ) x ) 118) x + 1 x ) 15

16 119) 1-1 x x 119) 120) x - x x - x ) 121) 1 x + 6 x ) 122) x 2 - x x x ) 16

17 12) x x ) 124) x x x ) 125) x x ) 17