Final Exam Review - MAT 0028

Transcription

1 Final Exam Review - MAT 0028 All questions on the final exam are multiple choice. You will be graded on your letter choices only - no partial credit will be awarded. To maximize the benefit of this review, you should work out each question without the use of notes, textbooks or the assistance of others. Check your answers, be prepared to ask questions, and practice! Simplify. 1) (-10) 28 B) ) B) ) ( ) 5-9 B) Evaluate the expression for x = -2, y = - 3, z = z 4) x -38 B) Evaluate the expression for x = -2, y = -3, z = 4. 5) 8x - y 2-7 B) Write the number in scientific notation. 6) 84,000, x 10-6 B) 8.4 x x x ) x 10-3 B) 1.06 x x x 10 4 Simplify the expression. Write the result using positive exponents only. 6p-2 8) 7p8 6 7p 16 B) 6 7p 10 6p10 7 6p16 7 Fall '08 - page 1

2 9) x4 x 9 1 x 5 B) - 1 x 5 x 5 -x 5 Use the product rule to simplify. Write the results using exponents. 10) (9x)(5x5)(x7) 14x 12 B) 45x 12 45x 13 15x 13 11) B) Simplify the expression. Write the result using positive exponents only. 12) x -8 x6 1 x 2 B) x 2 1 x 14 x 14 Use the power rule and/or the power of a product or quotient rules to simplify the expression. 13) x6y 4 x 10 y 5 B) x 24 y x 10 y x 24 y 4 Simplify the expression. 14) B) ) (-3x6yz8) 2 6x 12 yz 16 B) -6x 12 yz 16 9x 12 y 2 z 16-9x 12 y 2 z 16 16) -8x0-16 B) x ) (-2x)0-1 B) Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. 18) -6y ; binomial B) -6; monomial 4; binomial 0; binomial 19) -13y3 + 6y4-7 4; binomial B) 7; trinomial 4; trinomial 8; trinomial Fall '08 - page 2

3 Simplify the following by combining like terms. 20) -8r + 12r3 + 7r3-13r -2r B) -21r + 19r 3-2r 3 cannot be simplified Simplify the expression. 21) (2z + 6) 24z + 1 B) 14z z z + 67 Add or subtract as indicated. 22) (8x6-16x4 + 13) - (4x6 + 2x4 + 8) -9x 10 B) 4x 6-18x x 6-12x x 6-18x Add or subtract as indicated. 23) (6x2 - xy - y2) + (x2 + 5xy + 6y2) 7x 2 + 4xy + 5y 2 B) 7x2 + 6xy + 7y 2 5x 2-6xy - 7y 2 6x2 + 5xy + 6y 2 Multiply. 24) 7x(12x - 9) 84x 2-63x B) 12x 2-63x 84x 2-9x 21x 2 Find the product. 25) (5z - 8)(4z - 5) 9z 2-13 B) 20z 2 + 7z z 2-57z z Multiply. 26) (6a - 7)2 6a B) 6a 2-84a a 2-84a a ) (5p + 13)(5p - 13) 25p p B) 25p 2-130p p p ) (x + 2y)(x + 3y) x + 5xy + 6y B) x 2 + 2xy + 6y 2 x 2 + 5xy + 5y 2 x 2 + 5xy + 6y 2 Perform the division. 24x6 + 56x5 + 40x4 29) 8x5 3x x B) 8x + 7 3x + 7 3x + 56x x Fall '08 - page 3

4 30) 6x8-12x6-2x8 6x x 2 B) x x x 6 Factor out the GCF from the polynomial. 31) 40x (20x - 5) B) 10(4x) 10(4x - 1) 5(8x - 2) 32) 15m9-24m7-30m2 m2(15m 7-24m 5-30) B) 3m 2 (5m 7-8m 5-10) No common factor 3(5m 9-8m 7-10m 2 ) Factor the trinomial completely. If the polynomial cannot be factored, write "prime." 33) x2-6x - 16 (x - 8)(x + 2) B) (x - 16)(x + 1) (x + 8)(x - 2) prime 34) x2 + 13x + 40 (x - 5)(x + 1) B) (x - 5)(x + 8) (x + 5)(x + 8) prime Factor the trinomial completely. 35) 5x2-20x + 20 prime B) 5(x - 4)(x + 1) 5(x - 2)(x - 2) (x - 2)(5x - 10) 36) x2-14xy + 49y2 (x + 7y)2 B) (x - 7y) 2 (x - 7y)(x + 7y) x 2-14xy + 49y 2 37) x2 + 16x + 64 (x + 8)(x - 8) B) (x - 8) 2 (x + 8) 2 prime Factor the binomial completely. 38) 81x2-64 (9x + 8)2 B) (9x - 8)2 (9x + 8)(9x - 8) prime Factor the polynomial completely. 39) 2xy - 10x + 7y - 35 (2x - 5)(y + 7) B) (2x + 7)(y - 5) (2x + y)(7y - 5) (2x + 7y)(y - 5) 40) 8x2 + 6x - 9 (2x - 3)(4x + 3) B) (8x + 3)(x - 3) (2x + 3)(4x - 3) prime polynomial Fall '08 - page 4

5 Simplify the expression. 41) y2 + 5y + 6 y 2 + 8y + 12 y + 3 y + 6 B) - y2 + 5y + 6 y 2 + 8y y + 1 8y + 2 5y + 6 8y ) 7k k B) Multiply. Simplify if possible. 43) k2 + 9k + 20 k k + 40 k k - 8 k2 + 8k k 2-4k - 32 B) k2 + 8k k - 8 k k k k - 8 Find the quotient and simplify. 21x ) 7x B) (x - 1) (21x - 21) 7x - 7 Perform the indicated operation. Simplify if possible. 6 45) 15 + x + x x 8 15 B) x x 8 30 x x 46) 6x x x - 7 6x - 42 x - 14 B) x Rewrite the rational expression as an equivalent rational expression with the given denominator. x 47) x + 5 = 3x x 3x + 15 B) 5x 3x + 15 x 3x x + 15 Fall '08 - page 5

6 Solve the equation. 48) 7(y - 6) = 9y B) no solution 49) x2 - x = 20 x = -4, x = -5 B) x = -4, x = 5 x = 4, x = 5 x = 1, x = 20 50) 4.5m m = m B) 0 all real numbers no solution 51) x = x B) ) 3x2-21x + 30 = 0-2, -5 B) 0, 2, 5 3, 2, 5 2, 5 53) x 2 - x 5 = B) ) -7(x + 7) = 2 x - 9(x - 4) 149 B) 77 all real numbers no solution Solve the inequality. Graph the solution set. 55) -14r (6r + 10) {r r 3} B) {r r 3} {r r > 3} {r r < 3} Fall '08 - page 6

7 56) -9x x < 4-2x + 8 {x x 10} B) {x x > 2} {x x 10} {x x < 2} Write the sentence as an equation. Use x to represent "a number." 57) Twelve subtracted from four times a number yields x = 12 B) 4(x - 12) = 12 4x - 12 = 12 12(4 - x) = 12 Translate the question into a proportion. Do not solve. 58) A punch recipe calls for mixing 2 parts of orange juice with 5 parts of apple juice. Find how much orange juice should be mixed with 80 ounces of apple juice. x 5 = 80 B) 80 2 x = 2 x 5 80 = 5 x 2 80 = 2 5 Solve. 59) A phone costs $64 and a battery recharger costs $57. What is the total price for purchasing these items if the sales tax rate is 9%? $ B) $ $10.89 $ ) During an intramural basketball game, Team A scored 19 fewer points than Team B. Together, both teams scored a total of 151 points. How many points did Team A score during the game? 66 points B) 67 points 85 points 75 points Solve the equation for the specified variable. 61) P = Fd t for t t = Fd - P B) t = P Fd t = Fd P t = P - Fd Divide and simplify ) 4 6 B) Find the root. Assume that all variables represent positive numbers. 63) y 16 y 4 B) y 8 4 y y4 Fall '08 - page 7

8 Simplify the radical expression. Assume that all variables represent positive real numbers. 64) 300k 7 q 8 10q 4 3k 7 B) 10k 3 q 4 3k 10k 3 q k 7 q 8 3k Add or subtract as indicated. 65) B) Add or subtract as indicated. 66) B) Graph the linear equation. 67) x = 6 B) Fall '08 - page 8

9 68) y = x - 2 B) Graph the linear equation. 69) x - 3y = -12 B) Find the intercept. 70) The y-intercept for the equation: 4y - 2x = -10 (-5, 0) B) (- 5 2, 0) (0, - 5 ) (5, 0) 2 Fall '08 - page 9

10 71) The x-intercept for the equation: 8y - 2x = -4 (- 1 2, 0) B) (0, - 1 ) (2, 0) (-2, 0) 2 Find the slope of the line. 72) -5x + 2y = 7 m = 5 B) m = 5 2 m = 10 m = 2 5 Write the equation of the line with the given slope, m, and y-intercept, (0, b). 73) m = 2 3 ; b = 3 y = x + 3 B) y = x - 3 y = 2 3 x + 3 y = 2 3 x - 3 Find the slope of the line that passes through the points. 74) (4, -9) and (-1, -6) 3 5 B) Fall '08 - page 10