Review Topics. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Review Topics MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. On the real number line, label the points with the given coordinates. 1) 11,- 11 1) D) ) 4, - 4 ) D) Simplify the expression. 3) D) ) 4) (-) 4) D) not a real number The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the hypotenuse. ) 6, 7, 8 ) right triangle; 6 right triangle; 8 right triangle; 7 D) not right triangle 1

2 Tell whether the expression is a polynomial. If it is, give its degree. 6) 7x4 - Polynomial; degree Polynomial; degree 7 Polynomial; degree 4 D) Not a polynomial 6) Find the quotient and the remainder. 7) 48x + 4x - 11 divided by 6x 8x + 7x - 11 ; remainder 0 48x + 4; remainder ) 8x + 7; remainder -11 D) 8x - 4; remainder 0 Factor completely. If the polynomial cannot be factored, say it is prime. 8) 9x - 1 (3x + 1) (3x - 1)(3x + 1) (3x - 1) D) prime 8) Use synthetic division to find the quotient and the remainder. 9) x + 13x + 8 is divided by x + 9 x + 4; remainder 8 x + 4; remainder -8 x + ; remainder 0 D) x + 4; remainder 0 9) Use synthetic division to determine whether x - c is a factor of the given polynomial. 10) x3-11x + 0x + 96; x + 3 Yes No 10) Reduce the rational expression to lowest terms. x + 11) 10x + 14x ) x + 10x + 14x x + x + x + 14 D) x x + Perform the indicated operations and simplify the result. Leave the answer in factored form. 1) 11 1x - 1 6x 4 3x 3 8x 1 D) 3 4x 1) Find the LCM of the given polynomials. 13) x + 6x +, -x - -(x + )(x + 1) -(x- )(x + 1) -(x- )(x - 1) D) -(x + )(x - 1) 13) 14) x + 7x + 1, 6x (x + 4)(x - 3) 6(x - 4)(x + 3) 6(x + 4)(x + 3) D) 6(x - 4)(x - 3) 14)

3 Simplify the expression. Assume that all variables are positive when they appear. 1) 3-7x18y36-3x6y1 9x6y1 3x6y1 D) -3x9y18 1) 16) 7 16) D) 1 Simplify the expression. 8 /3 17) 7 17) D) ) -3-4/ ) D) not a real number Simplify the expression. Express the answer so that only positive exponents occur. Assume that all variables are positive. 19) x3/8 x/8 19) 1 x x1/64 D) x1/8 x 0) (-x 4/) x-4/7-3x3/7-3x4/7 -x4/7 D) -x3/7 0) Simplify the expression. Assume that all variables are positive when they appear. 1) D) ) ) ) D) Find the real solutions of the equation. 3) x = -1 {1} {-1} {-} D) {} 3) 3

4 Simplify the expression. Assume that all variables are positive when they appear. 4) 18xy 4) 3x y 3 x y 9x y D) x 18y ) ( )( 11-4) D) 7 ) 6) (7-8) D) ) Find the LCM of the given polynomials. 7) x - 1, 1 - x (x - 1) or (1 - x) x + 1 (x - 1)(1 - x) D) -1 7) Perform the indicated operations and simplify the result. Leave the answer in factored form. 8) 10 x x - 1 8) x 10 - x x + 10 D) x x ) 9) x x x 36 1 D) x 36 30) 3 x x + 3x + 19 x + 1x ) 3 9 3x + 19 D) 1 3 4

5 Solve the equation. 31) 8 9 x = ) D) 6 3) 4(x - ) = 7(x + 3) {-9} {-13} {17} D) {9} 3) 33) x = ) D) ) 3) x - = 3 x + 4 {-6} {-14} {17} D) {6} - x + 7 = 7 x (x + 7)(x + 14) {-14} {-7} {-7, -14} D) no real solution 34) 3) 36) t3-6t = 0 {0,-6} {-6} {6} D) {0, 6} 36) 37) 6x + 9 = {- 3,- 7 3 } { 3, 7 3 } {- 4 9,- 14 } D) no solution 9 37) 38) (x + 1) + 4 = 8 {-7, 0} {-, 3} {-, 0} D) {-7, 1} 38) Solve the equation by factoring. 39) x = 0 {100} {10} {10, -10} D) {-10} 39) 40) x - 60x + 36 = 0 {- 6 } { 6 } {6 } D) {- 6 } 40) 41) 6x + 1 x = ) {- 1, - } {1, } {6, } D) {- 1, }

6 4) x = x x + 6 {6, -1} {36, 1} {36, -1} D) {6, 1} 4) Solve the equation by the Square Root Method. 43) (x - ) = 81 {4,-14} {14,-4} {7, -} D) {,-7} 43) What number should be added to complete the square of the expression? 44) x - 8x D) 16 44) 4) x + 6 x 4) D) 7 Solve the equation by completing the square. 46) x + 10x + 3 = 0 { + } {- -, - + } { - 3, + 3} D) { } 46) 47) x - x - 4 = 0 {-4, - 1 } {-1, } 47) { - 1, + 1 } D) { 1-1, } Find the real solutions, if any, of the equation. Use the quadratic formula. 48) x + 8x - = 0 {4 + 1} {-4-1, } {-4-1, } D) {-1-1, } 48) 49) 6x = 7x {0, } {6 7, } {0, 6 7 } D) {0} 49) 0) x = -1x - 1 { -1-34, } { -6-34, } 4 0) { -6-38, } D) { -6-34, } 6

7 Find the LCM of the given polynomials. 1) x - 10, 10 - x -1 x + 10 (x - 10)(10 - x) D) (x - 10) or (10 - x) 1) Perform the indicated operations and simplify the result. Leave the answer in factored form. ) 9 x x - 1 ) x x x 9 - x x + 9 D) 9 3) 3) 4 + x x x 1 x 16 D) 16 4) x x + 3 x + 9 x + 8x + 1 4) x + 9 D) 10 Solve the equation. ) - 6 x = ) D) - 1 6) 3(x - 3) = (x + 3) {-6} {4} {9} D) {-4} 6) 7) x = ) D)

8 8) 9) 9 x - 3 = x + 3 {17} {4} {-4} D) {-1} x + 8 = x (x + 8)(x + 16) {-16} {-8} {-8, -16} D) no real solution 8) 9) 60) t3-9t = 0 {9} {-9} {0, -9} D) {0, 9} 60) Perform the indicated operations and simplify the result. Leave the answer in factored form. 61) 6 x + 8 x - 14x - 30 x(x - ) 30x - 14 x( - x) 14x - 30 x( - x) D) 30x - 14 x(x - ) 61) 6) x - 9 x x - 9 x - 6 6) (x - 9) (x - 1)(x - 6) -(x - 9) (x - 1)(x - 6) -7(x - 9) (x - 1)(x - 6) D) 0 Reduce the rational expression to lowest terms. 63) y + y + 6 y + 11y ) y y + 18 y + 3 y y + y + 6 y + 11y + 18 D) y y + 3 Perform the indicated operations and simplify the result. Leave the answer in factored form. 64) 4x - 4 9x x 8x - 8 3x + 64x + 3 9x3 36x 3-36x 8x - 8x 9x D) 9x 64) 6) x - 4 7x + 14 x - x - 6) (x - )(x - ) 7(x + ) 1 7 x - 7 D) x - 8

9 66) x - x 66) 8x - 8 x x 8 x (x - 1) 8x(x - 1) 8 x D) 40(x + 1) x3 67) x - 1x x ) 4x (x - 6) 49 1 D) x - 1x + 36 (x - 6) Use synthetic division to find the quotient and the remainder. 68) x + 8x4 + 1x3 + 1x + 1x - 16 is divided by x + 6 x4 + x3 + 3x + 3x + 3; remainder 4 x3 + x + 3x + 3; remainder x4 + x3 + 3x + 3x + ; remainder 0 D) x4 + x3 + 3x + 3x - 3; remainder 68) Factor completely. If the polynomial cannot be factored, say it is prime. 69) x + 16x + 64 (x + 8)(x - 8) (x - 8) x + 16x + 64 D) (x + 8) 69) 70) 10x + 1x + 9 (10x + 3)(x + 3) (x - 3)(x - 3) (x + 3)(x + 3) D) prime 70) 71) (x + 1) - 9 (x + 10)(x - 8) x + x - 8 (x + 4)(x - ) D) (x + )(x - 4) 71) Find the quotient and the remainder. 7) 6x + 17x - 8 divided by x + 4 6x - 7; remainder 0 6x - 7; remainder 7 x - 7; remainder 0 D) 6x + 7; remainder 0 7) 73) x4 + 6x + 7 divided by x + 1 x + ; remainder x + x + 1; remainder 73) x + ; remainder 0 D) x + x + 1 ; remainder 0 9

10 Tell whether the expression is a polynomial. If it is, give its degree. 74) 7x - 4 x 74) Polynomial; degree Polynomial; degree 1 Polynomial; degree -1 D) Not a polynomial Add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 7) (-9x + 4) - (-x3 - x + 3) x3-7x + 1-8x3 + x - 3-8x3 - x + 1 D) x3-11x + 7 7) 76) 8(1 - y3) + (1 + y + y + y3) 3y3 + y + y y3 - y + y y3 + - ay + y + 13 D) -3y3 + y + y ) Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. 77) (x - 10)(x + 10) 77) 4x - 40x x + 40x x D) x + 40x ) (9x - 11) 9x x - 198x x - 198x + 11 D) 81x ) 79) (x + )3 4x6 + 10x3 + 1,6 8x3 + 60x + 10x + 1 4x + 0x + D) 8x3 + 60x + 60x ) Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 80 feet. 80) A person who is 6 feet tall is standing on the beach and looks out onto the ocean. Suddenly, a ship appears on the horizon. How far is the ship from the shore? Round to the nearest tenth of a mile mi 4. mi 3 mi D) 18.1 mi 80) Solve the problem. 81) Find the area A of a triangle with height in and base 8 in. A = 40 in A = 0 in A = 40 in D) A = 0 in 8) Find the area A and circumference C of a circle of radius 9 yd. Express the answer in terms of π. A = 18π yd; C = 18π yd A = 34π yd; C = 9π yd A = 81π yd; C = 18π yd D) A = 36π yd; C = 9π yd 83) Find the volume V of a rectangular box with length 4 ft, width 7 ft, and height ft. V = 17 ft3 V = 80 ft3 V = 196 ft3 D) V = 140 ft3 81) 8) 83) 84) Find the volume V of a right circular cylinder with radius 14 cm and height 17 cm. Express the answer in terms of π. V = 38π cm3 V = 119π cm3 V = 333π cm3 D) V = 833π cm3 84) 10

11 8) Find the area of the shaded region. Express the answer in terms of π. 8) π square units 64-3π square units 16π + 64 square units D) 64-16π square units 86) A rectangular patio has dimensions 10 feet by 1 feet. The patio is surrounded by a border with a uniform width of feet. Find the area of the border. 116 ft 84 ft 18 ft D) 4 ft 86) The triangles are similar. Find the missing length x and the missing angles A, B, C. 87) 87) x = 4 units; A = 40 ; B = 9 ; C = 4 x = 8 units; A = 4 ; B = 40 ; C = 9 x = 8 units; A = 9 ; B = 40 ; C = 4 D) x = 4 units; A = 9 ; B = 40 ; C = 4 Solve. If necessary, round to the nearest tenth. 88) If a flagpole 1 feet tall casts a shadow that is 8 feet long, find the length of the shadow cast by an antenna which is 7 feet tall. 1.8 ft 34 ft 0.3 ft D) 36 ft 88) Use a calculator to evaluate the expression. Round the answer to three decimal places. 89) (1.11) D) ) 11

12 Simplify the expression. 90) D) 90) 91) (3-3) -1 91) D) 1 9 Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. 9) (x9y-1) 8 9) x 7 y8 x7y8 y 8 x7 D) 1 x7y8 93) 3x-1 7y-1-93) 49x 9y 9y 49x 49y 9x D) 9x 49y Evaluate the expression using the given value of the variables. 94) -3x-1y for x = 1, y = D) -1 94) 9) x - 4y for x =, y = D) 3 9) Insert <, >, or = to make the statement true. 96).3 > = < 96) Write the statement as an inequality. 97) y is greater than or equal to 0 y 0 y 0 y < 0 D) y > 0 97) 1

13 Graph the numbers on the real number line. 98) x > - 98) D) Evaluate the expression using the given values. 9x - 8y 99) x = 8, y = x D) ) 100) x - y x = -6, y = D) ) Express the statement as an equation involving the indicated variables. 101) The perimeter P of a rectangle is twice the sum of its length l and its width w. P = (l + w) P = lw P = l + w D) P = lw 101) 10) The surface area S of a sphere is 4 times π times the square of the radius r. S = 4πr S = 4πr S = πr D) S = 4π r 10) Determine which value(s), if any, must be excluded from the domain of the variable in the expression. x - 103) x ) x = x = 81 x = 9, x = -9 D) x = 9 104) x + x - x3 - x x = 0 x =, x = - x =, x = -, x = 0 D) x =, x = 0 104) 13

14 Insert <, >, or = to make the statement true. 10) = < > 10) Write the statement as an inequality. 106) y is greater than or equal to 60 y 60 y 60 y > 60 D) y < ) Graph the numbers on the real number line. 107) x > 7 107) D)

15 Answer Key Testname: ONLINE REVIEW TOPICS 1) B ) D 3) D 4) C ) D 6) C 7) C 8) B 9) B 10) B 11) B 1) D 13) A 14) C 1) A 16) B 17) D 18) C 19) B 0) A 1) A ) B 3) C 4) A ) B 6) A 7) A 8) B 9) A 30) A 31) B 3) D 33) B 34) D 3) D 36) D 37) A 38) D 39) C 40) C 41) A 4) C 43) C 44) D 4) A 46) B 47) D 48) B 49) C 0) D 1

16 Answer Key Testname: ONLINE REVIEW TOPICS 1) D ) B 3) A 4) D ) C 6) B 7) B 8) B 9) D 60) D 61) A 6) B 63) B 64) C 6) C 66) A 67) C 68) D 69) D 70) C 71) C 7) A 73) A 74) D 7) A 76) D 77) C 78) C 79) B 80) C 81) B 8) C 83) D 84) C 8) D 86) A 87) C 88) D 89) A 90) A 91) A 9) A 93) A 94) B 9) C 96) C 97) B 98) A 99) D 100) D 16

17 Answer Key Testname: ONLINE REVIEW TOPICS 101) A 10) B 103) C 104) C 10) B 106) B 107) D 17