Algebra - Final Exam Review Part Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use intercepts and a checkpoint to graph the linear function. ) 20x - 30y = 20 ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Rewrite the given equation in slope-intercept form by solving for y. 2) 4x - 0y = 40 2) A) y = 4x + 40 B) y = - 2 5 x + 4 C) y = 5 2 x + 0 D) y = 2 5 x - 4 Find the slope and the y-intercept of the line. 3) 5y - 4x = 5 3) A) m = 4 5 ; b = B) m = 4 5 ; b = - C) m = - 5 4 ; b = - D) m = - 4 5 ; b = Solve the problem. 4) A truck rental company rents a moving truck one day by charging $35 plus $0.07 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 20 miles? A) C(x) = 35x + 0.07; $4200.07 B) C(x) = 0.07x + 35; $35.84 C) C(x) = 0.07x + 35; $43.40 D) C(x) = 0.07x - 35; -$26.60 4) Write the point-slope form of the line satisfying the conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation in function notation. 5) Slope = -2, passing through (5, 2) 5) A) f(x) = - 2x - 2 B) f(x) = 2x - 2 C) f(x) = - 2x + 2 D) f(x) = - 2 x - 6
6) Passing through (6, 38) and (7, 43) 6) A) f(x) = - 5 x + 96 B) f(x) = 5 5 x + 84 5 C) f(x) = -5x + 68 D) f(x) = 5x + 8 Solve. 7) When making a telephone call using a calling card, a call lasting 5 minutes cost $0.95. A call lasting 3 minutes cost $.75. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of a making a call lasting x minutes. A) y = -0.x +.45 B) y = 0.x + 0.45 C) y = 0x - 98 D) y = 0.x -.25 20 7) 8) A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 28 ounces of water. After it has been filling for seconds, the gauge indicates the bottle contains 58 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that models the amount of water in the bottle in terms of x. A) y = 5x + 47 B) y = x + 27 C) y = -5x + 53 D) y = 5x + 3 5 8) Find the slope. 9) Find the slope of a line perpendicular to the line y = 6 x - 3. 9) 5 A) - 5 6 B) undefined C) 6 5 D) -3 0) Find the slope of a line parallel to the line -6x + 3y = 3. 0) A) - 2 B) 2 C) undefined D) 3 ) Find the slope of a line parallel to the line x = 2. ) A) 0 B) 2 C) undefined D) 2 Use the given conditions to write an equation for the line in slope-intercept form. 2) Passing through (5, -5) and parallel to the line whose equation is y = -4x + 9. 2) A) y = - 4x + 5 B) y = - 4x - 5 C) y = 4x - 5 D) y = - 4 x - 5 4 3) Passing through (2, 5) and perpendicular to the line whose equation is y = 2x + 9. 3) A) y = 2 x - 6 B) y = - 2 x + 6 C) y = - 2x - 2 D) y = - 2 x - 6 2
Determine whether the given ordered pair is a solution to the system. 4) (-, -3) 4x + y = -7 2x + 4y = -4 A) no B) yes 5) (6, 4) x + y = -2 x - y = -0 A) yes B) no 4) 5) Solve the system by graphing. 6) 4x + y = -9 6x + 2y = -2 6) A) B) {(-3, 3)} C) {(3, 3)} D) {(x,y) 4x + y = -9} Solve the system by the substitution method. 7) x = -3y + 3 3x - 7y = -7 A) Dependent; {(x,y) x = -3y + 3} B) {(0, )} C) D) {(, 0)} 7) Solve the system by the addition method. 8) 3x + 6y = 3 2x + 9y = -8 A) {(-5, 2)} B) C) Dependent; {(x,y) 3x + 6y = 3} D) {(5, -2)} 8) Solve the system by any method. 9) 5x - 6y = 2 5x - 8y = 8 9) A) ( 2, - 5 ) B) C) (2, 8) D) {x 5x - 6y = 2} 2 3
20) 2 x + 2 y = 2 20) x - y = 2 A) (8, -4) B) C) (-8, -3) D) (7, -3) Determine if the system has one solution, is dependent, or is inconsistent 2) x + y = -8 x + y = 9 A) dependent B) one solution C) inconsistent 2) 22) 9x + y = 4-45x - 5y = -20 A) one solution B) inconsistent C) dependent 22) Solve. 23) One number is 6 less than a second number. Twice the second number is 9 less than 5 times the first. Find the two numbers. A) 8 and 4 B) 6 and 2 C) -3 and -7 D) 7 and 3 24) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 3 bags of potato chips for $2.75. Another customer buys 5 hot dogs and 2 bags of potato chips for $3.75. Find the cost of each item. A) $2.25 for a hot dog; $.25 for a bag of potato chips B) $2.25 for a hot dog; $.50 for a bag of potato chips C) $.25 for a hot dog; $2.25 for a bag of potato chips D) $2.50 for a hot dog; $.50 for a bag of potato chips 25) Julie and Eric row their boat (at a constant speed) 55 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes hours. Find the rate of the current. A) 2.5 mph B) 4 mph C) 8 mph D) 3 mph 23) 24) 25) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the inequality. Other than, graph the solution set on a number line. 26) 9x - 9 3x - 2 26) 27) -3(4x - 0) < -5x + 3 27) Solve the linear inequality. Other than, graph the solution set on a number line. 28) 5(4x + 5) - 4x < 4(6 + 4x) - 6 28) 4
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the intersection of the sets. 29) {-4, -, 3, 5} {3, 5, 9} 29) A) {3, 5, 9} B) {-4, -, 3, 5, 9} C) {-4, -, 3, 5} D) {3, 5} SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. 30) 5x - 4 26 30) 3) -3x -9 or 4x > 2x - 8 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the solution set for the equation. 32) 8x - 3-7 = -3 32) A) {- 3 8 } B) C) {- 3 8, - 9 8 } D) {9 8, 3 8 } 33) 3x + 8 + 3 = 9 33) A) B) {- 2 3, - 4 3 } C) {- 4, - 7 4 } D) {2 3, 4 3 } SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve and graph the solution set on a number line. 34) x - 7 < 4 34) 35) 8x - 2-3 < 4 35) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve. 36) A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds. Solve the inequality. A) 40 - x 0.75; [39.25, 40.75] B) x - 40 0.75 ; (, 40.75] C) x + 0.75 40; [39.25, ) D) 40 + x 0.75; [39.25, 40.75] 36) 5
Simplify the expression. 37) t5 t6 t6 37) A) t2 B) t36 C) t7 D) t 38) (y8) 5 38) A) y3 B) 5y40 C) 5y8 D) y40 39) (-7x4y5) 2 39) A) -49x8y0 B) 49x8y0 C) 49x6y25 D) -4x8y0 Multiply the monomials. 40) (4x4y)(0x3y5) 40) A) 40x2y5 B) 40x7y6 C) 40x7y5 D) 4x7y5 Use the quotient rule to simplify the expression. 4) 0m 20n5 2m9n3 A) 5m39n8 B) 0mn2 C) 5mn2 D) 5n2 4) Use the quotient to a power rule to simplify. 6t3 2 42) 3s4 42) A) 4t 5 s6 B) 4t 6 s4 C) 2t 6 s8 D) 4t 6 s8 Simplify. The exponents in the answer should be positive integers. 43) ( 2 ) -3 43) A) 6 B) -8 C) 8 D) 8 44) 9x-8 44) 9 A) -72x B) -9x<b> C) D) 43,046,72x8 x8 45) y -9 y3 45) A) y6 B) y27 C) y2 D) y2 Find the product. 46) -7x(3x2-3x - 4) 46) A) -2x3 + 2x2 + 28 B) -2x2 + 2x + 28 C) -2x3-3x - 4 D) -2x3 + 2x2 + 28x 6
47) (3x + 8)(x + 5) 47) A) 3x2-46x + 40 B) x2 + 40x + 23 C) x2 + 23x - 46 D) 3x2 + 23x + 40 Find the area of the shaded region. 48) 48) (6x - 0) (5x + 0) A) 30x2-50x - 00 B) 30x2 + 0x - 00 C) 30x2 + 0x + 00 D) 30x2 + 0x - 00 Find the product. 49) (x2 + 8)(x2 + 6) 49) A) x4-4x2-48 B) x4 + 4x2 + 96 C) x4 + 48x2 + 48 D) x4 + 4x2 + 48 Find the special product. 50) (5p + 2)(5p - 2) 50) A) 25p2-20p - 44 B) 25p2-44 C) 25p2 + 20p - 44 D) p2-44 Find the product. 5) (x - 9)(x2 + 9x + 9) 5) A) x3 + 90x + 8 B) x3-8x2-72x - 8 C) x3 + 8x2 + 72x + 8 D) x3-72x - 8 Factor the GCF from the polynomial. 52) 6x + 36 52) A) 26x B) 6x + 6 C) 6(x + 36) D) 6(x + 6) 53) 8x8 + 64x6 53) A) x8(8x2 + 64) B) 8x7(x + 8x) C) 8(x8 + 8x6) D) 8x6(x2 + 8) 54) 27y3-6y2 + 5y 54) A) 3y(9y3-2y2 + 5y) B) y(27y2-6y + 5) C) 3y(9y2-2y + 5) D) 3(9y3-2y2 + 5y) Factor the trinomial completely. If the polynomial cannot be factored, write "prime." 55) x2 + x - 20 55) A) (x - 5)(x + 4) B) (x - 4)(x + 5) C) (x + )(x - 20) D) prime 56) x2-4x - 32 56) A) (x - 8)(x + 4) B) (x - 32)(x + ) C) (x + 8)(x - 4) D) prime 7
57) x2 + 0x + 24 57) A) (x - 6)(x + 4) B) (x - 6)(x + ) C) (x + 6)(x + 4) D) prime Solve the equation by factoring. 58) x(2x + 6) = 0 58) A) {0, 3} B) {0, -3} C) 0, - 3 D) 0, 3 59) (x - 6)(6x + 8) = 0 59) A) - 6, B) {-3, 6} C) - 3 3, D) {-6, 3} 6 60) x2 + 9x - 22 = 0 60) A) {-, } B) {-, 2} C) {, 2} D) {, -2} 8