Elementary Algebra Sample Review Questions 1) Simplify: (x 8 ) 7 1) ) Multiply and simplify any radicals in your answer. Assume that all variables represent positive real numbers. ( 11 + 5)( 17-5) ) 3) Evaluate: - 5 x - 8 for x = 11 3) 9 4) Divide. 4x 9 + 3x 4-36x 4x 4) 5) Solve for the variable. q + 3 = 7 5) 6) Solve: 11x - 7 > 10x - 4 6) 7) Solve by using the square root property. x = 144 7) 8) Solve: 3z(8z - 5) = 0 8) 9) Multiply and simplify any radicals in your answer. Assume that all variables represent positive real numbers. (6 11 + 7)( 11 + 9) 9) 10) Find the slope of a straight line that passes through the given pair of points. (-9, -6) and (-3, 8) 11) Find the missing coordinate to complete the ordered pair. y = -x + 8 (4, ) 10) 11) 1) Factor: 35x 5 y + 45xy 3 1) 13) Simplify: 4(-)(4)() 13) 14) Solve by using the square root property. 3x - 15 = 0 14) 15) Solve for the indicated variable: F = 9 C + 3 for C 15) 5 1
16) Scores in golf can be positive or negative integers. For example, a score of 8 over par can be represented by +8 and a score of 1 under par can be represented by -1. If Donna had scores of 5 over par, 7 under par, and 8 under par for three games of golf, what was her total score? 16) 17) Solve for the indicated variable: P = L + W for L 17) 18) Solve for y: 4(y + 3) = 5(y - 5) 18) 19) Solve for the indicated variable: A = 1 bh for b 19) 0) Divide: s 8 t 9 s t 0) 1) Solve for x: 6x + x = 1 1) ) Solve for h. V = 1 Bh ) 3 3) Write an algebraic expression for the quantity. Let y represent the unknown value. Four less than three-fourths of a number. 3) 4) Factor: 40x + 0 4) 5) A local animal shelter accepts abandoned cats and dogs. They usually receive three times as many cats as dogs. They estimate that 80% of the cats and 90% of the dogs that come in need some kind of medical treatment. If they treated 97 animals last year, how many cats and dogs did they take in? 6) Double the sum of a number and 6 is the same as 15 more than triple the same number. Find the number. 5) 6) 7) Find the area of a triangle whose altitude is 5 inches and whose base is 17 inches. 7) 8) Solve: -8x + 9 + 6x = -3x + 14 8) 9) Solve: 6x + 4 = - + x 9)
30) 30 marbles are to be divided into three bags so that the second bag has three times as many marbles as the first bag and the third bag has twice as many as the first bag. If x is the number of marbles in the first bag, find the number of marbles in each bag. 31) For three days in a row, volunteers picked up trash on a particular beach. They picked up a total of 615 pounds. On the second day they collected 1 pounds more than on the first day. On the third day, they picked up 4 pounds less than on the first day. How many pounds of trash did they pick up on the first day? 3) Larry makes $18 per hour for a 40-hour week and time an a half for every hour over 40 hours. If Larry made $1098 last week, how many overtime hours did he work? 33) A triangular region has a perimeter of 101 meters. The first side is two-thirds of the second side. The third side is 11 meters shorter than the second side. What are the lengths of the three sides of the triangular region? 34) Divide. Leave your answer in exponent form. Assume that all variables in any 11x 9 y denominator are nonzero. 66x y 7 30) 31) 3) 33) 34) 35) Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. x14 x 13 35) 36) Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that year was $700, how much did Kevin invest in the mutual fund? 37) Write an algebraic expression for the quantity. Let x represent the unknown value. Five fewer than a number. 36) 37) 38) Simplify: -15x 8 y 3 5x 5 y 11 38) 39) Factor: 9x - 108 + xy - 1y 39) 3
40) Factor: x 7-10x 6 + 9x 5 40) 41) The sum of two numbers is 10, and the sum of their squares is 5. Find the numbers. 41) 4) Factor: 49x - 9 4) 43) Solve: 3x x + - 6 x - = 3x + 1 x - 4 43) 44) Solve: 6 x + 3x + 3 x + x + 3 44) 45) A line has a slope of -5. What is the slope of a line parallel to it? 45) 46) Find an equation of the line with slope 7 and y-intercept (0, -5). 46) 47) Find the slope and y- intercept: y = -4x + 6 47) 48) Solve the system by graphing. 48) 3x + y = -1 x + y = - 49) Dmitri needs 7 liters of a 43% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 49% solution and the other an unlimited supply of the 35% solution. How many liters of each solution should Dmitri use? 49) 4
50) Solve: x - 6y = - -7x - 7y = -35 50) 51) A sphere has an area A and a radius r. The radius of the sphere is r = Rewrite this expression by rationalizing the denominator and simplifying. A 4. 5) Multiply and simplify any radicals in your answer. Assume that all variables represent positive real numbers. ( 11 + 5)( 17-5) 51) 5) 53) Solve: ( - 19x) = 86 53) 54) Solve: 49x - 5 = 8x 54) 55) Solve: x = 3-8x 55) 56) Translate the English statement into an inequality. The number of people the school can hold is at most 10. (Use the variable p for number of people.) 57) Solve for x: x - 1 6 = 5 1 56) 57) 58) The rectangular part of the field shown below is 169 yd long and the diameter of each semicircle is 16 yd. Find the cost of fertilizing the field at $0.35 per square yard. 58) 59) A number divided by eight is 168. What is the number? 59) 60) Factor: 9x + 18x + 8 60) 61) Multiply: (-4x - 1)(-x - 7) 61) 5
6) A window washer accidentally drops a bucket from the top of a 64-foot building. The height h of the bucket after t seconds is given by h = -16t + 64. When will the bucket hit the ground? 6) 63) Multiply. (4x + 1)(x + 11) 63) 64) Solve for x: 7 = 11x 3 64) 65) Holly bought a sweater on sale for 40% off the original price. If she saved $36, what was the original price? 65) 66) Find the slope and the y-intercept. y = -4x + 6 66) 67) Graph the region described by the inequality. 4x + y - 67) 68) Simplify: 68) 16y - 49x xy 4 y - 7 x 69) Write in scientific notation. 57,000,000 69) 70) Solve by the quadratic formula. If there are no real roots, say so. m + 8m + 5 = 0 70) 6
71) Simplify. Be sure to rationalize all denominators. Assume that all variables 5 represent positive real numbers. 71) 7) Complete the ordered pairs so that each is a solution of the linear equation. Then plot each solution and graph the equation by connecting the points by a straight line. y = x + 6 (0, ) (1, ) (-1, ) 7) 73) Use the Pythagorean theorem to find the length of the third side of the right triangle. Leave any irrational answers in radical form. 73) 6 10 b 74) Write in scientific notation. 0.00015 74) 75) Multiply. (x - 8y)(x + y) 75) 76) Translate the graph to an inequality using the variable x. 76) 77) Find the solution to the system of equations by the substitution method. x + 4y = 7-7x + 3y = -3 77) 7
78) Graph the equation by plotting the intercepts. y = 1 x + 3 78) 79) Write an algebraic expression for the quantity. Let x represent the unknown value. Eight greater than a number. 79) 80) Solve the inequality. 15x - 15 > 5(x + ) 80) 81) Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $9.45. How many dimes did she deposit? 8) Perform the indicated operations. (6x - 18x + 1) - (3x + 3x - 10) 81) 8) 83) Factor. x - 17x + 7 83) 84) Factor by grouping. 9x - 108 + xy - 1y 84) 85) Factor. x - 0x + 50 85) 86) On a buying trip in Los Angeles, Rosaria Perez ordered 10 pieces of jewelry: a number of bracelets at $5 each and a number of necklaces at $7 each. She wrote a check for $780 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase? 87) Find the area of a circular flower bed whose diameter is 3056 feet. (Use = 3.14 as an approximate value.) 86) 87) 8
88) ABC phone company charges $0 per month plus 3 per minute for phone calls. XYZ phone company charges $16 per month plus 5 per minute for phone calls. How many minutes of phone calls should be made each month to make XYZ phone company a better deal? 88) 89) Write an equation of the line. 89) 90) Write an algebraic expression for the quantity. Let x represent the unknown value. A value decreased by five. 91) The distance that an object falls when it is dropped varies directly as the square of the amount of time since it was dropped. An object falls 18 feet in seconds. Find the distance the object falls in 4 seconds. 9) Translate to an inequality. The distance is less than 459 inches. 90) 91) 9) 93) Factor: 15x + 6x + 8 93) 94) A random check of air flights last month showed that 109 of the 160 flights checked arrived on time. If the inspectors check 50 flights next month, how many can be expected to arrive on time? (Round to the nearest whole number.) 95) Simplify. Be sure to rationalize the denominator. Assume that all variables represent positive real numbers. - 3 + 3 94) 95) 96) Combine like terms: 4a + 8b - 4 + 3b + 7a + 6 96) 9
Answer Key Testname: SHORT REVIEW- ELEMENTARY ALGEBRA 1) x 56 ) 187 + 85-55 - 5 3) - 17 9 4) 6x 7 + 8x - 9 5) q = 46 6) x > 3 7) x = ±1 8) z = 5 8, z = 0 9) 195 + 68 11 10) 7 3 11) (4, 4) 1) 5xy(7x 4 + 9y ) 13) -64 14) x = ± 5 15) C = 5 (F - 3) 9 16) -10 or 10 under par 17) L = P - W 18) y = 37 19) b = A h 0) s 6 t 8 1) x = 3 ) h = 3V B 3) 3x 4-4 4) 0(x + 1) 5) 90 dogs, 70 cats 6) -3 7) 4.5 in. 8) x = 5 9) x = - 3 30) 1st bag = 5 marbles; nd bag = 15 marbles; 3rd bag = 10 marbles 31) 1 pounds 3) 14 hours 33) first side = 8 m; second side = 4 m; third side = 31 m 10
Answer Key Testname: SHORT REVIEW- ELEMENTARY ALGEBRA x 34) 7 6y 5 35) x 36) $000 37) x - 5 38) - 3x3 5y 8 39) (x - 1)(9 + y) 40) x 5 (x - 9)(x - 1) 41) 4 and 6 4) (7x + 3)(7x - 3) 43) No solution 44) 5 x 45) -5 46) y = 7 x - 5 47) m = -4; (0, 6) 48) (1, -4) 49) 49% solution: 4 liters; 35% solution: 3 liters 50) (4, 1) A 51) r = 5) 187 + 85-55 - 5 53) x = ± 86 19 54) x = 5 7, x = - 1 7 55) x = -4 ± 19 56) p 10 57) x = 7 1 58) $1016.74 59) 1344 60) (3x + 4)(3x + ) 61) 8x + 30x + 7 6) sec 63) 4x + 56x + 13 64) x = 6 77 65) $90.00 66) m = -4; (0, 6) 11
Answer Key Testname: SHORT REVIEW- ELEMENTARY ALGEBRA 67) 68) 4x + 7y 69) 5.7 107 70) m = -4 ± 6 71) 10 7) (0, 6) (1, 8) (-1, 4) 73) 8 74) 1.5 10-4 75) x - 6xy - 16y 76) x - 77) (3, 6) 1
Answer Key Testname: SHORT REVIEW- ELEMENTARY ALGEBRA 78) 79) x + 8 80) x > 5 81) 198 dimes 8) 3x - 1x + 83) (x - 8)(x - 9) 84) (x - 1)(9 + y) 85) (x - 5)(x - 5) 86) 30 bracelets and 90 necklaces 87) 7,331,1.76 ft 88) Less than 00 minutes 89) y = x - 6 90) x - 5 91) 51 feet 9) x < 459 93) (3x + 4)(5x + ) 94) 170 flights 5-66 95) 19 96) 11a + 11b + 13