Spring 2011 Name Math 115 Elementary Algebra Review Wednesday, June 1, 2011 All problems must me done on 8.5" x 11" lined paper. Solve. Label any contradictions or identities. 1) -4x + 2(3x - 3) = 5-9x 2) 7x - (3x - 1) = 2 3) 2x 5 - x 3 = 2 4) 15 14 x + 1 14 x = 6x + 1 7 + 13 14 x 5) -4.2q = -22.4-1.4q 6) -10.8q + 1.8 = -17.8-1.0q Solve the formula for the indicated letter. 7) F = 9 C + 32 for C 5 8) a + b = s + r for r 9) 1 a + 1 b = 1 c for c Solve and graph. Write the solution is interval notation and set builder notation. 10) -7x - 10 > -8x - 14 11) -20r - 10-5(3r + 11) Convert the percent notation in the sentence to decimal notation. 12) The unemployment rate was 9.9% for the month. Convert to decimal notation. 13) 73% Convert the decimal notation in the sentence to percent notation. 14) Property is assessed at 0.13 of market value. 1
Convert to percent notation. 2 15) 25 Solve. 16) What is 5% of 300 17) 23 is 4% of what number? 18) What percent of 110 is 55? Solve the problem. 19) If Gloria received a 9 percent raise and is now making $27,250 a year, what was her salary before the raise? Round to the nearest dollar if necessary. 20) After receiving a discount of 7.5% on its bulk order of typewriter ribbons, John's Office Supply pays $3885. What was the price of the order before the discount? Round to the nearest dollar if necessary." Translate the sentence to an algebraic inequality. 21) John weighs at least 125 pounds. Use an inequality and the five-step process to solve the problem. 22) One side of a rectangle is 7 inches and the other side is x inches. What values of x will make the perimeter at most 32? Determine where the point is located. 23) (-6, 10) 24) (0, -19) 2
Graph the equation. 25) x + y = 4 Find the intercepts for the equation. 26) 2x + y = -10 Solve the problem. 27) To the nearest dollar, the average tuition at a public four-year college was $3052 in 1997 and $3249 in 2000. Find, to the nearest dollar per year, the rate at which tuition was increasing. 28) Angie walks 21 feet in 3 seconds towards the front of a train that is moving at 70 feet per second. What is Angie's rate of travel with respect to the land? 29) The following graph shows data for a recent train ride from New York to Toronto. At what rate did the train travel? Time of Day (PM) 3
Use the graph to solve the problem. 30) Find the rate of change in the value of Bob's car. Year Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 31) (8, -5) and (-1, -7) 32) (8, -7) and (8, 7) 33) (-9, 6) and (2, 6) 34) (4, 5) and (9, 3) Solve the problem. 35) An old house has a basement stairway that has steps with 7.25 inch risers and 9 inch treads. What is the slope of the stairway? Find the slope and the y-intercept of the line. 36) 4x + 3y = 29 37) y = 15 4 x - 3 Write the equation of the line given the slope and y-intercept. 38) Slope - 7 ; y-intercept (0, 9) 5 4
Graph the linear equation. 39) y = - 6 5 x - 5 Determine whether the pair of equations represents perpendicular lines. 40) 3x - 4y = -12 8x + 6y = -12 41) 9x + 3y = 12 6x + 2y = 10 Determine whether the pair of equations represents parallel lines. 42) 6x + 2y = 8 18x + 6y = 26 43) 3x - 4y = 6 8x + 6y = 6 Write a slope-intercept equation of the line whose graph is described. 44) Parallel to the graph of y = 3x - 7; y-intercept (0, -5) 45) Perpendicular to the graph of 2x + y = 2; y-intercept (0, -5) Find an equation in point-slope form of the line having the specified slope and containing the point indicated. 46) m = 6; (4, 3) Write an equation of the line containing the specified point and parallel or perpendicular, as indicated, to the given line. Write your final answer in slope-intercept form. 47) (0, 7), parallel to -3x + y = 1 5
48) (0, -6), perpendicular to y = -2x + 2 Find an equation of the line containing the given pair of points. Write your final answer in slope-intercept form. 49) (-2, 7) and (5, -4) Graph on a plane. 50) 5x + y -1 Identify the base and the exponent. 51) (10x)15 52) -610 Simplify. Assume that no denominator is zero and that 00 is not considered. 53) (6x5)(2x3) 54) 24k 3 6k Simplify. 55) (-5a5)3 Simplify. Assume that no denominator is zero and that 00 is not considered. x5y 5 56) z3 Express using positive exponents. Then, if possible, simplify. 57) (-3 )-2 6
Simplify. Do not use negative exponents in your answer. 58) (x7y-6z-5)(x-2y-5z10) 59) 35x -6yz2 5x2y4z 60) (2m2n-5) 4 61) x5y5 wz6-5 Convert to decimal notation. 62) 1.97 103 63) 8.89 10-4 Express using positive exponents. Then, if possible, simplify. 5-2 64) 6 Convert to scientific notation. 65) 34,036 66) 0.00000085108 Perform the indicated operation. Write the answer in scientific notation. 67) 10 10-9 5 10-7 68) (8.0 10-4)(8.5 108) Determine the leading term, leading coefficient, and the degree of the polynomial. 69) 7a2 + 15a5-5a Combine like terms. Write the answer in descending order. 70) 11 14 x 6+ 9x3-2 - 4x3-9 14 x 6 + 3 71) 96.8x2-81.2x + 75.6 + 96.4x - 26.2x2-29.4 Evaluate the polynomial. 72) -2x3-6x2 - x - 32 for x = -3 7
Add. 73) (6-4x7 + 5x9 + 5x8) + (-3x8-5x7-9 + 7x9) Subtract. 74) (3x6 + 6x8 + 4-5x7) - (8-8x7 + 8x8-9x6) 75) Subtract (-14a3 + 11a2) from (16a3-9a2) Multiply. 76) -11x(12x + 1) 77) (2x + 6)(x - 8) 78) (x + 9 )(x - 9 ) 79) (3x - 11)(3x + 11) 80) (x + 4)(x2 - x + 8) 81) (x - 5)(x2 + 5x + 25) 82) (x + 3)(x2-3x + 9) 83) (n + 16)2 84) (9m + 2)2 Add or subtract, as indicated. 85) (3x2y + 2xy) - (6x2y + 6xy2) - (5xy + 2xy2) Multiply. 86) (5x + 6y)2 87) (x + y - 2)(x + y + 2) 88) (9m - 7w)(9m + 7w) Divide. 89) 27x 6-30x2 + 15x 3x 8
Divide. 90) (p2 + 6 p - 7 ) (p + 8 ) Factor out the largest common factor. 91) 5x2-30x 92) 12x7y9 + 36x5y6-18x2y4 Factor by grouping, if possible. 93) 4x3-5x2 + 20x - 25 Factor completely. If the polynomial is prime, state this. 94) y2 + 7y - 30 95) 60-4x - x2 96) x5 + 9x4-22x3 97) x2 + 1 4 x - 1 8 98) x2 + 3xy - 18y2 99) 12x2 + 17x + 6 100) 7x2 + 29x - 30 101) -30a2-5a + 75 102) 15x2 + 19xy + 6y2 103) x2-18xy + 81y2 104) 5a2 + 60a + 180 105) y2-64 106) 81x2 + 16 107) 49k2-16m2 9
108) x4-1 Factor completely. 109) x3-8 110) 27c3 + 125 111) x6 + 1 112) z6-1 Solve using the principle of zero products. 113) (y - 7)(6y + 17) = 0 Solve by factoring and using the principle of zero products. 114) b2 + 18b = 0 115) b2 + 14b = 0 116) x2 - x = 20 117) x2 + 7x - 18 = 0 118) 4k2-9 = 0 119) x2 - x = 12 120) x2 + 3x - 18 = 0 121) 9k2-49 = 0 122) 5x2-30x + 40 = 0 123) 2x2 + 4 = x2 + 5x 124) x(x - 1) = 90 125) 2k2 = 15k - 25 10
Find the x-intercept(s) and y-intercept. 126) y = x2 + 3x - 4 Solve the problem. 127) The product of two consecutive integers is 55 more than their sum. Find the integers. 128) The product of the page numbers on two facing pages of a book is 272. Find the page numbers. 129) A 10-ft ladder is leaning against a building. If the bottom of the ladder is 6 ft from the base of the building, how high does the ladder reach? 130) A triangle is 3 cm wider than it is tall. The area is 44 cm2. Find the width (length of the base). h + 3 Simplify. 131) 72 Solve. Try factoring first. If factoring is not possible or is difficult, use the quadratic formula. 132) 2m2 + 6m + 2 = 0 133) 5n2 = -8n - 1 Simplify, if possible. 134) 6x 2-18x 9x2-27x 135) y 2 + 10y + 21 y2 + 14y + 49 Multiply and, if possible, simplify. 136) x 2 + 13x - 30 x6 8x x + 15 11
Divide and, if possible, simplify. 137) x2-16 x2 + 12x + 36 3x + 12 x2 + 4x - 12 Perform the indicated operation. Simplify, if possible. 3x + 24 138) x2-2x - 8 - x + 20 x2-2x - 8 139) 2 y2-3y + 2 + 6 y2-1 140) 4 x - 6 + 1 6 - x Simplify. 141) 5 a2b4-6 a3b 4 a3b + 7 ab2 142) 4 x2-4 + 1 x - 2 7 x2-4 + 4 x + 2 Solve. If no solution exists, state this. 5 143) x - 8 = 2 x + 5 144) x - 10 x + 8 = 9 x + 8 145) 3 y + 5-5 y - 5 = 8 y2-25 146) y y2 + 13y + 36 + y y2-16 = y y2 + 5y - 36 147) x x + 7-7 x - 7 = x 2 + 49 x2-49 Solve. 148) Martha can rake the leaves in her yard in 4 hours. Her younger brother can do the job in 5 hours. How long will it take them to do the job if they work together? 12
149) One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone? Solve the problem. 150) A loaded moving truck is traveling 25 mph faster than a freight train. In the time it takes the train to travel 160 miles, the truck travels 260 miles. Find the speed of the truck. 151) A boat goes 360 miles downstream in the same time it can go 300 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water. 152) For the pair of similar triangles, find the value of a. 15 12 5 3 4 153) Ivan, who is 1.81 m tall, wishes to find the height of a tree with a shadow 32.83 m long. He walks 21.24 m from the base of the tree along the shadow of the tree until his head is in a position where the tip of his shadow exactly overlaps the end of the tree top's shadow. How tall is the tree? Round to the nearest hundredth. Solve. 154) Sven can type 30 words per minute. How many words would he type in 1 4 hour (15 minutes)? Determine whether the ordered pair is a solution of the system of equations. Remember to use alphabetical order of variables. 155) (2, 1); x + 3y = 5 4x + 3y = 11 13
Solve the system graphically. y = 4 3 x - 8 156) x + y = -1 Identify the system as consistent or inconsistent, and dependent or independent. x + 6y = 20 157) 2x + 12y = 40 158) 3x = y + 3 6x - 2y = 3 Solve using the substitution method. 3x + y = 13 159) 2x + 9y = -8 Solve the system of equations using substitution. 160) x + y = 4 x + y = -7 Solve using the elimination method. -7x + 7y = -28 161) -3x - 4y = -12 Solve using the elimination method. 162) 3x + 5y = -2-6x - 10y = 4 Solve the problem. 163) The sum of two numbers is 32, and their difference is 12. What are the numbers? 14
164) Two angles are supplementary. One angle is 212 less than three times the other. Find the measures of the angles. 165) Two angles are complementary. The sum of the first angle plus twice the second angle is 148. Find the measures of the angles. 166) The speed of a current is 6 mph. If a boat travels 52 miles downstream in the same time that it takes to travel 26 miles upstream, what is the speed of the boat in still water? 167) There were 510 people at a play. The admission price was $3.00 for adults and $1.00 for children. The admission receipts were $1030. How many adults and children attended? 168) How many liters of a 20%-alcohol solution must be mixed with 50 liters of a solution that is 80% alcohol to get a solution that is 30% alcohol? 169) Walt made an extra $7000 last year from a part-time job. He invested part of the money at 10% and the rest at 7%. He made a total of $640 in interest. How much was invested at 7%? 15