Algebra, Answer Key

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate. 1) -7 - 2 (-4) - (-5) A) 10 2) |-17 - 12| A) 5 Simplify. 3) 2x - 5(3 + x) A) 2x - 15 B) -6 C) 6 D) -4 B) 29 C) -5 D) -29 B) 3x - 15 C) -3x - 15 D) x - 2 Solve. 4) 8w - 1 = 9 - 10w 9 A) 5 B) 5 9 9 5 D) - 93 23 D) 1 C) - 1 4 5) -6x + 7(-3x - 5) = -58 - 4x A) - 1 B) 3 C) 6) Determine the number of solutions there are when solving the equation: x - 4 = x + 3 A) No solutions B) Infinitely many C) One solution 7) Solve the inequality: A) a > -8 -2a - 19 > -3 B) a ≥ -8 C) a < -8 8) Graph the inequality on a number line: a < -6 A) -9 -8 -7 -6 -5 -4 D) a ≤-8 B) -3 C) -9 -8 -7 -6 -5 -4 -3 -9 -8 -7 -6 -5 -4 -3 D) -9 -8 -7 -6 -5 -4 -3 Write the phrase as a mathematical expression. Use x to represent the number. Combine like terms if possible. 9) Five times a number, added to the sum of the number and six. A) 5x + 6 B) 6x C) 11x D) (x + 6) + 5x 1 10) The temperature, t, in degrees Fahrenheit, of water being heated is F = 67 + 1 m where m is the number of 4 minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit? A) 9 minutes B) 6 minutes C) 24 minutes D) 12 minutes 11) The trout population in Clear Lake is decreasing be about 60 fish per year. This year there are about 430 fish in the lake. Write an expression fro the number of trout in the lake t years from now. B) 60t = 430 C) t = 430 - 60 D) 370t A) 430 - 60t 12) Pat weighs 250 pounds and decides to go on a diet. Pat looses 3 pounds per week. What is the equation for Patʹs weight, W, in terms of the number of weeks, t, since going on the diet? B) W = -3t C) W = 3 - 250t D) W = 250 - 3t A) W = 250 + 3t 13) Which table could be described by a linear equation? B) x 1 2 3 A) x 0 2 5 y 4 7 10 y 4 6 8 Find the linear equation for the data. 14) x 1 2 3 4 5 y 3 0 -3 -6 -9 A) y = x - 6 B) y = -3x - 6 C) x 2 3 4 y 4 9 16 D) x -2 0 2 y 4 0 4 C) y = x + 6 D) y = -3x + 6 Determine whether the ordered pair is a solution for the given equation. 15) y = 9 - x, (4, 5) A) Yes B) No 16) Find the intercepts of the graph: 25x - 30y = 1200 A) (25, 0), (0, -40) C) (48, -40), (12000, 0) 2 B) (48, 0), (-40, 0) D) (48, 0), (0, -40) Use the graph to solve the problem. 17) Find the rate of change of the temperature of the water being heated. 80 75 70 65 60 -1 1 2 3 4 5 6 7 Minutes since heating started (marked in 1 minute increments) A) 1 degree per minute B) 5 degrees per minute C) 2.5 degrees per minute D) 2 degrees per minute 18) The cost of housing and tuition at State University is given by C = 200 + 25u, where u is the number of units you take. What does the slope of the graph tell you? B) Tuition at State University is increasing. A) Housing costs $200. C) How many units you are taking. D) Tuition costs $25 per unit. 19) The equation below gives the number of acres of rain-forest left in the world, where y is in millions of square kilometers, and x is the nubmer of years since 1950. 100y + 8x = 1140 What does the y-intercept of the graph tell you? A) There are 100 million square kilometers of rain-forest left. B) In 8 years, there will be 100 million square kilomethers of rain-forest left. C) In 1950, ther were 11.4 million square kilometers of rain forest. D) The rain-forest is shrinking by 8 million square kilometers per year. Identify the coordinates of each point in the graph. 20) 6 5 4 3 2 1 -6 -5 -4 -3 -2 -1-1 -2 -3 -4 -5 -6 A) (-4, -5) y 1 2 3 4 5 6x C) (7, -4) B) (-4, 5) 3 D) (5, -4) Find the slope of the line. 21) y 10 5 -10 -5 10 x 5 -5 -10 A) 1 3 B) -3 C) - 22) Find the slope of the line joining (1, 4) and (-6, -2) 2 6 B) A) 5 7 C) 1 3 D) 3 6 7 D) 1 4 23) Which of these graphs below is the graph of a line through the point (0, 4) with slope A) 7 6 B) 10 y 10 5 5 -10 y -5 5 10 x -10 -5 -5 -5 -10 -10 C) 5 10 x 5 10 x D) 10 y 10 5 5 -10 -5 y 5 10 x -10 -5 -5 -5 -10 -10 4 Find the equation of the line in slope-intercept form. 24) y 5 4 3 2 1 -5 -4 -3 -2 -1 -1 1 2 3 4 5x -2 -3 -4 -5 A) y = -2x - 1 B) y = 2x + 1 25) Find an equation for the line of Ssope A) y = 2 x+7 3 B) y = - C) y = x + 2 D) y = 1/2x + 1 2 that passes through (3, 5) 3 2 x+7 3 C) y = 2 x-7 3 D) y = - 2 x-7 3 Graph the equation. 26) 3x - 9y = 18 B) A) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 C) 5 10 x 5 10 x D) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 5 Solve the problem . 27) Betsy doesnʹt trust banks, so her savings are hidden under her mattress. Hsien-Ta has his savings in an investment at simple interest. In approximately what year did they have the same amount? A) 1986 B) 1989 C) 1988 D) 1996 28) Solve the system of equations: 3x + 4y = 12 6x + 5y = 6 A) (12, -6) B) 9x + 9y = 18 C) y = 29) What is the x-value of the solution to the system? -7x + 5y = 5 5x + 3y = 3 A) x=0 B) x=-1 -3 x+3 4 D) (-4, 6) C) x=2 D) No solutions C) 64,700 D) 647,000 Convert to decimal notation. 30) 6.47 x 105 A) 6,470,000 B) 323.5 Simplify. Do not use negative exponents in your answer. 31) (x-7 y9 )(x-4 y-4 ) A) x3 y5 B) y5 x11 C) x11 y5 D) 1 11 x y5 Simplify. 32) x2 + 10 x + 16 x +2 A) x + 8 B) x2 + 8 C) x3 - 14 D) x - 14 B) 49 + 14 m - m2 C) 14 - m2 D) 49 - m2 B) x2 + 15x + 15 C) 18x + 18 D) 4x + 11 Multiply. 33) ( 7 + m)( 7 - m) A) 49 - 14 m - m2 34) (x + 2)(3x + 9) A) 3x2 + 15x + 18 6 35) (x - 3)(7x2 + x + 8) A) 7x3 - 22x2 + 5x - 24 B) 7x3 + 20x2 + 5x - 24 D) 7x3 - 20x2 + 5x - 24 C) 7x3 - 20x2 + 11x - 24 Factor the trinomial. 36) y2 - 11y + 30 A) (y - 6)(y - 5) B) (y + 6)(y + 5) C) (y - 6)(y + 5) D) (y - 30)(y - 1) B) (x + 5)2 C) (x - 5)(x + 5) D) Not possible B) (15z + 4)(z - 4) C) (15z + 1)(z - 16) D) (3z - 4)(5z + 4) Factor. 37) x2 - 25 A) (x - 5)2 38) 15z 2 + 8z - 16 A) (3z + 4)(5z - 4) Multiply and reduce to lowest terms. z 2 + 14z + 49 z 2 + 6z 39) · z+7 z 2 - 36 A) z(z + 7) z+6 z z+6 C) z(z + 7) z-6 D) (z + 7) z-6 C) 7m m+7 D) 7 m 7 + m+7 m+7 40) Add: A) 1 B) m 41) Subtract: A) B) 2 x+2 x+2 x x2 + 2x + 4 x2 + 2x B) -x 2 C) 4 D) x2 + 2x + 4 4m + 3 m -2 + 2 2 m + 10 m + 21 m + 3 m - 28 42) Add: A) 5m+ 1 2 2m + 13 m - 7 B) 5 m + 1 C) 5 m 2 + 9 m + 17 (m + 7 )(m + 3 )(m - 4 ) D) 5 m 2 + 9 m + 17 (m - 7 )(m - 3 )(m + 4 ) Solve. 43) x x =2 7 4 A) 14 B) 56 3 C) 8 7 D) 28 44) 2 5 2 -1= 3x 3 x A) 7 5 B) 4 5 C) 1 D) 2 Solve the formula for the specified letter. A 45) P = for r 1 + rt A) r = P - tA B) r = A- P Pt C) r = P-1 At D) r = P-A 1+t Add. 46) (r + 4s + 1) - (5r - s) + (s + 4) A) -4r + 5s + 5 B) -4r + 6s + 5 C) -5r + 4s + 5 D) -6r + 6s + 5 Provide an appropriate response. 47) Identify the base and exponent in the Expression -3y2 A) Base: 2, exponent: y C) Base: 2, exponent: -3y B) Base: y, exponent: 2 D) Base: -3y, exponent: 2 Simplify. 48) m 5 · m 9 · m 8 A) m 66 y (-3xy2 )2 4 7 A) -18x y B) m 22 C) (3m)22 D) m 360 2 3 49) -2 x 3 7 B) 6 x y C) 6x6y10 D) none of these 50) The perimeter of a rectangle is 22 cm. The length is 7 cm longer than the width. What are the length and width of the rectangle? A) Length: 7 cm; width: 2 cm B) Length: 11 cm; width: 4 cm C) Length: 13 cm; width: 6 cm D) Length: 9 cm; width: 2 cm 51) Anne has 15 coins in her pocket consisting of nickels and dimes only. The total value of the coins is $1.25. Write a system of equations where x is the number of nickels and y is the number of dimes that you would use to answer the question ʺHow many nickels and how many dimes does she have?ʺ A) x + y = 1.25 B) x + y = 15 0.05x + 0.10y = 15 0.05x + 0.05y = 1.25 C) x + y = 15 D) x + y = 15 5x + 10y = 1.25 0.05x + 0.10y = 1.25 8 52) Alice starts jogging at 4 miles per hour. One half hour later, Bob jogs over the same route at 6 miles per hour. Set up a system of equations where x is the time of Alice and y is the time of Bob that you would use to answer the question ʺ How long will it take to Bob catch up with Alice?ʺ 1 1 B) 4x = 6y C) 4x = 6y D) 4x + 6y = A) 4x + 6y = 2 2 1 1 y x y x + = = 1 4x = 6y 2 2 x+y= 2 Solve. 53) How much pure acid (100%) should be mixed with 6 gallons of a 50% acid solution in order to get an 80% acid solution? A) 15 B) 3 C) 9 D) 24 54) Alexander and Judy are 32 miles apart on a calm lake paddling toward each other. Alexander paddles at 5 miles per hour, while Judy paddles at 8 miles per hour. How long will it take them to meet? 2 6 7 hrs B) 10 hrs C) 19 hrs D) 2 hrs A) 1 3 13 10 Solve the following equations. 55) 3x2 - 5x - 8 = 0 A) x = 3 ,x=1 8 56) 4x2 = -6x - 1 -3 ± 13 A) 4 B) x = B) 3 ,x=0 8 C) x = -6 ± 5 4 C) 57) One of the solutions of 2x2 - 4x = 7 is B) between 2 and 3 A) between 1 and 2 8 , x = -1 3 -3 ± 5 4 C) between 3 and 4 D) x = D) 3 , x = -1 8 -3 ± 5 8 D) between 4 and 5 Solve the problem . 58) A ball is dropped from a cliff that is 176 feet high. As it is falling, its height is given by the formula h = 176 - 16t 2 . How many seconds (in tenths) will it take for the ball to hit the ground (h = 0)? A) 1936 sec B) 12.6 sec C) 3.3 sec D) 13.3 sec B) 1, -7 C) 7, 1 D) 3, -3 Solve. 59) 2(x - 4)2 = 18 A) 13 9 Graph the equation. 60) y = x2 - 4 A) B) 10 y y 10 5 -10 5 -5 5 x 10 -10 -5 5 -5 -5 -10 -10 C) 10 x D) y y 15 10 10 5 5 -5 -10 -5 5 62) 6 32 - 3 18 A) 9 14 15 x -10 -5 Simplify the expression. 61) 36 - 81 A) - 3 5 10 -5 x 10 5 B) - C) -1.5 D) -3 B) 15 2 C) 2 14 D) 24 2 B) x = 38 C) x = 64 D) x = 36 3 Solve. 63) x+2=6 A) x = 34 Write a proportion that models the situation described. 64) 5 is to 12, as 3 is to x 3x 5 3 5 B) A) = = 1 12 x 12 C) 10 x 5 = 12 3 D) 5 12 = x 3 Solve the proportion. 2 5 65) = 9 x A) x = 10 B) x = 22 1 2 C) x = 2 1 2 D) x = 45 66) A recipe calls for 385 grams of flour and 220 grams of sugar. Write an equation to find how much sugar you should use with 350 grams of flour. 385 350 385 = x C) 220x + 350 = 385 D) = A) 385 + 220 = 350 + x B) 220 x 220 350 2x + 4 5 = 12 - x 3 67) Solve A) 4 4 11 B) 5 1 3 C) 8 68) Which table shows proportional variables B) A) y y x x 2 10 2 14 4 15 3 21 6 20 5 35 C) 11 D) 4.36 x 2 3 4 y 4 9 16 D) x 2 4 6 y 12 14 16 Answer Key 1) C 2) B 3) C 4) B 5) D 6) A 7) C 8) D 9) D 10) D 11) A 12) D 13) B 14) D 15) A 16) D 17) C 18) D 19) C 20) D 21) B 22) C 23) B 24) B 25) B 26) A 27) B 28) D 29) A 30) D 31) B 32) A 33) D 34) A 35) D 36) A 37) C 38) A 39) C 40) A 41) A 42) C 43) B 44) C 45) B 46) B 47) B 48) B 49) A 50) D 12 Answer Key 51) D 52) B 53) C 54) D 55) C 56) C 57) A 58) C 59) C 60) B 61) D 62) B 63) A 64) B 65) B 66) D 67) A 68) B 13