Algebra II Cumulative Test
Algebra II Cumulative Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Solve the equation.
____ 1.
a. / / b. / / c. / / d. /____ 2.
a. / x = or x = / c. / x = or x =b. / x = or x = / d. / x = or x =
____ 3.
a. / 1, –5 / c. / 1, –1b. / 5, –5 / d. / 5, –1
____ 4.
a. / 24; –40 / b. / 12 / c. / 40; –40 / d. / –4Solve the compound inequality. Graph the solution set.
____ 5. 5x + 2 ³ –28 and 9x – 14 £ 22
a. / x ³ –6 and x £ 4/ c. / x ³ or x £
b. / x ³ or x £ 4
/ d. / x ³ –6 and x £
____ 6. 3x – 1 < –1 or 7x + 3 > 17
a. / x < 0 or x > 2/ c. / x < or x >
b. / x < or x > 2
/ d. / x < 0 or x >
____ 7.
a. // c. /
b. /
/ d. /
Solve the inequality. Graph the solution.
____ 8.
a. // c. /
b. /
/ d. /
____ 9. This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of 3 and 4?
a. / / b. / / c. / / d. /____ 10. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 4 or greater than 6 in a single spin?
a. / / b. / / c. / / d. /____ 11. Assume a rabbit variety can be either long-haired (dominant) or short-haired (recessive). If a parent has one of each type of gene, then the two genes are equally likely to be passed to its offspring. If a rabbit has one or two dominant genes, it will be long-haired. What is the probability that a rabbit will be short-haired?
Gene from FatherG / g
Gene from / G / GG / Gg
Mother / g / Gg / gg
a. / / b. / / c. / / d. /
Graph the absolute value inequality.
____ 12. |x + 5| y – 2
a. / / c. /b. / / d. /
____ 13. A rental car agency charges a flat fee of $29.00 plus $1.75 per day to rent a certain car. Another agency charges a fee of $24.00 plus $3.00 per day to rent the same car.
a. / Write a system of equations to represent the cost c for renting a car at each agency for d days.b. / Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
a. / a.
b. 7 / c. / a.
b. 7
b. / a.
b. 4 / d. / a.
b. 4
Solve the system by the method of substitution.
____ 14.
a. / (–2, 2, 1) / b. / (2, –2, 1) / c. / (2, 2, 1) / d. / (2, 2, –1)____ 15.
a. / (3, –1, –1) / b. / (–3, –1, –1) / c. / (–3, –1, 1) / d. / (–3, 1, –1)____ 16. A group of 39 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.
a. / ; 13 adults, 26 children / c. / ; 26 adults; 19 childrenb. / ; 19 adults; 26 children / d. / ; 26 adults, 13 children
Use the elimination method to solve the system.
____ 17.
a. / infinite solutions / c. / (–7, –4)b. / (7, 4) / d. / no solutions
Solve the system of inequalities by graphing.
____ 18.
a. / / c. /b. / / d. /
____ 19.
a. / / c. /b. / / d. /
____ 20. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula , where x is the number of units produced per week, in thousands.
a. / How many units should the company produce per week to earn the maximum profit?b. / Find the maximum weekly profit.
a. / 4,000 units; $200 / c. / 2,000 units; $200
b. / 2,000 units; $1000 / d. / 4,000 units; $400
____ 21. Find .
a. / 2 / b. / / c. / / d. / –8____ 22. Identify the graph of the complex number .
a. / / c. /b. / / d. /
Solve the quadratic equation by completing the square.
____ 23.
a. / / c. /b. / / d. /
Rewrite the equation in vertex form.
____ 24.
a. / / c. /b. / / d. /
Use the Quadratic Formula to solve the equation.
____ 25.
a. / / c. /b. / / d. /
____ 26. Write 3x3 + 21x2 + 30x in factored form.
a. / 3x(x + 5)(x + 2) / c. / 3x(x + 2)(x – 5)b. / 5x(x + 2)(x + 3) / d. / 2x(x + 3)(x + 5)
____ 27. Write a polynomial function in standard form with zeros at 4, –3, and –5.
a. / / c. /b. / / d. /
____ 28. Divide by x + 2.
a. / , R 20 / c. /b. / , R –24 / d. /
Divide using synthetic division.
____ 29.
a. / 1 / c. /b. / / d. /
Factor the expression.
____ 30.
a. / / c. /b. / / d. /
____ 31. Solve . Find all complex roots.
a. / , / c. / ,b. / no solution / d. / ,
____ 32. In how many different orders can you line up 8 cards on a shelf?
a. / 8 / b. / 1,680 / c. / 40,320 / d. / 1Use Pascal’s Triangle to expand the binomial.
____ 33.
a. /b. /
c. /
d. /
____ 34. Determine the probability of getting four heads when tossing a coin four times.
a. / 0.5 / b. / 0.375 / c. / 0.25 / d. / 0.0625____ 35. Determine the probability that you will get 1 green light in a series of 6 lights. Assume red and green are equally likely occurrences.
a. / 9.38% / b. / 6% / c. / 0.94% / d. / 18.75%____ 36. There are 9 students participating in a spelling bee. In how many ways can the students who go first¸ second¸ and third in the bee be chosen?
a. / 362,880 ways / c. / 504 waysb. / 1 way / d. / 84 ways
____ 37. The Booster Club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk, coffee, tea, or cola. How many possible meal combinations are there?
a. / 10 / b. / 11 / c. / 28 / d. / 30____ 38. There are 7 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for 0¸ 1¸ or 2 judges. In how many different ways can a person vote?
a. / 35 / b. / 29 / c. / 21 / d. / 5Find the real-number root.
____ 39.
a. / –1.2 / c. / –0.72b. / 1.2 / d. / no real number root
Simplify the radical expression. Use absolute value symbols if needed.
____ 40.
a. / / b. / / c. / / d. /____ 41. Simplify . Assume that all variables are positive.
a. / / c. /b. / / d. / none of these
Divide and simplify. Assume that all variables are positive.
____ 42.
a. / / b. / / c. / / d. /Rationalize the denominator of the expression. Assume that all variables are positive.
____ 43.
a. / / c. /b. / / d. /
____ 44. Write the exponential expression in radical form.
a. / / b. / / c. / / d. /____ 45. Let and . Find .
a. / –67 / b. / 5 / c. / –21 / d. / –15____ 46. Let and . Find f(g(x)) and g(f(x)).
a. / f(g(x)) = 10x – 1; g(f(x)) = 10x + 7b. / f(g(x)) = 7x + 3; g(f(x)) = 10x + 7
c. / f(g(x)) = –7x – 3; g(f(x)) = –10x + 7
d. / f(g(x)) = –10x – 7; g(f(x)) = 7x + 3
____ 47. Graph and its inverse.
a. / / c. /b. / / d. /
____ 48. For the function , find .
a. / –9 / b. / 81 / c. / 9 / d. / –13Graph the function.
____ 49.
a. / / c. /b. / / d. /
____ 50. Write an exponential function for the graph.
a. / / b. / / c. / / d. /____ 51. Graph .
a. / / c. /b. / / d. /
____ 52. Graph .
a. / / c. /b. / / d. /
____ 53. Suppose you invest $2000 at an annual interest rate of 6.8% compounded continuously. How much will you have in the account after 15 years?
a. / $5,545.29 / b. / $32,110.96 / c. / $59,216.33 / d. / $5,546.39____ 54. How much money invested at 5% compounded continuously for 3 years will yield $820?
a. / $952.70 / b. / $818.84 / c. / $780.01 / d. / $705.78____ 55. Solve .
a. / / b. / / c. / / d. /____ 56. Solve . Round to the nearest ten-thousandth.
a. / 0.0090 / b. / 0.3103 / c. / 3.2222 / d. / 111____ 57. Solve . Round to the nearest ten-thousandth.
a. / 12.3308 / b. / 43.3013 / c. / 86.6025 / d. / 1875Use natural logarithms to solve the equation. Round to the nearest thousandth.
____ 58.
a. / 0.347 / b. / –0.199 / c. / 0.245 / d. / 0.173Simplify the rational expression. State any restrictions on the variable.
____ 59.
a. / / c. /b. / / d. /
Add or subtract. Simplify if possible.
____ 60.
a. / / c. /b. / / d. /
Simplify the complex fraction.
____ 61.
a. / / c. /b. / / d. / not here
____ 62. Two urns contain white balls and yellow balls. The first urn contains 7 white balls and 10 yellow balls and the second urn contains 7 white balls and 8 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
a. / / b. / / c. / / d. /Suppose S and T are mutually exclusive events. Find P(S or T).
____ 63. P(S) = 8%, P(T) = 77%
a. / 69% / b. / 85% / c. / 6.16% / d. / 616%Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci.
____ 64.
a. / ellipse with center (–3, 3), foci atb. / hyperbola with center (3, 3), foci at
c. / ellipse with center (3, –3), foci at
d. / hyperbola with center (–3, –3), foci at
____ 65.
a. / hyperbola with center (–5, –3), foci atb. / ellipse with center (–5, 3), foci at
c. / hyperbola with center (5, 3), foci at
d. / ellipse with center (5, –3), foci at
____ 66. The sequence 24, 30, 36, 42, 48, ..., 84 has 11 terms. Evaluate the related series.
a. / 510 / c. / 570b. / 264 / d. / 594
____ 67. Use summation notation to write the series 43 + 35 + 27 + ... for 12 terms.
a. / / c. /b. / / d. /
____ 68. If all possible results are equally likely, what is the probability that a spin of the spinner will land on a lower case letter or a vowel?