Algebra 2 / Trig Honors Start Time______Name______Review of Algebra Skills End Time ______Date______
Multiple Choice: Calculator Free Identify the letter of the choice that best completes the statement or answers the question.
____ 1. When simplifying an expression, you ____ perform operations inside grouping symbols first. a. always b. sometimes c. never ____ 2. A rational number is ____ a real number. a. always b. sometimes c. never
Simplify the expression.
____ 3. a. 297 b. 868 c. 437 d. 867 ____ 4. a. 13 b. –13 c. 12 d. –12 ____ 5. a. c. b. d. ____ 6. 3.7 – 1.8 – 3.67 + 4.4 – 1.34 a. –7.51 b. –1.29 c. 1.29 d. 8.63
____ 7. Evaluate the formula for B = 9 in.2 and h = 32 in. a. 288 in.3 b. 9.6 in.3 c. 32 in.3 d. 96 in.3 ____ 8. Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above ____ 9. Which set of numbers is the most reasonable to describe the number of desks in a classroom? a. whole numbers c. rational numbers b. irrational numbers d. integers ____ 10. The opposite of a negative number is ____ negative. a. always b. sometimes c. never ____ 11. Which number line model can you use to simplify –5 + 6? a. +6
–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 –5 + 6 = 11 b. +6
–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 –5 + 6 = 1 c. –6
–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 –5 + 6 = –11 d. –6
–11–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 –5 + 6 = 11 ____ 12. The product of two negative numbers is ____ positive. a. always b. sometimes c. never ____ 13. –12 (–2) a. 24 b. –6 c. –24 d. 6
____ 14. If a is a negative number, then is ____ equal to –1. a. always b. sometimes c. never
____ 15. Evaluate for a = 6 and b = 2. a. 12 b. 3 c. 4 d. 12 3 ____ 16. Use the Distributive Property to find the price of 7 CDs that cost $14.99 each. a. $105.00 b. $98.00 c. $104.93 d. $105.70 ____ 17. For every real number x, y, and z, the statement is ____ true. a. always b. sometimes c. never
Name the property the equation illustrates.
____ 18. 8.2 + (–8.2) = 0 a. Inverse Property of Addition b. Addition Property of 0 c. Identity Property of Addition d. Inverse Property of Multiplication ____ 19. 8 + 3.4 = 3.4 + 8 a. Inverse Property of Addition b. Associative Property of Addition c. Commutative Property of Addition d. Inverse Property of Multiplication ____ 20. 7 + (4 + 4) = (7 + 4) + 4 a. Inverse Property of Addition b. Associative Property of Addition c. Commutative Property of Multiplication d. Commutative Property of Addition ____ 21. (ab)3 = a(b3) a. Inverse Property of Multiplication b. Associative Property of Addition c. Associative Property of Multiplication d. Commutative Property of Multiplication ____ 22. Which of the scatter plots shows a positive correlation? a. y c. y 6 6
5 5
4 4
3 3
2 2
1 1
1 2 3 4 5 6 x 1 2 3 4 5 6 x
b. y d. y 6 6
5 5
4 4
3 3
2 2
1 1
1 2 3 4 5 6 x 1 2 3 4 5 6 x
Solve the equation.
____ 23. a. –80 b. 16 c. –16 d. 1.8 ____ 24. Which equation is an identity? a. c. b. d. ____ 25. Peter is reading a 193-page book. He has read three pages more than one fourth of the number of pages he hasn’t yet read. a. How many pages has he not yet read? b. Estimate how many days it will take Peter to finish the book if he reads about 8 pages per day. a. 144; about 18 days c. 152; about 19 days b. 147; about 18 days d. 141; about 18 days ____ 26. Carlos and Maria drove a total of 258 miles in 5 hours. Carlos drove the first part of the trip and averaged 53 miles per hour. Maria drove the remainder of the trip and averaged 51 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary. a. 3.5 hours b. 2.5 hours c. 1.8 hours d. 1.5 hours Find the range.
____ 27. 3 –9 7 –1 5 –4 2 a. 8 b. –1 c. 16 d. 2 ____ 28. Determine whether the statement is sometimes, always or never true. If ax + b – 4 = b and then . a. always b. sometimes c. never ____ 29. The perimeter of the rectangle is 24 cm. Find the value of x.
3 cm
3x cm
a. 3 b. 12 c. 8 d. 18 3
Which number is a solution of the inequality?
____ 30. b > 11.3 a. 15 b. 9 c. –14 d. 4 13 ____ 31. m 3 a. 3 b. 5 c. 2 d. –9 ____ 32. x(7 – x) > 8 a. 2 b. 8 c. –1 d. 0 ____ 33. a. 8 b. 18 c. 2 d. 1 ____ 34. a. 9 b. 5 c. 6 d. 6 11 11
Write the inequality in words.
____ 35. 5n – 10 > 26 a. Five times n less than ten is twenty-six. b. Ten plus five times a number is less than or equal to twenty-six. c. Ten less than five times a number is greater than twenty-six. d. Ten less than a number is less than or equal to twenty-six. Graph the inequality.
____ 36. a. –10 –8 –6 –4 –2 0 2 4 6 8 10 b. –10 –8 –6 –4 –2 0 2 4 6 8 10 c. –10 –8 –6 –4 –2 0 2 4 6 8 10 d. –10 –8 –6 –4 –2 0 2 4 6 8 10
Write an inequality for the graph.
____ 37. –10 –8 –6 –4 –2 0 2 4 6 8 10 a. b. x < –8 c. x > –8 d. x < 8
Identify the graph of the inequality from the given description.
____ 38. x is negative. a. c. –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 b. d. –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 ____ 39. x is at least –4.5. a. c. –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 b. d. –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –4 –3 –2 –1 0 1 2 3 4 5
Solve the inequality. Then graph your solution.
____ 40. a. c.
–32 –28 –24 –20 –16 –12 –8 –4 0 –32 –28 –24 –20 –16 –12 –8 –4 0 b. d.
–14 –12 –10 –8 –6 –4 –2 0 2 0 2 4 6 8 10 12 14 16 ____ 41. –2 < 4x – 10 < 6 a. 4 < x < 12 c. –16 < x < –8
–25 –20 –15 –10 –5 0 5 10 15 20 25 –25 –20 –15 –10 –5 0 5 10 15 20 25 b. 3 < x < 1 d. 2 < x < 4 –10 –8 –6 –4 –2 0 2 4 6 8 10 –10 –8 –6 –4 –2 0 2 4 6 8 10
____ 42. a. –36 < x < 14 c. –17 > x > 8
–40 –30 –20 –10 0 10 20 30 40 –20 –15 –10 –5 0 5 10 15 20 b. –17 < x < 8 d. –8 < x < 8
–20 –15 –10 –5 0 5 10 15 20 –8 –6 –4 –2 0 2 4 6 8
Solve the inequality.
1 2 5 ____ 43. + x + 3 9 6 a. 5 b. 17 c. 17 d. 7 x x x x 1 18 18 18 18
Write a compound inequality that the graph could represent.
____ 44. –5 –4 –3 –2 –1 0 1 2 3 4 5 a. c. b. d.
____ 45. –5 –4 –3 –2 –1 0 1 2 3 4 5 a. c. b. d.
Solve the compound inequality. Graph your solution.
____ 46. a. or c. or
–12 –10 –8 –6 –4 –2 0 2 4 6 8
–12 –10 –8 –6 –4 –2 0 2 4 6 8 b. or d. or
–12 –10 –8 –6 –4 –2 0 2 4 6 8 –12 –10 –8 –6 –4 –2 0 2 4 6 8
Solve the equation. If there is no solution, write no solution.
____ 47. a. x = 13 c. x = –1 b. x = 13 or x = –13 d. no solution ____ 48. The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write an absolute value inequality for the range of acceptable widths. a. c. b. d.
Solve the proportion.
____ 49.
a. 55 b. 2.2 c. 110 d. 1.8
____ 50. a. 32 b. 40 c. 64 d. 72 ____ 51. A package delivery company has determined that they can meet their schedules if they have 4 drivers for every 30 square miles of area they cover. If they want to offer service to a county of 75 square miles, how many drivers must they have? a. 12 drivers b. 10 drivers c. 15 drivers d. 9 drivers ____ 52. The cross products of a proportion are ____ equal. a. always b. sometimes c. never ____ 53. In similar triangles, corresponding angles are ____ congruent. a. always b. sometimes c. never ____ 54. Use the scale and map measurements to find the actual distance from New Wilmington to Sharon through Mercer. What is the actual distance if you travel from New Wilmington to Sharon through Volant?
1.25 in. Sharon
1 in. Mercer 1.75 in. New Wilmington
1.75 in.
Volant Scale 1 in. : 12 mi
a. 27 mi; 42 mi c. 13.5 mi; 21 mi b. 40.5 mi; 63 mi d. 54 mi; 84 mi ____ 55. What is 6% of 117? a. 5.97 b. 8.07 c. 7.02 d. 7.37 ____ 56. Susan earns a 5% commission on her computer sales. If she earned a $81.04 commission on a sale of a new system, what was the price of the system? a. $1134.56 b. $810.40 c. $162.08 d. $1620.80
Write an equation and solve. Round the final answer to the nearest tenth, if necessary.
____ 57. 68 is 78% of what number? a. ; 53 c. ; 59.3 b. ; 87.2 d. ; 90.7 ____ 58. If a > 0, then 125% of a is ____ less than or equal to a. a. sometimes b. always c. never ____ 59. Use the formula for simple interest, I = prt. Find p if I = $313.42, r = 2.5%, and t = 3 yr. a. $3,426.73 b. $4,429.67 c. $3,761.04 d. $4,178.93 ____ 60. The percent of change in two numbers is ____ greater than 100%. a. always b. sometimes c. never ____ 61. Teesha is in the French club. There are 26 students in the club. The French teacher will pick 3 students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide? a. 3 b. 29 c. 23 d. 3 26 26 26 29 ____ 62. The probability of the complement of an event is ____ less than the probability of the event itself. a. sometimes b. always c. never ____ 63. If you roll a number cube 60 times and use the results to calculate the experimental probability of rolling a 1, the experimental probability of rolling a 1 will ____ be less than the theoretical probability of rolling a 1. a. sometimes b. always c. never
____ 64. If A and B are independent events and P(A) and P(B) are both greater than , then P(A and B) is ____ greater than 1. a. sometimes b. always c. never ____ 65. Which graph is the most appropriate to describe a quantity decreasing at a steady rate? a. c.
b. d.
____ 66. The graph below shows how the cost of gasoline changes over one month. According to the graph, the cost of gasoline ______decreases. Cost
Time
a. always b. sometimes c. never ____ 67. A function is ______a relation. a. always b. sometimes c. never ____ 68. Identify the mapping diagram that represents the relation and determine whether the relation is a function.
a. c.
The relation is not a function. The relation is a function. b. d.
The relation is a function. The relation is not a function.
____ 69. Identify the mapping diagram that represents the relation and determine whether the relation is a function. a. c.
The relation is a function. The relation is not a function b. d.
The relation is a function. The relation is not a function. ____ 70. An equation of the form , where a, b, and c do not equal zero, is ______a direct variation. a. sometimes b. always c. never
Find the common difference of the arithmetic sequence.
____ 71. 9, 13, 17, 21, . . . a. 4 b. 4 c. 9 d. 22 1 9 13
Find the slope of the line.
y
5
4
3
2
1 ____ 72. –5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5
a. 1 b. 3 c. 3 d. 1 – 3 3 Find the slope and y-intercept of the line.
____ 73. 14x + 4y = 24 a. 2 c. 7 1 ; 6 ; 7 2 6 b. 7 d. 7 ; 6 ; 6 2 2
Write the slope-intercept form of the equation for the line.
y
5
4
3
2
1
–5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5 ____ 74. a. y = 3x 1 c. 1 y = x 1 3 b. y = 3x 1 d. 1 y = x 1 3
Match the equation with its graph.
____ 75. –7x + 7y = –49 a. y c. y 10 10
8 8
6 6
4 4
2 2
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –2 –2
–4 –4
–6 –6
–8 –8
–10 –10 b. y d. y 10 10
8 8
6 6
4 4
2 2
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –2 –2
–4 –4
–6 –6
–8 –8
–10 –10
____ 76. A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. a. y – 5 = 3(x + 1); y = 3x + 8 c.
b. d. y + 5 = –3(x – 1); y = –3x – 2 ;
Is the relationship shown by the data linear? If so, model the data with an equation.
____ 77. x y –9 –2 –5 –7 –1 –12 3 –17
a. 4 The relationship is linear; y + 2 = (x + 9). 5 b. 4 The relationship is linear; y + 9 = (x + 2). 5 c. The relationship is not linear. d. 5 The relationship is linear; y + 2 = (x + 9). 4
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
____ 78. 4x – 12y = 2; (10, –1) a. y = 3x + 29 c. y = 3x + 29 b. 1 d. 1 y = x + 29 y = x + 7 3 3 ____ 79. Which graph shows the best trend line for the following data.
a. Violin Competition c. Violin Competition 60 60
54 54
48 48
42 42
36 36 e e r r
o 30 o 30 c c S 24 S 24
18 18
12 12
6 6
2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 Practice (weeks) Practice (weeks) b. Violin Competition d. Violin Competition 60 60
54 54
48 48
42 42
36 36 e e r r
o 30 o 30 c c S S 24 24
18 18
12 12
6 6
2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 Practice (weeks) Practice (weeks)
Graph each equation by translating y = | x |.
____ 80. y = | x + 6 | a. y c. y 10 10
8 8
6 6
4 4
2 2
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –2 –2
–4 –4
–6 –6
–8 –8
–10 –10
b. y d. y 10 10
8 8
6 6
4 4
2 2
–10 –8 –6 –4 –2 2 4 6 8 10 x –10 –8 –6 –4 –2 2 4 6 8 10 x –2 –2
–4 –4
–6 –6
–8 –8
–10 –10
y
5
4
3
2
1 ____ 81. –5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5
Bella wants to write two equations to model the streets on this map. She can use y = x – 4 to describe Platte Way. Find one absolute value equation to describe Marteen Rd and Smith St. a. y = | x – 2 | – 3 c. y = | x + 3 | – 2 b. y = | x + 2 | – 3 d. y = | x – 3 | – 2 ____ 82. Which graph represents the following system of equations? y = 3x + 3 y = –x – 3 a. y c. y
4 4
2 2
–4 –2 O 2 4 x –4 –2 O 2 4 x
–2 –2
–4 –4
b. y d. y
4 4
2 2
–4 –2 O 2 4 x –4 –2 O 2 4 x
–2 –2
–4 –4
____ 83. What is the solution of the system of equations? y = 3x + 7 y = x – 9 a. (–1, –10) b. (–17, –8) c. (4, 19) d. (–8, –17)
Solve the system using elimination.
____ 84. 3x + y = 11 4x – y = 17 a. (–1, 4) b. (4, –1) c. (5, –4) d. (1, 4) ____ 85. 3x – 4y = –24 x + y = –1 a. (–4, 3) b. (0, 6) c. (3, 4) d. (4, 3) ____ 86. 3x – y = 28 3x + y = 14 a. (8, –4) b. (–7, 7) c. (7, –7) d. (–4, 8) ____ 87. Write the following inequality in slope-intercept form.
a. b. c. d.
Find the degree of the monomial. ____ 88. 7m6n5 a. 5 b. 11 c. 6 d. 7 ____ 89. 6x8y5 a. 5 b. 6 c. 13 d. 8
Simplify the difference.
____ 90. (4w2 – 4w – 8) – (2w2 + 3w – 6) a. 2w2 – 7w – 2 c. 2w2 – 1w – 14 b. 6w2 – 1w – 14 d. 6w2 + 7w + 2
Simplify the product.
____ 91. 8x2(4x2 + 4y6) a. 12x4 + 12x2y6 c. 12x4 + 12x2y6 b. 32x4 + 32x2y6 d. 32x4 + 32xy8
Factor the polynomial.
____ 92. 54c3d4 + 9c4d2 a. 9c3d2(d2 + 6c) c. 9c4d2(d2 + 6) b. 9c3d2(6d2 + c) d. 9c4d2(6d2 + 1) ____ 93. Find the GCF of the terms of the polynomial. 8x6 + 32x3 a. x3 b. 8x3 c. 8x3 d. 8x6
Find the square.
____ 94. (2x – 6)2 a. 4x2 – 24x + 36 c. 4x2 + 36 b. 4x2 – 8x + 36 d. 4x2 – 12x + 36 ____ 95. Find 332 using mental math. a. 1,089 b. 900 c. 999 d. 729
Find the product.
____ 96. (2n + 2)(2n – 2) a. 4n2 – 4 c. 4n2 + 2n – 4 b. 4n2 – 4n – 4 d. 4n2 + 4n – 4
Factor the expression.
____ 97. 36y2 – 84y – 147 a. (2y + 7)(6y – 7) c. (2y – 7)(18y + 21) b. 3(2y – 7)(6y + 7) d. 3(2y + 7)(6y + 7) ____ 98. a. c. b. d.
Factor by grouping.
____ 99. 3x2 + 7x – 6 a. (3x – 2)(x – 3) c. (x + 3)(3x + 2) b. (3x – 2)(x + 3) d. (3x + 2)(x – 3) ____ 100. 40p2 – 13p – 36 a. (8p + 9)(5p + 4) c. (8p – 9)(5p + 4) b. (8p – 9)(5p – 4) d. (8p + 9)(5p – 4)