regents algebra1 Flashcards

What's on the cards

1. What is the 20th term of the arithmetic sequence 4, 7, 10, 13, …? A. 61 B. 64 C. 79 D. 83
2. What is the value of x in the equation 0.5x − 4 = 8 − x ? A. 6 B. 8 C. 18 D. 24
3. The binomial 4x² − 25 is equivalent to A. 4(x + 5)(x − 5) B. 4(x − 5)(x − 5) C. (2x − 5)(2x + 5) D. (2x − 5)(2x − 5)
4. A function is defined by the following set of points: {(3, −4), (−4, 3), (1, 1), (x, 2)} What is a possible value for x? A. 1 B. 2 C. 3 D. −4
5. The expression (4xy²)³ is equivalent to A. 12x³y⁶ B. 12x³y⁸ C. 64x³y⁶ D. 64x³y⁸
6. Allison was asked to write a third-degree trinomial with a leading coefficient of 4 and a constant term of 5. Which expression satisfies these conditions? A. 4x³ − 5 B. 3x⁴ + 5 C. 4x³ + 8x² + 5 D. 3x⁴ + 2x³ − 5
7. Given the sequence 128, 64, 32, …, which formula could be used to find the nth term of this sequence? A. aₙ = 128(−2)ⁿ⁻¹ B. aₙ = 128(1/2)ⁿ⁻¹ C. aₙ = 128 − 2(n − 1) D. aₙ = 128 + (1/2)(n − 1)
8. When a bicyclist increases the pressure on the brakes, the speed of the bicycle decreases. This relationship can best be described as a A. negative correlation and causal relationship B. negative correlation and non-causal relationship C. positive correlation and causal relationship D. positive correlation and non-causal relationship
9. A garden club plans to plant 40 flowering plants this year. They will only purchase daffodils that cost $4 per plant and tulips that cost $5 per plant. All prices include tax. The club has $170 to spend on plants. Which equation could be used to find the number of daffodil plants, d, the club purchases? A. 4d + 5(170 − d) = 40 B. 4d + 5(40 − d) = 170 C. 5d + 4(170 − d) = 40 D. 5d + 4(40 − d) = 170
10. A function is defined as h(x) = x² − 3x + 1. What is the value of h(−1)? A. 1 B. 2 C. 3 D. 5
11. The zeros of p(x) = x(3x + 2)(x − 5) are A. −2/3 and 5, only B. 2/3 and −5, only C. −2/3, 0, 5 D. 2/3, 0, −5
12. If f(x) = 1.25ˣ and g(x) = 3x + 10, what is the smallest positive integer of x for which f(x) > g(x)? A. 18 B. 19 C. 67 D. 69
13. What is an equation of the line that passes through the points (2, 5) and (−2, −1)? A. y − 5 = (2/3)(x − 2) B. y − 5 = (3/2)(x − 2) C. y − 2 = (2/3)(x − 5) D. y − 2 = (3/2)(x − 5)
14. At a local high school, students were asked to name the sport they like to watch the most. The results are summarized in the table below. Male: Football 40, Basketball 35, Baseball 15. Female: Football 20, Basketball 40, Baseball 10. Approximately what percentage of female high school students preferred to watch basketball? A. 35 B. 40 C. 53 D. 57
15. An equation that yields the same solutions as x² − 10x − 24 = 0 is A. (x + 5)² = 1 B. (x − 5)² = 1 C. (x + 5)² = 49 D. (x − 5)² = 49
16. The function f(x) is shifted three units right and four units up. The result of this transformation is A. f(x − 3) + 4 B. f(x + 3) + 4 C. f(x + 4) − 3 D. f(x − 4) − 3
17. Hana was asked to solve a quadratic equation. Her first step is shown below. x² − 8x = 3; Step 1: x² − 8x + 16 = 3 + 16. The property that Hana used is the A. distributive property B. commutative property C. additive inverse property D. addition property of equality
18. A data set is given below: 28, 28, 28, 28, 32, 32, 34, 34, 40, 42. What is the value of the upper quartile of this data set? A. 28 B. 32 C. 34 D. 42
19. When −3x² + 7x − 1 is subtracted from 2x² − 3x + 10, the result is A. 5x² + 4x + 9 B. 5x² − 10x + 11 C. −5x² + 4x + 9 D. −5x² + 10x − 11
20. The value of a home in Buffalo can be modeled by the function V(t) = 96,949(1.0448)ᵗ, where V(t) is the value of the house after t years. What is the percent of increase in the value of the home each year? A. 1.0448% B. 0.0448% C. 0.448% D. 4.48%
21. A rod is an old English measure of distance that is equivalent to 5.5 yards. How many inches are 2.5 rods? [1 yard = 3 feet] A. 66 B. 165 C. 198 D. 495
22. For which function is the axis of symmetry x = −4? A. f(x) = −x² − 4x − 1 B. g(x) = −x² + 8x + 5 C. h(x) = x² + 8x + 3 D. k(x) = x² + x − 4
23. When f(x) = |4x + 2| and g(x) = 3x + 5 are graphed on the same set of axes, for which value of x is f(x) = g(x)? A. 1 B. 2 C. 3 D. 14
24. The expression x² − 26x − 120 is equivalent to A. (x + 4)(x − 30) B. (x − 4)(x + 30) C. (x − 20)(x + 6) D. (x + 20)(x − 6)
25. Students were asked to write a polynomial given the following conditions: • the degree of the expression is 3 • the leading coefficient is 2 • the constant term is −6 Which expression satisfies all three conditions? A. 4x − 6 + 3x² B. 3x² − 6x + 4 C. 4 − 6x + 2x³ D. 4x² + 2x³ − 6
26. The following function models the value of a diamond ring, in dollars, t years after it is purchased: v(t) = 500(1.08)ᵗ What was the original price of the ring, in dollars? A. $108 B. $460 C. $500 D. $540
27. When solving the following system of equations algebraically, Mason used the substitution method. 3x − y = 10 and 2x + 5y = 1. Which equation could he have used? A. 2(3x − 10) + 5x = 1 B. 2(−3x + 10) + 5x = 1 C. 2x + 5(3x − 10) = 1 D. 2x + 5(−3x + 10) = 1
28. When solving the equation 3(2x + 5) − 8 = 7x + 10, the first step could be 3(2x + 5) = 7x + 18. Which property justifies this step? A. addition property of equality B. commutative property of addition C. multiplication property of equality D. distributive property of multiplication over addition
29. If f(x) = √(x + 1) + 5, then what is the value of f(3)? A. 9 B. 7 C. 3 D. 10
30. Isabella wants to shift the graph of the function f(x) = (x + 5)² − 2 left 3 units. Which function represents the shifted graph? A. g(x) = (x + 2)² − 2 B. g(x) = (x + 8)² − 2 C. g(x) = (x + 5)² − 5 D. g(x) = (x + 5)² + 1
31. What are the zeros of f(x) = x(x² − 36)? A. 0, only B. 6, only C. 6 and −6, only D. 0, 6, and −6
32. The point (x, −6) lies on the graph of a parabola whose equation is y = −x² − x + 6. The value of x can be A. −3 or 2 B. −4 or 3 C. 3, only D. −4, only
33. The two-way frequency table below is a summary of concession stand sales for a football game. Concession Stand Sales (columns Soda, Water, Coffee, Total): Hot Dogs 50, 62, 46, 158; Pizza 120, 58, 4, 182; No Food 30, 20, 10, 60; Total 200, 140, 60, 400. Of the people making a purchase at the concession stand, what is the relative frequency of them buying pizza and a water? A. 0.58 B. 0.35 C. 0.455 D. 0.145
34. When Theodore was driving in Canada, his speed was 104 kilometers per hour. Theodore was asked to convert his metric speed to a different rate, using the following conversion: (104 km / 1 hr) • (1 hr / 60 min) • (1 min / 60 sec) • (0.6214 mi / 1 km) • (5280 ft / 1 mi). Assuming he did all the work correctly, what would the units be for Theodore’s rate? A. feet per second B. feet per minute C. seconds per foot D. minutes per foot
35. Which expression is equivalent to (−2x²)³? A. −2x⁵ B. −2x⁶ C. −8x⁵ D. −8x⁶
36. The table below shows the amount of a radioactive substance that remained for selected years. Year: 2000, 2001, 2005, 2010, 2014, 2017, 2019. Amount Remaining (grams): 750, 450, 219, 85, 25, 12, 8. To the nearest tenth, the average rate of change, in grams per year, from 2000 to 2014 is A. 39.1 B. 51.8 C. −39.1 D. −51.8
37. When 2x² − 3x + 4 is subtracted from x² + 2x − 5, the result is A. x² − 5x + 9 B. x² − x + 1 C. −x² + 5x − 9 D. −x² − x − 1
38. Which equation has the same solution as x² − 6x = 24? A. (x − 3)² = 24 B. (x − 6)² = 24 C. (x − 3)² = 33 D. (x − 6)² = 60
39. In a sequence, the first term is −2 and the common ratio is −3. The fourth term in this sequence is A. −162 B. −11 C. 24 D. 54
40. Which expression is equivalent to 100x² − 16? A. (50x − 8)(50x + 8) B. (50x − 8)(50x − 8) C. (10x − 4)(10x + 4) D. (10x − 4)(10x − 4)
41. Josie has $2.30 in dimes and quarters. She has two more dimes than quarters. Which equation below can be used to determine x, the number of quarters she has? A. 0.35(2x + 2) = 2.30 B. 0.25(x + 2) + 0.10x = 2.30 C. 0.25x + 0.10(x + 2) = 2.30 D. 0.25x + 0.10(x − 2) = 2.30
42. If g(x) = −2x² + 16, then g(−3) equals A. −20 B. −2 C. 34 D. 52
43. What are the zeros of f(x) = x² − 8x − 20? A. 10 and 2 B. 10 and −2 C. −10 and 2 D. −10 and −2
44. Which point lies on the graph of y = 3x² − (1/4)x + 3? A. (−2, 15.5) B. (−1, 5.75) C. (1, 6.25) D. (2, 15.5)
45. Given f(x) = x² and g(x) = 8x − 15 graphed on the same set of axes, which value(s) of x will make f(x) = g(x)? A. 3, only B. 9, only C. 3 and 5 D. 9 and 25
46. Which trinomial is written in standard form and has a constant term of five? A. x⁵ − 4x² + 10 B. 2x² + 6x⁴ + 5 C. 5x⁴ − 3x² + 1 D. 4x⁵ − 8x² + 5
47. When solving x² + 6x = −8 for x, a student wrote x² + 6x + 8 = 0 as their first step. Which property justifies this step? A. associative property B. commutative property C. zero property of addition D. addition property of equality
48. The tables below show the input and output values of four different functions. f(x): (−2, 6), (−1, 1), (0, −2), (1, −3), (2, −2), (3, 1). g(x): (−4, 3), (−3, 2), (−2, 1), (−1, 0), (0, 1), (1, 2). h(x): (−2, −1), (−1, −2), (0, −4), (1, −8), (2, −16), (3, −32). j(x): (−3, −11), (−2, −7), (−1, −3), (0, 1), (1, 5), (2, 9). Which table represents a linear function? A. f(x) B. g(x) C. h(x) D. j(x)
49. What is the solution set to the equation 3x² = 24x? A. {8} B. {0, 8} C. {0, −8} D. {0, 8, −8}
50. The table below shows the radioactivity level of a substance after the given time, t, in seconds. Time (seconds): 0, 1, 2, 3, 4. Radioactivity Level: 20, 10, 5, 2.5, 1.25. What is the average rate of change in radioactivity level over the interval 1 ≤ t ≤ 3? A. 3.75 B. −3.75 C. 4.6875 D. −4.6875
51. Fred recorded the number of minutes he read each day, from Monday through Friday. His results are shown in the table. Day: 1, 2, 3, 4, 5. Number of Minutes Read: 12, 16, 19, 27, 29. What is the correlation coefficient, to the nearest thousandth, and strength of the linear model of these data? A. 0.984 and strong B. 0.968 and strong C. 0.984 and weak D. 0.968 and weak
52. Given f(x) = x², which function will shift f(x) to the left 3 units? A. g(x) = x² + 3 B. h(x) = x² − 3 C. j(x) = (x − 3)² D. k(x) = (x + 3)²
53. The range of f(x) = |x + 2| − 5 is A. y ≥ −5 B. y ≥ 2 C. x ≥ −5 D. x ≥ 2
54. Which equation is always correct? A. a³ • aˣ = a³ˣ B. (a⁴)ˣ = a⁴⁺ˣ C. (ab)ˣ = aˣbˣ D. aˣ • bʸ = abˣ⁺ʸ
55. Three functions are given below. f(x) = −|x + 2| + 7; g(x) = (x − 3)² − 4; h(x) is given by the table x: −4, −3, −2, −1, 0, 1, 2 and h(x): 5, 0, −3, −4, −3, 0, 5. Which functions have the same y-intercept? A. f(x) and g(x) B. g(x) and h(x) C. f(x) and h(x) D. The functions all have different y-intercepts.
56. The sum of (x + 7)² and (x − 3)² is A. 2x² + 58 B. 2x⁴ + 58 C. 2x² + 8x + 58 D. 2x⁴ + 8x² + 58
57. When 6x³ − 2x + 8 is subtracted from 5x³ + 3x − 4, the result is A. x³ − 5x + 12 B. x³ + x + 4 C. −x³ + 5x − 12 D. −x³ + x + 4
58. The method of substitution was used to solve the system of equations below: 4x − 7y = 7 and x − y = −1. Which equation is a correct first step when using this method? A. x = y − 1 B. y = x − 1 C. 3x − 6y = 8 D. 5x − 8y = 6
59. In 2009, Usain Bolt, a sprinter from Jamaica, set the world record in the 100-meter dash with a time of 9.58 seconds. His approximate speed, in kilometers per hour, can be found using which conversion? A. (9.58 sec / 100 m) • (1 min / 60 sec) • (1 hr / 60 min) • (1000 m / 1 km) B. (100 m / 9.58 sec) • (60 sec / 1 min) • (60 min / 1 hr) • (1000 m / 1 km) C. (100 m / 9.58 sec) • (1 min / 60 sec) • (1 hr / 60 min) • (1 km / 1000 m) D. (100 m / 9.58 sec) • (60 sec / 1 min) • (60 min / 1 hr) • (1 km / 1000 m)
60. Which scenario represents an exponential relationship? A. Kirsten’s New Year’s resolution is to lose one pound each week. B. Sarah wants to increase her grade by 5 points each quarter. C. Tommy wants to reduce his spending by $50 each month. D. Dylan hopes to grow his business by 5% each month.
61. The geometry test scores for Andrea and Joe are shown in the table below. Andrea: 82, 87, 90, 84. Joe: 91, 78, 94, 67. Which statement about their test scores is correct? A. Both the mean and standard deviation of Andrea’s test scores are higher than Joe’s. B. Both the mean and standard deviation of Joe’s test scores are higher than Andrea’s. C. The mean of Andrea’s test scores is higher than Joe’s, but Joe’s standard deviation is higher than Andrea’s. D. The mean of Joe’s test scores is higher than Andrea’s, but Andrea’s standard deviation is higher than Joe’s.
62. Which polynomial has a degree of 3 and a leading coefficient of 2? A. 2x² + 3x + 1 B. 6x³ + 3x² − 2x C. 3x² + 2x + 2 D. 2x³ + x² + 4x
63. The expression (−3x² + 9) − (7x² − 5x + 4) is equivalent to A. −10x² + 5x + 5 B. −10x² + 5x + 13 C. −10x² − 5x + 5 D. −10x² − 5x + 13
64. The function h(x) is used to calculate the average height, in inches, of a tomato plant x weeks after it is transplanted. These data are represented in the table below. x: 2, 4, 6, 9, 12, 16. h(x): 6, 12, 24, 51, 60, 64. Between weeks 4 and 12, the average rate of change, in inches per week, is A. 6 B. 8 C. 48 D. 58
65. Chloe is solving the equation x² + 5x = 3x + 3. Her first step is shown below. Given: x² + 5x = 3x + 3; Step 1: x² + 2x − 3 = 0. Which property justifies this step? A. the zero product property B. the commutative property C. the distributive property D. the subtraction property of equality
66. Which function represents the graph of w(x) = |x| shifted 2 units to the right? A. g(x) = |x + 2| B. h(x) = |x − 2| C. q(x) = |x| + 2 D. r(x) = |x| − 2
67. Given the system of equations: y + 4x = 5 and 2x − 3y = 10. A step in solving this system by using the substitution method would be A. 2(5 − 4x) + 4x = 5 B. 2(5 + 4x) + 4x = 5 C. 2x − 3(5 − 4x) = 10 D. 2x − 3(5 + 4x) = 10
68. Which equation is equivalent to x² − 6x = 27? A. (x − 3)² = 27 − 9 B. (x − 3)² = 27 + 9 C. (x − 3)² = 27 + 36 D. (x − 3)² = 27 − 36
69. Which expression is equivalent to a⁸ − b⁶? A. (a⁴ − b³)² B. (a⁶ − b⁴)² C. (a⁴)² − (b³)² D. (a⁶)² − (b⁴)²
70. The sum of Tim’s age and Jack’s age is 44. Tim’s age is 4 less than 7 times Jack’s age, x. An equation that could be used to model this scenario is A. (7x − 4) + x = 44 B. (4 − 7x) + x = 44 C. 7x − 4 = 44 D. 4 − 7x = 44

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