Algebra 1 Regents Answers
Algebra 1 Regents answers for independent study: review 70 Part I multiple-choice questions from the June 2025, August 2025, January 2026 and June 2026 Algebra I Regents exams, each answer taken from the NYSED scoring key on nysedregents.org. Questions that need a graph, plot or picture are left out.
Multiple-choice questions from Part I of the New York State Regents Examinations in Algebra I given in June 2025, August 2025, January 2026 and June 2026. Every answer is the one in the New York State Education Department scoring key for that examination.
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01What is the 20th term of the arithmetic sequence 4, 7, 10, 13, …? A. 61 B. 64 C. 79 D. 83
A. 61 (NYSED scoring key, June 2026 Regents Algebra I, question 1: choice (1))
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“What is the 20th term of the arithmetic sequence 4, 7, 10, 13, ...? (1) 61 (3) 79 (2) 64 (4) 83”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 1 (nysedregents.org); answer from the June 2026 Scoring Key ↗02What is the value of x in the equation 0.5x − 4 = 8 − x ? A. 6 B. 8 C. 18 D. 24
B. 8 (NYSED scoring key, June 2026 Regents Algebra I, question 2: choice (2))
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“What is the value of x in the equation 0.5x 2 4 5 8 2 x ? (1) 6 (3) 18 (2) 8 (4) 24”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 2 (nysedregents.org); answer from the June 2026 Scoring Key ↗03The 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)
C. (2x − 5)(2x + 5) (NYSED scoring key, June 2026 Regents Algebra I, question 3: choice (3))
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“The binomial 4x2 2 25 is equivalent to (1) 4(x 1 5)(x 2 5) (3) (2x 2 5)(2x 1 5) (2) 4(x 2 5)(x 2 5) (4) (2x 2 5)(2x 2 5)”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 3 (nysedregents.org); answer from the June 2026 Scoring Key ↗04A 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
B. 2 (NYSED scoring key, June 2026 Regents Algebra I, question 4: choice (2))
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“A function is defined by the following set of points: {(3, 24), (24, 3), (1, 1), (x, 2)} What is a possible value for x? (1) 1 (3) 3 (2) 2 (4) 24”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 4 (nysedregents.org); answer from the June 2026 Scoring Key ↗05The expression (4xy²)³ is equivalent to A. 12x³y⁶ B. 12x³y⁸ C. 64x³y⁶ D. 64x³y⁸
C. 64x³y⁶ (NYSED scoring key, June 2026 Regents Algebra I, question 5: choice (3))
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“The expression (4xy2)3 is equivalent to (1) 12x3y6 (3) 64x3y6 (2) 12x3y8 (4) 64x3y8”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 5 (nysedregents.org); answer from the June 2026 Scoring Key ↗06Allison 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
C. 4x³ + 8x² + 5 (NYSED scoring key, June 2026 Regents Algebra I, question 6: choice (3))
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“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? (1) 4x3 2 5 (3) 4x3 1 8x2 1 5 (2) 3x4 1 5 (4) 3x4 1 2x3 2 5”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 6 (nysedregents.org); answer from the June 2026 Scoring Key ↗07Given 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)
B. aₙ = 128(1/2)ⁿ⁻¹ (NYSED scoring key, June 2026 Regents Algebra I, question 7: choice (2))
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“Given the sequence 128, 64, 32, ..., which formula could be used to find the nth term of this sequence? (1) an 5 128(22)n 2 1 (3) an 5 128 2 2(n 2 1) (2) an 5 128( 1 2) n 2 1 (4) an 5 128 1 1 2(n 2 1)”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 7 (nysedregents.org); answer from the June 2026 Scoring Key ↗08When 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
A. negative correlation and causal relationship (NYSED scoring key, June 2026 Regents Algebra I, question 8: choice (1))
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“When a bicyclist increases the pressure on the brakes, the speed of the bicycle decreases. This relationship can best be described as a (1) negative correlation and causal relationship (2) negative correlation and non-causal relationship (3) positive correlation and causal relationship (4) positive correlation and non-causal relationship”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 8 (nysedregents.org); answer from the June 2026 Scoring Key ↗09A 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
B. 4d + 5(40 − d) = 170 (NYSED scoring key, June 2026 Regents Algebra I, question 9: choice (2))
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“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? (1) 4d 1 5(170 2 d) 5 40 (3) 5d 1 4(170 2 d) 5 40 (2) 4d 1 5(40 2 d) 5 170 (4) 5d 1 4(40 2 d) 5 170”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 9 (nysedregents.org); answer from the June 2026 Scoring Key ↗10A function is defined as h(x) = x² − 3x + 1. What is the value of h(−1)? A. 1 B. 2 C. 3 D. 5
D. 5 (NYSED scoring key, June 2026 Regents Algebra I, question 10: choice (4))
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“A function is defined as h(x) 5 x2 2 3x 1 1. What is the value of h(21)? (1) 1 (3) 3 (2) 2 (4) 5”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 10 (nysedregents.org); answer from the June 2026 Scoring Key ↗11The 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
C. −2/3, 0, 5 (NYSED scoring key, June 2026 Regents Algebra I, question 11: choice (3))
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“The zeros of p(x) 5 x(3x 1 2)(x 2 5) are (1) 22 3 and 5, only (3) 22 3 , 0, 5 (2) 2 3 and 25, only (4) 2 3 , 0, 25”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 11 (nysedregents.org); answer from the June 2026 Scoring Key ↗12If 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
B. 19 (NYSED scoring key, June 2026 Regents Algebra I, question 12: choice (2))
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“If f (x) 5 1.25x and g (x) 5 3x 1 10, what is the smallest positive integer of x for which f (x) . g (x)? (1) 18 (3) 67 (2) 19 (4) 69”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 12 (nysedregents.org); answer from the June 2026 Scoring Key ↗13What 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)
B. y − 5 = (3/2)(x − 2) (NYSED scoring key, June 2026 Regents Algebra I, question 13: choice (2))
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“What is an equation of the line that passes through the points (2, 5) and (22, 21)? (1) y 2 5 5 2 3(x 2 2) (3) y 2 2 5 2 3(x 2 5) (2) y 2 5 5 3 2(x 2 2) (4) y 2 2 5 3 2(x 2 5)”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 13 (nysedregents.org); answer from the June 2026 Scoring Key ↗14At 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
D. 57 (NYSED scoring key, June 2026 Regents Algebra I, question 14: choice (4))
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“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. Football Basketball Baseball Male 40 35 15 Female 20 40 10 Approximately what percentage of female high school students preferred to watch basketball? (1) 35 (3) 53 (2) 40 (4) 57”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 14 (nysedregents.org); answer from the June 2026 Scoring Key ↗15An 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
D. (x − 5)² = 49 (NYSED scoring key, June 2026 Regents Algebra I, question 15: choice (4))
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“An equation that yields the same solutions as x2 2 10x 2 24 5 0 is (1) (x 1 5)2 5 1 (3) (x 1 5)2 5 49 (2) (x 2 5)2 5 1 (4) (x 2 5)2 5 49”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 15 (nysedregents.org); answer from the June 2026 Scoring Key ↗16The 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
A. f(x − 3) + 4 (NYSED scoring key, June 2026 Regents Algebra I, question 16: choice (1))
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“The function f (x) is shifted three units right and four units up. The result of this transformation is (1) f (x 2 3) 1 4 (3) f (x 1 4) 2 3 (2) f (x 1 3) 1 4 (4) f (x 2 4) 2 3”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 16 (nysedregents.org); answer from the June 2026 Scoring Key ↗17Hana 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
D. addition property of equality (NYSED scoring key, June 2026 Regents Algebra I, question 17: choice (4))
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“Hana was asked to solve a quadratic equation. Her first step is shown below. x2 2 8x 5 3 Step 1: x2 2 8x 1 16 5 3 1 16 The property that Hana used is the (1) distributive property (3) additive inverse property (2) commutative property (4) addition property of equality”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 17 (nysedregents.org); answer from the June 2026 Scoring Key ↗18A 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
C. 34 (NYSED scoring key, June 2026 Regents Algebra I, question 18: choice (3))
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“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? (1) 28 (3) 34 (2) 32 (4) 42”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 18 (nysedregents.org); answer from the June 2026 Scoring Key ↗19When −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
B. 5x² − 10x + 11 (NYSED scoring key, June 2026 Regents Algebra I, question 19: choice (2))
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“When 23x2 1 7x 2 1 is subtracted from 2x2 2 3x 1 10, the result is (1) 5x2 1 4x 1 9 (3) 25x2 1 4x 1 9 (2) 5x2 2 10x 1 11 (4) 25x2 1 10x 2 11”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 19 (nysedregents.org); answer from the June 2026 Scoring Key ↗20The 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%
D. 4.48% (NYSED scoring key, June 2026 Regents Algebra I, question 20: choice (4))
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“The value of a home in Buffalo can be modeled by the function V(t) 5 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? (1) 1.0448% (3) 0.448% (2) 0.0448% (4) 4.48%”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 20 (nysedregents.org); answer from the June 2026 Scoring Key ↗21A 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
D. 495 (NYSED scoring key, June 2026 Regents Algebra I, question 21: choice (4))
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“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 5 3 feet] (1) 66 (3) 198 (2) 165 (4) 495”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 21 (nysedregents.org); answer from the June 2026 Scoring Key ↗22For 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
C. h(x) = x² + 8x + 3 (NYSED scoring key, June 2026 Regents Algebra I, question 23: choice (3))
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“For which function is the axis of symmetry x 5 24? (1) f (x) 5 2x2 2 4x 2 1 (3) h(x) 5 x2 1 8x 1 3 (2) g(x) 5 2x2 1 8x 1 5 (4) k(x) 5 x2 1 x 2 4”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 17, 2026, question 23 (nysedregents.org); answer from the June 2026 Scoring Key ↗23When 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
C. 3 (NYSED scoring key, January 2026 Regents Algebra I, question 3: choice (3))
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“When f(x) 5 |4x 1 2| and g(x) 5 3x 1 5 are graphed on the same set of axes, for which value of x is f(x) 5 g(x)? (1) 1 (3) 3 (2) 2 (4) 14”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 3 (nysedregents.org); answer from the January 2026 Scoring Key ↗24The 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)
A. (x + 4)(x − 30) (NYSED scoring key, January 2026 Regents Algebra I, question 4: choice (1))
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“The expression x2 2 26x 2 120 is equivalent to (1) (x 1 4)(x 2 30) (3) (x 2 20)(x 1 6) (2) (x 2 4)(x 1 30) (4) (x 1 20)(x 2 6)”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 4 (nysedregents.org); answer from the January 2026 Scoring Key ↗25Students 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
D. 4x² + 2x³ − 6 (NYSED scoring key, January 2026 Regents Algebra I, question 6: choice (4))
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“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 26 Which expression satisfies all three conditions? (1) 4x 2 6 1 3x2 (3) 4 2 6x 1 2x3 (2) 3x2 2 6x 1 4 (4) 4x2 1 2x3 2 6”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 6 (nysedregents.org); answer from the January 2026 Scoring Key ↗26The 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
C. $500 (NYSED scoring key, January 2026 Regents Algebra I, question 8: choice (3))
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“The following function models the value of a diamond ring, in dollars, t years after it is purchased: v(t) 5 500(1.08)t What was the original price of the ring, in dollars? (1) $108 (3) $500 (2) $460 (4) $540”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 8 (nysedregents.org); answer from the January 2026 Scoring Key ↗27When 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
C. 2x + 5(3x − 10) = 1 (NYSED scoring key, January 2026 Regents Algebra I, question 10: choice (3))
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“When solving the following system of equations algebraically, Mason used the substitution method. 3x 2 y 5 10 2x 1 5y 5 1 Which equation could he have used? (1) 2(3x 2 10) 1 5x 5 1 (3) 2x 1 5(3x 2 10) 5 1 (2) 2(23x 1 10) 1 5x 5 1 (4) 2x 1 5(23x 1 10) 5 1”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 10 (nysedregents.org); answer from the January 2026 Scoring Key ↗28When 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
A. addition property of equality (NYSED scoring key, January 2026 Regents Algebra I, question 12: choice (1))
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“When solving the equation 3(2x 1 5) 2 8 5 7x 1 10, the first step could be 3(2x 1 5) 5 7x 1 18. Which property justifies this step? (1) addition property of equality (2) commutative property of addition (3) multiplication property of equality (4) distributive property of multiplication over addition”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 12 (nysedregents.org); answer from the January 2026 Scoring Key ↗29If f(x) = √(x + 1) + 5, then what is the value of f(3)? A. 9 B. 7 C. 3 D. 10
B. 7 (NYSED scoring key, January 2026 Regents Algebra I, question 14: choice (2))
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“If f(x) 5 x 1 1 1 5, then what is the value of f(3)? (1) 9 (3) 3 (2) 7 (4) 10”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 14 (nysedregents.org); answer from the January 2026 Scoring Key ↗30Isabella 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
B. g(x) = (x + 8)² − 2 (NYSED scoring key, January 2026 Regents Algebra I, question 15: choice (2))
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“Isabella wants to shift the graph of the function f(x) 5 (x 1 5)2 2 2 left 3 units. Which function represents the shifted graph? (1) g(x) 5 (x 1 2)2 2 2 (3) g(x) 5 (x 1 5)2 2 5 (2) g(x) 5 (x 1 8)2 2 2 (4) g(x) 5 (x 1 5)2 1 1”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 15 (nysedregents.org); answer from the January 2026 Scoring Key ↗31What 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
D. 0, 6, and −6 (NYSED scoring key, January 2026 Regents Algebra I, question 16: choice (4))
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“What are the zeros of f(x) 5 x(x2 2 36)? (1) 0, only (3) 6 and 26, only (2) 6, only (4) 0, 6, and 26”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 16 (nysedregents.org); answer from the January 2026 Scoring Key ↗32The 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
B. −4 or 3 (NYSED scoring key, January 2026 Regents Algebra I, question 17: choice (2))
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“The point (x, 26) lies on the graph of a parabola whose equation is y 5 2x2 2 x 1 6. The value of x can be (1) 23 or 2 (3) 3, only (2) 24 or 3 (4) 24, only”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 17 (nysedregents.org); answer from the January 2026 Scoring Key ↗33The 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
D. 0.145 (NYSED scoring key, January 2026 Regents Algebra I, question 18: choice (4))
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“The two-way frequency table below is a summary of concession stand sales for a football game. Concession Stand Sales 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? (1) 0.58 (3) 0.455 (2) 0.35 (4) 0.145”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 18 (nysedregents.org); answer from the January 2026 Scoring Key ↗34When 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
A. feet per second (NYSED scoring key, January 2026 Regents Algebra I, question 19: choice (1))
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“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: 1 min 0.6214 mi 5280 ft 1 hr 104 km 60 sec 1 km 1 mi 60 min 1 hr • • • • Assuming he did all the work correctly, what would the units be for Theodore’s rate? (1) feet per second (3) seconds per foot (2) feet per minute (4) minutes per foot”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 19 (nysedregents.org); answer from the January 2026 Scoring Key ↗35Which expression is equivalent to (−2x²)³? A. −2x⁵ B. −2x⁶ C. −8x⁵ D. −8x⁶
D. −8x⁶ (NYSED scoring key, January 2026 Regents Algebra I, question 20: choice (4))
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“Which expression is equivalent to (22x2)3? (1) 22x5 (3) 28x5 (2) 22x6 (4) 28x6”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 20 (nysedregents.org); answer from the January 2026 Scoring Key ↗36The 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
D. −51.8 (NYSED scoring key, January 2026 Regents Algebra I, question 21: choice (4))
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“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 (1) 39.1 (3) 239.1 (2) 51.8 (4) 251.8”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 21 (nysedregents.org); answer from the January 2026 Scoring Key ↗37When 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
C. −x² + 5x − 9 (NYSED scoring key, January 2026 Regents Algebra I, question 22: choice (3))
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“When 2x2 2 3x 1 4 is subtracted from x2 1 2x 2 5, the result is (1) x2 2 5x 1 9 (3) 2x2 1 5x 2 9 (2) x2 2 x 1 1 (4) 2x2 2 x 2 1”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 22 (nysedregents.org); answer from the January 2026 Scoring Key ↗38Which 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
C. (x − 3)² = 33 (NYSED scoring key, January 2026 Regents Algebra I, question 23: choice (3))
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“Which equation has the same solution as x2 2 6x 5 24? (1) (x 2 3)2 5 24 (3) (x 2 3)2 5 33 (2) (x 2 6)2 5 24 (4) (x 2 6)2 5 60”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 23 (nysedregents.org); answer from the January 2026 Scoring Key ↗39In 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
D. 54 (NYSED scoring key, January 2026 Regents Algebra I, question 24: choice (4))
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“In a sequence, the first term is 22 and the common ratio is 23. The fourth term in this sequence is (1) 2162 (3) 24 (2) 211 (4) 54”
— NYSED Regents High School Examination in Algebra I, Wednesday, January 21, 2026, question 24 (nysedregents.org); answer from the January 2026 Scoring Key ↗40Which 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)
C. (10x − 4)(10x + 4) (NYSED scoring key, August 2025 Regents Algebra I, question 1: choice (3))
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“Which expression is equivalent to 100x2 2 16? (1) (50x 2 8)(50x 1 8) (3) (10x 2 4)(10x 1 4) (2) (50x 2 8)(50x 2 8) (4) (10x 2 4)(10x 2 4)”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 1 (nysedregents.org); answer from the August 2025 Scoring Key ↗41Josie 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
C. 0.25x + 0.10(x + 2) = 2.30 (NYSED scoring key, August 2025 Regents Algebra I, question 2: choice (3))
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“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? (1) 0.35(2x 1 2) 5 2.30 (2) 0.25(x 1 2) 1 0.10x 5 2.30 (3) 0.25x 1 0.10(x 1 2) 5 2.30 (4) 0.25x 1 0.10(x 2 2) 5 2.30”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 2 (nysedregents.org); answer from the August 2025 Scoring Key ↗42If g(x) = −2x² + 16, then g(−3) equals A. −20 B. −2 C. 34 D. 52
B. −2 (NYSED scoring key, August 2025 Regents Algebra I, question 3: choice (2))
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“If g(x) 5 22x2 1 16, then g(23) equals (1) 220 (3) 34 (2) 22 (4) 52”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 3 (nysedregents.org); answer from the August 2025 Scoring Key ↗43What 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
B. 10 and −2 (NYSED scoring key, August 2025 Regents Algebra I, question 4: choice (2))
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“What are the zeros of f (x) 5 x2 2 8x 2 20? (1) 10 and 2 (3) 210 and 2 (2) 10 and 22 (4) 210 and 22”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 4 (nysedregents.org); answer from the August 2025 Scoring Key ↗44Which 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)
A. (−2, 15.5) (NYSED scoring key, August 2025 Regents Algebra I, question 5: choice (1))
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“Which point lies on the graph of y 5 3x2 2 1 4 x 1 3? (1) (22, 15.5) (3) (1, 6.25) (2) (21, 5.75) (4) (2, 15.5)”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 5 (nysedregents.org); answer from the August 2025 Scoring Key ↗45Given 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
C. 3 and 5 (NYSED scoring key, August 2025 Regents Algebra I, question 6: choice (3))
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“Given f (x) 5 x2 and g(x) 5 8x 2 15 graphed on the same set of axes, which value(s) of x will make f (x) 5 g(x)? (1) 3, only (3) 3 and 5 (2) 9, only (4) 9 and 25”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 6 (nysedregents.org); answer from the August 2025 Scoring Key ↗46Which 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
D. 4x⁵ − 8x² + 5 (NYSED scoring key, August 2025 Regents Algebra I, question 7: choice (4))
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“Which trinomial is written in standard form and has a constant term of five? (1) x5 2 4x2 1 10 (3) 5x4 2 3x2 1 1 (2) 2x2 1 6x4 1 5 (4) 4x5 2 8x2 1 5”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 7 (nysedregents.org); answer from the August 2025 Scoring Key ↗47When 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
D. addition property of equality (NYSED scoring key, August 2025 Regents Algebra I, question 8: choice (4))
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“When solving x2 1 6x 5 28 for x, a student wrote x2 1 6x 1 8 5 0 as their first step. Which property justifies this step? (1) associative property (2) commutative property (3) zero property of addition (4) addition property of equality”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 8 (nysedregents.org); answer from the August 2025 Scoring Key ↗48The 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)
D. j(x) (NYSED scoring key, August 2025 Regents Algebra I, question 9: choice (4))
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“The tables below show the input and output values of four different functions. x f(x) 22 6 21 1 0 22 1 23 2 22 3 1 x g(x) 24 3 23 2 22 1 21 0 0 1 1 2 x h(x) 22 21 21 22 0 24 1 28 2 216 3 232 x j(x) 23 211 22 27 21 23 0 1 1 5 2 9 Which table represents a linear function? (1) f (x) (3) h(x) (2) g(x) (4) j(x)”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 9 (nysedregents.org); answer from the August 2025 Scoring Key ↗49What is the solution set to the equation 3x² = 24x? A. {8} B. {0, 8} C. {0, −8} D. {0, 8, −8}
B. {0, 8} (NYSED scoring key, August 2025 Regents Algebra I, question 10: choice (2))
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“What is the solution set to the equation 3x2 5 24x? (1) {8} (3) {0, 28} (2) {0, 8} (4) {0, 8, 28}”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 10 (nysedregents.org); answer from the August 2025 Scoring Key ↗50The 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
B. −3.75 (NYSED scoring key, August 2025 Regents Algebra I, question 11: choice (2))
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“The table below shows the radioactivity level of a substance after the given time, t, in seconds. Time (seconds) Radioactivity Level 0 20 1 10 2 5 3 2.5 4 1.25 What is the average rate of change in radioactivity level over the interval 1 # t # 3? (1) 3.75 (3) 4.6875 (2) 23.75 (4) 24.6875”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 11 (nysedregents.org); answer from the August 2025 Scoring Key ↗51Fred 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
A. 0.984 and strong (NYSED scoring key, August 2025 Regents Algebra I, question 12: choice (1))
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“Fred recorded the number of minutes he read each day, from Monday through Friday. His results are shown in the table. Day Number of Minutes Read 1 12 2 16 3 19 4 27 5 29 What is the correlation coefficient, to the nearest thousandth, and strength of the linear model of these data? (1) 0.984 and strong (3) 0.984 and weak (2) 0.968 and strong (4) 0.968 and weak”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 12 (nysedregents.org); answer from the August 2025 Scoring Key ↗52Given 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
D. k(x) = (x + 3)² (NYSED scoring key, August 2025 Regents Algebra I, question 13: choice (4))
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“Given f (x) 5 x2, which function will shift f (x) to the left 3 units? (1) g(x) 5 x2 1 3 (3) j(x) 5 (x 2 3)2 (2) h(x) 5 x2 2 3 (4) k(x) 5 (x 1 3)2”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 13 (nysedregents.org); answer from the August 2025 Scoring Key ↗53The range of f(x) = |x + 2| − 5 is A. y ≥ −5 B. y ≥ 2 C. x ≥ −5 D. x ≥ 2
A. y ≥ −5 (NYSED scoring key, August 2025 Regents Algebra I, question 15: choice (1))
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“The range of f (x) 5 |x 1 2| 2 5 is (1) y $ 25 (3) x $ 25 (2) y $ 2 (4) x $ 2”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 15 (nysedregents.org); answer from the August 2025 Scoring Key ↗54Which equation is always correct? A. a³ • aˣ = a³ˣ B. (a⁴)ˣ = a⁴⁺ˣ C. (ab)ˣ = aˣbˣ D. aˣ • bʸ = abˣ⁺ʸ
C. (ab)ˣ = aˣbˣ (NYSED scoring key, August 2025 Regents Algebra I, question 16: choice (3))
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“Which equation is always correct? (1) a3 • ax 5 a3x (3) (ab)x 5 axbx (2) (a4)x 5 a4 1 x (4) ax • by 5 abx 1 y”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 16 (nysedregents.org); answer from the August 2025 Scoring Key ↗55Three 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.
A. f(x) and g(x) (NYSED scoring key, August 2025 Regents Algebra I, question 18: choice (1))
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“Three functions are given below. f (x) 5 2|x 1 2| 1 7 g (x) 5 (x 2 3)2 2 4 x h(x) 24 5 23 0 22 23 21 24 0 23 1 0 2 5 Which functions have the same y-intercept? (1) f (x) and g(x) (2) g (x) and h(x) (3) f (x) and h(x) (4) The functions all have different y-intercepts.”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 18 (nysedregents.org); answer from the August 2025 Scoring Key ↗56The sum of (x + 7)² and (x − 3)² is A. 2x² + 58 B. 2x⁴ + 58 C. 2x² + 8x + 58 D. 2x⁴ + 8x² + 58
C. 2x² + 8x + 58 (NYSED scoring key, August 2025 Regents Algebra I, question 19: choice (3))
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“The sum of (x 1 7)2 and (x 2 3)2 is (1) 2x2 1 58 (3) 2x2 1 8x 1 58 (2) 2x4 1 58 (4) 2x4 1 8x2 1 58”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 19 (nysedregents.org); answer from the August 2025 Scoring Key ↗57When 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
C. −x³ + 5x − 12 (NYSED scoring key, August 2025 Regents Algebra I, question 21: choice (3))
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“When 6x3 2 2x 1 8 is subtracted from 5x3 1 3x 2 4, the result is (1) x3 2 5x 1 12 (3) 2x3 1 5x 2 12 (2) x3 1 x 1 4 (4) 2x3 1 x 1 4”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 21 (nysedregents.org); answer from the August 2025 Scoring Key ↗58The 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
A. x = y − 1 (NYSED scoring key, August 2025 Regents Algebra I, question 23: choice (1))
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“The method of substitution was used to solve the system of equations below: 4x 2 7y 5 7 x 2 y 5 21 Which equation is a correct first step when using this method? (1) x 5 y 2 1 (3) 3x 2 6y 5 8 (2) y 5 x 2 1 (4) 5x 2 8y 5 6”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 23 (nysedregents.org); answer from the August 2025 Scoring Key ↗59In 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)
D. (100 m / 9.58 sec) • (60 sec / 1 min) • (60 min / 1 hr) • (1 km / 1000 m) (NYSED scoring key, August 2025 Regents Algebra I, question 24: choice (4))
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“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? (1) 9.58 sec 1 min 1 hr 1000 m 100 m 60 sec 60 min 1 km • • • (2) 100 m 60 sec 60 min 1000 m 9.58 sec 1 min 1 hr 1 km • • • (3) 100 m 1 min 1 hr 1 km 9.58 sec 60 sec 60 min 1000 m • • • (4) 100 m 60 sec 60 min 1 km”
— NYSED Regents High School Examination in Algebra I, Tuesday, August 19, 2025, question 24 (nysedregents.org); answer from the August 2025 Scoring Key ↗60Which 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.
D. Dylan hopes to grow his business by 5% each month. (NYSED scoring key, June 2025 Regents Algebra I, question 3: choice (4))
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“Which scenario represents an exponential relationship? (1) Kirsten’s New Year’s resolution is to lose one pound each week. (2) Sarah wants to increase her grade by 5 points each quarter. (3) Tommy wants to reduce his spending by $50 each month. (4) Dylan hopes to grow his business by 5% each month.”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 3 (nysedregents.org); answer from the June 2025 Scoring Key ↗61The 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.
C. The mean of Andrea’s test scores is higher than Joe’s, but Joe’s standard deviation is higher than Andrea’s. (NYSED scoring key, June 2025 Regents Algebra I, question 4: choice (3))
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“The geometry test scores for Andrea and Joe are shown in the table below. Andrea Joe 82 91 87 78 90 94 84 67 Which statement about their test scores is correct? (1) Both the mean and standard deviation of Andrea’s test scores are higher than Joe’s. (2) Both the mean and standard deviation of Joe’s test scores are higher than Andrea’s. (3) The mean of Andrea’s test scores is higher than Joe’s, but Joe’s standard”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 4 (nysedregents.org); answer from the June 2025 Scoring Key ↗62Which 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
D. 2x³ + x² + 4x (NYSED scoring key, June 2025 Regents Algebra I, question 5: choice (4))
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“Which polynomial has a degree of 3 and a leading coefficient of 2? (1) 2x2 1 3x 1 1 (3) 3x2 1 2x 1 2 (2) 6x3 1 3x2 2 2x (4) 2x3 1 x2 1 4x”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 5 (nysedregents.org); answer from the June 2025 Scoring Key ↗63The 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
A. −10x² + 5x + 5 (NYSED scoring key, June 2025 Regents Algebra I, question 6: choice (1))
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“The expression (23x2 1 9) 2 (7x2 2 5x 1 4) is equivalent to (1) 210x2 1 5x 1 5 (3) 210x2 2 5x 1 5 (2) 210x2 1 5x 1 13 (4) 210x2 2 5x 1 13”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 6 (nysedregents.org); answer from the June 2025 Scoring Key ↗64The 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
A. 6 (NYSED scoring key, June 2025 Regents Algebra I, question 7: choice (1))
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“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 h(x) 2 6 4 12 6 24 9 51 12 60 16 64 Between weeks 4 and 12, the average rate of change, in inches per week, is (1) 6 (3) 48 (2) 8 (4) 58”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 7 (nysedregents.org); answer from the June 2025 Scoring Key ↗65Chloe 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
D. the subtraction property of equality (NYSED scoring key, June 2025 Regents Algebra I, question 8: choice (4))
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“Chloe is solving the equation x2 1 5x 5 3x 1 3. Her first step is shown below. Given: x2 1 5x 5 3x 1 3 Step 1: x2 1 2x 2 3 5 0 Which property justifies this step? (1) the zero product property (2) the commutative property (3) the distributive property (4) the subtraction property of equality”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 8 (nysedregents.org); answer from the June 2025 Scoring Key ↗66Which 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
B. h(x) = |x − 2| (NYSED scoring key, June 2025 Regents Algebra I, question 9: choice (2))
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“Which function represents the graph of w(x) 5 |x| shifted 2 units to the right? (1) g(x) 5 |x 1 2| (3) q(x) 5 |x| 1 2 (2) h(x) 5 |x 2 2| (4) r(x) 5 |x| 2 2”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 9 (nysedregents.org); answer from the June 2025 Scoring Key ↗67Given 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
C. 2x − 3(5 − 4x) = 10 (NYSED scoring key, June 2025 Regents Algebra I, question 10: choice (3))
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“Given the system of equations: y 1 4x 5 5 2x 2 3y 5 10 A step in solving this system by using the substitution method would be (1) 2(5 2 4x) 1 4x 5 5 (3) 2x 2 3(5 2 4x) 5 10 (2) 2(5 1 4x) 1 4x 5 5 (4) 2x 2 3(5 1 4x) 5 10”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 10 (nysedregents.org); answer from the June 2025 Scoring Key ↗68Which 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
B. (x − 3)² = 27 + 9 (NYSED scoring key, June 2025 Regents Algebra I, question 11: choice (2))
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“Which equation is equivalent to x2 2 6x 5 27? (1) (x 2 3)2 5 27 2 9 (3) (x 2 3)2 5 27 1 36 (2) (x 2 3)2 5 27 1 9 (4) (x 2 3)2 5 27 2 36”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 11 (nysedregents.org); answer from the June 2025 Scoring Key ↗69Which expression is equivalent to a⁸ − b⁶? A. (a⁴ − b³)² B. (a⁶ − b⁴)² C. (a⁴)² − (b³)² D. (a⁶)² − (b⁴)²
C. (a⁴)² − (b³)² (NYSED scoring key, June 2025 Regents Algebra I, question 15: choice (3))
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“Which expression is equivalent to a8 2 b6? (1) (a4 2 b3)2 (3) (a4)2 2 (b3)2 (2) (a6 2 b4)2 (4) (a6)2 2 (b4)2”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 15 (nysedregents.org); answer from the June 2025 Scoring Key ↗70The 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
A. (7x − 4) + x = 44 (NYSED scoring key, June 2025 Regents Algebra I, question 17: choice (1))
VERIFIED AGAINST THE SOURCE
“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 (1) (7x 2 4) 1 x 5 44 (3) 7x 2 4 5 44 (2) (4 2 7x) 1 x 5 44 (4) 4 2 7x 5 44”
— NYSED Regents High School Examination in Algebra I, Wednesday, June 18, 2025, question 17 (nysedregents.org); answer from the June 2025 Scoring Key ↗Know questions we're missing?
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