PARCC - Partnership for Assessment of Readiness for College and Careers Advanced Mathematics Practice Questions 1 — Questions and Answers
Question 1: Factor completely: 6x² + 7x − 5
- (2x − 1)(3x + 5) (Correct answer)
- (2x + 1)(3x − 5)
- (3x − 1)(2x + 5)
- (6x − 1)(x + 5)
Correct answer: (2x − 1)(3x + 5)
Multiply 6 × (−5) = −30 and find two numbers that multiply to −30 and add to 7: those are 10 and −3. Rewrite as 6x² + 10x − 3x − 5, then factor by grouping: 2x(3x + 5) − 1(3x + 5) = (2x − 1)(3x + 5).
Question 2: If f(x) = 2x + 3 and g(x) = x² − 1, what is f(g(2))?
- 9 (Correct answer)
- 7
- 11
- 5
Correct answer: 9
First evaluate the inner function: g(2) = 2² − 1 = 3. Then apply f to that result: f(3) = 2(3) + 3 = 9. Composition is always evaluated inside-out.
Question 3: Solve for x: log₂(x + 3) = 4
- x = 11
- x = 13 (Correct answer)
- x = 7
- x = 19
Correct answer: x = 13
Convert the logarithmic equation to exponential form: 2⁴ = x + 3, which gives 16 = x + 3, so x = 13. Always check: log₂(13 + 3) = log₂(16) = 4 ✓
Question 4: What is the vertex of the parabola y = 2x² − 8x + 5?
- (2, −3) (Correct answer)
- (−2, 3)
- (2, 3)
- (4, −3)
Correct answer: (2, −3)
The x-coordinate of the vertex is x = −b/(2a) = −(−8)/(2·2) = 2. Substitute back: y = 2(4) − 8(2) + 5 = 8 − 16 + 5 = −3. Vertex is (2, −3).
Question 5: A geometric sequence has a first term of 3 and a common ratio of 2. What is the sum of the first 5 terms?
- 93 (Correct answer)
- 63
- 96
- 48
Correct answer: 93
The terms are 3, 6, 12, 24, 48. Using the formula Sₙ = a(rⁿ − 1)/(r − 1): S₅ = 3(2⁵ − 1)/(2 − 1) = 3(32 − 1)/1 = 3 × 31 = 93.
Question 6: When p(x) = x³ − 2x² + 3x − 4 is divided by (x − 2), what is the remainder?
- 2 (Correct answer)
- 0
- −2
- 4
Correct answer: 2
By the Remainder Theorem, the remainder when dividing by (x − 2) equals p(2). Evaluate: p(2) = 8 − 8 + 6 − 4 = 2. No long division needed.
PARCC - Partnership for Assessment of Readiness for College and Careers Advanced Mathematics Practice Questions 1
Factor completely: 6x² + 7x − 5