NCDAP College-Level Math 5 — Questions and Answers
Question 1: If a matrix A is 3×2 and matrix B is 2×4, what are the dimensions of AB?
- 3×4 (Correct answer)
- 2×2
- 4×3
- 2×4
Correct answer: 3×4
The product of a 3×2 and a 2×4 matrix is a 3×4 matrix.
Question 2: What is the sum of the infinite geometric series 8 + 4 + 2 + 1 + …?
- 16 (Correct answer)
- 12
- 24
- 8
Correct answer: 16
S = a/(1 − r) = 8/(1 − 0.5) = 16.
Question 3: Solve the system: x + y = 6, 2x − y = 3. What is x?
- 3 (Correct answer)
- 6
- 1
- 9
Correct answer: 3
Adding the equations: 3x = 9, so x = 3.
Question 4: What is the 10th term of the arithmetic sequence 5, 8, 11, 14, …?
- 32 (Correct answer)
- 35
- 29
- 38
Correct answer: 32
aₙ = 5 + (10 − 1)·3 = 5 + 27 = 32.
Question 5: Which value of x satisfies e^(2x) = 7?
- (ln 7)/2 (Correct answer)
- ln 7
- 7/2
- 2 ln 7
Correct answer: (ln 7)/2
Take ln of both sides: 2x = ln 7, so x = (ln 7)/2.
Question 6: A function is even if f(−x) = f(x). Which function is even?
- f(x) = x⁴ − 3x² (Correct answer)
- f(x) = x³ + x
- f(x) = x² + x
- f(x) = x⁵
Correct answer: f(x) = x⁴ − 3x²
f(−x) = (−x)⁴ − 3(−x)² = x⁴ − 3x² = f(x), confirming it is even.
Question 7: Find all solutions to sin(x) = −1/2 in [0, 2π).
- 7π/6 and 11π/6 (Correct answer)
- π/6 and 5π/6
- π/3 and 2π/3
- 5π/3 only
Correct answer: 7π/6 and 11π/6
sin is −1/2 at 7π/6 (third quadrant) and 11π/6 (fourth quadrant).
NCDAP College-Level Math 5
If a matrix A is 3×2 and matrix B is 2×4, what are the dimensions of AB?