NBT Mathematics Proficiency 3 — Questions and Answers
Question 1: Solve the simultaneous equations: x + y = 7 and 2x - y = 5
- x = 3, y = 4
- x = 4, y = 3 (Correct answer)
- x = 5, y = 2
- x = 2, y = 5
Correct answer: x = 4, y = 3
Add the equations: 3x = 12, so x = 4. Substitute: 4 + y = 7, so y = 3.
Question 2: What is the sum of the first 10 terms of an arithmetic sequence with first term 3 and common difference 4?
- 210 (Correct answer)
- 195
- 220
- 180
Correct answer: 210
Sₙ = n/2 × [2a + (n-1)d] = 10/2 × [2(3) + 9(4)] = 5 × [6 + 36] = 5 × 42 = 210.
Question 3: Solve for x: log₂(x) = 5
- x = 10
- x = 25
- x = 32 (Correct answer)
- x = 64
Correct answer: x = 32
log₂(x) = 5 means 2⁵ = x. 2⁵ = 32.
Question 4: Find the derivative of f(x) = 3x² - 4x + 1
- f'(x) = 6x - 4 (Correct answer)
- f'(x) = 3x - 4
- f'(x) = 6x + 1
- f'(x) = 3x² - 4
Correct answer: f'(x) = 6x - 4
Using the power rule: d/dx(3x²) = 6x, d/dx(-4x) = -4, d/dx(1) = 0. f'(x) = 6x - 4.
Question 5: In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?
- 54
- 81
- 162 (Correct answer)
- 486
Correct answer: 162
Tₙ = a × rⁿ⁻¹. T₅ = 2 × 3⁴ = 2 × 81 = 162.
Question 6: Solve for x: |2x - 3| = 7
- x = 5 or x = -2 (Correct answer)
- x = 5 or x = 2
- x = -2 or x = 3
- x = 5 or x = -5
Correct answer: x = 5 or x = -2
|2x - 3| = 7 gives two cases. Case 1: 2x - 3 = 7 → x = 5. Case 2: 2x - 3 = -7 → 2x = -4 → x = -2.
NBT Mathematics Proficiency 3
Solve the simultaneous equations: x + y = 7 and 2x - y = 5