NBT Mathematics Proficiency 3 — Questions and Answers
Question 1: What is the slope of the line passing through (1, 2) and (4, 11)?
- 3 (Correct answer)
- 2
- 4
- 9
Correct answer: 3
Slope = (11 − 2) ÷ (4 − 1) = 9 ÷ 3 = 3.
Question 2: The function f(x) = x² − 4x + 4 has its vertex at:
- (2, 0) (Correct answer)
- (0, 4)
- (−2, 0)
- (4, 4)
Correct answer: (2, 0)
f(x) = (x−2)² so the vertex is at (2, 0).
Question 3: Which of the following represents an arithmetic sequence?
- 3, 7, 11, 15, … (Correct answer)
- 2, 6, 18, 54, …
- 1, 4, 9, 16, …
- 5, 10, 20, 40, …
Correct answer: 3, 7, 11, 15, …
Each term increases by a constant difference of 4, making it arithmetic.
Question 4: For which value of x is the function g(x) = 1/(x − 5) undefined?
- 5 (Correct answer)
- 0
- 1
- −5
Correct answer: 5
The function is undefined when the denominator equals zero, i.e., x − 5 = 0, so x = 5.
Question 5: If f(x) = 2x + 1, what is f(f(3))?
- 15 (Correct answer)
- 7
- 13
- 9
Correct answer: 15
f(3) = 7, then f(7) = 2(7) + 1 = 15.
Question 6: The line y = −2x + 6 has a y-intercept of:
- 6 (Correct answer)
- −2
- 3
- −6
Correct answer: 6
In the form y = mx + c, the y-intercept c = 6.
Question 7: Which graph represents a function with a negative leading coefficient and two real roots?
- A downward-opening parabola that crosses the x-axis twice (Correct answer)
- An upward-opening parabola that doesn't cross the x-axis
- A straight line with negative slope
- An upward-opening parabola that crosses the x-axis twice
Correct answer: A downward-opening parabola that crosses the x-axis twice
A negative leading coefficient means the parabola opens downward; two real roots means it crosses the x-axis twice.
NBT Mathematics Proficiency 3
What is the slope of the line passing through (1, 2) and (4, 11)?