PSAT/NMSQT Algebra & Functions 3 — Questions and Answers
Question 1: If 2(x - 4) = 3x + 1, what is the value of x?
- -9 (Correct answer)
- 9
- -7
- 7
Correct answer: -9
Expanding gives 2x - 8 = 3x + 1, so -9 = x.
Question 2: What is the value of the expression (x^3 · x^4) when written as a single power of x?
- x^7 (Correct answer)
- x^12
- x^1
- x^34
Correct answer: x^7
When multiplying powers with the same base, add the exponents: 3 + 4 = 7.
Question 3: If g(x) = 5 - x and g(a) = 2, what is the value of a?
- 3 (Correct answer)
- -3
- 7
- -7
Correct answer: 3
Set 5 - a = 2, so a = 3.
Question 4: Which of the following is a factor of x^2 - 9?
- x - 3 (Correct answer)
- x - 9
- x + 9
- x^2
Correct answer: x - 3
x^2 - 9 is a difference of squares factoring to (x - 3)(x + 3).
Question 5: The cost C of renting a bike is C = 5 + 2h, where h is hours. What does the 2 represent?
- Cost per hour (Correct answer)
- Flat starting fee
- Total cost
- Number of bikes
Correct answer: Cost per hour
The coefficient 2 multiplies hours, so it is the cost added per hour.
Question 6: If 4x + 3 < 19, which value of x makes the inequality true?
- 3 (Correct answer)
- 5
- 4
- 6
Correct answer: 3
Solving gives x < 4, so only x = 3 satisfies the inequality.
Question 7: What is the vertex of the parabola y = (x - 2)^2 + 5?
- (2, 5) (Correct answer)
- (-2, 5)
- (2, -5)
- (5, 2)
Correct answer: (2, 5)
In vertex form y = (x - h)^2 + k, the vertex is (h, k) = (2, 5).
PSAT/NMSQT Algebra & Functions 3
If 2(x - 4) = 3x + 1, what is the value of x?