PSAT/NMSQT Math: Heart of Algebra 2 — Questions and Answers
Question 1: If 5x - 3 = 2x + 12, what is the value of x?
- 3
- 5 (Correct answer)
- 9
- 15
Correct answer: 5
Subtract 2x and add 3: 3x = 15, so x = 5.
Question 2: A line has slope 2 and passes through (0, -4). What is its equation?
- y = 2x - 4 (Correct answer)
- y = -4x + 2
- y = 2x + 4
- y = -2x - 4
Correct answer: y = 2x - 4
With slope 2 and y-intercept -4, the line is y = 2x - 4.
Question 3: What is the solution to the system y = x + 1 and y = 3x - 5?
- (2, 3)
- (3, 4) (Correct answer)
- (-3, -2)
- (1, 2)
Correct answer: (3, 4)
Set x + 1 = 3x - 5, giving 2x = 6, x = 3, y = 4.
Question 4: If 3(x - 2) = 18, what is x?
- 6
- 8 (Correct answer)
- 4
- 12
Correct answer: 8
Divide by 3 to get x - 2 = 6, so x = 8.
Question 5: A taxi charges $3 plus $2 per mile. Which expression gives the cost for m miles?
- 2 + 3m
- 3 + 2m (Correct answer)
- 5m
- 6m
Correct answer: 3 + 2m
The flat fee is $3 plus $2 times the number of miles m.
Question 6: If 2x + 4y = 20, what is x in terms of y?
- x = 10 - 2y (Correct answer)
- x = 20 - 4y
- x = 10 + 2y
- x = 5 - y
Correct answer: x = 10 - 2y
Subtract 4y then divide by 2: x = (20 - 4y)/2 = 10 - 2y.
Question 7: What is the slope of the line through (1, 2) and (4, 11)?
- 2
- 3 (Correct answer)
- 4
- 9
Correct answer: 3
Slope = (11 - 2)/(4 - 1) = 9/3 = 3.
PSAT/NMSQT Math: Heart of Algebra 2
If 5x - 3 = 2x + 12, what is the value of x?