Core Academic Skills Assessment Mathematics: Algebra and Functions 3 — Questions and Answers
Question 1: A line has equation 4x − 2y = 8. What is its slope and y-intercept?
- slope = 2, y-intercept = −4 (Correct answer)
- slope = −2, y-intercept = 4
- slope = 4, y-intercept = −8
- slope = 2, y-intercept = 4
Correct answer: slope = 2, y-intercept = −4
Rewrite as y = 2x − 4; slope is 2 and y-intercept is −4.
Question 2: Which of the following is a factor of x² − x − 12?
- (x − 4) (Correct answer)
- (x + 3) only
- (x − 3)
- (x + 12)
Correct answer: (x − 4)
x² − x − 12 = (x − 4)(x + 3), so (x − 4) is a factor.
Question 3: If h(x) = 2x + 1 and k(x) = x², what is k(h(3))?
- 49 (Correct answer)
- 19
- 37
- 7
Correct answer: 49
h(3) = 7, then k(7) = 7² = 49.
Question 4: Solve the inequality: −3x + 6 > 12.
- x < −2 (Correct answer)
- x > −2
- x < 2
- x > 6
Correct answer: x < −2
−3x > 6 → x < −2 (inequality flips when dividing by a negative).
Question 5: Which equation represents a line parallel to y = (2/3)x − 5?
- y = (2/3)x + 7 (Correct answer)
- y = (3/2)x − 5
- y = −(2/3)x + 1
- y = (2/3)x − 5
Correct answer: y = (2/3)x + 7
Parallel lines have the same slope (2/3) but different y-intercepts.
Question 6: What is the solution set of x² = 25?
- x = 5 or x = −5 (Correct answer)
- x = 5 only
- x = −5 only
- x = ±√5
Correct answer: x = 5 or x = −5
Taking the square root of both sides gives x = ±5.
Question 7: A car rental company charges $30 per day plus $0.15 per mile. Which function gives the total cost C for d days and m miles?
- C = 30d + 0.15m (Correct answer)
- C = 30m + 0.15d
- C = 30 + 0.15(d + m)
- C = 0.15d + 30m
Correct answer: C = 30d + 0.15m
The daily rate multiplies by days and the mileage rate multiplies by miles: C = 30d + 0.15m.
Core Academic Skills Assessment Mathematics: Algebra and Functions 3
A line has equation 4x − 2y = 8.
What is its slope and y-intercept?