Core Academic Skills Assessment Mathematics: Algebra and Functions 5 — Questions and Answers
Question 1: Which expression is equivalent to 3(x − 2)² − 5?
- 3x² − 12x + 7 (Correct answer)
- 3x² − 12x − 5
- 3x² − 6x + 7
- 3x² + 12x + 7
Correct answer: 3x² − 12x + 7
Expand: 3(x² − 4x + 4) − 5 = 3x² − 12x + 12 − 5 = 3x² − 12x + 7.
Question 2: If f(x) = 5x − 3, what is f⁻¹(x)?
- (x + 3)/5 (Correct answer)
- (x − 3)/5
- 5x + 3
- 1/(5x − 3)
Correct answer: (x + 3)/5
To find the inverse, swap x and y then solve: x = 5y − 3 → y = (x + 3)/5.
Question 3: A sequence is defined by aₙ = 3n − 2. What is the 10th term?
- 28 (Correct answer)
- 30
- 25
- 32
Correct answer: 28
a₁₀ = 3(10) − 2 = 30 − 2 = 28.
Question 4: Which inequality is represented by the graph of a dashed line y = x + 2 with shading below it?
- y < x + 2 (Correct answer)
- y > x + 2
- y ≤ x + 2
- y ≥ x + 2
Correct answer: y < x + 2
A dashed boundary means strict inequality, and shading below means y is less than the line.
Question 5: What are the x-intercepts of y = x² − 4x − 5?
- x = 5 and x = −1 (Correct answer)
- x = −5 and x = 1
- x = 5 and x = 1
- x = −5 and x = −1
Correct answer: x = 5 and x = −1
Factor: (x − 5)(x + 1) = 0, giving x = 5 and x = −1.
Question 6: If three times a number decreased by 7 equals twice the number increased by 4, what is the number?
- 11 (Correct answer)
- 3
- −11
- 7
Correct answer: 11
3n − 7 = 2n + 4 → n = 11.
Question 7: Which of the following best describes the transformation from f(x) = x² to g(x) = (x + 4)²?
- Shift left 4 units (Correct answer)
- Shift right 4 units
- Shift up 4 units
- Shift down 4 units
Correct answer: Shift left 4 units
Replacing x with (x + 4) shifts the graph horizontally to the left by 4 units.
Core Academic Skills Assessment Mathematics: Algebra and Functions 5
Which expression is equivalent to 3(x − 2)² − 5?