Core Academic Skills Assessment Mathematics: Algebra and Functions 2 â Questions and Answers
Question 1: If f(x) = 3x² â 2x + 1, what is f(â2)?
- 17 (Correct answer)
- 9
- â7
- 13
Correct answer: 17
f(â2) = 3(4) â 2(â2) + 1 = 12 + 4 + 1 = 17.
Question 2: Which value of x satisfies |2x â 5| = 9?
- x = 7 or x = â2 (Correct answer)
- x = 7 only
- x = â2 only
- x = 2 or x = â7
Correct answer: x = 7 or x = â2
2x â 5 = 9 gives x = 7; 2x â 5 = â9 gives x = â2.
Question 3: A function is defined as g(x) = (x + 3)/(x â 2). For which value of x is g(x) undefined?
- x = 2 (Correct answer)
- x = â3
- x = 0
- x = 3
Correct answer: x = 2
The function is undefined when the denominator equals zero: x â 2 = 0, so x = 2.
Question 4: What is the slope of the line passing through (â1, 4) and (3, â4)?
- â2 (Correct answer)
- 2
- â1/2
- 1/2
Correct answer: â2
Slope = (â4 â 4)/(3 â (â1)) = â8/4 = â2.
Question 5: If 5(x â 3) = 2x + 6, what is x?
- 7 (Correct answer)
- 3
- â1
- 9
Correct answer: 7
5x â 15 = 2x + 6 â 3x = 21 â x = 7.
Question 6: Which expression is equivalent to (2xÂły²)(3xyâ´)?
- 6xâ´yâś (Correct answer)
- 5xâ´yâś
- 6xÂłyâś
- 6xâ´yâ¸
Correct answer: 6xâ´yâś
Multiply coefficients (2¡3 = 6) and add exponents: x^(3+1) = xâ´, y^(2+4) = yâś.
Question 7: The graph of y = âx² + 4 opens in which direction and has what y-intercept?
- Opens downward; y-intercept 4 (Correct answer)
- Opens upward; y-intercept 4
- Opens downward; y-intercept â4
- Opens upward; y-intercept â4
Correct answer: Opens downward; y-intercept 4
The negative leading coefficient means the parabola opens downward, and setting x = 0 gives y = 4.
Core Academic Skills Assessment Mathematics: Algebra and Functions 2
If f(x) = 3x² â 2x + 1, what is f(â2)?