DSAT Math Algebra 2 — Questions and Answers
Question 1: If 3x - 7 = 2x + 5, what is the value of x?
- 6
- 12 (Correct answer)
- 2
- -2
Correct answer: 12
Subtracting 2x from both sides gives x - 7 = 5, so x = 12.
Question 2: Which value of x satisfies |2x - 4| = 10?
- x = 7 only
- x = -3 only
- x = 7 or x = -3 (Correct answer)
- x = 3 or x = -7
Correct answer: x = 7 or x = -3
Setting 2x - 4 = 10 gives x = 7, and setting 2x - 4 = -10 gives x = -3.
Question 3: A line passes through (0, -3) and (4, 5). What is its equation?
- y = 2x - 3 (Correct answer)
- y = 2x + 3
- y = -2x - 3
- y = 0.5x - 3
Correct answer: y = 2x - 3
The slope is (5 - (-3))/(4 - 0) = 2 and the y-intercept is -3, giving y = 2x - 3.
Question 4: If f(x) = 4x² - 9, which expression equals f(x) in factored form?
- (2x - 3)(2x + 3) (Correct answer)
- (4x - 3)(x + 3)
- (2x - 9)(2x + 1)
- (x - 3)(4x + 3)
Correct answer: (2x - 3)(2x + 3)
4x² - 9 is a difference of squares: (2x)² - 3² = (2x - 3)(2x + 3).
Question 5: What is the solution set of 5 - 2x ≥ 11?
- x ≥ -3
- x ≤ -3 (Correct answer)
- x ≥ 3
- x ≤ 3
Correct answer: x ≤ -3
Subtracting 5 gives -2x ≥ 6, then dividing by -2 (flip inequality) gives x ≤ -3.
Question 6: If (x + 3)(x - 5) = 0, what are the solutions for x?
- x = 3 and x = -5
- x = -3 and x = 5 (Correct answer)
- x = 3 and x = 5
- x = -3 and x = -5
Correct answer: x = -3 and x = 5
Setting each factor equal to zero: x + 3 = 0 → x = -3 and x - 5 = 0 → x = 5.
Question 7: For what value(s) of x is the expression (x² - 16)/(x - 4) undefined?
- x = 4 only (Correct answer)
- x = -4 only
- x = 4 or x = -4
- x = 0
Correct answer: x = 4 only
The expression is undefined when the denominator equals zero: x - 4 = 0, so x = 4.
DSAT Math Algebra 2
If 3x - 7 = 2x + 5, what is the value of x?