DSAT Advanced Math 2

Question 1

Which of the following is equivalent to (x² - 9) / (x - 3) for x ≠ 3?

Accepted Answer

x + 3

Answer

Factor the numerator as (x-3)(x+3), then cancel (x-3) to get x+3.

Question 2

If f(x) = 3x² - 2x + 1, what is f(-2)?

Accepted Answer

17

Answer

f(-2) = 3(4) - 2(-2) + 1 = 12 + 4 + 1 = 17.

Question 3

The function g(x) = x² - 6x + 8 has zeros at x = 2 and x = 4. What is the vertex of g(x)?

Accepted Answer

(3, -1)

Answer

The vertex x-coordinate is the midpoint of the zeros: (2+4)/2 = 3, and g(3) = 9 - 18 + 8 = -1.

Question 4

Which expression is equivalent to (2x³y²)(3xy⁴)?

Accepted Answer

6x⁴y⁶

Answer

Multiply coefficients (2×3=6) and add exponents: x^(3+1)=x⁴ and y^(2+4)=y⁶, giving 6x⁴y⁶.

Question 5

If 2^(x+1) = 32, what is the value of x?

Accepted Answer

4

Answer

32 = 2⁵, so 2^(x+1) = 2⁵ means x+1 = 5, giving x = 4.

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