DSAT Advanced Math 5

Question 1

Which of the following is equivalent to x^(3/2)?

Accepted Answer

Both A and C

Answer

x^(3/2) = x^1 · x^(1/2) = x√x, and also x^(3/2) = (x³)^(1/2) = √(x³); both A and C are correct.

Question 2

The graph of f(x) = x² is shifted 3 units left and 2 units up. What is the new equation?

Accepted Answer

y = (x+3)² + 2

Answer

Shifting left 3 replaces x with (x+3) and shifting up 2 adds 2: y = (x+3)² + 2.

Question 3

If p(x) = x³ - 2x² - x + 2, which of the following is a factor?

Accepted Answer

x - 2

Answer

p(2) = 8 - 8 - 2 + 2 = 0, so (x-2) is a factor by the Factor Theorem.

Question 4

What is the product of the complex numbers (3 + 2i) and (1 - i)?

Accepted Answer

5 - i

Answer

(3+2i)(1-i) = 3 - 3i + 2i - 2i² = 3 - i + 2 = 5 - i (since i² = -1).

Question 5

The equation y = 2x² - 8x + 6 can be rewritten in vertex form as:

Accepted Answer

y = 2(x-2)² - 2

Answer

Complete the square: y = 2(x²-4x) + 6 = 2(x-2)² - 8 + 6 = 2(x-2)² - 2.

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