SAT Math Practice (Medium–Hard): Quadratics & Exponents (With Solutions)

These questions target common SAT Math score-boosters: quadratics and exponent rules. Work timed, then review the solutions.

Question 1

What are the solutions to x^2 − 5x + 6 = 0?

• A. x = 2 and x = 3

• B. x = −2 and x = −3

• C. x = 1 and x = 6

• D. x = −1 and x = −6

Step-by-step solution

Factor the quadratic: x^2 − 5x + 6 = (x − 2)(x − 3).

Set each factor equal to 0: x − 2 = 0 or x − 3 = 0.

Solve: x = 2 or x = 3.

Final answer: x = 2 and x = 3

Question 2

If 2^(x+1) = 16, what is the value of x?

• A. 2

• B. 3

• C. 4

• D. 5

Step-by-step solution

Rewrite 16 as a power of 2: 16 = 2^4.

So 2^(x+1) = 2^4.

Equate exponents: x + 1 = 4.

Subtract 1: x = 3.

Final answer: 3

Question 3

For the quadratic y = x^2 − 8x + 12, what is the x-coordinate of the vertex?

• A. 2

• B. 4

• C. 6

• D. 8

Step-by-step solution

For y = ax^2 + bx + c, the vertex x-coordinate is −b/(2a).

Here a = 1 and b = −8.

Compute: −(−8)/(2·1) = 8/2 = 4.

Final answer: 4

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