Digital SAT Math Algebra Practice Flashcards

A system of equations is given: 2x + y = 7 and x − y = 2. What is the value of x + y?

Answer: 4

Adding both equations: 3x = 9, so x = 3. Substitute into x − y = 2: y = 1. Therefore x + y = 4.

The function g is defined by g(x) = (x + 3)² − 4. For what value of x does g(x) reach its minimum?

Answer: −3

The vertex form (x + 3)² − 4 has its minimum at x = −3 (where the squared term equals zero).

If f(x) = 3x − 2 and g(x) = x² + 1, what is f(g(2))?

Answer: 13

g(2) = 4 + 1 = 5. Then f(5) = 3(5) − 2 = 13.

The graph of y = kx + 3 passes through the point (2, 9). What is the value of k?

Answer: 3

Substitute (2, 9): 9 = 2k + 3 → 2k = 6 → k = 3.

Which of the following inequalities is equivalent to −3x + 6 ≤ 15?

Answer: x ≥ −3

Subtract 6: −3x ≤ 9. Divide by −3 (flip inequality): x ≥ −3.

If a linear function passes through (0, −4) and has slope 2, at which x-value does it cross the x-axis?

Answer: 2

Equation: y = 2x − 4. Set y = 0: 2x − 4 = 0 → x = 2.

If p and q are positive integers and 2p + 3q = 17, which of the following could be the value of p?

Answer: 7

If p = 7: 2(7) + 3q = 17 → 14 + 3q = 17 → 3q = 3 → q = 1, a positive integer.