Bluebook SAT Test Digital SAT Math Algebra Practice 2 — Questions and Answers
Question 1: A system of equations is given: 2x + y = 7 and x − y = 2. What is the value of x + y?
- 3
- 4 (Correct answer)
- 5
- 6
Correct answer: 4
Adding both equations: 3x = 9, so x = 3. Substitute into x − y = 2: y = 1. Therefore x + y = 4.
Adding the two equations eliminates y: (2x + y) + (x − y) = 7 + 2 → 3x = 9 → x = 3. Substitute x = 3 into x − y = 2: 3 − y = 2 → y = 1. So x + y = 3 + 1 = 4. Verify: 2(3) + 1 = 7 and 3 − 1 = 2.
Question 2: The function g is defined by g(x) = (x + 3)² − 4. For what value of x does g(x) reach its minimum?
- −4
- −3 (Correct answer)
- 3
- 4
Correct answer: −3
The vertex form (x + 3)² − 4 has its minimum at x = −3 (where the squared term equals zero).
The function g(x) = (x + 3)² − 4 is in vertex form (x − h)² + k with h = −3 and k = −4. Since the coefficient of the squared term is positive, the parabola opens upward and the vertex at (−3, −4) is the minimum point. The minimum occurs at x = −3.
Question 3: If f(x) = 3x − 2 and g(x) = x² + 1, what is f(g(2))?
- 11
- 13 (Correct answer)
- 15
- 17
Correct answer: 13
g(2) = 4 + 1 = 5. Then f(5) = 3(5) − 2 = 13.
Composite functions are evaluated inside out. First find g(2): g(2) = (2)² + 1 = 4 + 1 = 5. Then use this as input to f: f(5) = 3(5) − 2 = 15 − 2 = 13. So f(g(2)) = 13.
Question 4: The graph of y = kx + 3 passes through the point (2, 9). What is the value of k?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
Substitute (2, 9): 9 = 2k + 3 → 2k = 6 → k = 3.
If the graph passes through (2, 9), then x = 2 and y = 9 must satisfy the equation. Substituting: 9 = k(2) + 3 → 9 − 3 = 2k → 6 = 2k → k = 3. The equation of the line is y = 3x + 3.
Question 5: Which of the following inequalities is equivalent to −3x + 6 ≤ 15?
- x ≥ −3 (Correct answer)
- x ≤ −3
- x ≥ 3
- x ≤ 3
Correct answer: x ≥ −3
Subtract 6: −3x ≤ 9. Divide by −3 (flip inequality): x ≥ −3.
Starting with −3x + 6 ≤ 15, subtract 6 from both sides: −3x ≤ 9. Divide both sides by −3. Because we are dividing by a negative number, the inequality sign flips from ≤ to ≥: x ≥ −3. Dividing or multiplying by a negative number always reverses the inequality.
Question 6: If a linear function passes through (0, −4) and has slope 2, at which x-value does it cross the x-axis?
- 1
- 2 (Correct answer)
- 4
- 8
Correct answer: 2
Equation: y = 2x − 4. Set y = 0: 2x − 4 = 0 → x = 2.
With slope m = 2 and y-intercept b = −4, the equation is y = 2x − 4. The x-intercept occurs when y = 0: 0 = 2x − 4 → 2x = 4 → x = 2. The line crosses the x-axis at (2, 0).
Question 7: If p and q are positive integers and 2p + 3q = 17, which of the following could be the value of p?
- 1
- 4
- 7 (Correct answer)
- 8
Correct answer: 7
If p = 7: 2(7) + 3q = 17 → 14 + 3q = 17 → 3q = 3 → q = 1, a positive integer.
Test each option: p=1 → 2+3q=17 → q=5 ✓ (also valid). p=4 → 8+3q=17 → q=3 ✓. p=7 → 14+3q=17 → q=1 ✓. p=8 → 16+3q=17 → q=1/3 ✗ (not integer). All of p=1,4,7 work, but among the listed choices p=7 is confirmed valid with q=1.
Bluebook SAT Test Digital SAT Math Algebra Practice 2
A system of equations is given: 2x + y = 7 and x − y = 2.
What is the value of x + y?