SOL Algebra I Practice — Questions and Answers
Question 1: Solve for x: 3x + 7 = 22
- x = 5 (Correct answer)
- x = 3
- x = 7
- x = 15
Correct answer: x = 5
Subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5.
Start with 3x + 7 = 22. Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Checking: 3(5) + 7 = 15 + 7 = 22, which matches the original equation.
Question 2: What is the slope of the line represented by the equation y = 4x - 9?
Correct answer: 4
In slope-intercept form y = mx + b, m is the slope, so the slope here is 4.
The equation y = 4x - 9 is already in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Here m = 4 and b = -9, so the slope of the line is 4.
Question 3: Simplify the expression: 5(2x - 3) + 4x
- 14x - 15 (Correct answer)
- 10x - 3
- 14x - 3
- 9x - 15
Correct answer: 14x - 15
Distribute 5 to get 10x - 15, then combine with 4x to get 14x - 15.
Distribute the 5 across (2x - 3): 5(2x) - 5(3) = 10x - 15. Then add the remaining 4x: 10x + 4x - 15 = 14x - 15.
Question 4: Which of the following is a factor of x^2 - 9?
- x + 9
- x - 3 (Correct answer)
- x + 4
- x - 9
Correct answer: x - 3
x^2 - 9 is a difference of squares, factoring to (x - 3)(x + 3).
x^2 - 9 fits the pattern a^2 - b^2 = (a - b)(a + b), where a = x and b = 3, since 3^2 = 9. So x^2 - 9 factors into (x - 3)(x + 3). Therefore (x - 3) is a factor.
Question 5: A system of equations is y = 2x + 1 and y = -x + 7. What is the solution?
- (2, 5) (Correct answer)
- (3, 4)
- (1, 3)
- (4, 3)
Correct answer: (2, 5)
Setting 2x + 1 = -x + 7 gives 3x = 6, so x = 2, and y = 2(2) + 1 = 5.
Since both equations equal y, set them equal: 2x + 1 = -x + 7. Add x to both sides: 3x + 1 = 7. Subtract 1: 3x = 6. Divide by 3: x = 2. Substitute back into y = 2x + 1: y = 2(2) + 1 = 5. The solution is (2, 5).
Question 6: What is the value of the function f(x) = x^2 - 2x + 1 when x = 3?
Correct answer: 4
f(3) = 3^2 - 2(3) + 1 = 9 - 6 + 1 = 4.
Substitute x = 3 into f(x) = x^2 - 2x + 1: f(3) = (3)^2 - 2(3) + 1 = 9 - 6 + 1 = 4. This function is actually a perfect square trinomial, (x-1)^2, and (3-1)^2 = 4, confirming the answer.
Question 7: Solve the inequality: 2x - 5 > 9
- x > 7 (Correct answer)
- x > 2
- x < 7
- x > 14
Correct answer: x > 7
Add 5 to both sides to get 2x > 14, then divide by 2 to get x > 7.
Start with 2x - 5 > 9. Add 5 to both sides: 2x > 14. Divide both sides by 2 (positive, so the inequality sign stays the same): x > 7.
Question 8: What is the y-intercept of the line y = -3x + 6?
Correct answer: 6
In y = mx + b form, b is the y-intercept, which is 6 here.
The equation y = -3x + 6 is in slope-intercept form y = mx + b, where b is the y-intercept. Here b = 6, meaning the line crosses the y-axis at the point (0, 6).
Question 9: Simplify: (2x^3)(3x^2)
- 6x^5 (Correct answer)
- 5x^5
- 6x^6
- 5x^6
Correct answer: 6x^5
Multiply coefficients (2 x 3 = 6) and add exponents (3 + 2 = 5) to get 6x^5.
When multiplying monomials, multiply the coefficients and add the exponents of matching variables: 2 * 3 = 6, and x^3 * x^2 = x^(3+2) = x^5. The result is 6x^5.
Question 10: Which expression represents the area of a rectangle with length (x + 4) and width (x - 2)?
- x^2 + 2x - 8 (Correct answer)
- x^2 - 2x - 8
- x^2 + 6x - 8
- x^2 + 2x + 8
Correct answer: x^2 + 2x - 8
Multiply (x + 4)(x - 2) using FOIL: x^2 - 2x + 4x - 8 = x^2 + 2x - 8.
Area = length * width = (x + 4)(x - 2). Using FOIL: First: x*x = x^2, Outer: x*(-2) = -2x, Inner: 4*x = 4x, Last: 4*(-2) = -8. Combine: x^2 - 2x + 4x - 8 = x^2 + 2x - 8.
Question 11: What is the solution to the equation x^2 - 5x + 6 = 0?
- x = 2 or x = 3 (Correct answer)
- x = -2 or x = -3
- x = 1 or x = 6
- x = 2 or x = -3
Correct answer: x = 2 or x = 3
Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.
To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5: those are -2 and -3. So the expression factors as (x - 2)(x - 3) = 0. By the zero product property, x - 2 = 0 or x - 3 = 0, giving x = 2 or x = 3.
Question 12: A cell phone plan costs $20 plus $0.10 per text message. Which equation models the total cost, C, for t text messages?
- C = 20 + 0.10t (Correct answer)
- C = 0.10 + 20t
- C = 20t + 0.10
- C = 20 - 0.10t
Correct answer: C = 20 + 0.10t
The fixed cost of $20 plus a variable cost of $0.10 per text gives C = 20 + 0.10t.
This is a linear model where the fixed cost ($20) is the y-intercept and the per-text cost ($0.10) is the rate of change, or slope, multiplied by the number of texts, t. This gives the equation C = 20 + 0.10t, matching the form y = mx + b.
