Q. Solve the inequality 5x - 7 < 3.
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A.
x < 2
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B.
x > 2
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C.
x < 1
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D.
x > 1
Solution
Step 1: Add 7 to both sides: 5x < 10. Step 2: Divide by 5: x < 2.
Correct Answer:
A
— x < 2
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Q. What is the value of x in the equation 3(x - 1) = 2x + 4?
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A.
x = 1
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B.
x = 2
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C.
x = 3
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D.
x = 4
Solution
Step 1: Distribute: 3x - 3 = 2x + 4. Step 2: Subtract 2x from both sides: x - 3 = 4. Step 3: Add 3 to both sides: x = 7.
Correct Answer:
B
— x = 2
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Q. What is the value of x in the equation 4x - 7 = 5?
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A.
x = 1
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B.
x = 2
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C.
x = 3
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D.
x = 4
Solution
Add 7 to both sides: 4x = 12. Then divide by 4: x = 3.
Correct Answer:
B
— x = 2
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Q. What is the value of x in the polynomial equation x^3 - 4x^2 + x = 0?
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A.
x = 0, 1, 4
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B.
x = 0, 2, 3
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C.
x = 1, 2, 3
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D.
x = 0, -1, -4
Solution
Factor out x: x(x^2 - 4x + 1) = 0. Thus, x = 0 or solve x^2 - 4x + 1 = 0.
Correct Answer:
A
— x = 0, 1, 4
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Q. What is the vertex of the parabola represented by the equation y = x^2 - 4x + 4?
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A.
(2, 0)
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B.
(0, 4)
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C.
(4, 0)
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D.
(2, 4)
Solution
The vertex can be found using the formula x = -b/(2a). Here, a = 1, b = -4, so x = 2. Substitute x back to find y: y = 0.
Correct Answer:
A
— (2, 0)
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Q. Which of the following is a polynomial?
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A.
3x^2 + 2x - 1
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B.
1/x + 2
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C.
sqrt(x) + 3
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D.
ln(x)
Solution
A polynomial is a sum of terms with non-negative integer exponents. 3x^2 + 2x - 1 fits this definition.
Correct Answer:
A
— 3x^2 + 2x - 1
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Q. Which of the following represents a linear equation?
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A.
y = 2x + 3
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B.
y = x^2 + 1
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C.
y = sqrt(x)
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D.
y = ln(x)
Solution
A linear equation is in the form y = mx + b. y = 2x + 3 fits this form.
Correct Answer:
A
— y = 2x + 3
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Q. Which of the following represents the equation of a line with a slope of -3 and y-intercept of 2?
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A.
y = -3x + 2
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B.
y = 3x + 2
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C.
y = -3x - 2
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D.
y = 3x - 2
Solution
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Correct Answer:
A
— y = -3x + 2
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