Q. Which of the following is the result of (x + 2)(x - 2)?
-
A.
x^2 - 4
-
B.
x^2 + 4
-
C.
x^2 - 2
-
D.
x^2 + 2
Solution
Use the difference of squares: (x + 2)(x - 2) = x^2 - 4.
Correct Answer:
A
— x^2 - 4
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Q. Which of the following is the result of factoring x^2 + 5x + 6?
-
A.
(x + 2)(x + 3)
-
B.
(x - 2)(x - 3)
-
C.
(x + 1)(x + 6)
-
D.
(x - 1)(x - 6)
Solution
The polynomial factors to (x + 2)(x + 3) since 2 and 3 multiply to 6 and add to 5.
Correct Answer:
A
— (x + 2)(x + 3)
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Q. Which of the following is the solution set for the inequality 2x + 1 ≥ 5?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 1 from both sides: 2x ≥ 4. Step 2: Divide by 2: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. Which of the following is the solution set for the inequality 2x + 3 > 7?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.
Correct Answer:
B
— x > 2
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Q. Which of the following is the solution set for the inequality x + 2 > 3?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 5
-
D.
x > 5
Solution
To solve the inequality, subtract 2 from both sides: x > 1.
Correct Answer:
B
— x > 1
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Q. Which of the following is the solution set for the inequality x + 3 > 2?
-
A.
x > -1
-
B.
x < -1
-
C.
x > 1
-
D.
x < 1
Solution
To solve the inequality, subtract 3 from both sides: x > -1.
Correct Answer:
A
— x > -1
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Q. Which of the following is the solution set for the inequality x + 4 > 2?
-
A.
x > -2
-
B.
x < -2
-
C.
x > 6
-
D.
x < 6
Solution
Step 1: Subtract 4 from both sides: x > -2.
Correct Answer:
A
— x > -2
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Q. Which of the following is the solution set for the inequality x^2 - 4 > 0?
-
A.
(-∞, -2) ∪ (2, ∞)
-
B.
(-2, 2)
-
C.
[-2, 2]
-
D.
[2, ∞)
Solution
Factor: (x - 2)(x + 2) > 0. The solution is x < -2 or x > 2.
Correct Answer:
A
— (-∞, -2) ∪ (2, ∞)
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Q. Which of the following is the solution to the equation 3x + 4 = 10?
-
A.
x = 2
-
B.
x = 3
-
C.
x = 4
-
D.
x = 1
Solution
Subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.
Correct Answer:
A
— x = 2
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Q. Which of the following is the solution to the equation 4x^2 - 12x + 9 = 0?
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 4
Solution
Step 1: Factor the equation: (2x - 3)(2x - 3) = 0. Step 2: Set the factor to zero: 2x - 3 = 0. Step 3: Solve for x: x = 3/2.
Correct Answer:
B
— x = 2
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Q. Which of the following is the solution to the inequality 2x + 1 > 3?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 1 from both sides: 2x > 2. Step 2: Divide by 2: x > 1.
Correct Answer:
B
— x > 1
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Q. Which of the following is the solution to the inequality 2x + 3 ≥ 7?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 4. Step 2: Divide both sides by 2: x ≥ 2.
Correct Answer:
B
— x ≥ 2
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Q. Which of the following is the solution to the inequality: -4x + 1 < 3?
-
A.
x > -1/2
-
B.
x < -1/2
-
C.
x > 1/2
-
D.
x < 1/2
Solution
Step 1: Subtract 1 from both sides: -4x < 2. Step 2: Divide by -4 (reverse inequality): x > -1/2.
Correct Answer:
B
— x < -1/2
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Q. Which of the following is the solution to the inequality: 2x + 3 ≥ 11?
-
A.
x ≥ 4
-
B.
x ≤ 4
-
C.
x > 4
-
D.
x < 4
Solution
Step 1: Subtract 3 from both sides: 2x ≥ 8. Step 2: Divide by 2: x ≥ 4.
Correct Answer:
A
— x ≥ 4
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Q. Which of the following is the standard form of a linear equation?
-
A.
y = mx + b
-
B.
Ax + By = C
-
C.
y = ax^2 + bx + c
-
D.
x^2 + y^2 = r^2
Solution
The standard form of a linear equation is Ax + By = C.
Correct Answer:
B
— Ax + By = C
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Q. Which of the following is the standard form of a quadratic equation?
-
A.
ax^2 + bx + c = 0
-
B.
y = mx + b
-
C.
ax + b = c
-
D.
x^2 + y^2 = r^2
Solution
The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.
Correct Answer:
A
— ax^2 + bx + c = 0
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Q. Which of the following is the standard form of the equation of a line with slope 5 and y-intercept -3?
-
A.
y = 5x - 3
-
B.
5x + y = -3
-
C.
y = -5x + 3
-
D.
5x - y = 3
Solution
The slope-intercept form is y = mx + b.\n1. y = 5x - 3 can be rearranged to 5x - y = 3.\nThus, the standard form is 5x - y = 3.
Correct Answer:
B
— 5x + y = -3
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Q. Which of the following lines is parallel to the line y = -1/2x + 3?
-
A.
y = 1/2x - 1
-
B.
y = -1/2x + 1
-
C.
y = 2x + 3
-
D.
y = -2x + 3
Solution
Parallel lines have the same slope.\nThe slope of the given line is -1/2, so a parallel line must also have a slope of -1/2.
Correct Answer:
B
— y = -1/2x + 1
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Q. Which of the following pairs of triangles are congruent by the ASA criterion?
-
A.
Angle A = 30°, Angle B = 60°, Side AB = 5 cm
-
B.
Angle A = 30°, Angle B = 60°, Side AC = 5 cm
-
C.
Angle A = 60°, Angle B = 30°, Side AB = 5 cm
-
D.
Angle A = 60°, Angle B = 30°, Side AC = 5 cm
Solution
For ASA, two angles and the included side must be equal. The second option meets this criterion.
Correct Answer:
B
— Angle A = 30°, Angle B = 60°, Side AC = 5 cm
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Q. Which of the following points lies inside the circle with center (0, 0) and radius 5?
-
A.
(3, 4)
-
B.
(5, 0)
-
C.
(6, 0)
-
D.
(0, 5)
Solution
Distance from (0,0) to (3,4) is √(3² + 4²) = 5, which is on the circle. (5,0) and (0,5) are on the circle, (6,0) is outside.
Correct Answer:
A
— (3, 4)
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Q. Which of the following points lies on the line defined by the equation y = 2x + 1?
-
A.
(0, 1)
-
B.
(1, 2)
-
C.
(2, 5)
-
D.
(3, 6)
Solution
For (2, 5): y = 2(2) + 1 = 5, so (2, 5) lies on the line.
Correct Answer:
C
— (2, 5)
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Q. Which of the following points lies on the line y = 2x + 1?
-
A.
(0, 1)
-
B.
(1, 2)
-
C.
(2, 5)
-
D.
(3, 6)
Solution
Substituting x=2: y = 2(2) + 1 = 5, so (2, 5) lies on the line.
Correct Answer:
C
— (2, 5)
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Q. Which of the following quadrilaterals has all sides equal and all angles equal?
-
A.
Rectangle
-
B.
Rhombus
-
C.
Square
-
D.
Trapezoid
Solution
A square is defined as a quadrilateral with all sides equal and all angles equal (90 degrees).
Correct Answer:
C
— Square
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Q. Which of the following represents a linear equation?
-
A.
y = 2x + 3
-
B.
y = x^2 + 1
-
C.
y = sqrt(x)
-
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 a quadratic equation?
-
A.
x + 1 = 0
-
B.
x^2 - 4x + 4 = 0
-
C.
3x^3 + 2 = 0
-
D.
5x - 2 = 0
Solution
A quadratic equation is in the form ax^2 + bx + c = 0. The second option fits this form.
Correct Answer:
B
— x^2 - 4x + 4 = 0
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Q. Which of the following represents the binomial expansion of (x + 2)^2?
-
A.
x^2 + 4
-
B.
x^2 + 4x + 4
-
C.
x^2 + 2x + 2
-
D.
x^2 + 2
Solution
Step 1: Use the formula (a + b)^2 = a^2 + 2ab + b^2. Step 2: Here, a = x and b = 2. Step 3: The expansion is x^2 + 2(2)x + 2^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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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?
-
A.
y = -3x + 2
-
B.
y = 3x + 2
-
C.
y = -3x - 2
-
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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Q. Which of the following represents the equation of a line with a slope of 2 and y-intercept of -3?
-
A.
y = 2x + 3
-
B.
y = 2x - 3
-
C.
y = -2x + 3
-
D.
y = -2x - 3
Solution
The slope-intercept form is y = mx + b. Here, m = 2 and b = -3, so y = 2x - 3.
Correct Answer:
B
— y = 2x - 3
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Q. Which of the following represents the expression 2x^2 + 8x factored?
-
A.
2x(x + 4)
-
B.
2(x^2 + 4)
-
C.
x(2x + 8)
-
D.
2(x + 4)
Solution
Step 1: Factor out the common term 2x: 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Which of the following represents the factored form of x^2 + 5x + 6?
-
A.
(x + 2)(x + 3)
-
B.
(x - 2)(x - 3)
-
C.
(x + 1)(x + 6)
-
D.
(x - 1)(x - 6)
Solution
Factor the polynomial: x^2 + 5x + 6 = (x + 2)(x + 3).
Correct Answer:
A
— (x + 2)(x + 3)
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