Q. Find the solution set for the inequality -x + 5 ≤ 2.
-
A.
x ≥ 3
-
B.
x ≤ 3
-
C.
x ≥ 5
-
D.
x ≤ 5
Solution
-x + 5 ≤ 2 => -x ≤ -3 => x ≥ 3.
Correct Answer: B — x ≤ 3
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Q. Find the solution set for the inequality 2(x - 1) ≥ 3.
-
A.
x ≥ 2.5
-
B.
x ≤ 2.5
-
C.
x ≥ 1.5
-
D.
x ≤ 1.5
Solution
2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.5.
Correct Answer: A — x ≥ 2.5
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Q. Find the solution set for the inequality 2(x - 1) ≥ 3x + 4.
-
A.
x ≤ -6
-
B.
x ≥ -6
-
C.
x < -6
-
D.
x > -6
Solution
2(x - 1) ≥ 3x + 4 => 2x - 2 ≥ 3x + 4 => -x ≥ 6 => x ≤ -6.
Correct Answer: A — x ≤ -6
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Q. Find the solution set for the inequality 2(x - 1) ≥ 4.
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
2(x - 1) ≥ 4 => x - 1 ≥ 2 => x ≥ 3.
Correct Answer: D — x ≥ 3
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Q. Find the solution set for the inequality 2x + 1 ≤ 3x - 4.
-
A.
x < 5
-
B.
x > 5
-
C.
x ≤ 5
-
D.
x ≥ 5
Solution
2x + 1 ≤ 3x - 4 => 1 + 4 ≤ x => x ≥ 5.
Correct Answer: C — x ≤ 5
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Q. Find the solution set for the inequality 2x + 3 < 5x - 1.
-
A.
x < 4/3
-
B.
x > 4/3
-
C.
x < 2/3
-
D.
x > 2/3
Solution
2x + 3 < 5x - 1 => 4 < 3x => x > 4/3.
Correct Answer: B — x > 4/3
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Q. Find the solution set for the inequality 2x + 3 ≥ 7.
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
2x + 3 ≥ 7 => 2x ≥ 4 => x ≥ 2.
Correct Answer: D — x ≥ 2
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Q. Find the solution set for the inequality 2x + 4 < 3x - 1.
-
A.
x < 5
-
B.
x > 5
-
C.
x ≤ 5
-
D.
x ≥ 5
Solution
2x + 4 < 3x - 1 => 5 < x => x > 5.
Correct Answer: B — x > 5
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Q. Find the solution set for the inequality 2x + 4 ≤ 10.
-
A.
x ≤ 3
-
B.
x < 3
-
C.
x ≥ 3
-
D.
x > 3
Solution
2x + 4 ≤ 10 => 2x ≤ 6 => x ≤ 3.
Correct Answer: C — x ≥ 3
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Q. Find the solution set for the inequality 2x + 4 ≥ 8.
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
2x + 4 ≥ 8 => 2x ≥ 4 => x ≥ 2.
Correct Answer: D — x ≥ 2
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Q. Find the solution set for the inequality 2x + 5 ≤ 3x - 1.
-
A.
x ≤ 6
-
B.
x ≥ 6
-
C.
x < 6
-
D.
x > 6
Solution
2x + 5 ≤ 3x - 1 => 5 + 1 ≤ 3x - 2x => 6 ≤ x => x ≥ 6.
Correct Answer: C — x < 6
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Q. Find the solution set for the inequality 2x - 4 > 0.
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
2x - 4 > 0 => 2x > 4 => x > 2.
Correct Answer: B — x > 2
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Q. Find the solution set for the inequality 2x - 7 < 3.
-
A.
x < 5
-
B.
x > 5
-
C.
x < 4
-
D.
x > 4
Solution
Add 7 to both sides: 2x < 10. Then divide by 2: x < 5.
Correct Answer: A — x < 5
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Q. Find the solution set for the inequality 3x + 1 ≤ 10.
-
A.
x ≤ 3
-
B.
x < 3
-
C.
x ≥ 3
-
D.
x > 3
Solution
3x + 1 ≤ 10 => 3x ≤ 9 => x ≤ 3.
Correct Answer: A — x ≤ 3
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Q. Find the solution set for the inequality 3x + 2 ≤ 11.
-
A.
x ≤ 3
-
B.
x < 3
-
C.
x ≥ 3
-
D.
x > 3
Solution
3x + 2 ≤ 11 => 3x ≤ 9 => x ≤ 3.
Correct Answer: A — x ≤ 3
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Q. Find the solution set for the inequality 3x + 4 ≤ 10.
-
A.
x ≤ 2
-
B.
x < 2
-
C.
x ≥ 2
-
D.
x > 2
Solution
3x + 4 ≤ 10 => 3x ≤ 6 => x ≤ 2.
Correct Answer: A — x ≤ 2
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Q. Find the solution set for the inequality 3x + 5 ≥ 2x + 8.
-
A.
x ≥ 3
-
B.
x ≤ 3
-
C.
x ≥ 5
-
D.
x ≤ 5
Solution
3x + 5 ≥ 2x + 8 => x ≥ 3.
Correct Answer: A — x ≥ 3
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Q. Find the solution set for the inequality 3x - 7 ≤ 2.
-
A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x ≤ 1
-
D.
x ≥ 1
Solution
Add 7 to both sides: 3x ≤ 9. Then divide by 3: x ≤ 3.
Correct Answer: C — x ≤ 1
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Q. Find the solution set for the inequality 6 - 2x ≤ 0.
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
6 - 2x ≤ 0 => -2x ≤ -6 => x ≥ 3.
Correct Answer: B — x > 3
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Q. Find the solution set for the inequality 6 - 3x ≤ 0.
-
A.
x ≥ 2
-
B.
x < 2
-
C.
x ≤ 2
-
D.
x > 2
Solution
6 - 3x ≤ 0 => -3x ≤ -6 => x ≥ 2.
Correct Answer: A — x ≥ 2
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Q. Find the solution set for the inequality 7 - 3x > 1.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer: B — x > 2
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Q. Find the solution set for the inequality 8x + 1 ≤ 5.
-
A.
x ≤ 0.5
-
B.
x < 0.5
-
C.
x ≥ 0.5
-
D.
x > 0.5
Solution
8x + 1 ≤ 5 => 8x ≤ 4 => x ≤ 0.5.
Correct Answer: A — x ≤ 0.5
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Q. Find the solution set for the inequality x + 2 > 3.
-
A.
x > 1
-
B.
x < 1
-
C.
x > -1
-
D.
x < -1
Solution
x + 2 > 3 => x > 1.
Correct Answer: A — x > 1
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Q. Find the solutions of the equation 2sin(x) + √3 = 0.
-
A.
x = 5π/6
-
B.
x = 7π/6
-
C.
x = π/6
-
D.
x = 11π/6
Solution
Solving gives sin(x) = -√3/2, so x = 7π/6 and 11π/6.
Correct Answer: B — x = 7π/6
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Q. Find the solutions of the equation 2sin(x) - 1 = 0 in the interval [0, 2π].
-
A.
π/6, 5π/6
-
B.
π/4, 3π/4
-
C.
π/3, 2π/3
-
D.
π/2, 3π/2
Solution
The solutions are x = π/6 and x = 5π/6.
Correct Answer: A — π/6, 5π/6
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Q. Find the solutions of the equation 2sin(x) - 1 = 0.
-
A.
π/6
-
B.
5π/6
-
C.
7π/6
-
D.
11π/6
Solution
The solutions are x = π/6 and x = 5π/6.
Correct Answer: A — π/6
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Q. Find the sum of the roots of the equation 3x^2 - 12x + 9 = 0.
Solution
The sum of the roots is given by -b/a = 12/3 = 4.
Correct Answer: B — 4
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Q. Find the unit vector in the direction of the vector (3, 4).
-
A.
(0.6, 0.8)
-
B.
(0.8, 0.6)
-
C.
(1, 1)
-
D.
(0.5, 0.5)
Solution
Magnitude = √(3^2 + 4^2) = 5. Unit vector = (3/5, 4/5) = (0.6, 0.8).
Correct Answer: A — (0.6, 0.8)
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Q. Find the unit vector in the direction of the vector (3, 4, 0).
-
A.
(0.6, 0.8, 0)
-
B.
(0.3, 0.4, 0)
-
C.
(1, 1, 0)
-
D.
(0, 0, 1)
Solution
Magnitude = √(3^2 + 4^2) = 5. Unit vector = (3/5, 4/5, 0) = (0.6, 0.8, 0).
Correct Answer: A — (0.6, 0.8, 0)
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Q. Find the unit vector in the direction of the vector (4, 3).
-
A.
(4/5, 3/5)
-
B.
(3/5, 4/5)
-
C.
(1, 0)
-
D.
(0, 1)
Solution
Unit vector = (4, 3) / √(4^2 + 3^2) = (4, 3) / 5 = (4/5, 3/5).
Correct Answer: A — (4/5, 3/5)
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