Algebra
Q. What is the solution to the inequality 4x - 1 ≤ 3x + 2?
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A.
x ≤ 3
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B.
x ≥ 3
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C.
x < 3
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D.
x > 3
Solution
4x - 1 ≤ 3x + 2 => x ≤ 3.
Correct Answer: A — x ≤ 3
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Q. What is the solution to the inequality 4x - 5 < 3x + 2?
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A.
x < 7
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B.
x > 7
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C.
x < -7
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D.
x > -7
Solution
4x - 5 < 3x + 2 => x < 7.
Correct Answer: A — x < 7
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Q. What is the solution to the inequality 4x - 5 ≥ 3?
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A.
x < 2
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B.
x > 2
-
C.
x ≤ 2
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D.
x ≥ 2
Solution
4x - 5 ≥ 3 => 4x ≥ 8 => x ≥ 2.
Correct Answer: D — x ≥ 2
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Q. What is the solution to the inequality 4x - 7 < 9?
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A.
x < 4
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B.
x < 3
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C.
x > 4
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D.
x > 3
Solution
4x - 7 < 9 => 4x < 16 => x < 4.
Correct Answer: B — x < 3
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Q. What is the solution to the inequality 5 - 2x < 1?
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A.
x > 2
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B.
x < 2
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C.
x > 3
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D.
x < 3
Solution
Subtract 5 from both sides: -2x < -4. Then divide by -2 (reverse the inequality): x > 2.
Correct Answer: A — x > 2
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Q. What is the solution to the inequality 5 - 2x ≤ 1?
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A.
x ≥ 2
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B.
x ≤ 2
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C.
x < 2
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D.
x > 2
Solution
5 - 2x ≤ 1 => -2x ≤ -4 => x ≥ 2.
Correct Answer: A — x ≥ 2
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Q. What is the solution to the inequality 5 - 2x ≤ 3?
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A.
x ≥ 1
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B.
x ≤ 1
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C.
x > 1
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D.
x < 1
Solution
5 - 2x ≤ 3 => -2x ≤ -2 => x ≥ 1.
Correct Answer: B — x ≤ 1
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Q. What is the solution to the inequality 6 - 3x ≥ 0?
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A.
x < 2
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B.
x > 2
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C.
x ≤ 2
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D.
x ≥ 2
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer: C — x ≤ 2
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Q. What is the solution to the inequality 6x + 2 < 14?
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A.
x < 2
-
B.
x > 2
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C.
x < 3
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D.
x > 3
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer: A — x < 2
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Q. What is the solution to the inequality 6x + 2 ≤ 14?
-
A.
x ≤ 2
-
B.
x < 2
-
C.
x ≥ 2
-
D.
x > 2
Solution
6x + 2 ≤ 14 => 6x ≤ 12 => x ≤ 2.
Correct Answer: A — x ≤ 2
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Q. What is the solution to the inequality 6x + 4 < 2x + 20?
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A.
x < 4
-
B.
x > 4
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
6x + 4 < 2x + 20 => 4x < 16 => x < 4.
Correct Answer: A — x < 4
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Q. What is the solution to the inequality 6x + 4 ≤ 2x + 16?
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A.
x ≤ 3
-
B.
x ≥ 3
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
6x + 4 ≤ 2x + 16 => 4x ≤ 12 => x ≤ 3.
Correct Answer: B — x ≥ 3
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Q. What is the solution to the inequality 7 - 3x > 1?
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A.
x < 2
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B.
x > 2
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C.
x < 3
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D.
x > 3
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer: A — x < 2
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Q. What is the solution to the inequality 7 - 3x < 1?
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A.
x > 2
-
B.
x < 2
-
C.
x ≤ 2
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D.
x ≥ 2
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer: A — x > 2
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Q. What is the solution to the inequality 7x + 2 > 5?
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A.
x > 0.5
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B.
x < 0.5
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C.
x ≥ 0.5
-
D.
x ≤ 0.5
Solution
7x + 2 > 5 => 7x > 3 => x > 0.5.
Correct Answer: A — x > 0.5
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Q. What is the solution to the inequality 7x + 2 > 5x + 6?
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A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7x + 2 > 5x + 6 => 2x > 4 => x > 2.
Correct Answer: B — x > 2
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Q. What is the solution to the inequality 7x + 2 < 5?
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A.
x < -1
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B.
x > -1
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C.
x < 1
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D.
x > 1
Solution
7x + 2 < 5 => 7x < 3 => x < -1.
Correct Answer: A — x < -1
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Q. What is the solution to the inequality 7x + 3 > 24?
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A.
x < 3
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B.
x > 3
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C.
x ≤ 3
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D.
x ≥ 3
Solution
7x + 3 > 24 => 7x > 21 => x > 3.
Correct Answer: B — x > 3
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Q. What is the solution to the inequality 7x + 5 < 2x + 20?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 4
-
D.
x > 4
Solution
7x + 5 < 2x + 20 => 5x < 15 => x < 3.
Correct Answer: A — x < 3
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Q. What is the solution to the inequality 7x - 4 < 3x + 8?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 2
-
D.
x > 2
Solution
7x - 4 < 3x + 8 => 4x < 12 => x < 3.
Correct Answer: B — x > 3
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Q. What is the solution to the inequality 8 - 2x > 0?
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A.
x < 4
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B.
x > 4
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C.
x < 2
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D.
x > 2
Solution
8 - 2x > 0 => -2x > -8 => x < 4.
Correct Answer: B — x > 4
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Q. What is the solution to the inequality x/2 - 1 ≤ 3?
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A.
x ≤ 8
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B.
x ≥ 8
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C.
x ≤ 6
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D.
x ≥ 6
Solution
x/2 - 1 ≤ 3 => x/2 ≤ 4 => x ≤ 8.
Correct Answer: A — x ≤ 8
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Q. What is the solution to the inequality x/3 - 2 ≤ 1?
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A.
x ≤ 9
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B.
x ≥ 9
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C.
x < 9
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D.
x > 9
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer: A — x ≤ 9
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Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
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A.
81
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B.
64
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C.
100
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D.
125
Solution
The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.
Correct Answer: A — 81
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Q. What is the sum of the coefficients in the expansion of (x + 1)^5?
Solution
The sum of the coefficients is found by substituting x = 1, so (1 + 1)^5 = 2^5 = 32.
Correct Answer: D — 32
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Q. What is the sum of the coefficients in the expansion of (x + 1)^7?
Solution
The sum of the coefficients is found by substituting x = 1, giving (1 + 1)^7 = 2^7 = 128.
Correct Answer: A — 128
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Q. What is the sum of the complex numbers 2 + 3i and 4 - 5i?
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A.
6 - 2i
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B.
6 + 2i
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C.
2 - 2i
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D.
2 + 2i
Solution
The sum is (2 + 4) + (3 - 5)i = 6 - 2i.
Correct Answer: A — 6 - 2i
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Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
Solution
S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Correct Answer: A — 1.5
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Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?
-
A.
90
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B.
100
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C.
110
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D.
120
Solution
The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.
Correct Answer: A — 90
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Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?
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A.
n/2 * (2 + (n-1) * 3)
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B.
n * (2 + 3n)/2
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C.
3n^2/2 + n/2
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D.
n * (n + 1)
Solution
The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).
Correct Answer: A — n/2 * (2 + (n-1) * 3)
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