Q. What is the solution to the inequality 5 - 2x ≤ 3?
-
A.
x ≥ 1
-
B.
x ≤ 1
-
C.
x > 1
-
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?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
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?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
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?
-
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?
-
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?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
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?
-
A.
x > 2
-
B.
x < 2
-
C.
x ≤ 2
-
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?
-
A.
x > 0.5
-
B.
x < 0.5
-
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?
-
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?
-
A.
x < -1
-
B.
x > -1
-
C.
x < 1
-
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?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
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?
-
A.
x < 4
-
B.
x > 4
-
C.
x < 2
-
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?
-
A.
x ≤ 8
-
B.
x ≥ 8
-
C.
x ≤ 6
-
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?
-
A.
x ≤ 9
-
B.
x ≥ 9
-
C.
x < 9
-
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 standard deviation of the data set {10, 12, 23, 23, 16, 23, 21, 16}?
Solution
Mean = 19.5, Variance = 25, Standard Deviation = √25 = 5.
Correct Answer: A — 5
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Q. What is the standard deviation of the data set {10, 12, 23, 23, 16, 23, 21}?
-
A.
5.5
-
B.
4.5
-
C.
6.5
-
D.
3.5
Solution
Mean = 19.14, Variance = 20.25, Standard Deviation = √20.25 = 4.5.
Correct Answer: B — 4.5
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Q. What is the standard deviation of the data set {4, 8, 6, 5, 3}?
-
A.
1.58
-
B.
2.58
-
C.
3.58
-
D.
4.58
Solution
Mean = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 6.56. Standard Deviation = √6.56 ≈ 2.56.
Correct Answer: B — 2.58
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Q. What is the standard deviation of the data set: 1, 2, 3, 4, 5?
Solution
Mean = 3. Standard Deviation = sqrt[((1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2)/5] = sqrt[2] = 1.414.
Correct Answer: A — 1
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Q. What is the standard form of the equation of a parabola that opens upwards with vertex at the origin?
-
A.
y^2 = 4ax
-
B.
x^2 = 4ay
-
C.
y^2 = -4ax
-
D.
x^2 = -4ay
Solution
The standard form of a parabola that opens upwards is given by x^2 = 4ay.
Correct Answer: B — x^2 = 4ay
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Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
-
A.
81
-
B.
64
-
C.
100
-
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?
-
A.
6 - 2i
-
B.
6 + 2i
-
C.
2 - 2i
-
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 natural numbers?
Solution
Sum = 1 + 2 + 3 + 4 + 5 = 15.
Correct Answer: B — 15
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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
-
B.
100
-
C.
110
-
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, ...?
-
A.
n/2 * (2 + (n-1) * 3)
-
B.
n * (2 + 3n)/2
-
C.
3n^2/2 + n/2
-
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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