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The derivative of x⁵ with respect to x is:
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Correct answer: 5x⁴
The power rule gives 5x⁴.
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The integral of 4x with respect to x is:
- 1 4x² + c
- 2 2x² + c
- 3 x² + c
- 4 4 + c
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Correct answer: 2x² + c
The power rule gives 2x².
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The roots of x² − 3x − 10 = 0 are:
- 1 3 and −10
- 2 −5 and 2
- 3 5 and −2
- 4 10 and −1
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Correct answer: 5 and −2
The equation factors as (x − 5)(x + 2).
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The value of sin² 30° + cos² 30° is:
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Correct answer: 1
The identity sin²θ + cos²θ = 1 holds for every angle.
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The value of 5C2 is:
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Correct answer: 10
5C2 = (5 × 4) ÷ 2 = 10.
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The sum of the integers from 1 to 10 is:
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Correct answer: 55
The sum is 10 × 11 ÷ 2 = 55.
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The value of log₂ 16 is:
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Correct answer: 4
2⁴ = 16.
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The slope of the line through (0, 1) and (2, 5) is:
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Correct answer: 2
Slope = (5 − 1) ÷ (2 − 0) = 2.
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The determinant of the matrix with rows (4, 3) and (2, 1) is:
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Correct answer: −2
The determinant is 4 × 1 − 3 × 2 = −2.
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The value of i³ is:
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Correct answer: −i
i³ = i² × i = −i.
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The solutions of 2x² − 8 = 0 are:
- 1 8 and −8
- 2 2 and −2
- 3 2 only
- 4 4 and −4
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Correct answer: 2 and −2
x² = 4, so x = 2 or x = −2.
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The distance between (−3, 0) and (0, 4) is:
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Correct answer: 5
The distance is √(9 + 16) = 5.
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The derivative of 3x² + 2x at x = 1 is:
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Correct answer: 8
The derivative is 6x + 2, which is 8 at x = 1.
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The value of the integral of (2x + 1) from 0 to 1 is:
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Correct answer: 2
The antiderivative is x² + x, which is 2 at x = 1.
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If 3x + 2y = 12 and x = 2, then y is:
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Correct answer: 3
Put x = 2 to get 2y = 6, so y = 3.
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The sum of the roots of x² − 6x + 8 = 0 is:
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Correct answer: 6
The sum of the roots is −b ÷ a = 6, and the roots are 2 and 4.
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The value of sin 90° + cos 0° is:
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Correct answer: 2
Both values are 1.
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The value of 6C2 is:
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Correct answer: 15
6C2 = (6 × 5) ÷ 2 = 15.
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The 10th term of the arithmetic progression 4, 7, 10, … is:
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Correct answer: 31
a + 9d = 4 + 27 = 31.
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The sum of the first 5 terms of the geometric progression 2, 4, 8, … is:
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Correct answer: 62
The sum is 2 × (2⁵ − 1) ÷ (2 − 1) = 62.
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The slope of the line y = −2x + 5 is:
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Correct answer: −2
In y = mx + c the slope is m.
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The value of log₁₀ 100 is:
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Correct answer: 2
10² = 100.
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The determinant of the matrix with rows (3, 2) and (1, 4) is:
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Correct answer: 10
The determinant is 3 × 4 − 2 × 1 = 10.
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The solutions of x² = 16 are:
- 1 8 and −8
- 2 4 only
- 3 4 and −4
- 4 16 and −16
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Correct answer: 4 and −4
Both 4 and −4 give 16 when squared.
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