Algebra, sequences and functions MCQs with Answers: ECAT Mathematics

All questions with answers

What are the roots of x^2 - 5x + 6 = 0?
- 1 1 and 6
- 2 2 and 3
- 3 -2 and -3
- 4 -1 and 6
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Correct answer: 2 and 3

Factorise as (x - 2)(x - 3) = 0, so x = 2 or x = 3.

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What is the sum of the roots of 2x^2 - 7x + 3 = 0?
- 1 7/2
- 2 -7/2
- 3 3/2
- 4 -3/2
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Correct answer: 7/2

For ax^2 + bx + c = 0 the sum of the roots is -b/a = 7/2.

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For which values of k does x^2 + kx + 9 = 0 have equal roots?
- 1 k = 3 only
- 2 k = 9 only
- 3 k = 6 or -6
- 4 k = 3 or -3
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Correct answer: k = 6 or -6

Equal roots need discriminant zero: k^2 - 36 = 0, so k = 6 or k = -6.

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What is the 10th term of the arithmetic progression 3, 7, 11, ...?
- 1 39
- 2 43
- 3 40
- 4 36
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Correct answer: 39

The nth term is a + (n - 1)d = 3 + 9 x 4 = 39.

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What is the sum of the first 10 terms of the geometric progression 1, 2, 4, 8, ...?
- 1 512
- 2 1024
- 3 1023
- 4 2047
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Correct answer: 1023

S = a(r^n - 1) / (r - 1) = (2^10 - 1) / 1 = 1023.

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What is the coefficient of x^2 in the expansion of (1 + x)^5?
- 1 5
- 2 10
- 3 20
- 4 15
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Correct answer: 10

The coefficient is 5C2 = 10.

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If f(x) = 2x + 3, then the inverse function f^-1(x) is:
- 1 (x + 3) / 2
- 2 2x - 3
- 3 (x - 3) / 2
- 4 x / 2 - 3
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Correct answer: (x - 3) / 2

Let y = 2x + 3. Then x = (y - 3) / 2, so f^-1(x) = (x - 3) / 2.

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What is the domain of f(x) = sqrt(x - 4)?
- 1 x > 4
- 2 x >= 4
- 3 x <= 4
- 4 All real numbers
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Correct answer: x >= 4

The expression under the square root must be at least zero, so x - 4 >= 0 and x >= 4.

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What is the sum to infinity of the series 1 + 1/2 + 1/4 + 1/8 + ...?
- 1 1
- 2 2
- 3 4
- 4 It has no sum
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Correct answer: 2

S = a / (1 - r) = 1 / (1 - 1/2) = 2.

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