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Algebra, inequalities and counting
9 NET Mathematics questions with answers and explanations.
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What is the sum of the squares of the roots of x^2 - 3x + 2 = 0?
- 1 3
- 2 4
- 3 5
- 4 9
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Correct answer: 5
The roots are 1 and 2, so the sum of the squares is 1 + 4 = 5.
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If x^2 - 5x + 6 = 0 has roots alpha and beta, what is alpha^2 + beta^2?
- 1 25
- 2 13
- 3 11
- 4 5
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Correct answer: 13
Sum = 5 and product = 6, so alpha^2 + beta^2 = 25 - 12 = 13.
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How many terms are there in the expansion of (a + b)^8?
- 1 8
- 2 7
- 3 10
- 4 9
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Correct answer: 9
The expansion of (a + b)^n has n + 1 terms, so here there are 9.
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The sum of the first n natural numbers is 210. What is n?
- 1 19
- 2 20
- 3 21
- 4 15
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Correct answer: 20
n(n + 1) / 2 = 210 gives n(n + 1) = 420, which is true for n = 20.
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Which values of x satisfy |x - 2| < 3?
- 1 x < 5
- 2 x > -1
- 3 -1 < x < 5
- 4 x < -1 or x > 5
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Correct answer: -1 < x < 5
|x - 2| < 3 means -3 < x - 2 < 3, so -1 < x < 5.
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What is the remainder when x^3 - 2x^2 + x - 5 is divided by x - 2?
- 1 -3
- 2 3
- 3 0
- 4 -5
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Correct answer: -3
By the remainder theorem, substitute x = 2: 8 - 8 + 2 - 5 = -3.
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What is log base 10 of 0.001?
- 1 3
- 2 -3
- 3 -2
- 4 0.001
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In how many different ways can the letters of the word BOOK be arranged?
- 1 24
- 2 6
- 3 12
- 4 8
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Correct answer: 12
There are 4 letters with the letter O repeated twice, so the number of arrangements is 4! / 2! = 12.
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What is the value of 5C2?
- 1 20
- 2 10
- 3 5
- 4 25