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Quiz Chapter 1: Variation

10 questions · Form 5 Mathematics Bab 1: Variation

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Given that y varies inversely as x and y = 8 when x = 2. Find the value of y when x = 4.

  1. C. 16
  2. A. 1
  3. B. 4
  4. D. 32
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Answer: B

y = kx => 8 = k2 => k = 16. Equation: y = 16x. When x = 4, y = 164 = 4.

2. If y varies inversely as x, the graph of y against 1x is a:

  1. A. Straight line passing through the origin
  2. B. Curved hyperbola
  3. C. Parabola opening upwards
  4. D. Horizontal straight line above x-axis
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Answer: A

For y = kx, plotting y against (1x) treats (1x) as the independent variable X, yielding y = kX, a straight line through origin.

3. Given that y varies inversely as (x + 2). If y = 3 when x = 2, find x when y = 2.

  1. D. 2
  2. A. 4
  3. B. 6
  4. C. 3
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Answer: A

y = kx + 2 => 3 = k2 + 2 => k = 12. When y = 2 => 2 = 12x + 2 => 2x + 4 = 12 => 2x = 8 => x = 4.

4. Which of the following graphs represents y varying directly as x?

  1. A. A straight line passing through the origin (0,0)
  2. B. A hyperbola curve in the first quadrant
  3. C. A straight line with a negative y-intercept
  4. D. A horizontal straight line
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Answer: A

Direct variation y = kx is a linear relationship passing through the origin (0,0).

5. The table below shows some values of p and q. If p varies directly as the square of q, find the equation connecting p and q if p = 18 when q = 3.

  1. A. p = 2q²
  2. B. p = 6q
  3. C. p = 2q
  4. D. p = 18q²
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Answer: A

p ∝ q² => p = kq². Substituting p = 18, q = 3 => 18 = k(3²) => 18 = 9k => k = 2. Thus, p = 2q².

6. If p ∝ qr and p = 4 when q = 8 and r = 6, find the value of r when p = 12 and q = 16.

  1. A. 8
  2. C. 3
  3. B. 4
  4. D. 2
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Answer: B

p = kq/r => 4 = k86 => k = 3. Equation: p = 3qr. When p = 12, q = 16 => 12 = 316r => 12 = 48r => r = 4.

7. If y varies directly as x, which graph yields a straight line with gradient k?

  1. A. y against x
  2. B. y against 1x
  3. C. y against x²
  4. D. 1y against x
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Answer: A

For y = kx, plotting y on the vertical axis against x on the horizontal axis yields a gradient equal to k.

8. The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. If R = 4 when L = 100 and d = 2, find R when L = 200 and d = 4.

  1. B. 2
  2. A. 8
  3. C. 4
  4. D. 1
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Answer: B

R = kL/d² => 4 = k1002² => 4 = 25k => k = 0.16. New R = 0.162004² = 3216 = 2.

9. If y is inversely proportional to x², what is the effect on y if x is tripled?

  1. A. y is divided by 9
  2. B. y is multiplied by 9
  3. C. y is divided by 3
  4. D. y is multiplied by 3
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Answer: A

y_new = k3x² = k9x² = (19) y. Thus, y is divided by 9.

10. If y varies inversely as the square root of x, and y = 5 when x = 16, calculate the value of k.

  1. A. 80
  2. C. 1.25
  3. B. 20
  4. D. 400
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Answer: B

y = k / √x => 5 = k / √16 => 5 = k4 => k = 20.

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