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Quiz Chapter 1: Variation

10 questions · Form 5 Mathematics Bab 1: Variation

10 questions · plays in fullscreen

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 g varies directly as h and inversely as the cube of f. Write the full expression for g in terms of h, f, and constant k.

  1. A. g = k hf³
  2. B. g = k f³ / h
  3. C. g = k h f³
  4. D. g = kh f³
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Answer: A

Directly as h means h is in numerator; inversely as f³ means f³ is in denominator: g = k hf³.

2. 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.

3. Variable A varies directly as B1/3). When B = 27, A = 6. Calculate A when B = 64.

  1. B. 8
  2. A. 12
  3. C. 16
  4. D. 4
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Answer: B

A = k B1/3) => 6 = k (271/3)) => 6 = 3k => k = 2. When B = 64 => A = 2 (641/3)) = 2(4) = 8.

4. 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.

5. It is given that y varies directly as x and inversely as z. If y = 6 when x = 4 and z = 2, express y in terms of x and z.

  1. D. y = 12xz
  2. B. y = 3xz
  3. C. y = 48xz
  4. A. y = 3xz
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Answer: B

y = kx/z => 6 = k42 => 6 = 2k => k = 3. Therefore, y = 3xz.

6. If W varies jointly as V and the square of T, write the relationship in variation form.

  1. A. W ∝ VT²
  2. B. W ∝ VT²
  3. C. W ∝ V²T
  4. D. W ∝ 1VT²
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Answer: B

Jointly as V and the square of T translates to W ∝ V × T² = VT².

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. 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.

9. 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.

10. Given p ∝ q³ / r, if q is doubled and r is halved, what happens to p?

  1. C. p increases by 4 times
  2. D. p stays the same
  3. A. p increases by 16 times
  4. B. p decreases by 8 times
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Answer: A

p_new = k(2q)³ / (r2) = k8q³0.5r = 16 (kq³ / r) = 16p. Hence, p increases by 16 times.

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