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Quiz Chapter 1: Variation

10 questions · Form 5 Mathematics Bab 1: Variation

Question 1 of 10Score: 0

If x ∝ y^n and x = 54 when y = 3 with k = 2, find the value of n.

Full Question List & Answer Key

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1. If x ∝ y^n and x = 54 when y = 3 with k = 2, find the value of n.

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

x = k y^n => 54 = 2(3^n) => 27 = 3^n => 3³ = 3^n => n = 3.

2. 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).

3. The time T taken to complete a job varies inversely as the number of workers W. If 6 workers take 10 hours, how many hours will 15 workers take?

  1. C. 25 hours
  2. A. 4 hours
  3. B. 8 hours
  4. D. 2 hours
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Answer: A

T = kW => 10 = k6 => k = 60. Equation: T = 60W. For W = 15 => T = 6015 = 4 hours.

4. 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.

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. 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.

7. If y varies directly as x, and y = 12 when x = 3, find the constant of variation, k.

  1. B. 36
  2. A. 4
  3. C. 0.25
  4. D. 15
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Answer: A

Since y ∝ x, y = kx. Substituting y = 12 and x = 3 gives 12 = 3k, so k = 4.

8. 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.

9. 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.

10. The volume V of a cylinder varies directly as its height h and the square of its radius r. If V = 154 cm³ when r = 7 cm and h = 1, find constant k (use π ≈ 227).

  1. C. 227
  2. A. 722
  3. B. 1
  4. D. 3.14
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Answer: C

V = k r² h => 154 = k (7²)(1) => 154 = 49k => k = 15449 = 227.

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