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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. 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.

3. 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.

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. Given that E varies directly as m and the square of v. If m = 2 and v = 3 when E = 9, calculate E when m = 4 and v = 5.

  1. D. 25
  2. B. 50
  3. A. 100
  4. C. 75
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Answer: B

E = kmv² => 9 = k(2)(3²) => 9 = 18k => k = 0.5. New E = 0.5(4)(5²) = 2(25) = 50.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

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