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Quiz Chapter 6: Linear Law

10 questions · Form 4 Additional Mathematics Bab 6: Linear Law

Question 1 of 10Score: 0

A graph of y² against x has a gradient of -2 and passes through (4, 10). What is the value of the vertical intercept c?

Full Question List & Answer Key

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

1. A graph of y² against x has a gradient of -2 and passes through (4, 10). What is the value of the vertical intercept c?

  1. 18
  2. 2
  3. 14
  4. -18
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Answer: A

Y = mX + c => 10 = -2(4) + c => 10 = -8 + c => c = 18.

2. A straight line plot of lg y against x has a Y-intercept of 0.6021. Find the value of constant a if y = a b^x.

  1. 4
  2. 2
  3. 3
  4. 5
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Answer: A

c = lg a = 0.6021 => a = 100.6021 ≈ 4.

3. Given the equation y = a √x + b/√x, which transformation yields a straight line with Y-intercept b when plotted against x?

  1. Plot y√x against x
  2. Plot y against √x
  3. Plot y/√x against x
  4. Plot y² against x
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Answer: A

Multiply y = a√x + b/√x by √x: y√x = ax + b. Plotted Y = y√x against X = x, gradient m = a and vertical intercept c = b.

4. If y - x = p x² + q, what variables should be plotted on the vertical and horizontal axes to obtain a straight line with gradient p?

  1. Vertical axis: y - x, Horizontal axis: x²
  2. Vertical axis: y, Horizontal axis: x²
  3. Vertical axis: yx, Horizontal axis: x
  4. Vertical axis: y - x, Horizontal axis: x
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Answer: A

Comparing y - x = p x² + q with Y = mX + c gives Y = y - x, X = x², gradient m = p, and intercept c = q.

5. Variables x and y are connected by p^x y = q. Express this in linear form Y = mX + c.

  1. lg y = (-lg p)x + lg q
  2. lg y = (lg p)x + lg q
  3. lg y = (lg q)x - lg p
  4. y = -p x + q
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Answer: A

Take lg on both sides: lg(p^x y) = lg q => x lg p + lg y = lg q => lg y = (-lg p)x + lg q.

6. Convert the non-linear equation y = ax² + bx into linear form Y = mX + c when plotting yx against x.

  1. Y = yx, X = x, m = a, c = b
  2. Y = y, X = x², m = a, c = b
  3. Y = yx, X = x², m = b, c = a
  4. Y = xy, X = x, m = a, c = b
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Answer: A

Dividing both sides of y = ax² + bx by x gives yx = ax + b. Comparing with Y = mX + c gives Y = yx, X = x, gradient m = a, and vertical intercept c = b.

7. Variables x and y are related by y = ax + b. A graph of xy against x gives a straight line with gradient 4 and y-intercept 6. Find the values of a and b.

  1. a = 6, b = 4
  2. a = 4, b = 6
  3. a = -6, b = 4
  4. a = 6, b = -4
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Answer: A

Multiply y = ax + b by x: xy = bx + a. Thus Y = xy, X = x, gradient m = b = 4, and intercept c = a = 6.

8. The variables x and y satisfy y = h x^k. When lg y is plotted against lg x, the line passes through (0, 1) and (2, 7). Find the value of k.

  1. 3
  2. 1
  3. 2
  4. 4
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Answer: A

Equation: lg y = k lg x + lg h. Gradient m = 7 - 12 - 0 = 62 = 3. Since gradient m = k, k = 3.

9. A plot of lg y against lg x gives a line with gradient m = 0.5 and Y-intercept c = 0.3010. Express y in terms of x.

  1. y = 2√x
  2. y = 2x
  3. y = 0.5√x
  4. y = 100.5)√x
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Answer: A

lg y = 0.5 lg x + 0.3010 => lg y = lg(x0.5) + lg(100.3010) = lg(x0.5) + lg 2 = lg(2√x) => y = 2√x.

10. Variables x and y are related by y = 2x² + kx. When xy is plotted against x³, the graph is a straight line. What is the vertical intercept?

  1. k
  2. 2
  3. 2k
  4. k2
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Answer: A

Multiply y = 2x² + kx by x: xy = 2x³ + k. Comparing with Y = mX + c where Y = xy and X = x³ gives gradient m = 2 and vertical intercept c = k.

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