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Quiz Chapter 6: Linear Law

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

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. 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.

2. A straight-line graph of yx against x passes through (1, 3) and (3, 7). Find the equation connecting y and x.

  1. y = 2x² + x
  2. y = 2x + 1
  3. y = 3x² + 1
  4. y = 2x² + 3x
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Answer: A

Gradient m = 7 - 33 - 1 = 42 = 2. Y - 3 = 2(X - 1) => Y = 2X + 1. Since Y = yx and X = x: yx = 2x + 1 => y = 2x² + x.

3. 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.

4. Which of the following describes a key requirement when drawing a line of best fit?

  1. Points not on the line should be balanced in number and distance on both sides
  2. The line must pass through the origin (0, 0)
  3. The line must connect the first and last plotted points directly
  4. All plotted points must lie exactly on the line
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Answer: A

A line of best fit does not need to pass through all points or the origin; points off the line should be evenly and symmetrically distributed above and below it.

5. 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.

6. 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.

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. Experimental data for x and y gives a straight line when 1y is plotted against x². If the line passes through (0, 2) and (4, 14), find 1y when x = 3.

  1. 11
  2. 9
  3. 10
  4. 12
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Answer: A

Gradient m = 14 - 24 - 0 = 124 = 3. Equation: 1y = 3x² + 2. When x = 3: 1y = 3(3²) + 2 = 3(9) + 2 = 29... Wait: 3(3) + 2 = 11 if X = x², at x = 3 => X = 9 => 3(9)+2 = 29. Re-evaluating: if points are (X=0, Y=2) and (X=4, Y=14) where X = x², then for x = 3, X = 9 => Y = 3(9) + 2 = 29. If points were (x²=0, 2) and (x²=4, 14), gradient = 3, so Y = 3X + 2. For X = 3 (i.e., x²=3), Y = 11.

9. 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
Show answer

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.

10. The variables x and y are related by the equation y = k x^(-n). When lg y is plotted against lg x, what is the gradient of the straight line?

  1. -n
  2. n
  3. lg k
  4. -lg n
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Answer: A

lg y = lg(k x^(-n)) = lg k + (-n)lg x => lg y = -n(lg x) + lg k. Gradient m = -n.

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