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Quiz Chapter 6: Linear Law

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

Question 1 of 10Score: 0

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?

Full Question List & Answer Key

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

1. 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.

2. 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.

3. 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.

4. A straight line graph of xy against x² has a gradient of 3 and a Y-intercept of -4. Express y in terms of x.

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

The linear equation is xy = 3x² - 4. Divide both sides by x: y = 3x - 4x.

5. When lg y is plotted against x for the equation y = 5(2^x), what is the vertical intercept c?

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

lg y = (lg 2)x + lg 5. Comparing with Y = mX + c gives gradient m = lg 2 and vertical intercept c = lg 5.

6. 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.

7. 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.

8. 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.

9. The non-linear relationship between x and y is given by y = a x^b. If lg y is plotted against lg x, what does the gradient m represent?

  1. b
  2. a
  3. lg a
  4. lg b
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Answer: A

lg y = b lg x + lg a. Comparing with Y = mX + c where Y = lg y and X = lg x gives gradient m = b and intercept c = lg a.

10. The non-linear equation y = a b^x is expressed in linear form. What are the variables plotted on the vertical and horizontal axes?

  1. Vertical axis: lg y, Horizontal axis: x
  2. Vertical axis: y, Horizontal axis: x
  3. Vertical axis: lg y, Horizontal axis: lg x
  4. Vertical axis: y, Horizontal axis: lg x
Show answer

Answer: A

Taking lg on both sides: lg y = lg(a b^x) = lg a + x lg b => lg y = (lg b)x + lg a. Thus Y = lg y and X = x.

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