arrow_backBack to Study Resources

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. 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
Show answer

Answer: A

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

2. 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
Show answer

Answer: A

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

3. 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
Show answer

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.

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
Show answer

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. 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.

6. 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
Show answer

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.

7. 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
Show answer

Answer: A

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

8. 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
Show answer

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.

9. 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
Show answer

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.

10. A line of best fit passes through points (2, 5) and (6, 17) on a plot of yx against x². Find the gradient m.

  1. 3
  2. 4
  3. 2.5
  4. 2
Show answer

Answer: A

Gradient m = 17 - 56 - 2 = 124 = 3.

Sponsored