Foundation November 2021 Paper 3 Q21
21
(a) A straight line has the equation \(y = 2x - 1\).
Write down the gradient of the line. [1]
(b) Here are the equations of four straight lines.\[y = 2x + 3 \qquad y = 1 - x \qquad y = \tfrac{1}{2}x + 4 \qquad y = x - 1\]
(i) Which of the four straight lines is parallel to \(y = 2x - 1\)? [1]
(ii) A student says
\(y = \frac{1}{2}x + 4\) is the steepest of the four straight lines because it has the largest number added.
Explain why the student is wrong. [1]
(c) Here is part of the graph of \(y = 2x - 1\).
The line continues to the right.
Will the line pass above, below or through the point (45, 90)?
Show how you decide. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 2 cao | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) \(y = 2x + 3\) | 1 | Allow, “The first one” oe for \(y = 2x + 3\) | |
| (ii) Comment: Rejecting 4 [as gradient] and/or indicating \(2 \gt \dfrac{1}{2}\) | 1 | See appendix | |
Appendix
Exemplar responses for Q21b(ii)
| Response | Mark | |
|---|---|---|
| The number before \(x\) is bigger in the first one | Compares the numbers for gradient | 1 |
| The 4 is not the gradient, it is the y intercept. The gradient is ½ | OK, Rejects gradient | 1 |
| Because it is only half whereas \(y = 2x + 3\) is the steepest | BOD ½ for gradient and implied comparison with 2 | 1 |
| The number added is the [\(y\)] intercept and not the gradient | OK, rejects constant | 1 |
| It has the smallest gradient which is ½ | BOD implied comparison of gradients | 1 |
| You halve the \(x\) making it closer to \(x\) | inconclusive statement and doesn’t compare numbers | 0 |
| It’s actually the least steep | True but no reason given | 0 |
| Because ½ isn’t the highest number | Doesn’t compare the gradients ½ and 2. There are lots of “numbers” | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(2 \times 45 - 1\) soi 89 or \((90 + 1) \div 2\) soi 45.5 oe | M1 | ||
| Below | A1 | ||