Foundation November 2019 Paper 2 Q13
13
(a)
(i) Sketch the graph of \(y = 2\).
[2]
(ii) Sketch the graph of \(y = x + 1\).
[2]
(iii) Ceri says that the graphs of \(y = 2\) and \(y = x + 1\) cross at the point \((2, 3)\).
Explain the error in her answer. [1]
(b) Oliver has sketched the graph of \(y = x^2\) below.
Make two comments about the accuracy of his sketch. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) \(y = 2\) sketched correctly with 2 indicated on \(y\)-axis as y-intercept | 2 | M1 for a horizontal line | Condone good freehand |
| (ii) \(y = x + 1\) sketched correctly with 1 indicated as \(y\)-intercept | 2 | M1 for any straight line with positive gradient or for \(y\)- intercept at 1 | Condone good freehand |
| (iii) \(y\)-value where they cross has to be 2 oe | 1 | Isw extra statements. Accept eg (2, 3) is not on \(y = 2\) as the y coordinate is 3 they cross at (1, 2) they cross when \(x = 1\) See AG | |
Exemplar responses
Exemplar responses for Q13aiii
| Response | Mark | |
|---|---|---|
| 1 | y = 2 won’t go higher than 2 to cross at 3 (implies y values) | 1 |
| 2 | Her answer wouldn’t be accurate because y = 2 so wouldn’t cross the point of 3 | 1 |
| 3 | the first graph only equals to two ( it shows y = 2 ) the x = 1 | 1 |
| 4 | y = 2 only goes through y = 2 not y = 3 so not (2,3) | 1 |
| 5 | Because it needs to go through x = 1 (can BOD imply the x coordinate is 1) | BOD 1 |
| 6 | y = 2 will not show a cross at (2,3) due to not being 1 and being y = 2 | 0 |
| 7 | Because they are not on the same graph – they are both on different graphs | 0 |
| 8 | Y is in y axis meanwhile y = x+1 does not = to (2,3) coordinates | 0 |
| 9 | she added 2+1 = 3 and used 2 for x (if they had also stated ‘instead of y’ it would score 1) | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Should go through (0, 0) oe Should be a curve oe No numbers on axis/axes oe It is symmetrical oe | 2 | B1 for each to a max of 2 | If more than two comments, mark the best two See AG |
Exemplar responses
Exemplar responses for Q13b
| Response | Mark | |
|---|---|---|
| 1 | Its meant to be a smooth curve | 1 |
| 2 | He hasn’t placed the numbers on the graph | 1 |
| 3 | The curve is not a perfect curve. | 1 |
| 4 | The curve isn’t accurate as it has edges. | 1 |
| 5 | it doesn’t flow, has used a ruler to connect his points. | 1 |
| 6 | His lines are not curvy they are crooked | 1 |
| 7 | It’s not an actual curve | 1 |
| 8 | “central point isn’t on O” | 1 |
| 9 | The bottom should start at zero as there is no numbers for it to pass through | 1 |
| 10 | It doesn’t touch the centre of the graph (‘origin’ implied) | 1 |
| 11 | it is sketched with a ruler. | 1 |
| 12 | He has used a ruler so it will affect the reliability (this is ok to imply ‘it is not a curve’) | 1 |
| 13 | The line should be drawn freehand not with a ruler (BOD implies a curve) | BOD 1 |
| 14 | There are pointy sides with each coordinate (‘pointy sides’ implies ‘not a curve’) | BOD 1 |
| 15 | The line he makes was meant to be round and his was a straight line (BOD ‘straight line’ rather than ‘ straight lines’) | BOD 1 |
| 16 | does not fully meet the x axis and lines are not fully straight (they are) | 1, 0 |
| 17 | The curved line (U) is not touching the x-axis | 0, 1 |
| 18 | The curve is symmetrical (‘it is not a curve but it is symmetrical’ scores 1,1) | 0, 1 |
| 19 | the line is too blacky and show a stiff movement of the graph (‘stiff movement’ unclear) | 0, 0 |
| 20 | The bottom of the arch needs to be on the line (‘arch’ is wrong way up, ‘on the line’ could be x axis or y axis therefore choice) | 0, 0 |
| 21 | Each side is the same (the sides are ‘mirror images’ would score) | 0 |
| 22 | It is a curve (it’s not) | 0 |
| 23 | No marking on the graph (‘marking’ not enough to imply scale/numbers) | 0 |
| 24 | This sketch is not one line they have not done one single line what flows (‘single line’ will not score, ‘single curve’ will) | 0 |
| 25 | Should be a smooth line (‘smooth line’ does not imply curve) | 0 |
| 26 | The sketch does not start at the point O | 0 |
| 27 | He was accurate with the shape of the graph as it should look like a ‘U’ (‘wasn’t accurate’ in this statement would be fine) | 0 |
| 28 | He has joined each point together (‘with straight lines’ missing) | 0 |
| 29 | connected the points instead of a fluient line (‘with straight lines’ missing) | 0 |
| 30 | It doesn’t match y = x squared (needs to state why) | 0 |
| 31 | It is not going fully around, it stops | 0 |