Foundation June 2019 Paper 2 Q9
9 Simon has \(x\) sweets.
Yuen has 2 more sweets than Simon.
Giulia has 3 times as many sweets as Yuen.
Simon, Yuen and Giulia have a total of \(T\) sweets.
Give your formula in its simplest form. (3)
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
| e.g. \(x + 2\) or \(3x + 6\) or \(3(x + 2)\) | M1 |
| e.g. \(x + x + 2 + 3x + 6\) or \(5x + 8\) or \(x + x + 2 + 3(x + 2)\) | M1 |
| \(T = 5x + 8\) | A1 |
| (3) |
Notes
M1: dep
A1: accept \(T = 8 + 5x\)
(SC B2 \(T = 5x + a\) where \(a \ne 0\) or \(T = bx + 8\) where \(b \ne 0\))
| Scheme | Marks |
|---|---|
e.g. \(r - 7 = 4g\) or \(\dfrac{r}{4} = g + \dfrac{7}{4}\) or \(-4g = 7 - r\) or \(-g = \dfrac{7 - r}{4}\) or \(-g = \dfrac{r - 7}{4}\) oe or \(\dfrac{r - 7}{4}\) oe | M1 |
| \(g = \dfrac{r - 7}{4}\) | A1 |
| (2) |
Notes
M1: for a first step of subtracting 7 or dividing by 4 in a correct equation
A1: oe
Note: the printed scheme lists \(-g = \dfrac{r - 7}{4}\) among the correct first steps. This is not a correct equation: from \(-4g = 7 - r\) it should be \(-g = \dfrac{7 - r}{4}\) (or \(g = \dfrac{r - 7}{4}\)).
| Scheme | Marks |
|---|---|
| e.g. \(6y - 2y = 8 + 3\) or \(2y - 6y = -3 - 8\) oe e.g. \(4y - 3 = 8\) or \(6y = 2y + 11\) or \(-3 = -4y + 8\) or \(6y - 11 = 2y\) | M1 |
| e.g. \(4y = 11\) or \(-4y = -11\) or | M1 |
| \(\dfrac{11}{4}\) | A1 |
| (3) | |
| (8 marks) |
Notes
M1: for correct rearrangement with \(y\) terms on one side and numbers on the other side e.g. \(6y - 2y = 8 + 3\)
or
for the correct simplification of either \(y\) terms or numbers on one side in a correct equation e.g. \(4y - 3 = 8\) or \(6y = 2y + 11\)
M1: for correct rearrangement with \(y\) terms on one side and numbers on the other and correct simplification of terms on both sides
or for \(4y - 11 = 0\)
or for \(11 - 4y = 0\)