Foundation June 2023 Paper 2R Q16
16
(a) Factorise \(6y - 27\) (1)
(b) Expand \(p(p - 2)\) (1)
\(T = 5g + 4r\)
(c) Work out the value of \(r\) when \(T = 46\) and \(g = 17\) (3)
\(P = m^2 - 4c\)
(d) Work out the value of \(P\) when \(m = -5\) and \(c = 3\) (2)
(e) Expand and simplify \((x + 5)(x - 7)\) (2)
| Scheme | Marks |
|---|---|
| \(3(2y - 9)\) | B1 |
| (1) |
Notes
B1: accept \(3(-9 + 2y)\)
| Scheme | Marks |
|---|---|
| \(p^2 - 2p\) | B1 |
| (1) |
Notes
B1: accept \(-2p + p^2\)
| Scheme | Marks |
|---|---|
\(46 = 5 \times 17 + 4r\) oe or \(46 = 85 + 4r\) oe oe or \(46 - 5 \times 17\;(= 4r)\) oe or \(46 - 85\;(= 4r)\) oe or \(r = \dfrac{T - 5g}{4}\) | M1 |
\((r =)\;\dfrac{46 - 85}{4}\) oe or \((r =)\;\dfrac{46 - 5 \times 17}{4}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: –9.75 | A1 |
| (3) |
Notes
A1: oe eg \(\dfrac{-39}{4}\)
| Scheme | Marks |
|---|---|
| 25 ± ……. or ……. – 12 or \((-5)^2 - 4 \times 3\) or \((-5)^2 - 4(3)\) or \(-5 \times -5 - 4 \times 3\) or \(-5 \times -5 - 4(3)\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 13 | A1 |
| (2) |
Notes
M1: for either 25 or –12 in the correct place or the correct substitution shown with brackets around –5
A1: (M0A0 for –37 without any working)
| Scheme | Marks |
|---|---|
| \(x^2 + 5x - 7x - 35\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(x^2 - 2x - 35\) | A1 |
| (2) | |
| (9 marks) |
Notes
M1: for any 3 correct terms or for 4 out of 4 correct terms ignoring signs or for \(x^2 - 2x \ldots\) or for \(\ldots -2x - 35\)
A1: oe
Ignore solutions/roots if correct expansion seen