Foundation June 2022 Paper 2R Q23
23
(a) Solve \(p = \dfrac{3p - 5}{10}\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(b) Simplify \(a^0\) where \(a \gt 0\) (1)
(c) Simplify fully \(\dfrac{3xy^3}{6x^2y}\) (2)
(d) Factorise fully \(10c^3d^2 + 15cd^4\) (2)
| Scheme | Marks |
|---|---|
| eg \(10p = 3p - 5\) or \(p = \dfrac{3p}{10} - \dfrac{5}{10}\) oe, eg \(p = 0.3p - 0.5\) | M1 |
| eg \(10p - 3p = -5\) or \(7p = -5\) or \(p - \dfrac{3p}{10} = -\dfrac{5}{10}\) or \(0.7p = -0.5\) | M1ft |
| \(-\dfrac{5}{7}\) | A1 |
| (3) |
Notes
M1: for a correct first step – multiplying both sides by 10 correctly or writing the RHS as 2 terms each over 10 or each term as a decimal [must be in a correct equation]
M1ft: (ft a 3 term equation) for collecting terms in \(p\) on one side and number the other
A1: (dep on at least M1) for \(-\dfrac{5}{7}\) oe, accept −0.71(4...) allow −0.7 if you have seen \(-\dfrac{5}{7}\) or −5 ÷ 7
| Scheme | Marks |
|---|---|
| 1 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\dfrac{y^2}{2x}\) | B2 |
| (2) |
Notes
B2: for \(\dfrac{y^2}{2x}\) oe eg \(\dfrac{0.5y^2}{x}\), \(0.5y^2x^{-1}\), \(\dfrac{y^2x^{-1}}{2}\), \(\dfrac{1}{2xy^{-2}}\) oe
If not B2, award B1 for 2 of number, \(x\), \(y\) correct eg \(\dfrac{ky^2}{x}\) where \(k \ne \dfrac{1}{2}\) or \(\dfrac{y^2}{2x^m}\) where \(m \ne 1\) or \(0.5y^2\) or \(\dfrac{y^p}{2x}\) where \(p \ne 2\)) oe [one term can be missing with 2 correct for B1]
| Scheme | Marks |
|---|---|
| \(5cd^2(2c^2 + 3d^2)\) | B2 |
| (2) | |
| (8 marks) |
Notes
B2: for \(5cd^2(2c^2 + 3d^2)\)
B1 for a correct partial factorisation eg \(5(2c^3d^2 + 3cd^4)\) or \(cd^2(10c^2 + 15d^2)\) or \(5d^2(2c^3 + 3cd^2)\) or \(5c(2c^2d^2 + 3d^4)\) or \(5cd(2c^2d + 3d^3)\) etc or \(5cd^2\)(a 2 term expression with just one error)