Foundation November 2024 Paper 1 Q20
20
(a) Simplify \(\left(p^3\right)^5\) (1)
(b) Expand and simplify \(2n(4n + 3) + n(n - 4)\) (2)
(c) Solve \(\dfrac{2x + 5}{3} = 4 - x\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
| \(p^{15}\) | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| \(8n^2 + 6n + n^2 - 4n\) | M1 |
| \(9n^2 + 2n\) | A1 |
| (2) |
Notes
M1: for expanding with at least 3 correct terms (must see for example, \(8n^2\) and not just \(2n \times 4n\))(can assume that no sign in front of a number is a + if terms written in a list or table)
A1: oe \(2n + 9n^2\) or \(n(9n + 2)\) or \(n(2 + 9n)\)
| Scheme | Marks |
|---|---|
eg \(2x + 5 = 12 - 3x\) or \(\dfrac{2}{3}x + \dfrac{5}{3} = 4 - x\) oe | M1 |
eg \(2x + 3x = 12 - 5\) or \(5x = 7\) or \(5 - 12 = -3x - 2x\) or \(-7 = -5x\) or \(\dfrac{2}{3}x + x = 4 - \dfrac{5}{3}\) oe or \(\dfrac{5}{3}x = \dfrac{7}{3}\) oe | M1 |
Working required Answer: \(\dfrac{7}{5}\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: for removal of fraction and multiplying out RHS correctly by 3
or
separating fraction (LHS) in an equation
M1: ft (dep on 4 terms) correctly rearranging their 4 term equation for terms in \(x\) on one side of equation and number terms on the other
A1: oe eg 1.4 or \(1\dfrac{2}{5}\) dep on M2