Foundation January 2022 Paper 2 Q16
16
(a) Expand and simplify \(\quad x(2x - 3) + 7(2x + 1) - 5\) (3)
(b) Expand and simplify \(\quad (y + 4)(2 - y)\) (2)
(c) Factorise fully \(\quad 15b^5c - 35b^3c^9\) (2)
| Scheme | Marks |
|---|---|
| \(2x^2 - 3x + 14x + 7 \quad (-5)\) | M1 |
| M1 | |
| \(2x^2 + 11x + 2\) | A1 |
| (3) |
Notes
M1: for at least 3 correct terms for the multiplying of the 2 brackets
M1: 2 of the 3 correct terms in an expression in the form \(ax^2 + bx + c\) where \(a\), \(b\) and \(c\) are integers
A1: can be any order
| Scheme | Marks |
|---|---|
| \(2y - 4y + 8 - y^2\) | M1 |
| \(8 - 2y - y^2\) | A1 |
| (2) |
Notes
M1: for 3 correct terms or
for 4 correct terms ignoring signs or
\(\ldots - 2y - y^2\) or
\(8 - 2y - \ldots\)
A1: Any order but simplified.
| Scheme | Marks |
|---|---|
| \(5b^3c(3b^2 - 7c^8)\) | B2 |
| (2) | |
| (7 marks) |
Notes
B2: fully correct or
B1 for a correct partial factorisation with at least two terms outside the bracket eg \(5b^3(3b^2c - 7c^9)\) or \(5c\,(3b^5 - 7b^3c^8)\) etc
or the fully correct factor outside the bracket with a two term expression in terms of \(b\) and \(c\) inside the bracket eg \(5b^3c(15b^2 - c^8)\)