Higher June 2023 Paper 2 Q5
5.
(a) Solve \(7x - 5 = 2x + 3\). [2]
(b) Roza is buying bananas and apples.
She buys \(x\) bananas which cost 30 pence each.
She buys 2 more apples than the number of bananas she buys.
Her apples cost 25 pence each.
She pays a total of £5.45.
Use an algebraic method to find the number of bananas Roza buys. [4]
She buys \(x\) bananas which cost 30 pence each.
She buys 2 more apples than the number of bananas she buys.
Her apples cost 25 pence each.
She pays a total of £5.45.
Use an algebraic method to find the number of bananas Roza buys. [4]
(c) Factorise \(x^2 + 5x + 4\). [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(5x = 8\) | B1 | |
| \(x = 1.6\) or \(\dfrac{8}{5}\) ISW | B1 | FT from \(ax = 8,\ a \ne 1\) or \(5x = b\) Accept \(\dfrac{8}{a}\) or \(\dfrac{b}{5}\) but if on FT either simplifies to an integer the answer must be given as an integer. ‘\(x\) =’ can be omitted but must not be wrong if there. Correct answer implies first B1. |
| Scheme | Marks | Comments |
|---|---|---|
| (number of apples =) \(x + 2\) si | B1 | Not implied by use of numerical trials Note: do not award B1 for \(x + 2 = 545\) oe |
| \(30x + 25(x + 2) = 545\) oe | M1 | FT ‘their \(x + 2\)’ providing binomial in \(x\); brackets may be omitted |
| \(55x + 50 = 545\) oe | m1 | Expands the brackets and simplifies |
| \(x = 9\) | A1 | CAO (no FT as needs to be an integer answer) If M0A0 award either: SC2 for an answer of 9 if unsupported or from trials. SC1 if 9 only seen in embedded working. |
| Scheme | Marks | Comments |
|---|---|---|
| \((x + 1)(x + 4)\) | B2 | B1 for a pair of brackets that expand to give \(x^2 + 5x \pm a\) OR \(x^2 \pm bx + 4\) |
| (8) |