Higher November 2024 Paper 1 Q8
8
(a)
(i) Factorise \(x^2 + 5x - 24\) (2)
(ii) Hence, solve \(x^2 + 5x - 24 = 0\) (1)
(b) Solve the inequality \(3y + 5 \gt 7y - 10\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
| (i) \((x \pm 8)(x \pm 3)\) or \(x(x - 3) + 8(x - 3)\) or \(x(x + 8) - 3(x + 8)\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \((x + 8)(x - 3)\) | A1 |
| (2) | |
| (ii) Answer: –8 and 3 | B1 |
| (1) |
Notes
M1: for \((x \pm 8)(x \pm 3)\) or
\((x + a)(x + b)\) where \(ab = -24\) or
\(a + b = 5\) and, \(a\) and \(b\) are integers
A1: for \((x + 8)(x - 3)\)
Allow any letter for \(x\)
Must be in the form \((x + a)(x + b)\) where \(a\) and \(b\) are integers
B1: must ft from their answer in (a)(i)
ft from their incorrect factors in the form \((x + a)(x + b)\)
Award B0 for –8 and 3 if no marks scored in (a)(i)
| Scheme | Marks |
|---|---|
| \(3y - 7y \gt -10 - 5\) or \(5 + 10 \gt 7y - 3y\) | M1 |
| \(-4y \gt -15\) or \(15 \gt 4y\) or \(y = \dfrac{15}{4}\) oe or | M1 |
Working required Answer: \(y \lt \dfrac{15}{4}\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: allow use of = or condone incorrect inequality sign
M1: allow use of = or condone incorrect inequality sign
A1: dep on M1
oe eg \(y \lt 3.75\) or \(\dfrac{15}{4} \gt y\) or \(3.75 \gt y\)
Must have correct sign on answer line
NB Sight of correct answer in working space and just \((y =)\;\dfrac{15}{4}\) oe on answer line gains M2 only