4MA0 Higher January 2015 Paper 4 Q12
12
(a) Factorise \(c^2 - 5c\) (2)
(b) Simplify \(d^5 \times d^7\) (1)
(c) Factorise \(x^2 + x - 30\) (2)
(d) Make \(b\) the subject of \(P = \dfrac{1}{2}ab^2\) (2)
(e) Solve \(\dfrac{2x + 1}{3} + \dfrac{x - 5}{2} = 4\)
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| \(c(c - 5)\) | B2 |
| (2) |
Notes
B2: Award B2 also for \((c \pm 0)(c - 5)\) or \(c \times (c - 5)\)
B1 for factors which, when expanded and simplified, give two terms, one of which is correct
| Scheme | Marks |
|---|---|
| \(d^{12}\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \((x + 6)(x - 5)\) | B2 |
| (2) |
Notes
B2: B1 for \((x \pm 6)(x \pm 5)\)
| Scheme | Marks |
|---|---|
| \(\dfrac{2P}{a} = b^2\) | M1 |
| \(b = \sqrt{\dfrac{2P}{a}}\) | A1 |
| (2) |
Notes
M1: oe with \(b^2\) as the subject
A1: oe with \(b\) as the subject or \(b = \pm\sqrt{\dfrac{2P}{a}}\)
| Scheme | Marks |
|---|---|
eg. \(2(2x + 1) + 3(x - 5) = 6 \times 4\) or \(\dfrac{2(2x + 1)}{6} + \dfrac{3(x - 5)}{6} = 4\) | M1 |
eg. \(4x + 2 + 3x - 15 = 24\) or \(\dfrac{4x + 2}{6} + \dfrac{3x - 15}{6} = 4\) | M1 |
| eg. \(4x + 3x = 37\) or \(-4x - 3x = -37\) or \(7x = 37\) or \(-7x = -37\) \(7x = 24 + 15 - 2\) or \(-7x = 2 - 24 - 15\) | M1 |
| \(5\frac{2}{7}\) | A1 |
| (4) | |
| (11 marks) |
Notes
M1: for clear intention to multiply both sides by 6 or by a multiple of 6 or
write both fractions with a common denominator
M1: for correct expansion of brackets in a correct equation
M1: for isolating terms in \(x\) in a correct equation or \(7x - 37 = 0\) or \(37 - 7x = 0\)
A1: oe eg. \(\dfrac{37}{7}\) Award 4 marks if answer is correct and at least one method mark scored
Accept 5.285714… rounded or truncated to 3 or more sig figs