Foundation January 2019 Paper 1 Q13
13
(a) Expand and simplify \(\;(e + 3)(e - 5)\) (2)
(b) Solve \(\;y = \dfrac{2y + 1}{5}\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(c) Solve \(\;x^2 + 3x - 18 = 0\)
Show your working clearly. (3)
Show your working clearly. (3)
| Scheme | Marks |
|---|---|
| \(e^2 + 3e - 5e - 15\) | M1 |
| \(e^2 - 2e - 15\) | A1 |
| (2) |
Notes
M1: for 3 correct terms or
for 4 correct terms ignoring signs or
\(e^2 - 2e + k\) for non-zero \(k\)
or \(\ldots - 2e - 15\)
| Scheme | Marks |
|---|---|
| \(5y = 2y + 1\) or \(y = \dfrac{2y}{5} + \dfrac{1}{5}\) | M1 |
E.g. \(5y - 2y = 1\) or \(3y = 1\) or \(3y - 1 = 0\) or \(\dfrac{3y}{5} = \dfrac{1}{5}\) | M1 |
| \(\dfrac{1}{3}\) oe | A1 |
| (3) |
Notes
M1: for a correct first step
M1: for collecting terms in \(y\) in a correct equation
A1: dep on at least M1 for \(\dfrac{1}{3}\) oe
e.g. \(0.\dot{3}\), 0.3333…
This part is excluded from the general rule that a correct answer, unless clearly obtained by an incorrect method, implies a correct method.
| Scheme | Marks |
|---|---|
| \((x + 6)(x - 3)\ (= 0)\) or \(x(x + 6) - 3(x + 6)\ (= 0)\) or \(x(x - 3) + 6(x - 3)\ (= 0)\) | M1 |
| \((x + 6)(x - 3)\ (= 0)\) or for \(x + 6 = 0\) oe and \(x - 3 = 0\) oe | A1 |
| \(x = -6\), \(x = 3\) | B1 |
| (3) | |
| (8 marks) |
Notes
M1: for \((x \pm 6)(x \pm 3)\ (= 0)\) or for \((x + a)(x + b)\) with \(ab = -18\) or \(a + b = 3\)
A1: for correct factors
B1: ft
dep on at least M1
This part is excluded from the general rule that a correct answer, unless clearly obtained by an incorrect method, implies a correct method.