4MA0 Higher January 2016 Paper 4 Q9
9
(a) Expand \(x(x + 2)\) (1)
(b) Solve the inequality \(4x - 7 \gt 3\) (2)
(c) Solve \(\dfrac{3 - 5m}{4} = 8\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
| \(x^2 + 2x\) | B1 |
| (1) |
Notes
B1: \(2x + x^2\) or \(x2 + x^2\)
| Scheme | Marks |
|---|---|
| \(4x \gt 3 + 7\) or \(4x \gt 10\) | M1 |
| \(x \gt 2.5\) | A1 |
| (2) |
Notes
M1: for \(4x \gt 3 + 7\) or \(4x \gt 10\) or
\(4x = 3 + 7\) or \(4x = 10\) or \(x = 2.5\) or
\(x \lt 2.5\) or an answer of 2.5 following \(x \gt 2.5\) in working
A1: allow \(x \gt \dfrac{10}{4}\) oe
must have correct inequality sign
| Scheme | Marks |
|---|---|
| \(3 - 5m = 8 \times 4\) or \(3 - 5m = 32\) or \(32 + 5m = 3\) | M1 |
| \(-5m\) = ‘32’ – 3 or 3 – ‘32’ = \(5m\) \(-5m = 29\) or \(-29 = 5m\) | M1 |
| −5.8 | A1 |
| (3) |
Notes
M1: Multiplying both sides by 4 as a correct first step
M1: for isolating \(5m\) or \(-5m\) in a correct equation
A1: oe eg \(\dfrac{-29}{5}\) dependent on at least M1
Alternative for (c)
| Scheme | Marks |
|---|---|
| \(\dfrac{-5m}{4} = 8 - \dfrac{3}{4}\) or \(\dfrac{5m}{4} = \dfrac{3}{4} - 8\) | M1 |
| \(-5m = \left(8 - \dfrac{3}{4}\right) \times 4\) or \(5m = \left(\dfrac{3}{4} - 8\right) \times 4\) | M1 |
| −5.8 | A1 |
Notes
M1: For using quarters (or a multiple of 4) and isolating the term in \(m\) in a correct equation
M1: For isolating \(5m\) or \(-5m\) in a correct equation.
A1: oe eg \(\dfrac{-29}{5}\) dependent on at least M1