4MA0 Higher January 2017 Paper 3 Q5
5
(a) Factorise \(\;7h + h^2\) (1)
(b) Expand and simplify \(\;4(p + 5) + 7(p - 2)\) (2)
\(D = 7c^2 + f\)
(c) Work out the value of \(D\) when \(c = -2\) and \(f = 5\) (2)
(d) Solve \(\;5(q - 3) = 12 - q\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(e) Solve the inequality \(\;3 - 7t \geqslant 31\) (2)
| Scheme | Marks |
|---|---|
| \(h(7 + h)\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(4p + 20 + 7p - 14\) | M1 |
| \(11p + 6\) | A1 |
| (2) |
Notes
M1: Any 3 terms correct
A1: cao
NB \(11p + 6\) followed by, for example, \(17p\) scores M1 A0
| Scheme | Marks |
|---|---|
| \(7 \times (-2)^2 + 5\) or \(7 \times 4 + 5\) or \(7(-2)^2 + 5\) | M1 |
| 33 | A1 |
| (2) |
Notes
M1: for correct substitution
or 7 × 4 or 28
| Scheme | Marks |
|---|---|
\(5q - 15\) (\(= 12 - q\)) or \(q - 3 = \dfrac{12}{5} - \dfrac{q}{5}\) | M1 |
| E.g. \(5q + q = 12 + 15\) or \(6q = 27\) | M1 |
| 4.5 | A1 |
| (3) |
Notes
M1: For a correct equation with the \(q\) terms collected on one side of the equation and the non \(q\) terms on the other side.
ft from \(5q - 3 = 12 - q\) for this mark only
A1: for 4.5 or \(\dfrac{9}{2}\) oe dep on at least M1
| Scheme | Marks |
|---|---|
| \(-7t \geqslant 31 - 3\) or \(7t \leqslant 3 - 31\) oe | M1 |
| \(t \leqslant -4\) | A1 |
| (2) | |
| (10 marks) |
Notes
M1: \(-7t \geqslant 31 - 3\) or \(7t \leqslant 3 - 31\) or – 4 or \(t \geqslant -4\)
accept an equation or the wrong inequality sign in the working
A1: or for \(-4 \geqslant t\)