4MA0 Higher June 2016 Paper 4 Q15
15
(a) Write \(\dfrac{x + 3}{5} + \dfrac{x - 2}{3}\) as a single fraction in its simplest form. (3)
(b) Simplify \((8a^9e^6)^{\frac{1}{3}}\) (2)
(c) Solve \(\dfrac{2}{3}y + \dfrac{3}{8}y = 5\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
| Scheme | Marks |
|---|---|
| Eg \(\dfrac{3(x + 3)}{3 \times 5} + \dfrac{5(x - 2)}{3 \times 5}\) or \(\dfrac{3(x + 3) + 5(x - 2)}{3 \times 5}\) oe | M1 |
| Eg \(\dfrac{3x + 9 + 5x - 10}{3 \times 5}\) or \(\dfrac{3x + 9}{3 \times 5} + \dfrac{5x - 10}{3 \times 5}\) oe | M1 |
| \(\dfrac{8x - 1}{15}\) | A1 |
| (3) |
Notes
M1: For a common denominator as part of 1 or 2 fractions (must be a correct expression)
M1: For a correct expansion of brackets as part of 1 or 2 fractions (must be a correct expression)
A1: cao
Do not ISW
| Scheme | Marks |
|---|---|
| M1 | |
| \(2a^3e^2\) | A1 |
| (2) |
Notes
M1: For two of 2, \(a^3\), \(e^2\) in a product with three terms
A1: Do not ISW
| Scheme | Marks |
|---|---|
Eg \(\dfrac{16 + 9}{24}y\) (= 5) or \(\dfrac{16}{24}y + \dfrac{9}{24}y\) (= 5) or \(\dfrac{25}{24}y\) (= 5) or \(y\left(\dfrac{2}{3} + \dfrac{3}{8}\right)\) (= 5) or \(y(0.\dot{6} + 0.375)\) (= 5) or \(1.041\dot{6}y\) (= 5) or \(24 \times \dfrac{2}{3}y + 24 \times \dfrac{3}{8}y = 24 \times 5\) | M1 |
Eg \(25y = 5 \times 24\) or \(25y = 120\) or \(y = 5 \div 1\dfrac{1}{24}\) or \(y = \dfrac{5}{1.041\dot{6}}\) or \(y = \dfrac{5}{\frac{2}{3} + \frac{3}{8}}\) | M1 |
| 4.8 | A1oe |
| (3) |
Notes
M1: For simplifying the LHS or multiplying both sides by 24
M1: Dep on 1st M1 gained
For the removal of the denominator(s) as part of a correct equation or for correctly isolating \(y\)
A1oe: Dep on 1st M1 gained.
ScM2 for \(16y + 9y = 120\)
M0A0 for trial and improvement
NB: Decimals must be exact to gain any credit:
Eg Award M0 for \(y(0.667 + 0.375)\)