Higher November 2020 Paper 2 Q11
11
(a) Simplify fully \(\left(8e^{15}\right)^{\frac{2}{3}}\) (2)
(b) Express \(\left(\dfrac{y}{2}\right)^{-4}\) in the form \(ay^n\) where \(a\) and \(n\) are integers. (2)
(c) Solve \(\dfrac{4x - 2}{3} - \dfrac{5 - 3x}{4} = 6\)
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| \(4e^{10}\) | B2 |
| (2) |
Notes
B2: (B1 for \(4e^k\) or \(ke^{10}\))
| Scheme | Marks |
|---|---|
A correct first step eg \(\dfrac{y^{-4}}{2^{-4}}\) or \(\left(\dfrac{y^4}{16}\right)^{-1}\) or \(\dfrac{y^{-4}}{0.0625}\) or \(\left(\dfrac{2}{y}\right)^4\) or \(\dfrac{16}{y^4}\) or \(\left(\dfrac{1}{\frac{y}{2}}\right)^4\) or \(\dfrac{1}{\left(\frac{y}{2}\right)^4}\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(16y^{-4}\) | A1 |
| (2) |
Notes
M1: or for \(16y^p\) where \(p \neq -4\)
| Scheme | Marks |
|---|---|
eg \(12 \times \dfrac{4x - 2}{3} - 12 \times \dfrac{5 - 3x}{4} = 12 \times 6\) or eg \(4(4x - 2) - 3(5 - 3x) = 12 \times 6\) or eg \(\dfrac{4(4x - 2)}{12} - \dfrac{3(5 - 3x)}{12}\;(= 6)\) or eg \(\dfrac{4(4x - 2) - 3(5 - 3x)}{12}\;(= 6)\) oe | M1 |
| eg \(16x - 8 - 15 + 9x = 6 \times 12\) | M1 |
| eg \(16x + 9x = 72 + 8 + 15\) | M1 |
| Working required Answer: 3.8 | A1 |
| (4) | |
| (8 marks) |
Notes
M1: for clear intention to multiply all terms by 12 or a multiple of 12
or to express LHS as two fractions over 12 or a multiple of 12 or as a single fraction with a denominator of 12 or a multiple of 12
(if expanded numerator, allow one sign error)
M1: expanding brackets and multiplying both sides by denominator with no more than one sign error
M1: for correct rearrangement of a correct equation with terms in \(x\) isolated
A1: oe, award full marks for a correct answer if at least M1 scored