Higher June 2021 Paper 1 Q5
5
(a) Expand and simplify \(3x(2x + 3) - x(3x + 5)\) (2)
(b) Make \(t\) the subject of the formula \(p = at - d\) (2)
Given that \(\dfrac{w^5 \times w^n}{w^3} = w^{10}\)
(c) work out the value of \(n\). (2)
| Scheme | Marks |
|---|---|
| \(6x^2 + 9x - 3x^2 - 5x\) | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(3x^2 + 4x\) | A1 |
| (2) |
Notes
M1: expansion with at least 3 correct terms (must see for example, \(6x^2\) and not just \(3x \times 2x\))(can assume that no sign in front of a number is a + if terms written in a list or table)
A1: or \(4x + 3x^2\) or \(x(3x + 4)\) or \(x(4 + 3x)\)
| Scheme | Marks |
|---|---|
| eg \(p + d = at\) or \(-at = -d - p\) or \(\dfrac{p}{a} = \dfrac{at}{a} - \dfrac{d}{a}\) oe | M1 |
Working not required, so correct answer scores full marks Answer: \(t = \dfrac{p + d}{a}\) | A1 |
| (2) |
Notes
M1: Correct first stage in rearrangement
A1: oe eg \(t = \dfrac{p}{a} + \dfrac{d}{a}\) or \(t = \dfrac{-d - p}{-a}\)
Must have “\(t =\)” either in working or on answer line
| Scheme | Marks |
|---|---|
\(w^2 \times w^n = w^{10}\) or \(w^5 \times w^n = w^{13}\) or \(w^5 \times w^{n - 3} = w^{10}\) or \(\dfrac{w^{5 + n}}{w^3} = w^{10}\) oe or \(5 + n - 3 = 10\) or \(2 + n = 10\) or \(5 + n = 13\) | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 8 | A1 |
| (2) | |
| (6 marks) |
Notes
M1: A correct first stage simplifying at least one index in a correct equation
or
a clearly correct subsequent stage showing correct use of a rule of indices
eg \(w^5 \times w^n = w^{30}\) and \(w^n = w^{30 - 5}\)
or
a correct equation using indices only
A1: accept \(w^8\)
(trial and error gains full marks if correct and no marks if incorrect unless a rule of indices is clearly shown)