Higher June 2023 Unit 1 Q3
3.
(a) Simplify each of the following.
Circle your answer in each case.
Circle your answer in each case.
(i) \(m^4 \times m^3 =\) [1]
\(m^7\) \(m^{12}\) \(m^{43}\) \(7m\) \(12m\)
(ii) \(\dfrac{m^{15}}{m^5} =\) [1]
\(m^{75}\) \(\dfrac{1}{m^3}\) \(m^3\) \(m^{10}\) \(\dfrac{1}{m^{10}}\)
(b) Write down an expression for the \(n\)th term of the following sequence. [2]
4, 11, 18, 25, ………
(c) List all of the integers that satisfy the following inequality. [2]\[13 \lt 2n \lt 19\]
Integers are ……………………
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(m^7\) | B1 | |
| (ii) \(m^{10}\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(7n - 3\) | B2 | Mark final answer. B1 for sight of \(7n\). Allow notation of \(n7\) or \(7{\times}n\) or \(n\times 7\) for \(7n\). Allow \(N\) for \(n\), but penalise –1 for use of a different letter. |
| Scheme | Marks | Comments |
|---|---|---|
| 7, 8 and 9 | B2 | Answer line takes precedence. Award B2 for all three integers and no extras. Award B1 for one of the following indicated as a final answer:
|