Higher June 2022 Paper 6 Q4
4 You are given that
\[\frac{10a^k \times a^8}{ma^5} = \frac{2a^7}{5}\]where \(k\) and \(m\) are integers.
Find the value of \(k\) and the value of \(m\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 4 and 25 nfww | 4 | B3 for \(\dfrac{10a^4 \times a^8}{25a^5} = \dfrac{2a^7}{5}\) | Otherwise, condone embedded answers for M marks only |
| OR B2 for \(k = 4\) or M1 for any correct simplification of \(\dfrac{a^k \times a^8}{a^5} = a^7\) eg \([a^k \times]\ a^3\ [= a^7]\) or \([a^k \times a^8 =]\ a^{12}\), \(a^k = a^4\), \(\dfrac{a^{k+8}}{[a^5]}\ [= a^7]\), \(k + 8 - 5 = 7\) oe | M1 applying correctly a law of indices, may be seen within an attempt to simplify with other coefficients | ||
| AND B2 for \(m = 25\) or M1 for \(\dfrac{10}{m} = \dfrac{2}{5}\) oe | Allow \([m =]\ 10 \times 5 \div 2\) | ||