1. A-level exam technique
Key command words
Exact: Indicates that answers should not be rounded (e.g. 𝜋 rather than ). Analytic working is required rather than direct calculation, though note Casio scientific calculators often give exact answers.
Hence: Indicates that the previous part of the question should be used. (Hence or otherwise is also a big hint that the previous part of the question is useful)
Find, Solve, Calculate: Working may be necessary to answer the question but no justification required. A solution could be obtained by efficient use of a calculator.
Give, State, Write down: Neither working nor justification is required.

2. Prove, Show that, Verify, Determine, Detailed Reasoning
Each of the above indicate that working and justification are required.
Prove: requires a high level of mathematical detail, clearly defining variables and always giving a concise conclusion.
Show that: Explanation has to be sufficiently detailed to cover every step of the working, including the conclusion.
Verify: A little less than above, uses a clear substitution of a given value to justify the statement.
Determine: Justification should be given for any results, including working where appropriate. Steps may involve using a calculator to find numerical solutions.
“In this question you must show detailed reasoning”: A full solution that leads to a conclusion, showing a detailed and complete analytical method. Note, this command word means you cannot use GDC as a method step (though it might still be useful for checking your answer).

3. Answer the following questions according to the command words
Verify that 𝑒 4 is a root of ln 𝑥 4 =12 ln 𝑥 (3)
Find the roots of ln 𝑥 4 =12 ln 𝑥 (3)
Find the exact roots of ln 𝑥 4 =12 ln 𝑥 (5)
In this question you must show detailed reasoning Find all roots of ln 𝑥 4 =12 ln 𝑥 (6)

4. You can do this!
Clear mathematical working. Careful use of notation.
Some “free” marks using common sense. Otherwise lots of practice!

5. Integration Solve each of the following integrals:
𝑥+1 𝑥+2 𝑑𝑥 𝑥 𝑒 𝑥 2 𝑑𝑥 𝑥 3 ln 𝑥 𝑑𝑥 𝑒 4𝑥 1−𝑒 2𝑥 𝑑𝑥

6. Bonus problems