Stage 8 - Q1 - 2 marks
Factorise fully.
Hint
Identify the common numerical and variable factors, then divide every term by them.
Stage 8 - Q2 - 2 marks
Factorise fully.
Hint
Identify the common numerical and variable factors, then divide every term by them.
Stage 8 - Q3 - 3 marks
Factorise fully.
Hint
Identify the common numerical and variable factors, then divide every term by them.
Stage 8 - Q4 - 3 marks
Factorise fully.
Hint
Identify the common numerical and variable factors, then divide every term by them.
Stage 8 - Q5 - 4 marks
A rectangle has area \(11x+22\) square units and width 11 units. Find its length as an expression.
Hint
Identify the common numerical and variable factors, then divide every term by them.
Stage 8 - Q6 - 4 marks
A rectangle has area \(77x+88\) square units and width 11 units. Find its length as an expression.
Hint
Identify the common numerical and variable factors, then divide every term by them.
Stage 8 - Q7 - 5 marks
A pupil writes \(18x^{2}-24x=3x(6x-8)\). Explain why this is correct but incomplete, and factorise fully.
Hint
Check whether the terms remaining inside have a common factor.
Stage 8 - Q8 - 5 marks
Show that \(15n^{2}+10n\) is always divisible by 5 for an integer n. Is it always divisible by 10? Justify.
Hint
Use factorisation for the universal claim and one counterexample for the stronger claim.
Stage 8 - Q9 - 5 marks
Find the integer k so that \(12x^{2}+kx\) has highest common factor \(6x\) and the remaining bracket is \(2x+5\).
Hint
Work backwards by expanding the intended factors.
Stage 8 - Q10 - 5 marks
The expression \(6n^{2}+9n\) is divisible by 9 for some positive integers n. Find a rule describing exactly which n work, and justify it.
Hint
Factor out \(3n\) and ask when one further factor of 3 is available.