Chapter 8: Review

Resolve the chapter problem

The outer area is $(x+6)(x+4)=x^2+10x+24$. The opening area is $x(x+2)=x^2+2x$.

Subtract the opening area from the outer area: $x^2+10x+24-(x^2+2x)=8x+24$ square centimetres. For $x=5$, the frame area is $8(5)+24=64$ square centimetres.

The expression can also be factorised as $8(x+3)$, which provides a check by expansion.

Mixed practice

For each question, choose a method and explain why it applies. Check by reversing the operation when possible.

1. Simplify $4a+3-2a+6$.
2. Expand $3(2x-5)$.
3. Factorise $12y+18$.
4. Find $2n^2+1$ when $n=-3$.
5. Make $t$ the subject of $v=u+at$.
6. Higher only: expand $(x-1)(x+2)(x+4)$.
7. Estimate then calculate the value of $8x+24$ when $x=5$.

Reflect

Write one algebraic skill you can now use with more confidence. Name one question you would like to practise again.