Algebraic notation, expanding and factorising – Year 10 GCSE maths test to download as PDF

Non-calculator. Given \(p=4\) and \(q=-3\).

1. Work out \(3p-2q\). (2 marks)
2. Simplify \(5x^2+3x-2x^2+4x\). (2 marks)

Calculator allowed.

1. Expand and simplify \((x+7)(x-3)\). (2 marks)
2. Factorise \(x^2-8x+15\). (1 mark)
3. Factorise fully \(6x^2y-9xy^2\). (1 mark)

A rectangular field has length \((3x+2)\) m and width \((x+4)\) m. A farmer puts a fence round the field.

1. Show that the perimeter is \(8x+12\) metres. (2 marks)
2. The fence costs £5 per metre and the perimeter is 52 m. Find \(x\) and the total cost of the fence. (2 marks)

Show that \((2n+3)^2-(2n-3)^2\) is a multiple of 8 for every whole number \(n\). (4 marks)

Higher tier.

1. Factorise \(2x^2-5x-12\). (2 marks)
2. Hence solve \(2x^2-5x-12=0\). (1 mark)
3. Simplify \(\dfrac{x^2-16}{x^2+x-12}\). (1 mark)