Algebra worksheet — GCSE Higher

1.A garden path runs along the line 4x + y = 12. A drainage pipe must be laid perpendicular to the path, passing through the point (3, 1) where a sprinkler sits. Work out the equation of the pipe's line, giving your answer in the form y = mx + c.

2.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

3.Simplify 5a/6 − a/3

4.A proof that the product of two consecutive even numbers is always a multiple of 8 begins: Let the two consecutive even numbers be 2n and 2n + 2, so their product is 2n(2n + 2) = 4n(n + 1). Which line correctly completes the proof?

5.Solve 3x + 14 = 8x − 6

6.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

7.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

8.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).

9.Work out the value of n² − n when n = −3

10.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

11.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

12.Factorise x² − 64.

13.Solve 2x² = 18.

14.Factorise 6x² − 7x − 3.

15.Which of these statements is an identity?