Algebra worksheet — GCSE Foundation

1.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

2.Solve the inequality 9 − 2x ≥ 1.

3.Make a the subject of the formula b = 20 − a.

4.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

5.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

6.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

7.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

8.Solve x² = 49.

9.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

10.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

11.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

12.x = 5. Work out the value of 3x² − 4.

13.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

14.Work out the value of 3a − 2b when a = 5 and b = 4

15.Work out the value of a² − 2b when a = −3 and b = 4.