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.A square tile has an area of 144 cm². Work out the side length of the tile.

3.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

4.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

5.Solve 3(2x − 1) = 27

6.Which of these values of x is a solution of x² + 2x − 15 = 0?

7.Work out the value of 3b − 4 when b = 6

8.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

9.Which of these is an equation, rather than an expression, a formula or an identity?

10.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

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

12.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

13.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

14.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

15.The point B has coordinates (−2, −2). In which quadrant is B?