Algebra worksheet — GCSE Foundation

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

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

3.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

4.Which expression means the same as 3 × a × b?

5.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

6.Solve 3x − 1 = 8

7.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

9.Which expression is equivalent to 3(2x − 5) + 4x?

10.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.

11.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

12.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

13.Solve 2x + 7 = x + 13

14.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

15.Which expression is equivalent to 4(x − 2) + 10?