Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 6x − (2x − 5)?

2.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

3.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

4.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

5.A point lies on the y-axis. What can be said about the x-coordinate of that point?

6.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

7.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

8.Which of these is a factor of 15x + 20?

9.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

10.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.

11.Solve the inequality 2(x − 1) ≤ 8.

12.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

13.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

14.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

15.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.