Algebra worksheet — GCSE Foundation

1.y = x + 4. Work out the value of y when x = 3.

2.Solve 3(2x − 1) = 27

3.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

4.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

5.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.

6.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?

7.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.

8.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

9.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

10.Write down the expression that means the same as (x + 7) ÷ 4.

11.Work out the distance of the point (−6, 4) from the x-axis.

12.A square has sides of length y cm. Write down an expression for the perimeter of the square.

13.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

14.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

15.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.