Algebra worksheet — GCSE Foundation

1.y = 5 − 2x. Work out the value of x when y = 11.

2.Which of these is an expression?

3.Simplify (5x² + 3x − 2) − (2x² − x + 5)

4.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

5.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

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

7.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

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

9.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

10.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.

11.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

12.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

13.Factorise x² − 64.

14.Which expression means 'y squared, multiplied by 3'?

15.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.