Algebra worksheet — GCSE Foundation

1.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

2.Which of these is a formula?

3.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

4.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

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

6.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

7.Expand and simplify 2(a + 6) − 2(a − 7)

8.Which expression means 'triple c, then add double d'?

9.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

10.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.

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

12.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

13.Solve 4x + 3 = 19

14.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

15.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.