Algebra worksheet — GCSE Foundation

1.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

2.Which of these quadratic graphs does NOT cross the x-axis at all?

3.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

4.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

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

6.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

8.Simplify 2b − 1 + 2b − 4 + 2b

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

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

11.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

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

13.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.

14.Make x the subject of the formula y = 4x − 3.

15.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.