Algebra worksheet — GCSE Foundation

1.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.

2.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

3.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

4.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

5.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

6.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

7.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

8.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

9.Solve the inequality 4x + 1 > 2x + 9.

10.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

11.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

12.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

13.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

14.Make m the subject of the formula w = m − 8.

15.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.