Algebra worksheet — GCSE Foundation

1.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

2.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

3.Which of these equations is equivalent to 5x − 2 = 3x + 8?

4.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

5.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

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

7.Solve 2x − 2 = 2

8.Solve 4x² − 9 = 0.

9.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

10.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

11.Which expression means the same as 3 × a × b?

12.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

13.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.

14.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

15.Make x the subject of the formula y = 3(x + 2).