Algebra worksheet — GCSE Foundation

1.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

2.Solve 2x − 2 = 2

3.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

4.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

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

6.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

7.The point B has coordinates (−2, −2). In which quadrant is B?

8.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

9.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

10.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

11.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

12.Which of these rules generates the sequence 6, 11, 16, 21, …?

13.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

14.Factorise fully 12x² + 18x.

15.Which expression is equivalent to 2(x + 6)?