Algebra worksheet — GCSE Foundation

1.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

2.Which of these statements is an equation with exactly one solution?

3.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

4.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

5.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

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.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

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.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

10.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

11.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

12.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

13.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

14.Simplify 2b − 1 + 2b − 4 + 2b

15.a = 2 and b = 5. Work out the value of ab².