Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 5x − (x + 3)?

2.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

3.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

4.Expand 2(x + 12)

5.A square tile has an area of 144 cm². Work out the side length of the tile.

6.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.

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

8.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

9.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

10.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.

11.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

12.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

13.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

14.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

15.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.