Algebra worksheet — GCSE Foundation

1.Solve x² − 5x + 6 = 0 by factorising.

2.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

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

4.Solve x/4 + 1 = 3

5.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

6.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.

7.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.

8.A number machine adds 5 to its input. Work out the output when the input is 0.

9.Write down the expression that means 5 more than half of n.

10.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

11.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

12.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

13.Work out the value of 5y + 9 when y = 0

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

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