Algebra worksheet — GCSE Foundation

1.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

2.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

3.Which expression is equivalent to 3(2x − 5) + 4x?

4.Which expression means 'y squared, multiplied by 3'?

5.A square has sides of length y cm. Write down an expression for the perimeter of the square.

6.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

7.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

8.Work out the y-intercept of the graph of y = x² + 3x − 10.

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

10.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

11.Make x the subject of the formula y = x/2 − 5.

12.Solve the inequality 3x + 6 ≤ 0.

13.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

14.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

15.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.