Algebra worksheet — GCSE Foundation

1.Which of these points lies in the first quadrant?

2.Solve x² = 81.

3.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

4.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

7.Work out the value of 2x² when x = −3

8.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

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

10.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

11.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

12.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

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

14.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

15.Solve 6x + 4 = 28