Algebra worksheet — GCSE Foundation

1.a = 3 and b = 5. Work out the value of a²b.

2.Work out the gradient of the straight line with equation 3y = 12 − 6x.

3.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

4.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

5.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

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

7.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

8.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

9.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

10.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

11.Solve x² = 49.

12.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

13.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

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

15.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.