Algebra worksheet — GCSE Foundation

1.Which of these is a formula, rather than an expression, an equation, or an identity?

2.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

3.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

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

5.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

6.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

7.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

8.Which of these equations describes a vertical line?

9.The point A is at (5, −3). In which quadrant does A lie?

10.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

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

12.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.

13.Which of these is a term, rather than a whole expression, an equation, or a formula?

14.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.

15.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.