Algebra worksheet — GCSE Foundation

1.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

2.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

3.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

4.Solve 3x − 5 = 4.

5.Solve 6x − 5 = 3x + 13.

6.Write down the expression that means the same as w ÷ 6.

7.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

8.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.

9.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

10.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

11.Solve 4x² − 9 = 0.

12.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

13.Work out the value of 3a − 2b when a = 5 and b = 4

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

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