Algebra worksheet — GCSE Foundation

1.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

2.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?

3.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

5.Solve the inequality 2(3x − 1) ≥ 4x + 8.

6.Which of these is an inequality?

7.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

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 is an equation, rather than an expression, a formula or an identity?

10.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

11.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?

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

13.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

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

15.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.