Algebra worksheet — GCSE Foundation

1.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

2.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

3.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

4.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

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

6.Which expression means 'add 3 to n, then multiply the result by 4'?

7.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

8.Simplify 5x + 3y − 2x + y.

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

10.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.

11.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

12.Solve the inequality x − 10 < −3.

13.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

14.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

15.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.