Algebra worksheet — GCSE Foundation

1.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

2.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

3.Solve the inequality 3x − 1 ≤ 11.

4.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

5.Which of these is an expression?

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

7.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.

8.Make x the subject of the formula y = 4(x − 6).

9.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

10.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

11.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

12.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

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

14.x = 5. Work out the value of 3x² − 4.

15.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.