Algebra worksheet — GCSE Foundation

1.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

2.Work out the coordinates of the reflection of (6, −3) in the y-axis.

3.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.

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

5.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.

6.Write down the expression that means the same as p + p + p + q.

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

8.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

9.Which of these is an inequality?

10.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

11.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

12.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

13.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

14.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

15.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.