Algebra worksheet — GCSE Foundation

1.Which expression means 'triple c, then add double d'?

2.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

3.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

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

5.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

6.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.

7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

8.In which quadrant does the point (−3, 0.5) lie?

9.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

10.Which of these is a formula?

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

12.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

13.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.

14.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

15.Which of these is an identity?