Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

2.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

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

4.Write down the gradient of the line with equation y = 7x − 2.

5.A square has sides of length y cm. Write down an expression for the perimeter of the square.

6.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

7.Solve 5x − 9 = 16

8.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

9.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

10.Which expression is equivalent to 4(x − 2) + 10?

11.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

12.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.

13.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

14.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

15.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.