Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

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

3.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

4.Write down 0.2x with its coefficient written as a fraction in its simplest form.

5.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.

6.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

7.Write down the expression that means the same as w ÷ 6.

8.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

9.Solve x² = 49.

10.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

11.A vertical line passes through the point (4, 7). Write down the equation of this line.

12.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

13.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

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

15.Which expression is equivalent to 7x − 3(2x − 6)?