Algebra worksheet — GCSE Foundation

1.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

2.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.

3.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

4.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.

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

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

7.Which of these is an equation, rather than an expression, a formula or an identity?

8.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

9.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

10.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

11.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

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

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

14.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

15.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.