Algebra worksheet — GCSE Foundation

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

2.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.

3.Solve 2x + 1 = 9

4.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

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

6.Write down the number of terms in the expression 4x² − 7x + 3.

7.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

8.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

9.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

10.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

11.A number machine multiplies its input by 5. Work out the output when the input is −1.

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

13.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

14.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

15.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.