Algebra worksheet — GCSE Foundation

1.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.

2.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.

3.Solve 2x + 7 = x + 13

4.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

5.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

6.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

7.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

8.Make x the subject of the formula y = x + 7.

9.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

10.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

11.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

12.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).

13.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

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

15.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?