Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

2.Work out the value of 3a − 2b when a = 5 and b = 4

3.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

4.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

5.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

6.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

7.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

8.How many turning points does the graph of y = x² − 7x + 10 have?

9.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

10.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

11.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

12.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

13.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.

14.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

15.Which of these points lies in the first quadrant?