Algebra worksheet — GCSE Foundation

1.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

2.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

3.Make x the subject of the formula y = 4x − 3.

4.Solve 6x + 4 = 28

5.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

6.Write down the expression that means the same as p + p + p + q.

7.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

8.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

9.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

10.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

11.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

12.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

13.Solve 3(2x − 1) = 27

14.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

15.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.