Algebra worksheet — GCSE Foundation

1.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

2.Write down the gradient of the line with equation y = 6 + 4x.

3.Which of these statements is an equation with exactly one solution?

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

5.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

6.Solve x² − 5x + 6 = 0 by factorising.

7.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

8.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

9.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

10.Work out the gradient of the straight line with equation 3y = 12 − 6x.

11.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

12.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

13.Which expression means the same as a × a × a?

14.Write down the first four terms of the sequence with nth term 6n − 5.

15.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.