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.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

3.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

4.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

5.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

6.Solve the inequality 5 − x ≤ 2.

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

8.Which expression is equivalent to 3(2x − 5) + 4x?

9.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

10.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

11.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

13.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.

14.Solve (2x + 1)/3 = 5

15.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.