Algebra worksheet — GCSE Foundation

1.y = 5x − 1. Work out the value of y when x = 3.

2.Solve x² − 100 = 0.

3.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.

4.Which of these is a term, rather than a whole expression, an equation, or a formula?

5.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

6.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.

7.Write down the gradient of the line with equation y = 7x − 2.

8.Work out the value of 4p² − 3 when p = 2.5

9.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.

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

11.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

12.Work out the value of 3n − 2 when n = 1

13.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

14.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

15.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).