Algebra worksheet — GCSE Foundation

1.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

2.Factorise fully 5x + 5y − 5

3.The point A is at (5, −3). In which quadrant does A lie?

4.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

5.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

6.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.

7.Work out the value of 3b − 4 when b = 6

8.Write down the expression that means the same as m × m × m × n.

9.Which of these is a factor of 15x + 20?

10.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

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.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

13.n = 3. Work out the value of (2n)².

14.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

15.Write down the gradient of the line with equation y = −x + 3.