Algebra worksheet — GCSE Foundation

1.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

2.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

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

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

5.Which of these rules generates the sequence 6, 11, 16, 21, …?

6.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

7.Write down the number of terms in the expression 4x² − 7x + 3.

8.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

9.Work out the value of 5a + 2 when a = 3

10.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.

11.Solve 4(x − 3) = 2x + 6.

12.Work out the value of 3a − 2b when a = 5 and b = 4

13.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.

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

15.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.