Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

2.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

3.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.

4.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

5.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

6.Work out the value of 2x² when x = −3

7.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

8.Which of these is an equation, rather than an expression, a formula or an identity?

9.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

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

11.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

12.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

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

14.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

15.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.