Algebra worksheet — GCSE Foundation

1.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

2.Work out the value of 2(x + 2) when x = −5

3.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

4.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

5.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

6.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.

7.A number machine adds 6 to its input. Work out the output when the input is −4.

8.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

9.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

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

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

12.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

13.Make c the subject of the formula k = 6c.

14.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

15.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?