Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

2.Which expression is equivalent to 0.5(4x + 6) − x?

3.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

4.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

5.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

6.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.

7.y = x + 4. Work out the value of y when x = 3.

8.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

9.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

10.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

11.Write down the expression that means the same as (x + 7) ÷ 4.

12.Which of these values of x is a solution of x² + 2x − 15 = 0?

13.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.

14.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

15.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.