Algebra worksheet — GCSE Foundation

1.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

2.Factorise fully 56x − 24

3.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

4.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

5.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

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

7.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

8.In which quadrant does the point (−3, 0.5) lie?

9.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

10.Solve x/4 + 1 = 3

11.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

12.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

13.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

14.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

15.a = 3 and b = 5. Work out the value of a²b.