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.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

3.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

4.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

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

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

8.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.

9.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

10.A point lies on the y-axis. What can be said about the x-coordinate of that point?

11.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

12.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

13.Make x the subject of the formula y = (x − 4)/5.

14.Solve the inequality 3x + 6 ≤ 0.

15.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.