Algebra worksheet — GCSE Foundation

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

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

3.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

4.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.

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

6.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.

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

8.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

9.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

10.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

11.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

12.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

13.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

14.Expand 2(x + 12)

15.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.