Algebra worksheet — GCSE Foundation

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

2.Solve 6x − 5 = 3x + 13.

3.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

4.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

5.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

6.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

7.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

8.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

9.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

10.Which of these is a formula?

11.Expand 2(x − 13)

12.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

13.Solve 7x − 5 = 3x + 11

14.Work out the value of 3b − 4 when b = 6

15.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.