Algebra worksheet — GCSE Foundation

1.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

2.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

3.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

4.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.

5.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.

6.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

7.Write down the gradient of the line with equation y = 6 + 4x.

8.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.

9.Simplify 2a + 3b − a + 2b − b

10.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

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

12.Work out the gradient of the straight line with equation 2x + y = 8.

13.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

14.Solve x² = 81.

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.