Algebra worksheet — GCSE Foundation

1.Write down the first four terms of the sequence with nth term 6n − 5.

2.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

3.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

4.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

5.Expand 4(2x − 3).

6.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

7.Two expressions are 4(x + 3) and 4x + 3. A student checks whether they are equivalent by substituting x = 2. Which statement correctly interprets the result?

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

9.Solve x² − 2x − 24 = 0.

10.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

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

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

13.Write down the expression that means the same as m × m × m × n.

14.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

15.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.