Algebra worksheet — GCSE Foundation

1.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

2.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.

3.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

4.a = 2 and b = 5. Work out the value of a²b.

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

6.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

7.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.

8.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

9.Solve x − 4 = −9

10.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

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

12.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.

13.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

14.Which expression means the same as 3 × a × b?

15.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.