Algebra worksheet — GCSE Foundation

1.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.

2.Write down the gradient of the line with equation y = −x + 3.

3.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

4.Expand and simplify 2(a + 6) − 2(a − 7)

5.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

6.Write down the expression that means 5 more than half of n.

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

8.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

9.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

10.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

11.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

12.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

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

14.Work out the value of 5y + 9 when y = 0

15.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.