Algebra worksheet — GCSE Foundation

1.Which of these is a factor of 15x + 20?

2.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

3.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

4.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

5.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

6.Write down the coefficient of p in the expression 7 − 4p + 9q.

7.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

8.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.

9.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

10.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.

11.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

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

13.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

14.Solve 2x² = 18.

15.Expand 2(x − 13)