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.A square has sides of length y cm. Write down an expression for the perimeter of the square.

3.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

4.Which expression means 'triple c, then add double d'?

5.Which of these statements is an equation with exactly one solution?

6.Solve 6x − 5 = 3x + 13.

7.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

8.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

9.Solve 7x − 5 = 3x + 11

10.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

11.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

12.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

13.Simplify 5x + 3y − 2x + y.

14.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

15.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.