Algebra worksheet — GCSE Foundation

1.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

2.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.

3.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

4.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

5.Write down the expression that means the same as 3 × y × y.

6.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

7.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

8.Solve 6x − 5 = 3x + 13.

9.Which expression is equivalent to 3(2x − 5) + 4x?

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

11.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

12.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

13.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

14.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

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