Algebra worksheet — GCSE Foundation

1.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.

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

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

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

5.Which expression is equivalent to 2(x + 6)?

6.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

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

8.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

9.Solve x² = 49.

10.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

11.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

12.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

13.A vertical line passes through the point (4, 7). Write down the equation of this line.

14.Work out the value of (x − 4)/2 + 3 when x = 10

15.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.