Algebra worksheet — GCSE Foundation

1.The diagram shows the graph of a function. Which equation could it represent?

2.Write down the gradient of the line with equation y = 6 + 4x.

3.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

4.Write down the expression that means the same as p + p + p + q.

5.Factorise fully 56x − 24

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

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

8.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

9.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.

10.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.

11.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

12.Work out the distance of the point (−6, 4) from the x-axis.

13.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

14.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

15.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.