Algebra worksheet — GCSE Foundation

1.Expand and simplify 2(a + 6) − 2(a − 7)

2.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

3.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

4.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

5.Which of these rules generates the sequence 6, 11, 16, 21, …?

6.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.

7.Simplify 5x + 3y − 2x + y.

8.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

9.Simplify x + x + 4

10.Which of these is an expression?

11.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

12.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

13.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

14.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

15.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.