Algebra worksheet — GCSE Foundation

1.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

2.x = 5. Work out the value of 3x² − 4.

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

4.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

5.Factorise fully 5x + 5y − 5

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

7.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

8.p = 4. Work out the value of 2p³.

9.Work out the value of 3n − 2 when n = 1

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

11.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.

12.The point A is at (5, −3). In which quadrant does A lie?

13.Factorise x² − 3x − 10.

14.Make x the subject of the formula y = 2x − 9.

15.Work out the gradient of the straight line with equation 3y = 12 − 6x.