Algebra worksheet — GCSE Foundation

1.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

2.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

3.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

4.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

5.In which quadrant does the point (−3, 0.5) lie?

6.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

7.Expand 7(a + 8)

8.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

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

10.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

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

12.Which of these equations describes a vertical line?

13.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.

14.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

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