Algebra worksheet — GCSE Foundation

1.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

2.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.

3.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

4.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

5.A number machine adds 5 to its input. Work out the output when the input is 0.

6.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

7.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

8.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

9.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

10.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

11.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

12.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

13.Simplify 2b − 1 + 2b − 4 + 2b

14.The point B has coordinates (−2, −2). In which quadrant is B?

15.Which of these equations describes a vertical line?