Algebra worksheet — GCSE Higher

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

2.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

3.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

4.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.

5.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

6.Solve the inequality x² + 6x + 9 > 0.

7.f(x) = x³ − 5x − 6. Given that f(2.6) = −1.424 and f(2.7) = 0.183, work out what this shows about the equation x³ − 5x − 6 = 0.

8.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

9.Which of these is a formula, rather than an expression, an equation, or an identity?

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

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

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

13.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

14.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

15.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.