Algebra worksheet — GCSE Higher

1.Factorise fully 5x + 5y − 5

2.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

3.Solve (3x + 2)/5 = (x + 4)/3

4.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

5.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.

6.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

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

8.A proof sets out to show that the sum of the squares of two consecutive odd numbers, written as 2n + 1 and 2n + 3, is always 2 more than a multiple of 8. Four attempts to expand (2n + 1)² + (2n + 3)² and reach a conclusion are shown below. Which attempt correctly proves this claim?

9.f(x) = 2x − 1. Work out ff(x).

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

11.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

12.Work out the value of n² − n when n = −3

13.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

14.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

15.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.