Algebra worksheet — GCSE Higher

1.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

2.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

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

4.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

5.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

6.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

7.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

10.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

11.The graph of y = x² − 4x is translated by the vector (3, 0). Work out the equation of the image, giving your answer in the form y = x² + bx + c.

12.Expand and simplify (x − 3)²

13.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.

14.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

15.Simplify (5x² + 3x − 2) − (2x² − x + 5)