Algebra worksheet — GCSE Higher

1.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

2.Simplify (x² − 9) ÷ (x² + 5x + 6).

3.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

4.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

5.Solve x² − 100 = 0.

6.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

7.Work out the period of the graph of y = cos x, in degrees.

8.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

9.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

10.A square patio of side length n slabs is surrounded by a single border of square paving slabs of the same size. For a patio with side length n, the total number of slabs used for the patio and its border together is 9 when n = 1, 16 when n = 2, 25 when n = 3, and 36 when n = 4. Work out an expression, in terms of n, for the total number of slabs.

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

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

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

14.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

15.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.