Algebra worksheet — GCSE Higher

1.The graph of y = f(x) has a maximum turning point at (5, 8). Which of these correctly gives the corresponding turning point on the graph of y = −f(x + 1), and its type?

2.A circle has centre (0, 0) and equation x² + y² = 25. Work out the x-coordinates of the two points where the circle crosses the line y = 3.

3.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

4.Work out the value of m² + 3m when m = −2

5.Factorise fully 12x² + 18x.

6.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).

7.The graph of y = f(x) has a minimum turning point at (3, 2). Write down the coordinates of the minimum turning point of the graph of y = f(x) + 5.

8.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.

9.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

10.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.

11.The equation x² − 4x − 1 = 0 can be solved using the iterative formula xₙ₊₁ = √(4xₙ + 1). The starting value is x₀ = 1, so x₁ is the value after the formula has been used once. Work out x₂ correct to 3 decimal places.

12.The curve y = 2x² − 12x + 7 has a minimum point. By completing the square, find the value of x at which the minimum occurs.

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

14.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

15.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.