Algebra worksheet — GCSE Higher

1.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

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

3.A proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?

4.Make x the subject of the formula y = 4(x − 6).

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

6.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

7.The graph of y = sin x is transformed onto the graph of y = sin x + 1. Which statement correctly describes the transformation and the new range of the graph?

8.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.

9.Solve the inequality 2(x − 1) ≤ 8.

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

11.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.

12.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

13.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.

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

15.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.