Algebra worksheet — GCSE Higher

1.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

2.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

3.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

4.f(x) = 3x − 2. Find f⁻¹(x).

5.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.

6.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

7.x = 5. Work out the value of 3x² − 4.

8.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.

9.A company's weekly profit, in £, is modelled by y = f(x), where x is the number of weeks since launch. The graph of y = f(x) has a maximum at (10, 45000). A rival company uses the same marketing strategy but starts trading 6 weeks later and has fixed costs £8000 higher every week, so its profit is modelled by y = f(x − 6) − 8000. In which week does the rival's maximum weekly profit occur, and what is it?

10.Factorise fully 5x + 5y − 5

11.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).

12.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

13.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

15.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?