Algebra worksheet — GCSE Higher

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

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

3.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

4.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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

6.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

7.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

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

9.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).

10.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

11.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.

12.A cyclist accelerates uniformly from rest to 6 m/s in 4 seconds, travels at a constant 6 m/s for 10 seconds, then decelerates uniformly to rest in 3 seconds. Work out the total distance the cyclist travels.

13.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

14.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

15.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.