Algebra worksheet — GCSE Higher

1.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.

2.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.

3.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

4.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

5.Solve 5x² − 15x = 0.

6.Points A(−1, 2) and B(5, 8) are the endpoints of a line segment. Work out the equation of the perpendicular bisector of AB.

7.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?

8.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

9.Which of these values of x is a solution of x² + 2x − 15 = 0?

10.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.

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

12.Which of these quadratic graphs does NOT cross the x-axis at all?

13.Solve 2x + 7 = x + 13

14.The simultaneous equations kx + 2y = 4 and 3x + y = 5 have no solution. Work out the value of k.

15.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.