Algebra worksheet — GCSE Higher

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

2.A circle has centre (0, 0) and equation x² + y² = 50. Work out the length of the diameter of the circle, correct to 1 decimal place.

3.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.

4.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.

5.A circular running track is modelled on a grid whose centre is the origin, where each unit represents 1 metre. A floodlight at the point (30, 40) stands on the edge of the track. A second floodlight stands on the edge of the track at the point (0, k), where k is positive. Work out the value of k.

6.Which of these statements is an equation with exactly one solution?

7.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

8.The equation x³ + 4x − 9 = 0 is to be solved by iteration. Work out which one of these iterative formulas comes from a correct rearrangement of that equation.

9.Work out the value of 2x² when x = −3

10.One solution of the equation x² − (k + 1)x + k = 0 is x = 3. Work out the value of k.

11.Work out the value of (x − 4)/2 + 3 when x = 10

12.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

13.Solve x² − 5x + 6 = 0 by factorising.

14.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

15.Simplify (5x² + 3x − 2) − (2x² − x + 5)