Algebra worksheet — GCSE Higher

1.By completing the square, find the turning point of the curve y = 2x² − 8x + 3.

2.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

3.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

4.The curve y = x² − 6 and the line y = 2x − 3 intersect at two points. Which pair of points is correct?

5.The graph of y = f(x) passes through the point (2, 7). The graph of y = f(x) + a passes through the point (2, 3). Work out the value of a.

6.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

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.Factorise fully 56x − 24

9.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.

10.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

12.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

13.Solve the inequality 2(x − 1) ≤ 8.

14.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

15.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.