Algebra worksheet — GCSE Higher

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

2.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

3.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

4.Which expression is equivalent to 6x − (2x − 5)?

5.Solve (2x + 1)/3 = 5

6.y = 5 − 2x. Work out the value of x when y = 11.

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

8.The graph of y = f(x) has a maximum turning point at (5, 8). Which of these correctly gives the corresponding turning point on the graph of y = −f(x + 1), and its type?

9.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

11.A tap fills a tank at a varying rate. A graph shows the rate of flow, in litres per minute, against time, in minutes. What does the area under this graph represent?

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

13.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

14.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

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