Algebra worksheet — GCSE Higher

1.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

2.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

3.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

4.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

5.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

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

7.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = −f(x) + 5 crosses the y-axis.

8.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.

9.Solve the inequality 9 − 2x ≥ 1.

10.By completing the square, find the turning point of the curve y = x² − 4x + 9.

11.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).

12.Solve the inequality 2(x − 1) ≤ 8.

13.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

14.Which of these is an identity?

15.x = 5. Work out the value of 3x² − 4.