Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

2.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.

3.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

4.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

5.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

6.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).

7.Factorise fully 12x² + 18x.

8.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

9.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

10.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

11.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

12.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?

13.Expand and simplify (x − 3)²

14.Which expression means 'triple c, then add double d'?

15.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).