Algebra worksheet — GCSE Higher

1.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

2.Ben is asked to find the inverse of f(x) = 4 − 3x. He writes f⁻¹(x) = (4 − x)/3. Which statement about Ben's answer is correct?

3.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

4.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?

5.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

6.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

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

8.Write down the first four terms of the sequence with nth term 6n − 5.

9.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

10.Factorise fully 12x² + 18x.

11.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

12.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

13.Which expression is equivalent to 3(2x − 5) + 4x?

14.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

15.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.