Algebra worksheet — GCSE Higher

1.Which of these rules generates the sequence 6, 11, 16, 21, …?

2.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).

3.A circular running track is modelled on a grid whose centre is the origin, where each unit represents 1 metre. A floodlight at the point (30, 40) stands on the edge of the track. A second floodlight stands on the edge of the track at the point (0, k), where k is positive. Work out the value of k.

4.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.

5.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?

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

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

8.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.

9.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

10.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.

11.Solve the inequality 3x − 1 ≤ 11.

12.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

13.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

14.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.

15.Which expression is equivalent to 7x − 3(2x − 6)?