Algebra worksheet — GCSE Higher

1.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

2.Which of these equations is equivalent to 5x − 2 = 3x + 8?

3.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

4.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

5.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.

6.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

7.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.

8.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

9.Expand and simplify 2(a + 6) − 2(a − 7)

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.A rectangular sheet of metal measures 20 cm by 12 cm. A square of side x cm is cut from each corner and the sides are folded up to make an open box of volume 200 cm³. This gives x³ − 16x² + 60x − 50 = 0, which can be solved using the iterative formula xₙ₊₁ = (16xₙ² − xₙ³ + 50)/60. The starting value is x₀ = 1, so x₁ is the value after the formula has been used once. Work out x₃, and use it to find the longer side of the base of the box correct to 1 decimal place.

12.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

13.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.

14.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

15.A tram travels between two stops. Its velocity-time graph consists of straight line segments joining the points (0, 0), (5, 20), (12, 20), (16, 4) and (20, 4), where time is in seconds and velocity is in m/s. Work out the average speed of the tram over the whole 20 seconds. Give your answer to 1 decimal place.