Algebra worksheet — GCSE Higher

1.The equation x³ = 6x + 20 can be solved using the iterative formula xₙ₊₁ = ∛(6xₙ + 20). Taking x₀ = 3, x₁ = 3.3620 correct to 4 decimal places. Using the full unrounded value of x₁, work out x₂ correct to 3 decimal places.

2.Solve 7x − 5 = 3x + 11

3.By completing the square, show that the curve y = x² − 14x + 50 never crosses the x-axis. Which statement gives the correct reason?

4.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

5.Write down the expression that means 5 more than half of n.

6.Write down the expression that means the same as (x + 7) ÷ 4.

7.Make x the subject of the formula y = (x − 4)/5.

8.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

9.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

10.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

11.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

12.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?

13.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

14.f(x) = 2x + 1. Work out the value of x for which f⁻¹(x) = 5.

15.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?