From Paper 1 (non-calculator), Higher
Solve 4(x + 3) = 7x − 9.
From Paper 1 (non-calculator), Higher
Solve x² − 2x − 24 = 0 by factorising.
From Paper 1 (non-calculator), Higher
A line passes through (-1, 2) and (3, 14). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.
From Paper 1 (non-calculator), Higher
Make x the subject of p = (2x − 7)/(x + 4).
From Paper 1 (non-calculator), Higher
Write x² − 8x + 5 in the form (x + p)² + q, and state the coordinates of the turning point of y = x² − 8x + 5.
From Paper 1 (non-calculator), Higher
Prove that the sum of the squares of any two consecutive integers is always odd.
From Paper 1 (non-calculator), Higher
Simplify fully (2x² + 7x + 3)/(x² − 9).
From Paper 1 (non-calculator), Higher
Solve the simultaneous equations
2x + 3y = 13
4x − y = 5
From Paper 1 (non-calculator), Higher
Find the nth term of the quadratic sequence 2, 8, 16, 26, 38, …
From Paper 1 (non-calculator), Higher
Expand and simplify (x + 1)(x + 2)(x − 3).
From Paper 1 (non-calculator), Higher
Factorise fully 2x² − 5x − 12.
From Paper 2 (calculator), Higher
Solve 3x² + 4x − 5 = 0. Give your answers to 2 decimal places.
From Paper 2 (calculator), Higher
Using x₀ = 2 and the iterative formula xₙ₊₁ = ∛(5 − 2xₙ), find x₁, x₂ and x₃ to 4 decimal places.
From Paper 2 (calculator), Higher
f(x) = 4x − 1 and g(x) = x² − 3. (a) Find fg(x). (b) Find f⁻¹(x). (c) Show that f(x) = g(x) can be written as x² − 4x − 2 = 0.
From Paper 2 (calculator), Higher
Solve 5x − 3 > 12 and −2 < x ≤ 5 together, and list the integers that satisfy both.
From Paper 2 (calculator), Higher
The circle x² + y² = 169 passes through the point P(5, 12). Find the equation of the tangent to the circle at P.
From Paper 3 (calculator), Higher
Solve the simultaneous equations
x² + y² = 25
y = 2x − 5
From Paper 3 (calculator), Higher
Solve 2x² − 9x + 3 = 0. Give your answers to 2 decimal places.
From Paper 3 (calculator), Higher
A line passes through (2, -3) and (6, 5). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.
From Paper 3 (calculator), Higher
The graph of y = x² + 2x − 3 is drawn. Use a tangent to estimate the gradient of the curve at x = 1, and explain why your answer is an estimate.
From Paper 3 (calculator), Higher
Solve x² + x − 12 < 0.
From Paper 3 (calculator), Higher
Solve cos x = −0.5 for 0° ≤ x ≤ 360°.
Score 0 / 72 · 0 of 22 marked
This paper is written by Plasmo in the style of the Edexcel GCSE Maths exam. It is not a past paper and is not produced or endorsed by the exam board.