From Paper 1 (non-calculator), Higher
Solve 3(x + 4) = 5x − 6.
From Paper 1 (non-calculator), Higher
Solve x² + 2x − 15 = 0 by factorising.
From Paper 1 (non-calculator), Higher
A line passes through (1, 3) and (4, 9). (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 y = (3x + 2)/(x − 5).
From Paper 1 (non-calculator), Higher
Write x² + 6x + 2 in the form (x + p)² + q, and state the coordinates of the turning point of y = x² + 6x + 2.
From Paper 1 (non-calculator), Higher
Prove that the difference between the squares of any two consecutive odd numbers is a multiple of 8.
From Paper 1 (non-calculator), Higher
Simplify fully (x² − 9)/(x² + x − 12).
From Paper 1 (non-calculator), Higher
Solve the simultaneous equations
3x + 2y = 16
5x − 2y = 0
From Paper 1 (non-calculator), Higher
Find the nth term of the quadratic sequence 4, 9, 18, 31, 48, …
From Paper 2 (calculator), Higher
Solve 2x² + 5x − 4 = 0. Give your answers to 2 decimal places.
From Paper 2 (calculator), Higher
Using x₀ = 1 and the iterative formula xₙ₊₁ = ∛(5 − 2xₙ), find x₁, x₂ and x₃ to 4 decimal places.
From Paper 2 (calculator), Higher
f(x) = 3x + 2 and g(x) = x² − 4. (a) Find fg(x). (b) Find f⁻¹(x). (c) Show that f(x) = g(x) can be written as x² − 3x − 6 = 0.
From Paper 2 (calculator), Higher
Solve 3x + 4 > 7 and −2 < x ≤ 5 together, and list the integers that satisfy both.
From Paper 2 (calculator), Higher
The circle x² + y² = 25 passes through the point P(3, 4). Find the equation of the tangent to the circle at P.
From Paper 3 (calculator), Higher
Solve the simultaneous equations
x² + y² = 25
y = x + 1
From Paper 3 (calculator), Higher
Solve 3x² − 7x − 2 = 0. Give your answers to 2 decimal places.
From Paper 3 (calculator), Higher
A line passes through (-2, 5) and (4, -7). (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 − 4x + 1 is drawn. Use a tangent to estimate the gradient of the curve at x = 3, and explain why your answer is an estimate.
From Paper 3 (calculator), Higher
Solve x² − 3x − 10 < 0.
From Paper 3 (calculator), Higher
Solve sin x = 0.5 for 0° ≤ x ≤ 360°.
Score 0 / 67 · 0 of 20 marked
This paper is written by Plasmo in the style of the AQA GCSE Maths exam. It is not a past paper and is not produced or endorsed by the exam board.