From Paper 4 (calculator), Higher
Solve 5x² + 2x − 6 = 0. Give your answers to 2 decimal places.
From Paper 4 (calculator), Higher
Using x₀ = 1.5 and the iterative formula xₙ₊₁ = ∛(5 − 2xₙ), find x₁, x₂ and x₃ to 4 decimal places.
From Paper 4 (calculator), Higher
f(x) = 2x + 7 and g(x) = x² − 5. (a) Find fg(x). (b) Find f⁻¹(x). (c) Show that f(x) = g(x) can be written as x² − 2x − 12 = 0.
From Paper 4 (calculator), Higher
Solve 4x + 9 > 3 and −2 < x ≤ 5 together, and list the integers that satisfy both.
From Paper 4 (calculator), Higher
The circle x² + y² = 100 passes through the point P(6, 8). Find the equation of the tangent to the circle at P.
From Paper 4 (calculator), Higher
The graph of y = f(x) has a turning point at (-1, 4). Write down the coordinates of the turning point of (a) y = f(x − 2) (b) y = −f(x).
From Paper 5 (non-calculator), Higher
Solve 5(x + 2) = 2x + 19.
From Paper 5 (non-calculator), Higher
Solve x² − 5x − 14 = 0 by factorising.
From Paper 5 (non-calculator), Higher
A line passes through (0, -4) and (5, 6). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.
From Paper 5 (non-calculator), Higher
Make x the subject of a = (5 + x)/(3x − 1).
From Paper 5 (non-calculator), Higher
Write x² + 10x + 7 in the form (x + p)² + q, and state the coordinates of the turning point of y = x² + 10x + 7.
From Paper 5 (non-calculator), Higher
Prove that (n + 5)² − (n + 3)² is always a multiple of 4.
From Paper 5 (non-calculator), Higher
Simplify fully (x² − 4x − 21)/(3x² + 9x).
From Paper 5 (non-calculator), Higher
Solve the simultaneous equations
5x + 2y = 24
3x − 4y = 4
From Paper 5 (non-calculator), Higher
Find the nth term of the quadratic sequence 2, 9, 22, 41, 66, …
From Paper 5 (non-calculator), Higher
Solve x² − 5x − 6 < 0.
From Paper 5 (non-calculator), Higher
Solve tan x = 1 for 0° ≤ x ≤ 360°.
From Paper 5 (non-calculator), Higher
Expand and simplify (x + 2)(x − 1)(x + 4).
From Paper 5 (non-calculator), Higher
Factorise fully 6x² + 11x − 10.
From Paper 5 (non-calculator), Higher
The graph of y = f(x) has a turning point at (3, -2). Write down the coordinates of the turning point of (a) y = f(x − 4) (b) y = −f(x).
From Paper 6 (calculator), Higher
Solve the simultaneous equations
x² + y² = 25
y = x − 1
From Paper 6 (calculator), Higher
Solve 4x² + 3x − 2 = 0. Give your answers to 2 decimal places.
From Paper 6 (calculator), Higher
A line passes through (-3, 1) and (1, -11). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.
From Paper 6 (calculator), Higher
Solve x² − 4x − 21 < 0.
From Paper 6 (calculator), Higher
Solve sin x = −√3/2 for 0° ≤ x ≤ 360°.
From Paper 6 (calculator), Higher
The graph of y = f(x) has a turning point at (2, 5). Write down the coordinates of the turning point of (a) y = f(x − 3) (b) y = −f(x).
Score 0 / 80 · 0 of 26 marked
This paper is written by Plasmo in the style of the OCR GCSE Maths exam. It is not a past paper and is not produced or endorsed by the exam board.