OCR A Level Maths November 2021 Paper 3: question paper and mark scheme (H240/03)

Try 3 A Level questions like these

Written and checked by us, not taken from the OCR paper. Tap "Worked answer" to see every step.

1. Trigonometry · 5 marks

   Solve $\text{cosec}^2 x + \cot^2 x = 3$ for $0^\circ \le x \le 360^\circ$.

   Worked answer

   1. M1 for using the identity $\text{cosec}^2 x = 1 + \cot^2 x$ to obtain $1 + 2\cot^2 x = 3$.
   2. M1 for rearranging to $\cot^2 x = 1$.
   3. M1 for taking the square root to find $\tan x = \pm 1$.
   4. A1 for finding the principal values $45^\circ$ and $135^\circ$.
   5. A1 for stating all four correct solutions: $45^\circ, 135^\circ, 225^\circ, 315^\circ$.

2. Numerical methods · 6 marks

   The equation $\cos x = x$ has a unique root $\alpha$ in $[0, 1]$. Using the iteration $x_{n+1} = \cos x_n$ with $x_0 = 0.5$, find $x_1$, $x_2$, $x_3$, and $x_4$ each to $4$ d.p. (Angle in radians.)

   Worked answer

   $x_1 = \cos 0.5 = 0.8776$   M1 A1. $x_2 = \cos 0.8776 = 0.6390$   A1. $x_3 = \cos 0.6390 = 0.8027$   A1. $x_4 = \cos 0.8027 = 0.6948$   A1 A1.

3. Kinematics · 5 marks

   A particle moving with constant acceleration passes three points $A$, $B$ and $C$, in that order, on a straight line. The distance $AB$ is $20 \text{ m}$ and the distance $AC$ is $84 \text{ m}$. The speed of the particle at $B$ is $12 \text{ m s}^{-1}$ and its speed at $C$ is $20 \text{ m s}^{-1}$. Find the acceleration of the particle and its speed at $A$.

   Worked answer

   1. M1 for $BC = 84 - 20 = 64 \text{ m}$.
   2. M1 for $v^2 = u^2 + 2as$ from $B$ to $C$: $20^2 = 12^2 + 2a(64)$.
   3. A1 for $128a = 256 \Rightarrow a = 2 \text{ m s}^{-2}$.
   4. M1 for $v^2 = u^2 + 2as$ from $A$ to $B$: $12^2 = u_A^2 + 2(2)(20)$.
   5. A1 for $u_A^2 = 64 \Rightarrow u_A = 8 \text{ m s}^{-1}$.

More on these topics: Trigonometry · Numerical methods · Kinematics

What this paper covers

Pure Mathematics and Mechanics: a pure section, then mechanics (3.01 to 3.04).

We haven't mapped this paper question by question yet, so these are the topics it can test, from the specification's paper structure. Each links to a page where you can learn the topic and then practise questions on it.

Pure

• Proof
• Algebra and functions
• Coordinate geometry
• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors

Mechanics

• Kinematics
• Forces and Newton's laws
• Moments

Practise these topics (opens the practice engine)

• Pure I
• Pure II
• Pure III (calculus)
• Mechanics

Formula booklet

A Level Mathematics A (H240): formulae printed in each question paper · OCR · H240 specification version 3.1 (current)

OCR has no separate formula booklet for H240: the formulae are printed on pages 2 and 3 of every question paper. The link opens OCR’s H240 assessment page, where the papers are. Checked against OCR’s own papers on 11 October 2026.