| 1 |
Hard +2.3 |
AQA |
Further Paper 2 |
2021 |
Q11 |
9 |
Vectors: Lines & Planes |
The Cartesian equation of the line $L _ { 1 }$ is
$$\frac { x + 1 } { 3 } = \fr... |
| 2 |
Hard +2.3 |
AQA |
Further Paper 2 |
2020 |
Q14 |
11 |
Polar coordinates |
The diagram shows the polar curve $C _ { 1 }$ with equation $r = 2 \sin \theta$
... |
| 3 |
Hard +2.3 |
Edexcel |
AEA |
2018 |
Q7 |
27 |
Parametric equations |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 4 |
Hard +2.3 |
Edexcel |
AEA |
2024 |
Q7 |
24 |
Circles |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 5 |
Hard +2.3 |
Edexcel |
AEA |
2024 |
Q6 |
18 |
Newton's laws and connected particles |
6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 6 |
Hard +2.3 |
OCR |
Further Mechanics |
2018 |
Q8 |
16 |
Momentum and Collisions 1 |
A point $O$ is situated a distance $h$ above a smooth horizontal plane, and a pa... |
| 7 |
Hard +2.3 |
OCR |
FM1 AS |
2018 |
Q6 |
9 |
Circular Motion 2 |
A fairground game involves a player kicking a ball, $B$, from rest so as to proj... |
| 8 |
Hard +2.3 |
OCR |
Further Additional Pure |
2018 |
Q4 |
12 |
Number Theory |
(i) (a) Find all the quadratic residues modulo 11.\\
(b) Prove that the equation... |
| 9 |
Hard +2.3 |
OCR |
Further Additional Pure |
2019 |
Q8 |
11 |
Number Theory |
In this question you must show detailed reasoning.
(a) Prove that $2 ( p - 2 ) ^... |
| 10 |
Hard +2.3 |
Edexcel |
AEA |
2007 |
Q6 |
17 |
Differentiation Applications |
(a) Find an expression, in terms of $x$, for the area $A$ of $R$.\\
(b) Show tha... |
| 11 |
Hard +2.3 |
Edexcel |
AEA |
2012 |
Q7 |
24 |
Trig Graphs & Exact Values |
7． $\left[ \arccos x \right.$ and $\arctan x$ are alternative notation for $\cos... |
| 12 |
Hard +2.3 |
Edexcel |
M5 |
2015 |
Q7 |
12 |
Moments of inertia |
7. (a) Find, using integration, the moment of inertia of a uniform solid hemisph... |
| 13 |
Hard +2.3 |
Edexcel |
M5 |
2013 |
Q4 |
13 |
Moments of inertia |
4. Show, using integration, that the moment of inertia of a uniform solid right ... |
| 14 |
Hard +2.3 |
OCR |
Further Additional Pure |
|
Q9 |
14 |
Number Theory |
(i) (a) Prove that $p \equiv \pm 1 ( \bmod 6 )$ for all primes $p > 3$.\\
(b) He... |
| 15 |
Hard +2.3 |
OCR |
Further Additional Pure |
2021 |
Q8 |
12 |
Number Theory |
(a) Solve the second-order recurrence system $\mathrm { H } _ { \mathrm { n } + ... |
| 16 |
Hard +2.3 |
OCR |
Further Additional Pure |
2023 |
Q4 |
7 |
Sequences and Series |
The sequence $\left\{ A _ { n } \right\}$ is given for all integers $n \geqslant... |
| 17 |
Hard +2.3 |
CAIE |
FP2 |
2013 |
Q11 EITHER |
|
Simple Harmonic Motion |
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{38694ab3-44cd-48d1... |
| 18 |
Hard +2.3 |
CAIE |
FP2 |
2015 |
Q11 EITHER |
|
Moments of inertia |
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{eb3dccaf-d151-472d... |
| 19 |
Hard +2.3 |
CAIE |
FP2 |
2015 |
Q11 EITHER |
|
Moments of inertia |
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{baea9836-ea05-442f... |
| 20 |
Hard +2.3 |
CAIE |
FP1 |
2018 |
Q11 OR |
|
Groups |
Let $V$ be the subspace of $\mathbb { R } ^ { 4 }$ spanned by
$$\mathbf { v } _... |
| 21 |
Hard +2.3 |
Edexcel |
AEA |
2013 |
Q6 |
16 |
Standard Integrals and Reverse Chain Rule |
6．（a）Starting from $[ \mathrm { f } ( x ) - \lambda \mathrm { g } ( x ) ] ^ { 2 ... |
| 22 |
Hard +2.3 |
Edexcel |
AEA |
2013 |
Q5 |
15 |
First order differential equations (integrating factor) |
5．In this question u and v are functions of $x$ ．Given that $\int \mathrm { u } ... |
| 23 |
Hard +2.3 |
Edexcel |
AEA |
2012 |
Q3 |
10 |
Addition & Double Angle Formulae |
3．The angle $\theta , 0 < \theta < \frac { \pi } { 2 }$ ，satisfies
$$\tan \thet... |
| 24 |
Hard +2.3 |
Edexcel |
AEA |
2009 |
Q2 |
9 |
Differentiating Transcendental Functions |
2. The curve $C$ has equation $y = x ^ { \sin x } , \quad x > 0$.\\
(a) Find the... |
| 25 |
Hard +2.3 |
Edexcel |
AEA |
2007 |
Q4 |
11 |
First order differential equations (integrating factor) |
4．The function $\mathrm { h } ( x )$ has domain $\mathbb { R }$ and range $\math... |
| 26 |
Hard +2.3 |
Edexcel |
AEA |
2006 |
Q7 |
20 |
Sequences and Series |
7.\\
\includegraphics[max width=\textwidth, alt={}, center]{0df09d8a-7478-4679-b... |
| 27 |
Hard +2.3 |
Edexcel |
AEA |
2005 |
Q3 |
9 |
Chain Rule |
3．Given that
$$\frac { \mathrm { d } } { \mathrm {~d} x } ( u \sqrt { } x ) = \... |
| 28 |
Hard +2.3 |
Edexcel |
AEA |
2003 |
Q5 |
17 |
Curve Sketching |
5．The function $f$ is given by
$$f ( x ) = \frac { 1 } { \lambda } \left( x ^ {... |
| 29 |
Hard +2.3 |
Edexcel |
AEA |
2023 |
Q7 |
15 |
Sequences and Series |
\begin{enumerate}
\setcounter{enumi}{6}
\item A sequence of non-zero real nu... |
| 30 |
Hard +2.3 |
Edexcel |
AEA |
2023 |
Q5 |
21 |
Conditional Probability |
5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 31 |
Hard +2.3 |
Edexcel |
AEA |
2022 |
Q6 |
24 |
Sequences and Series |
6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 32 |
Hard +2.3 |
Edexcel |
AEA |
2020 |
Q6 |
23 |
Integration by Substitution |
\begin{enumerate}
\setcounter{enumi}{5}
\item (a) Given that f is a function... |
| 33 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q7 |
18 |
Trig Proofs |
7．The variable $y$ is defined by
$$y = \ln \left( \sec ^ { 2 } x + \operatornam... |
| 34 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q6 |
18 |
Generalised Binomial Theorem |
6．Given that the coefficients of $x , x ^ { 2 }$ and $x ^ { 4 }$ in the expansio... |
| 35 |
Hard +2.3 |
OCR MEI |
S4 |
2016 |
Q1 |
24 |
Probability Generating Functions |
The random variable $X$ has a Cauchy distribution centred on $m$. Its probabilit... |
| 36 |
Hard +2.3 |
OCR MEI |
FP3 |
2014 |
Q3 |
24 |
Sequences and Series |
(a) A curve has intrinsic equation $s = 2 \ln \left( \frac { \pi } { \pi - 3 \ps... |
| 37 |
Hard +2.3 |
CAIE |
Further Paper 2 |
2024 |
Q8 |
14 |
Complex numbers 2 |
(a)By considering the binomial expansion of $\left( z + \frac { 1 } { z } \right... |
| 38 |
Hard +2.3 |
Edexcel |
F2 |
2017 |
Q7 |
15 |
Polar coordinates |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 39 |
Hard +2.3 |
Edexcel |
F1 |
2017 |
Q8 |
12 |
Conic sections |
8. The parabola $C$ has equation $y ^ { 2 } = 4 a x$, where $a$ is a positive co... |
| 40 |
Hard +2.3 |
CAIE |
Further Paper 3 |
2024 |
Q6 |
9 |
Non-constant acceleration |
A particle $P$ of mass 2 kg moving on a horizontal straight line has displacemen... |
| 41 |
Hard +2.3 |
CAIE |
Further Paper 3 |
2024 |
Q6 |
9 |
Non-constant acceleration |
A particle $P$ of mass 2 kg moving on a horizontal straight line has displacemen... |
| 42 |
Hard +2.3 |
CAIE |
Further Paper 2 |
2024 |
Q8 |
14 |
Complex numbers 2 |
(a) By considering the binomial expansion of $\left( z + \frac { 1 } { z } \righ... |
| 43 |
Hard +2.3 |
CAIE |
Further Paper 2 |
2023 |
Q5 |
10 |
Hyperbolic functions |
5\\
\includegraphics[max width=\textwidth, alt={}, center]{1fa404d4-5e14-4356-9b... |
| 44 |
Challenging +1.8 |
OCR |
Further Pure Core 2 |
2021 |
Q3 |
6 |
Polar coordinates |
The equation of a curve in polar coordinates is $r = \ln ( 1 + \sin \theta )$ fo... |
| 45 |
Challenging +1.8 |
OCR |
Further Mechanics |
2021 |
Q3 |
12 |
Momentum and Collisions 2 |
Two smooth circular discs $A$ and $B$ are moving on a horizontal plane. The mass... |
| 46 |
Challenging +1.8 |
OCR |
Further Mechanics |
2021 |
Q4 |
9 |
Momentum and Collisions |
Two particles $A$ and $B$, of masses $m \mathrm {~kg}$ and 1 kg respectively, ar... |
| 47 |
Challenging +1.8 |
OCR |
FP1 AS |
2021 |
Q3 |
7 |
Roots of polynomials |
In this question you must show detailed reasoning.\\
The cubic equation $5 x ^ {... |
| 48 |
Challenging +1.8 |
OCR |
FM1 AS |
2021 |
Q5 |
4 |
Momentum and Collisions 1 |
\end{gathered} > \begin{gathered}
3 u ( 1 + e ) ( 11 - 5 e ) \\
80
\end{gathered... |
| 49 |
Challenging +1.8 |
OCR |
FM1 AS |
2021 |
Q4 |
12 |
Momentum and Collisions 1 |
Three particles $A , B$ and $C$ are free to move in the same straight line on a ... |
| 50 |
Challenging +1.8 |
SPS |
SPS FM Pure |
2023 |
Q8 |
11 |
Integration using inverse trig and hyperbolic functions |
8. (a) Use a hyperbolic substitution and calculus to show that
$$\int \frac { x... |