| 1 |
Hard +2.5 |
OCR |
H240/03 |
2018 |
Q3 |
4 |
Function Transformations |
A sequence of three transformations maps the curve $y = \ln x$ to the curve $y =... |
| 2 |
Hard +2.3 |
CAIE |
Further Paper 2 |
2023 |
Q5 |
10 |
Hyperbolic functions |
5\\
\begin{tikzpicture}[scale=1.2]
% Axes
\draw[->] (-0.3,0) -- (5.5,0) node[rig... |
| 3 |
Hard +2.3 |
CAIE |
Further Paper 2 |
2024 |
Q8 |
14 |
Complex numbers 2 |
\begin{enumerate}[label=(\alph*)]
\item By considering the binomial expansion of... |
| 4 |
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... |
| 5 |
Hard +2.3 |
Edexcel |
F2 |
2017 |
Q7 |
15 |
Polar coordinates |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 6 |
Hard +2.3 |
CAIE |
Further Paper 2 |
2024 |
Q8 |
14 |
Complex numbers 2 |
\begin{enumerate}[label=(\alph*)]
\item By considering the binomial expansion of... |
| 7 |
Hard +2.3 |
OCR MEI |
FP3 |
2014 |
Q3 |
24 |
Sequences and Series |
\begin{enumerate}[label=(\alph*)]
\item A curve has intrinsic equation $s = 2 \l... |
| 8 |
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... |
| 9 |
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... |
| 10 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q7 |
18 |
Trig Proofs |
7.The variable $y$ is defined by
$$y = \ln \left( \sec ^ { 2 } x + \operatornam... |
| 11 |
Hard +2.3 |
Edexcel |
AEA |
2020 |
Q6 |
23 |
Integration by Substitution |
(a) Given that f is a function such that the integrals exist,\\
\begin{enumerate... |
| 12 |
Hard +2.3 |
Edexcel |
AEA |
2022 |
Q6 |
24 |
Sequences and Series |
6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 13 |
Hard +2.3 |
Edexcel |
AEA |
2023 |
Q5 |
21 |
Conditional Probability |
5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 14 |
Hard +2.3 |
Edexcel |
AEA |
2023 |
Q7 |
15 |
Sequences and Series |
\begin{enumerate}
\item A sequence of non-zero real numbers $a _ { 1 } , a _ {... |
| 15 |
Hard +2.3 |
Edexcel |
AEA |
2003 |
Q5 |
17 |
Curve Sketching |
5.The function $f$ is given by
$$f ( x ) = \frac { 1 } { \lambda } \left( x ^ {... |
| 16 |
Hard +2.3 |
Edexcel |
AEA |
2005 |
Q3 |
9 |
Chain Rule |
3.Given that
$$\frac { \mathrm { d } } { \mathrm {~d} x } ( u \sqrt { } x ) = \... |
| 17 |
Hard +2.3 |
Edexcel |
AEA |
2006 |
Q7 |
20 |
Sequences and Series |
7.\\
\includegraphics[max width=\textwidth, alt={}, center]{0df09d8a-7478-4679-b... |
| 18 |
Hard +2.3 |
Edexcel |
AEA |
2007 |
Q4 |
11 |
First order differential equations (integrating factor) |
4.The function $\mathrm { h } ( x )$ has domain $\mathbb { R }$ and range $\math... |
| 19 |
Hard +2.3 |
Edexcel |
AEA |
2009 |
Q2 |
9 |
Differentiating Transcendental Functions |
2. The curve $C$ has equation $y = x ^ { \sin x } , \quad x > 0$.
\begin{enumera... |
| 20 |
Hard +2.3 |
Edexcel |
AEA |
2012 |
Q3 |
10 |
Addition & Double Angle Formulae |
3.The angle $\theta , 0 < \theta < \frac { \pi } { 2 }$ ,satisfies
$$\tan \thet... |
| 21 |
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 } ... |
| 22 |
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 ... |
| 23 |
Hard +2.3 |
CAIE |
FP1 |
2018 |
Q11 OR |
|
Groups |
Let $V$ be the subspace of $\mathbb { R } ^ { 4 }$ spanned by
$$\mathbf { v } _... |
| 24 |
Hard +2.3 |
CAIE |
FP2 |
2015 |
Q11 EITHER |
|
Moments of inertia |
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{baea9836-ea05-442f... |
| 25 |
Hard +2.3 |
CAIE |
FP2 |
2015 |
Q11 EITHER |
|
Moments of inertia |
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{eb3dccaf-d151-472d... |
| 26 |
Hard +2.3 |
CAIE |
FP2 |
2013 |
Q11 EITHER |
|
Simple Harmonic Motion |
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{38694ab3-44cd-48d1... |
| 27 |
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... |
| 28 |
Hard +2.3 |
OCR |
Further Additional Pure |
2021 |
Q8 |
12 |
Number Theory |
\begin{enumerate}[label=(\alph*)]
\item Solve the second-order recurrence system... |
| 29 |
Hard +2.3 |
OCR |
Further Additional Pure |
|
Q9 |
14 |
Number Theory |
\begin{enumerate}[label=(\roman*)]
\item (a) Prove that $p \equiv \pm 1 ( \bmod ... |
| 30 |
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 ... |
| 31 |
Hard +2.3 |
Edexcel |
M5 |
2015 |
Q7 |
12 |
Moments of inertia |
7.\\
\begin{enumerate}[label=(\alph*)]
\item Find, using integration, the moment... |
| 32 |
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... |
| 33 |
Hard +2.3 |
Edexcel |
AEA |
2007 |
Q6 |
17 |
Stationary points and optimisation |
\begin{enumerate}[label=(\alph*)]
\item Find an expression, in terms of $x$, for... |
| 34 |
Hard +2.3 |
OCR |
Further Additional Pure |
2019 |
Q8 |
11 |
Number Theory |
In this question you must show detailed reasoning.
\begin{enumerate}[label=(\alp... |
| 35 |
Hard +2.3 |
OCR |
Further Additional Pure |
2018 |
Q4 |
12 |
Number Theory |
\begin{enumerate}[label=(\roman*)]
\item (a) Find all the quadratic residues mod... |
| 36 |
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... |
| 37 |
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... |
| 38 |
Hard +2.3 |
Edexcel |
AEA |
2024 |
Q7 |
24 |
Circles |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 39 |
Hard +2.3 |
Edexcel |
AEA |
2018 |
Q7 |
27 |
Parametric curves and Cartesian conversion |
7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwi... |
| 40 |
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... |
| 41 |
Hard +2.3 |
Pre-U |
Pre-U 9795/1 |
2014 |
Q9 |
2 |
Groups |
9\\
\begin{enumerate}[label=(\roman*)]
\item Explain why all groups of even orde... |
| 42 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q4 |
14 |
Implicit equations and differentiation |
Find the coordinates of the stationary points of the curve with equation
$$x^3 +... |
| 43 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q5 |
15 |
Trig Graphs & Exact Values |
\includegraphics{figure_1}
Figure 1 shows a sketch of part of the curve with eq... |
| 44 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q6 |
17 |
Curve Sketching |
\includegraphics{figure_2}
Figure 2 shows a sketch of part of two curves $C_1$ ... |
| 45 |
Hard +2.3 |
Edexcel |
AEA |
2002 |
Q7 |
18 |
Proof |
A student was attempting to prove that $x = \frac{1}{2}$ is the only real root o... |
| 46 |
Hard +2.3 |
Edexcel |
AEA |
2004 |
Q7 |
19 |
Sine and Cosine Rules |
Triangle $ABC$, with $BC = a$, $AC = b$ and $AB = c$ is inscribed in a circle. G... |
| 47 |
Hard +2.3 |
Edexcel |
AEA |
2008 |
Q4 |
13 |
Differentiating Transcendental Functions |
\includegraphics{figure_1}
Figure 1 shows a sketch of the curve $C$ with equati... |
| 48 |
Hard +2.3 |
AQA |
Further Paper 2 |
2020 |
Q8 |
9 |
3x3 Matrices |
\begin{enumerate}[label=(\alph*)]
\item Factorise $\begin{vmatrix} 2u + h + x & ... |
| 49 |
Hard +2.3 |
AQA |
Further Paper 2 |
2020 |
Q14 |
11 |
Polar coordinates |
The diagram shows the polar curve $C_1$ with equation $r = 2 \sin \theta$
The d... |
| 50 |
Hard +2.3 |
AQA |
Further Paper 2 |
2023 |
Q16 |
16 |
Simple Harmonic Motion |
A bungee jumper of mass $m$ kg is attached to an elastic rope.
The other end of ... |