Questions - OCR - A-Level Maths

OCR S1 2011 January Q5

10 marks Moderate -0.8

The number of free gifts that Jan receives in a week is denoted by $X$. Name a suitable probability distribution with which to model $X$, giving the value(s) of any parameter(s). State any assumption(s) necessary for the distribution to be a valid model. Assume now that your model is valid.
Find
(a) $\mathrm { P } ( X \leqslant 2 )$,
(b) $\mathrm { P } ( X = 2 )$.
Find the probability that, in the next 7 weeks, there are exactly 3 weeks in which Jan receives exactly 2 free gifts. 6
The diagram shows 7 cards, each with a digit printed on it. The digits form a 7 -digit number. \href{http://physicsandmathstutor.com}{physicsandmathstutor.com}
3
2
2
2
2

\multirow[t]{21}{*}{3
}
\multirow[t]{4}{*}{3
}
3
\href{http://physicsandmathstutor.com}{physicsandmathstutor.com}

OCR S1 2012 January Q7

8 marks Moderate -0.8

State a suitable distribution that can be used as a model for $X$, giving the value(s) of any parameter(s). State also any necessary condition(s) for this distribution to be a good model. Use the distribution stated in part (i) to find
$\mathrm { P } ( X = 4 )$,
$\mathrm { P } ( X \geqslant 4 )$.

OCR S2 2007 June Q4

6 marks Moderate -0.3

State two conditions needed for $X$ to be well modelled by a normal distribution.
It is given that $X \sim \mathrm {~N} \left( 50.0,8 ^ { 2 } \right)$. The mean of 20 random observations of $X$ is denoted by $\bar { X }$. Find $\mathrm { P } ( \bar { X } > 47.0 )$. 5 The number of system failures per month in a large network is a random variable with the distribution $\operatorname { Po } ( \lambda )$. A significance test of the null hypothesis $\mathrm { H } _ { 0 } : \lambda = 2.5$ is carried out by counting $R$, the number of system failures in a period of 6 months. The result of the test is that $\mathrm { H } _ { 0 }$ is rejected if $R > 23$ but is not rejected if $R \leqslant 23$.
State the alternative hypothesis.
Find the significance level of the test.
Given that $\mathrm { P } ( R > 23 ) < 0.1$, use tables to find the largest possible actual value of $\lambda$. You should show the values of any relevant probabilities. 6 In a rearrangement code, the letters of a message are rearranged so that the frequency with which any particular letter appears is the same as in the original message. In ordinary German the letter $e$ appears $19 \%$ of the time. A certain encoded message of 20 letters contains one letter $e$.
Using an exact binomial distribution, test at the $10 \%$ significance level whether there is evidence that the proportion of the letter $e$ in the language from which this message is a sample is less than in German, i.e., less than $19 \%$.
Give a reason why a binomial distribution might not be an appropriate model in this context. 7 Two continuous random variables $S$ and $T$ have probability density functions as follows. $$\begin{array} { l l } S : & f ( x ) = \begin{cases} \frac { 1 } { 2 } & - 1 \leqslant x \leqslant 1 \\ 0 & \text { otherwise } \end{cases} \\ T : & g ( x ) = \begin{cases} \frac { 3 } { 2 } x ^ { 2 } & - 1 \leqslant x \leqslant 1 \\ 0 & \text { otherwise } \end{cases} \end{array}$$
Sketch on the same axes the graphs of $y = \mathrm { f } ( x )$ and $y = \mathrm { g } ( x )$. [You should not use graph paper or attempt to plot points exactly.]
Explain in everyday terms the difference between the two random variables.
Find the value of $t$ such that $\mathrm { P } ( T > t ) = 0.2$. 8 A random variable $Y$ is normally distributed with mean $\mu$ and variance 12.25. Two statisticians carry out significance tests of the hypotheses $\mathrm { H } _ { 0 } : \mu = 63.0 , \mathrm { H } _ { 1 } : \mu > 63.0$.
Statistician $A$ uses the mean $\bar { Y }$ of a sample of size 23, and the critical region for his test is $\bar { Y } > 64.20$. Find the significance level for $A$ 's test.
Statistician $B$ uses the mean of a sample of size 50 and a significance level of $5 \%$.
(a) Find the critical region for $B$ 's test.
(b) Given that $\mu = 65.0$, find the probability that $B$ 's test results in a Type II error.
Given that, when $\mu = 65.0$, the probability that $A$ 's test results in a Type II error is 0.1365 , state with a reason which test is better. 9 (a) The random variable $G$ has the distribution $\mathrm { B } ( n , 0.75 )$. Find the set of values of $n$ for which the distribution of $G$ can be well approximated by a normal distribution.
(b) The random variable $H$ has the distribution $\mathrm { B } ( n , p )$. It is given that, using a normal approximation, $\mathrm { P } ( H \geqslant 71 ) = 0.0401$ and $\mathrm { P } ( H \leqslant 46 ) = 0.0122$.
Find the mean and standard deviation of the approximating normal distribution.
Hence find the values of $n$ and $p$.

OCR S4 2010 June Q3

7 marks Challenging +1.8

Assuming that all rankings are equally likely, show that $\mathrm { P } ( R \leqslant 17 ) = \frac { 2 } { 231 }$. The marks of 5 randomly chosen students from School $A$ and 6 randomly chosen students from School $B$, who took the same examination, achieving different marks, were ranked. The rankings are shown in the table.
Rank 1 2 3 4 5 6 7 8 9 10 11
School $A$ $A$ $A$ $B$ $A$ $A$ $B$ $B$ $B$ $B$ $B$
For a Wilcoxon rank-sum test, obtain the exact smallest significance level for which there is evidence of a difference in performance at the two schools.

OCR M1 2010 January Q5

11 marks Moderate -0.3

Find the value of $t$ when $A$ and $B$ have the same speed.
Calculate the value of $t$ when $B$ overtakes $A$.
On a single diagram, sketch the $( t , x )$ graphs for the two cyclists for the time from $t = 0$ until after $B$ has overtaken $A$.

OCR M1 2015 June Q3

8 marks Standard +0.3

Calculate the distance $A$ cycles, and hence find the period of time for which $B$ walks before finding the bicycle.
Find $T$.
Calculate the distance $A$ and $B$ each travel.

OCR M2 2008 January Q6

11 marks Standard +0.3

Show that the tension in the string is 4.16 N , correct to 3 significant figures.
Calculate $\omega$.
(ii) \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{982647bd-8514-40cf-b4ee-674f51df32c5-3_510_417_1238_904} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} The lower part of the string is now attached to a point $R$, vertically below $P$. $P B$ makes an angle $30 ^ { \circ }$ with the vertical and $R B$ makes an angle $60 ^ { \circ }$ with the vertical. The bead $B$ now moves in a horizontal circle of radius 1.5 m with constant speed $v _ { \mathrm { m } } \mathrm { m } ^ { - 1 }$ (see Fig. 2).
Calculate the tension in the string.
Calculate $v$.

OCR M2 2006 June Q6

11 marks Standard +0.3

Calculate the tension in the string and hence find the angular speed of $Q$. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d6d87705-be4b-407d-b699-69fb441d88a7-4_489_1358_1286_392} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} The particle $Q$ on the plane is now fixed to a point 0.2 m from the hole at $A$ and the particle $P$ rotates in a horizontal circle of radius 0.2 m (see Fig. 2).
Calculate the tension in the string.
Calculate the speed of $P$.

OCR M2 2008 June Q5

8 marks Standard +0.3

Show that the distance from the ball to the centre of mass of the toy is 10.7 cm , correct to 1 decimal place.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6ae57fe9-3b6f-46c2-95b8-d48903ed796b-3_312_1051_1509_587} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} The toy lies on horizontal ground in a position such that the ball is touching the ground (see Fig. 2). Determine whether the toy is lying in equilibrium or whether it will move to a position where the rod is vertical.

OCR M2 2009 June Q5

11 marks Standard +0.3

Fig. 1 Fig. 1 shows a uniform lamina $B C D$ in the shape of a quarter circle of radius 6 cm . Show that the distance of the centre of mass of the lamina from $B$ is 3.60 cm , correct to 3 significant figures. A uniform rectangular lamina $A B D E$ has dimensions $A B = 12 \mathrm {~cm}$ and $A E = 6 \mathrm {~cm}$. A single plane object is formed by attaching the rectangular lamina to the lamina $B C D$ along $B D$ (see Fig. 2). The mass of $A B D E$ is 3 kg and the mass of $B C D$ is 2 kg . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e85c2bf4-21a8-4d9a-93c5-d5679b2a8233-3_959_447_1123_849} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
Taking $x$ - and $y$-axes along $A E$ and $A B$ respectively, find the coordinates of the centre of mass of the object. The object is freely suspended at $C$ and rests in equilibrium.
Calculate the angle that $A C$ makes with the vertical.

OCR M2 2015 June Q7

11 marks Standard +0.8

Show that $\mu = \frac { 2 } { 3 }$. A small object of weight $a W \mathrm {~N}$ is placed on the ladder at its mid-point and the object $S$ of weight $2 W \mathrm {~N}$ is placed on the ladder at its lowest point $A$.
Given that the system is in equilibrium, find the set of possible values of $a$.

OCR M3 2009 January Q4

10 marks Standard +0.8

Show that $v ^ { 2 } = 9 + 9.8 \sin \theta$.
Find, in terms of $\theta$, the radial and tangential components of the acceleration of $P$.
Show that the tension in the string is $( 3.6 + 5.88 \sin \theta ) \mathrm { N }$ and hence find the value of $\theta$ at the instant when the string becomes slack, giving your answer correct to 1 decimal place.

OCR M3 2010 January Q6

13 marks Challenging +1.2

By considering the total energy of the system, obtain an expression for $v ^ { 2 }$ in terms of $\theta$.
Show that the magnitude of the force exerted on $P$ by the cylinder is $( 7.12 \sin \theta - 4.64 \theta ) \mathrm { N }$.
Given that $P$ leaves the surface of the cylinder when $\theta = \alpha$, show that $1.53 < \alpha < 1.54$.

OCR M3 2007 June Q6

13 marks Challenging +1.8

Show that, when $P$ is in equilibrium, $O P = 7.25 \mathrm {~m}$.
Verify that $P$ and $Q$ together just reach the safety net.
At the lowest point of their motion $P$ releases $Q$. Prove that $P$ subsequently just reaches $O$.
State two additional modelling assumptions made when answering this question.

OCR M3 2010 June Q3

8 marks Standard +0.3

Given that the coefficient of restitution between the sphere and the wall is $\frac { 1 } { 2 }$, state the values of $u$ and $v$. Shortly after hitting the wall the sphere $A$ comes into contact with another uniform smooth sphere $B$, which has the same mass and radius as $A$. The sphere $B$ is stationary and at the instant of contact the line of centres of the spheres is parallel to the wall (see Fig. 2). The contact between the spheres is perfectly elastic. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a8c1e5b3-4d8b-4795-9e9f-4c0db374112e-3_524_371_1503_888} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
Find, for each sphere, its speed and its direction of motion immediately after the contact.
$4 ~ O$ is a fixed point on a horizontal plane. A particle $P$ of mass 0.25 kg is released from rest at $O$ and moves in a straight line on the plane. At time $t \mathrm {~s}$ after release the only horizontal force acting on $P$ has magnitude $$\frac { 1 } { 2400 } \left( 144 - t ^ { 2 } \right) \mathrm { N } \quad \text { for } 0 \leqslant t \leqslant 12$$ and $$\frac { 1 } { 2400 } \left( t ^ { 2 } - 144 \right) \mathrm { N } \text { for } t \geqslant 12 .$$ The force acts in the direction of $P$ 's motion. $P$ 's velocity at time $t \mathrm {~s}$ is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
Find an expression for $v$ in terms of $t$, valid for $t \geqslant 12$, and hence show that $v$ is three times greater when $t = 24$ than it is when $t = 12$.
Sketch the $( t , v )$ graph for $0 \leqslant t \leqslant 24$.

OCR M3 2016 June Q3

10 marks Challenging +1.2

Find the speed of $A$ after the collision. Find also the component of the velocity of $B$ along the line of centres after the collision.
$B$ subsequently hits the wall.
Explain why $A$ and $B$ will have a second collision if the coefficient of restitution between $B$ and the wall is sufficiently large. Find the set of values of the coefficient of restitution for which this second collision will occur. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{4} \includegraphics[alt={},max width=\textwidth]{c0f31235-80aa-4838-844f-b706de55e7cd-3_193_1451_705_306}
\end{figure} $A$ and $C$ are two fixed points, 1.5 m apart, on a smooth horizontal plane. A light elastic string of natural length 0.4 m and modulus of elasticity 20 N has one end fixed to point $A$ and the other end fixed to a particle $B$. Another light elastic string of natural length 0.6 m and modulus of elasticity 15 N has one end fixed to point $C$ and the other end fixed to the particle $B$. The particle is released from rest when $A B C$ forms a straight line and $A B = 0.4 \mathrm {~m}$ (see diagram). Find the greatest kinetic energy of particle $B$ in the subsequent motion.
\includegraphics[max width=\textwidth, alt={}, center]{c0f31235-80aa-4838-844f-b706de55e7cd-3_586_533_1409_758} One end of a light inextensible string of length $a$ is attached to a fixed point $O$. A particle $P$ of mass $m$ is attached to the other end of the string and hangs at rest. $P$ is then projected horizontally from this position with speed $2 \sqrt { a g }$. When the string makes an angle $\theta$ with the upward vertical $P$ has speed $v$ (see diagram). The tension in the string is $T$.
Find an expression for $T$ in terms of $m , g$ and $\theta$, and hence find the height of $P$ above its initial level when the string becomes slack.
$P$ is now projected horizontally from the same initial position with speed $U$.
Find the set of values of $U$ for which the string does not remain taut in the subsequent motion.
\includegraphics[max width=\textwidth, alt={}, center]{c0f31235-80aa-4838-844f-b706de55e7cd-4_566_1013_255_525} Two uniform rods $A B$ and $A C$ are freely jointed at $A$. Rod $A B$ is of length $2 l$ and weight $W$; $\operatorname { rod } A C$ is of length $4 l$ and weight $2 W$. The rods rest in equilibrium in a vertical plane on two rough horizontal steps, so that $A B$ makes an angle of $\theta$ with the horizontal, where $\sin \theta = \frac { 4 } { 5 }$, and $A C$ makes an angle of $\varphi$ with the horizontal, where $\sin \varphi = \frac { 3 } { 5 }$ (see diagram). The force of the step acting on $A B$ at $B$ has vertical component $R$ and horizontal component $F$.
By taking moments about $A$ for the rod $A B$, find an equation relating $W , R$ and $F$.
Show that $R = \frac { 73 } { 50 } W$, and find the vertical component of the force acting on $A C$ at $C$.
The coefficient of friction at $B$ is equal to that at $C$. Given that one of the rods is on the point of slipping, explain which rod this must be, and find the coefficient of friction.

OCR M4 2008 June Q6

15 marks Challenging +1.3

Show that the moment of inertia of the lamina about the axis through $X$ is $\frac { 4 } { 3 } m a ^ { 2 }$.
At an instant when $\cos \theta = \frac { 3 } { 5 }$, show that $\omega ^ { 2 } = \frac { 6 g } { 5 a }$.
At an instant when $\cos \theta = \frac { 3 } { 5 }$, show that $R = 0$, and given also that $\sin \theta = \frac { 4 } { 5 }$ find $S$ in terms of $m$ and $g$.

OCR M4 2010 June Q6

12 marks Challenging +1.2

Show that $\theta = 0$ is a position of stable equilibrium.
Show that the kinetic energy of the system is $4 m a ^ { 2 } \dot { \theta } ^ { 2 }$.
By differentiating the energy equation, then making suitable approximations for $\sin \theta$ and $\cos \theta$, find the approximate period of small oscillations about the equilibrium position $\theta = 0$. \section*{[Question 7 is printed overleaf.]}

OCR M4 2013 June Q5

14 marks Standard +0.8

Find the magnitude and bearing of the velocity of $U$ relative to $P$.
Find the shortest distance between $P$ and $U$ in the subsequent motion.
(ii) Plane $Q$ is flying with constant velocity $160 \mathrm {~ms} ^ { - 1 }$ in the direction which brings it as close as possible to $U$.
Find the bearing of the direction in which $Q$ is flying.
Find the shortest distance between $Q$ and $U$ in the subsequent motion.
\includegraphics[max width=\textwidth, alt={}, center]{6e3d5f5e-7ffa-4111-903d-468fb4d20192-3_771_769_262_646} A square frame $A B C D$ consists of four uniform rods $A B , B C , C D , D A$, rigidly joined at $A , B , C , D$. Each rod has mass 0.6 kg and length 1.5 m . The frame rotates freely in a vertical plane about a fixed horizontal axis passing through the mid-point $O$ of $A D$. At time $t$ seconds the angle between $A D$ and the horizontal, measured anticlockwise, is $\theta$ radians (see diagram).
1. Show that the moment of inertia of the frame about the axis through $O$ is $3.15 \mathrm {~kg} \mathrm {~m} ^ { 2 }$.
2. Show that $\frac { \mathrm { d } ^ { 2 } \theta } { \mathrm {~d} t ^ { 2 } } = - 5.6 \sin \theta$.
3. Deduce that the frame can make small oscillations which are approximately simple harmonic, and find the period of these oscillations. The frame is at rest with $A D$ horizontal. A couple of constant moment 25 Nm about the axis is then applied to the frame.
4. Find the angular speed of the frame when it has rotated through 1.2 radians.

OCR M4 2015 June Q5

15 marks Challenging +1.8

Taking $H$ as the reference level for gravitational potential energy, show that the total potential energy $V$ of the system is given by $$V = m g \left( 2 \lambda r \cos \theta - 2 r \cos ^ { 2 } \theta - \lambda a \right)$$
Find the set of possible values of $\lambda$ so that there is more than one position of equilibrium.
For the case $\lambda = \frac { 3 } { 2 }$, determine whether each equilibrium position is stable or unstable.

OCR FP1 2011 January Q7

9 marks Moderate -0.8

Write down the matrix, $\mathbf { A }$, that represents a shear with $x$-axis invariant in which the image of the point $( 1,1 )$ is $( 4,1 )$.
The matrix $\mathbf { B }$ is given by $\mathbf { B } = \left( \begin{array} { c c } \sqrt { 3 } & 0 \\ 0 & \sqrt { 3 } \end{array} \right)$. Describe fully the geometrical transformation represented by $\mathbf { B }$.
The matrix $\mathbf { C }$ is given by $\mathbf { C } = \left( \begin{array} { l l } 2 & 6 \\ 0 & 2 \end{array} \right)$.
(a) Draw a diagram showing the unit square and its image under the transformation represented by $\mathbf { C }$.
(b) Write down the determinant of $\mathbf { C }$ and explain briefly how this value relates to the transformation represented by $\mathbf { C }$. 8 The quadratic equation $2 x ^ { 2 } - x + 3 = 0$ has roots $\alpha$ and $\beta$, and the quadratic equation $x ^ { 2 } - p x + q = 0$ has roots $\alpha + \frac { 1 } { \alpha }$ and $\beta + \frac { 1 } { \beta }$.
Show that $p = \frac { 5 } { 6 }$.
Find the value of $q$. 9 The matrix $\mathbf { M }$ is given by $\mathbf { M } = \left( \begin{array} { r r r } a & - a & 1 \\ 3 & a & 1 \\ 4 & 2 & 1 \end{array} \right)$.
Find, in terms of $a$, the determinant of $\mathbf { M }$.
Hence find the values of $a$ for which $\mathbf { M } ^ { - 1 }$ does not exist.
Determine whether the simultaneous equations $$\begin{aligned} & 6 x - 6 y + z = 3 k \\ & 3 x + 6 y + z = 0 \\ & 4 x + 2 y + z = k \end{aligned}$$ where $k$ is a non-zero constant, have a unique solution, no solution or an infinite number of solutions, justifying your answer.
Show that $\frac { 1 } { r } - \frac { 2 } { r + 1 } + \frac { 1 } { r + 2 } \equiv \frac { 2 } { r ( r + 1 ) ( r + 2 ) }$.
Hence find an expression, in terms of $n$, for $$\sum _ { r = 1 } ^ { n } \frac { 2 } { r ( r + 1 ) ( r + 2 ) }$$
Show that $\sum _ { r = n + 1 } ^ { \infty } \frac { 2 } { r ( r + 1 ) ( r + 2 ) } = \frac { 1 } { ( n + 1 ) ( n + 2 ) }$.

OCR FP1 2016 June Q8

10 marks Standard +0.3

Show that $\frac { 1 } { 2 r + 1 } - \frac { 1 } { 2 r + 3 } \equiv \frac { 2 } { ( 2 r + 1 ) ( 2 r + 3 ) }$.
Hence find $\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$, giving your answer as a single fraction.
Find $\sum _ { r = n } ^ { \infty } \frac { 1 } { ( 2 r + 1 ) ( 2 r + 3 ) }$, giving your answer as a single fraction.

OCR FP2 2010 January Q5

8 marks Standard +0.3

Using the definitions of $\sinh x$ and $\cosh x$ in terms of $\mathrm { e } ^ { x }$ and $\mathrm { e } ^ { - x }$, show that $$\cosh ^ { 2 } x - \sinh ^ { 2 } x \equiv 1$$ Deduce that $1 - \tanh ^ { 2 } x \equiv \operatorname { sech } ^ { 2 } x$.
Solve the equation $2 \tanh ^ { 2 } x - \operatorname { sech } x = 1$, giving your answer(s) in logarithmic form.
Express $\frac { 4 } { ( 1 - x ) ( 1 + x ) \left( 1 + x ^ { 2 } \right) }$ in partial fractions.
Show that $\int _ { 0 } ^ { \frac { 1 } { \sqrt { 3 } } } \frac { 4 } { 1 - x ^ { 4 } } \mathrm {~d} x = \ln \left( \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } - 1 } \right) + \frac { 1 } { 3 } \pi$.

OCR FP3 2011 January Q5

13 marks Standard +0.8

Find the general solution of the differential equation $$3 \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 5 \frac { \mathrm {~d} y } { \mathrm {~d} x } - 2 y = - 2 x + 13 .$$
Find the particular solution for which $y = - \frac { 7 } { 2 }$ and $\frac { \mathrm { d } y } { \mathrm {~d} x } = 0$ when $x = 0$.
Write down the function to which $y$ approximates when $x$ is large and positive.
$6 Q$ is a multiplicative group of order 12.
Two elements of $Q$ are $a$ and $r$. It is given that $r$ has order 6 and that $a ^ { 2 } = r ^ { 3 }$. Find the orders of the elements $a , a ^ { 2 } , a ^ { 3 }$ and $r ^ { 2 }$. The table below shows the number of elements of $Q$ with each possible order.
Order of element 1 2 3 4 6
Number of elements 1 1 2 6 2
$G$ and $H$ are the non-cyclic groups of order 4 and 6 respectively.
Construct two tables, similar to the one above, to show the number of elements with each possible order for the groups $G$ and $H$. Hence explain why there are no non-cyclic proper subgroups of $Q$.

OCR FP3 2007 June Q7

10 marks Standard +0.3

Show that $\left( z - \mathrm { e } ^ { \mathrm { i } \phi } \right) \left( z - \mathrm { e } ^ { - \mathrm { i } \phi } \right) \equiv z ^ { 2 } - ( 2 \cos \phi ) z + 1$.
Write down the seven roots of the equation $z ^ { 7 } = 1$ in the form $\mathrm { e } ^ { \mathrm { i } \theta }$ and show their positions in an Argand diagram.
Hence express $z ^ { 7 } - 1$ as the product of one real linear factor and three real quadratic factors.

Rank	1	2	3	4	5	6	7	8	9	10	11
School	\(A\)	\(A\)	\(A\)	\(B\)	\(A\)	\(A\)	\(B\)	\(B\)	\(B\)	\(B\)	\(B\)

Questions — OCR (4619 questions)

Browse by module

Browse by board

OCR S1 2011 January Q5

OCR S1 2012 January Q7

OCR S2 2007 June Q4

OCR S4 2010 June Q3

OCR M1 2010 January Q5

OCR M1 2015 June Q3

OCR M2 2008 January Q6

OCR M2 2006 June Q6

OCR M2 2008 June Q5

OCR M2 2009 June Q5

OCR M2 2015 June Q7

OCR M3 2009 January Q4

OCR M3 2010 January Q6

OCR M3 2007 June Q6

OCR M3 2010 June Q3

OCR M3 2016 June Q3

OCR M4 2008 June Q6

OCR M4 2010 June Q6

OCR M4 2013 June Q5

OCR M4 2015 June Q5

OCR FP1 2011 January Q7

OCR FP1 2016 June Q8

OCR FP2 2010 January Q5

OCR FP3 2011 January Q5

OCR FP3 2007 June Q7

\multirow[t]{21}{*}{3 }




















\multirow[t]{4}{*}{3 }



3

Order of element	1	2	3	4	6
Number of elements	1	1	2	6	2