Questions — Edexcel (9685 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Sort by: Default | Easiest first | Hardest first
Edexcel AEA 2017 Specimen Q1
8 marks Challenging +1.2
1.(a)For \(| y | < 1\) ,write down the binomial series expansion of \(( 1 - y ) ^ { - 2 }\) in ascending powers of \(y\) up to and including the term in \(y ^ { 3 }\) (b)Show that when it is convergent,the series $$1 + \frac { 2 x } { x + 3 } + \frac { 3 x ^ { 2 } } { ( x + 3 ) ^ { 2 } } + \ldots + \frac { r x ^ { r - 1 } } { ( x + 3 ) ^ { r - 1 } } + \ldots$$ can be written in the form \(( 1 + a x ) ^ { n }\) ,where \(a\) and \(n\) are constants to be found.
(c)Find the set of values of \(x\) for which the series in part(b)is convergent.
Edexcel AEA 2017 Specimen Q2
11 marks Challenging +1.8
2.(a)On separate diagrams,sketch the curves with the following equations.On each sketch you should label the exact coordinates of the points where the curve meets the coordinate axes.
  1. \(y = 8 + 2 x - x ^ { 2 }\)
  2. \(y = 8 + 2 | x | - x ^ { 2 }\)
  3. \(y = 8 + x + | x | - x ^ { 2 }\) (b)Find the values of \(x\) for which $$\left| 8 + x + | x | - x ^ { 2 } \right| = 8 + 2 | x | - x ^ { 2 }$$
Edexcel AEA 2017 Specimen Q3
12 marks Challenging +1.8
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-08_609_631_264_724} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure}
\includegraphics[max width=\textwidth, alt={}]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-08_172_168_781_1548}
Figure 1 shows a regular pentagon \(O A B C D\). The vectors \(\mathbf { p }\) and \(\mathbf { q }\) are defined by \(\mathbf { p } = \overrightarrow { O A }\) and \(\mathbf { q } = \overrightarrow { O D }\) respectively. Let \(k\) be the number such that \(\overrightarrow { D B } = k \overrightarrow { O A }\).
  1. Write down \(\overrightarrow { A C }\) in terms of \(\mathbf { p } , \mathbf { q }\) and \(k\) as appropriate.
  2. Show that \(\overrightarrow { C D } = - \mathbf { p } - \frac { 1 } { k } \mathbf { q }\)
  3. Hence find the value of \(k\) By considering triangle \(D B C\), or otherwise,
  4. find the exact value of \(\sin 54 ^ { \circ }\)
Edexcel AEA 2017 Specimen Q4
13 marks Challenging +1.8
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-12_428_897_251_593} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A particle of weight \(W\) lies on a rough plane.The plane is inclined to the horizontal at an angle \(\alpha\) where \(\tan \alpha = \frac { 3 } { 4 }\) .The coefficient of friction between the particle and the plane is \(\frac { 1 } { 2 }\) The particle is held in equilibrium by a force of magnitude 1.2 W .The force makes an angle \(\theta\) with the plane,where \(0 < \theta < \pi\) ,and acts in a vertical plane containing a line of greatest slope of the plane,as shown in Figure 2.
  1. Find the value of \(\theta\) for which there is no frictional force acting on the particle. The minimum value of \(\theta\) for the particle to remain in equilibrium is \(\beta\)
  2. Show that $$\beta = \arccos \left( \frac { \sqrt { 5 } } { 3 } \right) - \arctan \left( \frac { 1 } { 2 } \right)$$
  3. Find the range of values of \(\theta\) for which the particle remains in equilibrium with the frictional force acting up the plane.
Edexcel AEA 2017 Specimen Q5
13 marks Challenging +1.8
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-16_745_862_258_667} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Show that the area of the finite region between the curves \(y = \tan ^ { 2 } x\) and \(y = 4 \cos 2 x - 1\) in the interval \(- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }\), shown shaded in Figure 3, is given by $$2 \sqrt { 2 \sqrt { 3 } } - 2 \sqrt { 2 \sqrt { 3 } - 3 }$$
\includegraphics[max width=\textwidth, alt={}]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-16_2255_51_315_1987}
Edexcel AEA 2017 Specimen Q6
18 marks
6.(i)Eden,who is confused about the laws of logarithms,states that $$\left( \log _ { 5 } p \right) ^ { 2 } = \log _ { 5 } \left( p ^ { 2 } \right)$$ and \(\log _ { 5 } ( q - p ) = \log _ { 5 } q - \log _ { 5 } p\) However,there is a value of \(p\) and a value of \(q\) for which both statements are correct.
Determine these values.
(ii)(a)Let \(r \in \mathbb { R } ^ { + } , r \neq 1\) .Prove that $$\log _ { r } A = \log _ { r ^ { 2 } } B \Rightarrow A ^ { 2 } = B$$ (b)Solve $$\log _ { 4 } \left( 3 x ^ { 3 } + 26 x ^ { 2 } + 40 x \right) = 2 + \log _ { 2 } ( x + 2 )$$
\includegraphics[max width=\textwidth, alt={}]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-20_2261_53_317_1977}
Edexcel AEA 2017 Specimen Q7
25 marks Challenging +1.8
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-25_670_682_301_694} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} A circular tower of radius 1 metre stands in a large horizontal field of grass.A goat is attached to one end of a rope and the other end of the rope is attached to a fixed point \(O\) at the base of the tower.The goat cannot enter the tower. Taking the point \(O\) as the origin( 0,0 ),the centre of the base of the tower is at the point \(T ( 0,1 )\) ,where the unit of length is the metre. The rope has length \(\pi\) metres and you may ignore the size of the goat.
The curve \(C\) shown in Figure 4 represents the edge of the region that the goat can reach.
  1. Write down the equation of \(C\) for \(y < 0\) When the goat is at the point \(G ( x , y )\) ,with \(x > 0\) and \(y > 0\) ,as shown in Figure 4 ,the rope lies along \(O A G\) where \(O A\) is an arc of the circle with angle \(O T A = \theta\) radians and \(A G\) is a tangent to the circle at \(A\) .
  2. With the aid of a suitable diagram show that $$\begin{aligned} & x = \sin \theta + ( \pi - \theta ) \cos \theta \\ & y = 1 - \cos \theta + ( \pi - \theta ) \sin \theta \end{aligned}$$
  3. By considering \(\int y \frac { \mathrm {~d} x } { \mathrm {~d} \theta } \mathrm {~d} \theta\), show that the area, in the first quadrant, between \(C\), the positive \(x\)-axis and the positive \(y\)-axis can be expressed in the form $$\int _ { 0 } ^ { \pi } u \sin u \mathrm {~d} u + \int _ { 0 } ^ { \pi } u ^ { 2 } \sin ^ { 2 } u \mathrm {~d} u + \int _ { 0 } ^ { \pi } u \sin u \cos u \mathrm {~d} u$$
  4. Show that \(\int _ { 0 } ^ { \pi } u ^ { 2 } \sin ^ { 2 } u \mathrm {~d} u = \frac { \pi ^ { 3 } } { 6 } + \int _ { 0 } ^ { \pi } u \sin u \cos u \mathrm {~d} u\)
  5. Hence find the area of grass that can be reached by the goat.
Edexcel C1 Specimen Q1
3 marks Easy -1.2
  1. Calculate \(\sum _ { r = 1 } ^ { 20 } 5 + 2 r\)
  2. Find \(\int 5 x + 3 \sqrt { x } d x\)
  3. (a) Express \(\sqrt { } 80\) in the form \(a \sqrt { } 5\), where \(a\) is an integer.
    (b) Express \(( 4 - \sqrt { 5 } ) ^ { 2 }\) in the form \(b + c \sqrt { 5 }\), where \(b\) and \(c\) are integers.
  4. The points \(A\) and \(B\) have coordinates \(( 3,4 )\) and \(( 7 , - 6 )\) respectively. The straight line \(l\) passes through \(A\) and is perpendicular to \(A B\). Find an equation for \(l\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers. (5)
\begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{99113eec-7a88-4e26-9711-89253d0168ec-1_457_736_1316_747}
\end{figure} Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\).
The curve crosses the coordinate axes at the points \(( 0,1 )\) and \(( 3,0 )\). The maximum point on the curve is \(( 1,2 )\). On separate diagrams, sketch the curve with equation
Edexcel C1 Specimen Q6
9 marks Moderate -0.8
6. (a) Solve the simultaneous equations $$\begin{aligned} & y + 2 x = 5 \\ & 2 x ^ { 2 } - 3 x - y = 16 \end{aligned}$$ (b) Hence, or otherwise, find the set of values of \(x\) for which $$2 x ^ { 2 } - 3 x - 16 > 5 - 2 x$$
Edexcel C1 Specimen Q7
9 marks Moderate -0.8
  1. Ahmed plans to save \(\pounds 250\) in the year 2001, \(\pounds 300\) in 2002, \(\pounds 350\) in 2003, and so on until the year 2020. His planned savings form an arithmetic sequence with common difference £50.
    1. Find the amount he plans to save in the year 2011.
    2. Calculate his total planned savings over the 20 year period from 2001 to 2020.
    Ben also plans to save money over the same 20 year period. He saves \(\pounds A\) in the year 2001 and his planned yearly savings form an arithmetic sequence with common difference \(\pounds 60\). Given that Ben's total planned savings over the 20 year period are equal to Ahmed's total planned savings over the same period,
  2. calculate the value of \(A\).
Edexcel C1 Specimen Q8
11 marks Moderate -0.8
8. Given that $$x ^ { 2 } + 10 x + 36 = ( x + a ) ^ { 2 } + b$$ where \(a\) and \(b\) are constants,
  1. find the value of \(a\) and the value of \(b\).
  2. Hence show that the equation \(x ^ { 2 } + 10 x + 36 = 0\) has no real roots. The equation \(x ^ { 2 } + 10 x + k = 0\) has equal roots.
  3. Find the value of \(k\).
  4. For this value of \(k\), sketch the graph of \(y = x ^ { 2 } + 10 x + k\), showing the coordinates of any points at which the graph meets the coordinate axes.
Edexcel C1 Specimen Q9
11 marks Moderate -0.8
9. The curve \(C\) has equation \(y = \mathrm { f } ( x )\) and the point \(P ( 3,5 )\) lies on \(C\). Given that $$f ( x ) = 3 x ^ { 2 } - 8 x + 6$$
  1. find \(\mathrm { f } ( x )\).
  2. Verify that the point \(( 2,0 )\) lies on \(C\). The point \(Q\) also lies on \(C\), and the tangent to \(C\) at \(Q\) is parallel to the tangent to \(C\) at \(P\).
  3. Find the \(x\)-coordinate of \(Q\).
Edexcel C1 Specimen Q10
13 marks Moderate -0.8
10. The curve \(C\) has equation \(y = x ^ { 3 } - 5 x + \frac { 2 } { x } , x \neq 0\). The points \(A\) and \(B\) both lie on \(C\) and have coordinates \(( 1 , - 2 )\) and \(( - 1,2 )\) respectively.
  1. Show that the gradient of \(C\) at \(A\) is equal to the gradient of \(C\) at \(B\).
  2. Show that an equation for the normal to \(C\) at \(A\) is \(4 y = x - 9\). The normal to \(C\) at \(A\) meets the \(y\)-axis at the point \(P\). The normal to \(C\) at \(B\) meets the \(y\)-axis at the point \(Q\).
  3. Find the length of \(P Q\).
Edexcel FP2 2008 June Q1
5 marks Moderate -0.5
\begin{enumerate} \item Solve the differential equation \(\frac { \mathrm { d } y } { \mathrm {~d} x } - 3 y = x\) to obtain \(y\) as a function of \(x\). \item (a) Simplify the expression \(\frac { ( x + 3 ) ( x + 9 ) } { x - 1 } - ( 3 x - 5 )\), giving your answer in the form \(\frac { a ( x + b ) ( x + c ) } { x - 1 }\), where \(a , b\) and \(c\) are integers.
(b) Hence, or otherwise, solve the inequality \(\frac { ( x + 3 ) ( x + 9 ) } { x - 1 } > 3 x - 5 \quad\) (4)(Total \(\mathbf { 8 }\) marks) \item (a) Find the general solution of the differential equation \(3 \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - \frac { \mathrm { d } y } { \mathrm {~d} x } - 2 y = x ^ { 2 }\) (b) Find the particular solution for which, at \(x = 0 , y = 2\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3\).(6)(Total 14 marks) \item The diagram above shows the curve \(C _ { 1 }\) which has polar equation \(\boldsymbol { r } = \boldsymbol { a } ( \mathbf { 3 } + \mathbf { 2 } \boldsymbol { \operatorname { c o s } } \boldsymbol { \theta } ) , 0 \leq \theta < 2 \pi\) and the circle \(C _ { 2 }\) with equation \(\boldsymbol { r } = \mathbf { 4 } \boldsymbol { a } , 0 \leq \theta < 2 \pi\), where \(a\) is a positive constant.
Edexcel FP2 2008 June Q5
9 marks Standard +0.8
5. (a) Find, in terms of \(k\), the general solution of the differential equation $$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 4 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 3 x = k t + 5 , \text { where } k \text { is a constant and } t > 0 .$$ For large values of \(t\), this general solution may be approximated by a linear function.
(b) Given that \(k = 6\), find the equation of this linear function.(2)(Total 9 marks)
Edexcel FP2 2008 June Q6
10 marks Standard +0.8
6. (a) Find, in the simplest surd form where appropriate, the exact values of \(x\) for which $$\frac { x } { 2 } + 3 = \left| \frac { 4 } { x } \right|$$ (b) Sketch, on the same axes, the line with equation \(y = \frac { x } { 2 } + 3\) and the graph of \(y = \left| \frac { 4 } { x } \right| , \quad x \neq 0\).
(c) Find the set of values of \(x\) for which \(\frac { x } { 2 } + 3 > \left| \frac { 4 } { x } \right|\).
(2)(Total 10 marks)
Edexcel FP2 2008 June Q7
12 marks Standard +0.8
7. (a) Show that the substitution \(y = v x\) transforms the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x } { y } + \frac { 3 y } { x } , \quad x > 0 , \quad y > 0$$ into the differential equation $$x \frac { \mathrm {~d} v } { \mathrm {~d} x } = 2 v + \frac { 1 } { v } .$$ (b) By solving differential equation (II), find a general solution of differential equation (I) in the form \(y = \mathrm { f } ( x )\). Given that \(y = 3\) at \(x = 1\),
(c)find the particular solution of differential equation (I).(2)
Edexcel FP2 2008 June Q8
13 marks Challenging +1.8
8. The curve \(C\) shown in the diagram above has polar equation $$r = 4 ( 1 - \cos \theta ) , 0 \leq \theta \leq \frac { \pi } { 2 }$$ At the point \(P\) on \(C\), the tangent to \(C\) is parallel to the line \(\theta = \frac { \pi } { 2 }\).
  1. Show that \(P\) has polar coordinates \(\left( 2 , \frac { \pi } { 3 } \right)\). The curve \(C\) meets the line \(\theta = \frac { \pi } { 2 }\) at the point \(A\). The tangent to \(C\) at the initial line at the point \(N\). The finite region \(R\), shown shaded in \includegraphics[max width=\textwidth, alt={}]{863ef52d-ae75-450c-9eab-8102804868f5-2_737_561_1395_1329} the diagram above, is bounded by the initial line, the line \(\theta = \frac { \pi } { 2 }\), the arc \(A P\) of \(C\) and the line \(P N\).
  2. Calculate the exact area of \(R\).
Edexcel FP2 2008 June Q9
8 marks Challenging +1.2
9. $$\left( x ^ { 2 } + 1 \right) \frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = 2 y ^ { 2 } + ( 1 - 2 x ) \frac { \mathrm { d } y } { \mathrm {~d} x }$$
  1. By differentiating equation (I) with respect to \(x\), show that $$\left( x ^ { 2 } + 1 \right) \frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } } = ( 1 - 4 x ) \frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + ( 4 y - 2 ) \frac { \mathrm { d } y } { \mathrm {~d} x }$$ Given that \(y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 1\) at \(x = 0\),
  2. find the series solution for \(y\), in ascending powers of \(x\), up to and including the term in \(x _ { 3 }\).(4)
  3. Use your series to estimate the value of \(y\) at \(x = - 0.5\), giving your answer to two decimal places.(1)
Edexcel FP2 2008 June Q10
12 marks Standard +0.8
10. The point \(P\) represents a complex number \(z\) on an Argand diagram such that $$| z - 3 | = 2 | z |$$
  1. Show that, as \(z\) varies, the locus of \(P\) is a circle, and give the coordinates of the centre and the radius of the circle.(5) The point \(Q\) represents a complex number \(z\) on an Argand diagram such that $$| z + 3 | = | z - i \sqrt { } 3 |$$
  2. Sketch, on the same Argand diagram, the locus of \(P\) and the locus of \(Q\) as \(z\) varies.(5)
  3. On your diagram shade the region which satisfies $$| z - 3 | \geq 2 | z | \text { and } | z + 3 | \geq | z - i \sqrt { } 3 |$$
Edexcel FP2 2008 June Q11
13 marks Challenging +1.2
  1. De Moivre's theorem states that \(\quad ( \cos \theta + \mathrm { i } \sin \theta ) ^ { n } = \cos n \theta + \mathrm { i } \sin n \theta\) for \(n \in \Re\)
    1. Use induction to prove de Moivre's theorem for \(n \in \mathbb { Z } ^ { + }\).
    2. Show that \(\cos 5 \theta = 16 \cos ^ { 5 } \theta - 20 \cos ^ { 3 } \theta + 5 \cos \theta\)
    3. Hence show that \(2 \cos \frac { \pi } { 10 }\) is a root of the equation
    $$x ^ { 4 } - 5 x ^ { 2 } + 5 = 0$$
Edexcel M1 Specimen Q1
5 marks Moderate -0.8
  1. A particle \(P\) is moving with constant velocity \(( - 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). At time \(t = 6 \mathrm {~s} P\) is at the point with position vector \(( - 4 \mathbf { i } - 7 \mathbf { j } ) \mathrm { m }\). Find the distance of \(P\) from the origin at time \(t = 2 \mathrm {~s}\).
Edexcel M1 Specimen Q2
7 marks Moderate -0.3
2. Particle \(P\) has mass \(m \mathrm {~kg}\) and particle \(Q\) has mass \(3 m \mathrm {~kg}\). The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision \(P\) has speed \(4 u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) has speed \(k u \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(k\) is a constant. As a result of the collision the direction of motion of each particle is reversed and the speed of each particle is halved.
  1. Find the value of \(k\).
  2. Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted on \(P\) by \(Q\).
Edexcel M1 Specimen Q3
7 marks Moderate -0.8
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ab3c0d61-3cab-4050-8288-6052e8404eb1-06_182_872_310_543} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A small box is pushed along a floor. The floor is modelled as a rough horizontal plane and the box is modelled as a particle. The coefficient of friction between the box and the floor is \(\frac { 1 } { 2 }\). The box is pushed by a force of magnitude 100 N which acts at an angle of \(30 ^ { \circ }\) with the floor, as shown in Figure 1. Given that the box moves with constant speed, find the mass of the box.
Edexcel M1 Specimen Q6
10 marks Moderate -0.8
  1. A ball is projected vertically upwards with a speed of \(14.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point which is 49 m above horizontal ground. Modelling the ball as a particle moving freely under gravity, find
    1. the greatest height, above the ground, reached by the ball,
    2. the speed with which the ball first strikes the ground,
    3. the total time from when the ball is projected to when it first strikes the ground.