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 M1 Q1
6 marks Standard +0.3
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c762bd90-5b57-428a-a7a8-291a1a643a14-2_286_933_203_452} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} Figure 1 shows a non-uniform beam \(A B\) of mass 10 kg and length 6 m resting in a horizontal position on a single support 2 m from \(A\). The beam is supported at \(B\) by a vertical string. Given that the magnitude of the tension in the string is 1.5 times the magnitude of the reaction at the support, find the distance of the centre of mass of the beam from \(A\).
(6 marks)
Edexcel M1 Q2
9 marks Moderate -0.3
2. A ball of mass 2 kg moves on a smooth horizontal surface under the action of a constant force, \(\mathbf { F }\). The initial velocity of the ball is \(( 2 \mathbf { i } - 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) and 4 seconds later it has velocity \(( 10 \mathbf { i } + 9 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) where \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular, horizontal unit vectors.
  1. Making reference to the mass of the ball and the force it experiences, explain why it is reasonable to assume that the acceleration is constant.
  2. Find, giving your answers correct to 3 significant figures,
    1. the magnitude of the acceleration experienced by the ball,
    2. the angle which \(\mathbf { F }\) makes with the vector \(\mathbf { i }\).
Edexcel M1 Q3
9 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c762bd90-5b57-428a-a7a8-291a1a643a14-3_309_590_196_518} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Figure 2 shows a ball of mass 3 kg lying on a smooth plane inclined at an angle \(\alpha\) to the horizontal where \(\sin \alpha = \frac { 3 } { 5 }\). The ball is held in equilibrium by a force of magnitude \(P\) newtons, which acts at an angle of \(10 ^ { \circ }\) to the line of greatest slope of the plane.
  1. Suggest a suitable model for the ball. Giving your answers correct to 1 decimal place,
  2. find the value of \(P\),
  3. find the magnitude of the reaction between the ball and the plane.
Edexcel M1 Q4
9 marks Standard +0.3
4. A bullet of mass 50 g is fired horizontally at a wooden block of mass 4.95 kg which is lying at rest on a rough horizontal surface. The bullet enters the block at \(400 \mathrm {~ms} ^ { - 1 }\) and becomes embedded in the block.
  1. Find the speed with which the block begins to move. Given that the block decelerates uniformly to rest over a distance of 4 m ,
  2. show that the coefficient of friction is \(\frac { 2 } { g }\).
Edexcel M1 Q5
11 marks Standard +0.3
5. Two dogs, Fido and Growler, are playing in a field. Fido is moving in a straight line so that at time \(t\) his position vector relative to a fixed origin, \(O\), is given by \([ ( 2 t - 3 ) \mathbf { i } + t \mathbf { j } ]\) metres. Growler is stationary at the point with position vector \(( 2 \mathbf { i } + 5 \mathbf { j } )\) metres, where \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal perpendicular unit vectors.
  1. Find the displacement vector of Fido from Growler in terms of \(t\).
  2. Find the value of \(t\) for which the two dogs are closest.
  3. Find the minimum distance between the two dogs.
Edexcel M1 Q6
12 marks Standard +0.3
6. A particle moving in a straight line with speed \(5 U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) undergoes a uniform deceleration for 6 seconds which reduces its speed to \(2 \mathrm { Um } \mathrm { s } ^ { - 1 }\). It maintains this speed for 16 seconds before uniformly decelerating to rest in a further 2 seconds.
  1. Sketch a speed-time graph displaying this information.
  2. Find an expression for each of the decelerations in terms of \(U\). Given that the total distance travelled by the particle during this period of motion is 220 m ,
  3. find the value of \(U\).
Edexcel M1 Q7
19 marks Standard +0.3
7. A car of mass 1200 kg tows a trailer of mass 800 kg along a straight level road by means of a rigid towbar. The resistances to the motion of the car and the trailer are proportional to their masses. Given that the car experiences a resistance to motion of 300 N ,
  1. find the resistance to motion which the trailer experiences. Given that the engine of the car exerts a driving force of 3 kN ,
  2. find the acceleration of the system,
  3. show that the tension in the towbar is 1200 N . When the system has reached a speed of \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it continues at constant speed until an electrical fault causes the engine of the car to switch off. The brakes are used to apply a constant retarding force until the system comes to rest. Given that the retarding force of the brakes has magnitude 1 kN and assuming that the original resistances to motion of the car and the trailer remain constant,
  4. calculate the distance that the system travels during the braking period,
  5. find the magnitude and direction of the force exerted by the towbar on the car.
  6. Comment on the assumption that the original resistances to motion of the car and the trailer remain constant throughout the motion.
Edexcel M1 Q1
6 marks Easy -1.2
1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6fb27fe5-055a-4701-bd80-e66ebd57292a-2_403_550_214_609} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} Figure 1 shows a light, inextensible string fixed at one end to a point \(P\). The other end is attached to a small object of weight 10 N . The object is subjected to a horizontal force \(H\) so that the string makes an angle of \(30 ^ { \circ }\) with the vertical.
  1. Find the magnitude of the tension in the string.
  2. Show that the ratio of the magnitude of the tension to the magnitude of \(H\) is \(2 : 1\).
Edexcel M1 Q2
8 marks Moderate -0.8
2. A particle of mass 8 kg moves in a horizontal plane and is acted upon by three forces \(\mathbf { F } _ { 1 } = ( 5 \mathbf { i } - 3 \mathbf { j } ) \mathrm { N } , \mathbf { F } _ { 2 } = ( 3 \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }\) and \(\mathbf { F } _ { 3 } = ( 4 \mathbf { i } - 5 \mathbf { j } ) \mathrm { N }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.
  1. Find the magnitude, in newtons, of the resultant force which acts on the particle, giving your answer in the form \(k \sqrt { } 5\).
  2. Calculate, giving your answer in degrees correct to 1 decimal place, the angle the acceleration of the particle makes with the vector \(\mathbf { i }\).
Edexcel M1 Q3
9 marks Standard +0.3
3. A lorry accelerates uniformly from \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in 30 seconds.
  1. Find how far it travels while accelerating.
  2. Find, in seconds correct to 2 decimal places, the length of time it takes for the lorry to cover the first half of this distance.
    (6 marks)
Edexcel M1 Q4
10 marks Standard +0.3
4. In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors and \(O\) is a fixed origin. A pedestrian moves with constant velocity \(\left[ \left( 2 q ^ { 2 } - 3 \right) \mathbf { i } + ( q + 2 ) \mathbf { j } \right] \mathrm { ms } ^ { - 1 }\). Given that the velocity of the pedestrian is parallel to the vector \(( \mathbf { i } - \mathbf { j } )\),
  1. Show that one possible value of \(q\) is \({ } ^ { - } 1\) and find the other possible value of \(q\). Given that \(q = { } ^ { - } 1\), and that the pedestrian started walking at the point with position vector \(( 6 \mathbf { i } - \mathbf { j } ) \mathrm { m }\),
  2. find the length of time for which the pedestrian is less than 5 m from \(O\).
Edexcel M1 Q5
11 marks Standard +0.3
5. A sledgehammer of mass 12 kg is being used to drive a wooden post of mass 4 kg into the ground. A labourer moves the sledgehammer from rest at a point 0.5 m vertically above the post with constant acceleration \(16 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) directed towards the post.
  1. Find the velocity with which the sledgehammer hits the post. When the sledgehammer hits the post, they both move together with common speed, \(V\).
  2. Show that \(V = 3 \mathrm {~ms} ^ { - 1 }\). As the sledgehammer hits the post, the labourer relaxes his grip and applies no further force. The sledgehammer and post are brought to rest by the action of a resistive force from the ground of magnitude 1500 N .
  3. Find, in centimetres, the total distance that the sledgehammer and the post travel together before coming to rest.
Edexcel M1 Q6
12 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6fb27fe5-055a-4701-bd80-e66ebd57292a-4_252_726_194_561} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Figure 2 shows a picnic bench of mass 20 kg which consists of a horizontal plank of wood of length 2 m resting on two supports, each of which is 0.6 m from the centre of the plank. Luigi sits on the bench at its midpoint and his mother Maria sits at one end. Their masses are 40 kg and 75 kg respectively. By modelling the bench as a uniform rod and Luigi and Maria as particles,
  1. find the reaction at each of the two supports. Luigi moves to sit closer to his mother.
  2. Find how close Luigi can get to his mother before the reaction at one of the supports becomes zero.
  3. Explain the significance of a zero reaction at one of the supports.
Edexcel M1 Q7
19 marks Standard +0.8
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6fb27fe5-055a-4701-bd80-e66ebd57292a-5_417_1016_237_440} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure} Figure 3 shows a particle of mass 4 kg resting on the surface of a rough plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. It is connected by a light inextensible string passing over a smooth pulley at the top of the plane, to a particle of mass 5 kg which hangs freely. The coefficient of friction between the 4 kg mass and the plane is \(\mu\) and when the system is released from rest the 4 kg mass starts to move up the slope.
  1. Show that the acceleration of the system is \(\frac { 1 } { 9 } ( 3 - 2 \mu \sqrt { 3 } ) \mathrm { g } \mathrm { ms } ^ { - 2 }\).
  2. Hence, find the maximum value of \(\mu\). Given that \(\mu = \frac { 1 } { 2 }\),
  3. find the tension in the string in terms of \(g\),
  4. show that the magnitude of the force on the pulley is given by \(\frac { 5 } { 3 } ( 2 \sqrt { 3 } + 1 ) \mathrm { g }\). END
Edexcel M1 Q1
5 marks Moderate -0.8
  1. The resultant of two forces \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\) is \(( - 2 \mathbf { i } + 9 \mathbf { j } ) \mathrm { N }\).
Given that \(\mathbf { F } _ { \mathbf { 1 } } = ( 2 p \mathbf { i } - 3 q \mathbf { j } ) \mathrm { N }\) and \(\mathbf { F } _ { \mathbf { 2 } } = ( 5 q \mathbf { i } + 4 p \mathbf { j } ) \mathrm { N }\), calculate the values of \(p\) and \(q\).
(5 marks)
Edexcel M1 Q2
10 marks Moderate -0.8
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{10b4d660-3980-4204-b18d-5240dea61a45-2_321_666_584_534} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} Figure 1 shows a toy lorry being pulled by a piece of string, up a ramp inclined at an angle of \(25 ^ { \circ }\) to the horizontal. When the string is pulled with a force of 20 N parallel to the line of greatest slope of the ramp, the lorry is on the point of moving up the ramp. In a simple model of the situation, the ramp is considered to be smooth.
  1. Draw a diagram showing all the forces acting on the lorry.
  2. Find the weight of the lorry and the magnitude of the reaction between the lorry and the ramp, giving your answers to an appropriate degree of accuracy.
  3. Write down any modelling assumptions that you have made about
    1. the lorry,
    2. the string. In a more refined model, the ramp is assumed to be rough.
  4. State the effect that this would have on your answers to part (b).
Edexcel M1 Q3
11 marks Moderate -0.3
3. A cannon of mass 600 kg lies on a rough horizontal surface and is used to fire a 3 kg shell horizontally at \(200 \mathrm {~ms} ^ { - 1 }\).
  1. Find the impulse which the shell exerts on the cannon.
  2. Find the speed with which the cannon recoils. Given that the coefficient of friction between the cannon and the surface is 0.75 ,
  3. calculate, to the nearest centimetre, the distance that the cannon travels before coming to rest.
Edexcel M1 Q4
11 marks Moderate -0.8
4. The position of an aeroplane flying in a straight horizontal line at constant speed is plotted on a radar screen. At 2 p.m. the position vector of the aeroplane is \(( 80 \mathbf { i } + 5 \mathbf { j } )\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors directed east and north respectively relative to a fixed origin, \(O\), on the screen. Ten minutes later the position of the aeroplane on the screen is \(( 32 \mathbf { i } + 19 \mathbf { j } )\). Each unit on the screen represents 1 km .
  1. Find the position vector of the aeroplane at 2:30 p.m.
  2. Find the speed of the aeroplane in \(\mathrm { km } \mathrm { h } ^ { - 1 }\).
  3. Find, correct to the nearest degree, the bearing on which the aeroplane is flying.
Edexcel M1 Q5
11 marks Standard +0.3
5. A car on a straight test track starts from rest and accelerates to a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in 6 seconds. The car maintains this speed for a further 50 seconds before decelerating to rest. In a simple model of this motion, the acceleration and deceleration are assumed to be uniform and the magnitude of the deceleration to be 1.5 times that of the acceleration.
  1. Show that the total time for which the car is moving is 60 seconds.
  2. Sketch a velocity-time graph for this journey. Given that the total distance travelled is 1320 metres,
  3. find \(V\). In a more sophisticated model, the acceleration is assumed to be inversely proportional to the velocity of the car.
  4. Explain how the acceleration would vary during the first six seconds under this model.
    (2 marks)
Edexcel M1 Q6
12 marks Moderate -0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{10b4d660-3980-4204-b18d-5240dea61a45-4_250_1036_1251_422} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Figure 2 shows a bench of length 3 m being used in a gymnasium.
The bench rests horizontally on two identical supports which are 2.2 m apart and equidistant from the middle of the bench.
  1. Explain why it is reasonable to model the bench as a uniform rod. When a gymnast of mass 55 kg stands on the bench 0.1 m from one end, the bench is on the point of tilting.
  2. Find the mass of the bench. The first gymnast dismounts and a second gymnast of mass 33 kg steps onto the bench at a distance of 0.4 m from its centre.
  3. Show that the magnitudes of the reaction forces on the two supports are in the ratio \(5 : 3\).
    (6 marks)
Edexcel M1 Q7
15 marks Standard +0.2
7. A car of mass 1250 kg tows a caravan of mass 850 kg up a hill inclined at an angle \(\alpha\) to the horizontal where \(\sin \alpha = \frac { 1 } { 14 }\). The total resistance to motion experienced by the car is 400 N , and by the caravan is 500 N . Given that the driving force of the engine is 3 kN ,
  1. show that the acceleration of the system is \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\),
  2. find the tension in the towbar linking the car and the caravan. Starting from rest, the car accelerates uniformly for 540 m until it reaches a speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the top of the hill.
  3. Find v. At the top of the hill the road becomes level and the driver maintains the speed at which the car and caravan reached the top of the hill.
  4. Assuming that the resistance to motion on each part of the system is unchanged, find the percentage reduction in the driving force of the engine required to achieve this.
Edexcel M1 Q1
8 marks Moderate -0.8
  1. At time \(t = 0\), a particle of mass 2 kg has velocity \(( 8 \mathbf { i } + \lambda \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) where \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal perpendicular unit vectors and \(\lambda > 0\).
Given that the speed of the particle at time \(t = 0\) is \(17 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
  1. find the value of \(\lambda\). The particle experiences a constant retarding force \(\mathbf { F }\) so that when \(t = 5\), it has velocity \(( 3 \mathbf { i } + 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
  2. Show that \(\mathbf { F }\) can be written in the form \(\mu ( \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }\) where \(\mu\) is a constant which you should find.
    (5 marks)
Edexcel M1 Q2
8 marks Standard +0.3
2. A monk uses a small brush to clean the stone floor of a monastery by pushing the brush with a force of \(P\) Newtons at an angle of \(60 ^ { \circ }\) to the vertical. He moves the brush at a constant speed. The mass of the brush is 0.5 kg and the coefficient of friction between the brush and the floor is \(\frac { 1 } { \sqrt { 3 } }\). The brush is modelled as a particle and air resistance is ignored.
  1. Show that \(P = \frac { g } { 2 }\) Newtons.
  2. Explain why it is reasonable to ignore air resistance in this situation.
Edexcel M1 Q3
10 marks Standard +0.8
3. A small van of mass 1500 kg is used to tow a car of mass 750 kg by means of a rope of length 9 m joined to both vehicles. The van sets off with the rope slack and reaches a speed of \(2 \mathrm {~ms} ^ { - 1 }\) just before the rope becomes taut and jerks the car into motion. Immediately after the rope becomes taut, the van and car travel with common speed \(V \mathrm {~ms} ^ { - 1 }\).
  1. Show that \(V = \frac { 4 } { 3 }\).
  2. Calculate the magnitude of the impulse on the car when the rope tightens. The van and car eventually reach a steady speed of \(18 \mathrm {~ms} ^ { - 1 }\) with the rope taut when a child runs out into the road, 30 m in front of the van. The van driver brakes sharply and decelerates uniformly to rest in a distance of 27 m . It takes the driver of the car 1 second to react to the van starting to brake. He then brakes and the car decelerates uniformly at \(f \mathrm {~m} \mathrm {~s} ^ { - 2 }\), coming to rest before colliding with the van.
  3. Find the set of possible values of \(f\).
    (5 marks)
Edexcel M1 Q4
10 marks Standard +0.8
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4fe54579-ac77-46f9-85e1-2e95963d6b3e-3_467_348_201_708} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} Figure 1 shows a weight \(A\) of mass 6 kg connected by a light, inextensible string which passes over a smooth, fixed pulley to a box \(B\) of mass 5 kg . There is an object \(C\) of mass 3 kg resting on the horizontal floor of box \(B\). The system is released from rest. Find, giving your answers in terms of \(g\),
  1. the acceleration of the system,
  2. the force on the pulley.
  3. Show that the reaction between \(C\) and the floor of \(B\) is \(\frac { 18 } { 7 } \mathrm {~g}\) newtons.