Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
The equation of a curve is y = x ln(8 – x). The gradient of the curve is equal to 1 at only one point, when x = a.
A certain curve is such that its gradient at a general point with coordinates (x, y) is proportional to y²/x The curve passes through the points wi...
A curve has equation y = (3 cos x)/(2 + sin x) for −½π < x < ½π.
Let f(x) = (7x² – 15x + 8) / ((1-2x)(2-x)²).
Without using a calculator, express the complex number (2 + 6i)/(1-2i) in the form x + iy, where x and y are real.
The line l has equation r = 5i – 3j – k + λ(i – 2j + k). The plane p has equation (r - i - 2j).(3i + j + k) = 0. The line l intersects the plane p ...
Showing all necessary working, solve the equation (2eˣ + e⁻ˣ) / (eˣ – e⁻ˣ) = 4, giving your answer correct to 2 decimal places.
Showing all necessary working, express the complex number (2 + 3i) / (1 - 2i) in the form re^(iθ), where r > 0 and –π < θ < π. Give the values of r...
Let f(x) = (6x² + 8x + 9) / ((2 - x)(3 + 2x)²).
A particle of mass 0.2 kg moving in a straight line experiences a constant resistance force of 1.5 N. When the particle is moving at speed 2.5 m s⁻...
A high-speed train of mass 490 000 kg is moving along a straight horizontal track at a constant speed of 85 m s⁻¹. The engines are supplying 4080 k...
A van of mass 2500kg descends a hill of length 0.4 km inclined at 4° to the horizontal. There is a constant resistance to motion of 600 N and the s...
Two particles A and B, of masses m kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fi...
Coplanar forces, of magnitudes 15 N, 25 N and 30 N, act at a point B on the line ABC in the directions shown in the diagram. [Figure 5.1]
A particle is projected from a point P with initial speed u m s⁻¹ up a line of greatest slope PQR of a rough inclined plane. The distances PQ and Q...
A smooth ring R of mass mkg is threaded on a light inextensible string ARB. The ends of the string are attached to fixed points A and B with A vert...
A block of mass 5 kg is being pulled by a rope up a rough plane inclined at 6° to the horizontal. The rope is parallel to a line of greatest slope ...
The velocity of a particle moving in a straight line is vms¯¹ at time t seconds. The diagram shows a velocity-time graph which models the motion of...
Two particles P and Q, of masses 0.4 kg and 0.7 kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...
A particle moves in a straight line starting from a point O with initial velocity 1 ms¯¹. The acceleration of the particle at time t s after leavin...
A car of mass 1200 kg is driving along a straight horizontal road at a constant speed of 15 m s¯¹. There is a constant resistance to motion of 350 N.
A particle of mass 0.3 kg is released from rest above a tank containing water. The particle falls vertically, taking 0.8 s to reach the water surfa...
A small smooth ring R of mass 0.2 kg is threaded onto a light inextensible string ARB. The two ends of the string are attached to points A and B on...
A block is pushed along a horizontal floor by a force of magnitude 50N which acts at an angle of 20° to the horizontal (see diagram). The coefficie...
A particle of mass 1.2kg moves in a straight line AB. It is projected with speed 7.5 ms¯¹ from A towards B and experiences a resistance force. The ...
A runner sets off from a point P at time t = 0, where t is in seconds. The runner starts from rest and accelerates at 1.2ms¯² for 5s. For the next ...
Two particles P and Q, of masses 0.3 kg and 0.5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...
A van of mass 3200 kg travels along a horizontal road. The power of the van's engine is constant and equal to 36 kW, and there is a constant resist...
A particle moves in a straight line. The particle is initially at rest at a point O on the line. At time t s after leaving O, the acceleration a m ...
A small ball B is projected with speed 30ms¯¹ at an angle of 60° to the horizontal from a point on horizontal ground. Find the time after projectio...
A uniform object is made by attaching the base of a solid hemisphere to the base of a solid cone so that the object has an axis of symmetry. The ba...
A particle P of mass 0.4 kg is attached to a fixed point O by a light elastic string of natural length 0.5 m and modulus of elasticity 20 N. The pa...
A particle P of mass 0.5 kg is projected along a smooth horizontal surface towards a fixed point A. Initially P is at a point O on the surface, and...
A particle P of mass 0.1 kg is attached to one end of a light inextensible string of length 0.5 m. The other end of the string is attached to a fix...
Fig. 1 shows the cross-section ABCDE through the centre of mass G of a uniform prism. The cross-section consists of a rectangle ABCF from which a t...
A small object is projected with speed 24 m s¯¹ from a point O at the foot of a plane inclined at 45° to the horizontal. The angle of projection of...
A small ball B is projected with speed 38 m s⁻¹ at an angle of 30° to the horizontal from a point on horizontal ground. Find the speed of B when th...
A uniform solid object is made by attaching a cone to a cylinder so that the circumferences of the base of the cone and a plane face of the cylinde...
A small object is projected horizontally with speed V m s⁻¹ from a point O above horizontal ground. At time t s after projection, the horizontal an...
A particle P of mass 0.7 kg is attached to a fixed point O by a light elastic string of natural length 0.6 m and modulus of elasticity 15 N. The pa...
The diagram shows a uniform lamina ABCDEFGH. The lamina consists of a quarter-circle OAB of radius r m, a rectangle DEFG and two isosceles right-an...
A rough horizontal rod AB of length 0.45 m rotates with constant angular velocity 6 rad s⁻¹ about a vertical axis through A. A small ring R of mass...
A small ball B is projected with speed 30 m s⁻¹ at an angle of 60° to the horizontal from a point on horizontal ground. Find the time after project...
A small object is projected with speed 24 m s⁻¹ from a point O at the foot of a plane inclined at 45° to the horizontal. The angle of projection of...
9 people are to be divided into a group of 4, a group of 3 and a group of 2. In how many different ways can this be done?
A random variable X has the probability distribution shown in the following table, where p is a constant. X -1 0 1 2 4 P(X = x) p p 2p 2p 0.1
In an orchestra, there are 11 violinists, 5 cellists and 4 double bass players. A small group of 6 musicians is to be selected from these 20.
It is given that X ~ N(31.4, 3.6). Find the probability that a randomly chosen value of X is less than 29.4.
At the Nonland Business College, all students sit an accountancy examination at the end of their first year of study. On average, 80% of the studen...
The daily rainfall, x mm, in a certain village is recorded on 250 consecutive days. The results are summarised in the following cumulative frequenc...