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 diagram shows the curve y = √x cos x, for 0 < x < ¾π, and its minimum point M, where x = a. The shaded region between the curve and the x-axis ...
By sketching a suitable pair of graphs, show that the equation cosec x = 1 + e⁻½ˣ has exactly two roots in the interval 0 < x < π.
The diagram shows the curve y = (2 – x)e⁻½ˣ, and its minimum point M. [Figure 10.1]
Two lines have equations r = i + 2j + k + λ(ai + 2j – k) and r = 2i + j – k + µ(2i – j + k), where a is a constant.
A particle B of mass 5 kg is at rest on a smooth horizontal table. A particle A of mass 2.5 kg moves on the table with a speed of 6 m s⁻¹ and colli...
A car of mass 1400 kg is moving along a straight horizontal road against a resistance of magnitude 350 N.
Coplanar forces of magnitudes 8 N, 12 N, 10 N and P N act at a point in the directions shown in the diagram. The system is in equilibrium. [Figure ...
A particle P moves in a straight line. It starts from rest at a point O on the line and at time t s after leaving O it has acceleration a m s⁻², wh...
Two particles of masses 0.8 kg and 0.2 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The system is releas...
A car of mass 1500 kg is pulling a trailer of mass 750 kg up a straight hill of length 800 m inclined at an angle of sin⁻¹ 0.08 to the horizontal. ...
Three points A, B and C lie on a line of greatest slope of a plane inclined at an angle of 30° to the horizontal, with AB = 1 m and BC = 1m, as sho...
Two particles P and Q, of masses 0.2 kg and 0.5 kg respectively, are at rest on a smooth horizontal plane. P is projected towards Q with speed 2 m ...
A car of mass 1800 kg is travelling along a straight horizontal road. The power of the car's engine is constant. There is a constant resistance to ...
A block of mass m kg is held in equilibrium below a horizontal ceiling by two strings, as shown in the diagram. One of the strings is inclined at 4...
The diagram shows a velocity-time graph which models the motion of a car. The graph consists of four straight line segments. The car accelerates at...
A particle is projected vertically upwards with speed 40 m s⁻¹ alongside a building of height h m.
A block of mass 5 kg is placed on a plane inclined at 30° to the horizontal. The coefficient of friction between the block and the plane is μ.
A particle P moves in a straight line, starting from a point O with velocity 1.72 m s⁻¹. The acceleration a m s⁻² of the particle, t s after leavin...
Two particles A and B, 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 particle P is projected vertically upwards with speed v ms¯¹ from a point on the ground. P reaches its greatest height after 3 s.
A box of mass 5 kg is pulled at a constant speed a distance of 15 m up a rough plane inclined at an angle of 20° to the horizontal. The box moves a...
A string is attached to a block of mass 4 kg which rests in limiting equilibrium on a rough horizontal table. The string makes an angle of 24° abov...
Two small smooth spheres A and B, of equal radii and of masses 4 kg and m kg respectively, lie on a smooth horizontal plane. Initially, sphere B is...
A particle P moves in a straight line. It starts at a point O on the line and at time t s after leaving O it has velocity v m s¯¹, where v = 4t² – ...
A car of mass 1600 kg is pulling a caravan of mass 800 kg. The car and the caravan are connected by a light rigid tow-bar. The resistances to the m...
As shown in the diagram, particles A and B of masses 2 kg and 3 kg respectively are attached to the ends of a light inextensible string. The string...
Two ordinary fair dice, one red and the other blue, are thrown. Event A is 'the score on the red die is divisible by 3'. Event B is 'the sum of the...
The probability that a student at a large music college plays in the band is 0.6. For a student who plays in the band, the probability that she als...
Kayla is competing in a throwing event. A throw is counted as a success if the distance achieved is greater than 30 metres. The probability that Ka...
The random variable X takes each of the values 1, 2, 3, 4 with probability ¹/₄. Two independent values of X are chosen at random. If the two values...
The time in hours that Davin plays on his games machine each day is normally distributed with mean 3.5 and standard deviation 0.9.
The times, t minutes, taken by 150 students to complete a particular challenge are summarised in the following cumulative frequency table. Time tak...
Find the number of different ways in which the 10 letters of the word SHOPKEEPER can be arranged so that all 3 Es are together.
A fair six-sided die, with faces marked 1, 2, 3, 4, 5, 6, is thrown repeatedly until a 4 is obtained.
A bag contains 5 red balls and 3 blue balls. Sadie takes 3 balls at random from the bag, without replacement. The random variable X represents the ...
Pia runs 2 km every day and her times in minutes are normally distributed with mean 10.1 and standard deviation 1.3.
In a certain country, the weather each day is classified as fine or rainy. The probability that a fine day is followed by a fine day is 0.75 and th...
The following table gives the weekly snowfall, in centimetres, for 11 weeks in 2018 at two ski resorts, Dados and Linva. Dados 6 8 12 15 10 36 42 2...
Mr and Mrs Ahmed with their two children, and Mr and Mrs Baker with their three children, are visiting an activity centre together. They will divid...
The times taken to swim 100 metres by members of a large swimming club have a normal distribution with mean 62 seconds and standard deviation 5 sec...
An ordinary fair die is thrown until a 6 is obtained. Two ordinary fair dice are thrown together until a pair of 6s is obtained. The number of thro...
A committee of 6 people is to be chosen from 9 women and 5 men. The 9 women and 5 men include a sister and brother.
The 1300 train from Jahor to Keman runs every day. The probability that the train arrives late in Keman is 0.35.
The 8 letters in the word RESERVED are arranged in a random order.
Three coins A, B and C are each thrown once. • Coins A and B are each biased so that the probability of obtaining a head is 2/3. • Coin C is biased...
A particular piece of music was played by 91 pianists and for each pianist, the number of incorrect notes was recorded. The results are summarised ...
It is known that, on average, 1 in 300 flowers of a certain kind are white. A random sample of 200 flowers of this kind is selected.
In a survey, a random sample of 250 adults in Fromleigh were asked to fill in a questionnaire about their travel.
The masses, in kilograms, of female and male animals of a certain species have the distributions N(102, 27²) and N(170, 55²) respectively. Find the...
The diagram shows the probability density function, f(x), of a random variable X. For 0 ≤ x ≤ a, f(x) = k; elsewhere f(x) = 0. [Figure X.X]