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.
Let f(x) = 8x³ + 54x² - 17x-21.
Express 3 cos 2x - √3 sin 2x in the form Rcos(2x+α), where R > 0 and 0 < α < ½π. Give the exact values of R and α.
A container in the shape of a cuboid has a square base of side x and a height of (10-x). It is given that x varies with time, t, where t > 0. The c...
The equations of two straight lines are r=i+j+2ak+λ(3i+4j+ak) and r=-3i-j+4k+μ(−i+2j+2k) where a is a constant.
Use the substitution 2x = tan θ to find the exact value of ∫(from 0 to 1/2) 12 / (1+4x²)² dx. Give your answer in the form a+bπ, where a and b are ...
A car starts from rest and accelerates at 2ms⁻² for 10s. It then travels at a constant speed for 30s. The car then uniformly decelerates to rest ov...
Two forces of magnitudes 20N and FN act at a point P in the directions shown in the diagram. [Figure 2.1]
A train of mass 180000kg ascends a straight hill of length 1.5km, inclined at an angle of 1.5° to the horizontal. As it ascends the hill, the total...
A car of mass 1700kg is pulling a trailer of mass 300kg along a straight horizontal road. The car and trailer are connected by a light inextensible...
A straight slope of length 60m is inclined at an angle of 12° to the horizontal. A bobsled starts at the top of the slope with a speed of 5ms⁻¹. Th...
A particle moves in a straight line, starting from a point O. The velocity of the particle at time t s after leaving O is v m s⁻¹. It is given that...
A particle P of mass 0.2kg is projected vertically upwards from horizontal ground with speed 25ms⁻¹.
A cyclist and bicycle have a total mass of 72kg. The cyclist rides along a horizontal road against a total resistance force of 28 N. Find the total...
A particle P moves in a straight line. At time ts after leaving a point O on the line, P has velocity vms⁻¹, where v = 44t-6t² - 36.
Four coplanar forces of magnitude PN, 10N, 16N and 2N act at a point in the directions shown in the diagram. It is given that the forces are in equ...
A car has mass 1400kg. When the speed of the car is vms⁻¹ the magnitude of the resistance to motion is kv²N where k is a constant.
A particle of mass 0.8kg lies on a rough plane which is inclined at an angle of 28° to the horizontal. The particle is kept in equilibrium by a for...
Three particles A, B and C of masses 5kg, 1kg and 2kg respectively lie at rest in that order on a straight smooth horizontal track XYZ. Initially A...
Two particles P and Q of masses 2.5kg and 0.5kg respectively are connected by a light inextensible string that passes over a small smooth pulley fi...
Two particles P and Q of masses 0.2 kg and 0.5 kg respectively are at rest on a smooth horizontal plane. Particle P is projected with a speed 6ms⁻¹...
A particle of mass 0.2kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point on a verti...
A car travels along a straight road with constant acceleration a ms⁻², where a > 0. The car passes through points A, B and C in that order. The spe...
A particle travels in a straight line. The velocity of the particle at time t s after leaving a point O is v ms⁻¹, where v = kt²-4t+3. The distance...
A van of mass 4500 kg is towing a trailer of mass 750kg down a straight hill inclined at an angle of θ to the horizontal where sinθ = 0.05 . The va...
A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and her bicycle is 80 kg. There is a constant resistance fo...
The diagram shows a track ABCD which lies in a vertical plane. The section AB is a straight line inclined at an angle of 30° to the horizontal and ...
A summary of 20 values of x gives Σ(x−30) = 439, Σ(x−30)² = 12405. A summary of another 25 values of x gives Σ(x−30) = 470, Σ(x−30)² = 11346.
The lengths of the tails of adult raccoons of a certain species are normally distributed with mean 28 cm and standard deviation 3.3 cm.
The heights, in cm, of 200 adults in Barimba are summarised in the following table. Height (h cm) 130 ≤ h < 150 150 ≤ h < 160 160 ≤ h < 170 170 ≤ h...
A game for two players is played using a fair 4-sided dice with sides numbered 1, 2, 3 and 4. One turn consists of throwing the dice repeatedly up ...
In a certain area in the Arctic the probability that it snows on any given day is 0.7, independent of all other days.
Harry has three coins: • One coin is biased so that the probability of obtaining a head when it is thrown is 1/5. • The second coin is biased so th...
The eight digits 1, 2, 2, 3, 4, 4, 4, 5 are arranged in a line.
Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.3, independently...
Seva has a coin which is biased so that when it is thrown the probability of obtaining a head is ¹⁄₃. He also has a bag containing 4 red marbles an...
The weights of oranges can be modelled by a normal distribution with mean 131 grams and standard deviation 54 grams. Oranges are classified as smal...
The back-to-back stem-and-leaf diagram shows the annual salaries of 19 employees at each of two companies, Petral and Ravon. Petral 30 | 0 0 3 31 |...
Jasmine has one $5 coin, two $2 coins and two $1 coins. She selects two of these coins at random. The random variable X is the total value, in doll...
The residents of Mahjing were asked to classify their local bus service: * 25% of residents classified their service as good. * 60% of resident...
How many different arrangements are there of the 10 letters in the word REGENERATE?
The numbers on the faces of a fair six-sided dice are 1, 2, 2, 3, 3, 3. The random variable X is the total score when the dice is rolled twice.
In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m.
Box A contains 6 green balls and 3 yellow balls. Box B contains 4 green balls and x yellow balls. A ball is chosen at random from box A and placed ...
The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the followi...
Salah decides to attempt the crossword puzzle in his newspaper each day. The probability that he will complete the puzzle on any given day is 0.65,...
The 9 letters of the word RECORDERS are divided at random into two groups: a group of 5 letters and a group of 4 letters.
A bus station has exactly four entrances. In the morning the numbers of passengers arriving at these entrances during a 10-second period have the i...
The random variable X has the distribution N(31.2, 10.4²). Two independent random values of X, denoted by X₁ and X₂, are chosen. Find P(X₁ > 3X₂).
The time taken in minutes for a certain daily train journey has a normal distribution with standard deviation 5.8. For a random sample of 20 days t...
A random sample of 8 boxes of cereal from a certain supplier was taken. Each box was weighed and the masses in grams were as follows. 261 249 259 2...