Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
The line l has equation r = i + 2j + 3k + μ(2i – j – 2k).
Given that tan α = 12/5 and tan θ = 4/3, show that the coplanar forces shown in the diagram are in equilibrium. [Figure 1.1]
A particle P is projected vertically upwards with speed 25 m s⁻¹ from a point 3 m above horizontal ground.
A lorry has mass 12000 kg.
A particle of mass 1.3 kg rests on a rough plane inclined at an angle θ to the horizontal, where tan θ = 12/5. The coefficient of friction between ...
A particle P moves in a straight line from a fixed point O. The velocity v m s⁻¹ of P at time t s is given by v = t² – 8t + 12 for 0 ≤ t ≤ 8.
Two particles A and B, of masses 0.4 kg and 0.2 kg respectively, are connected by a light inextensible string. Particle A is held on a smooth plane...
Coplanar forces of magnitudes 40 N, 32 N, PN and 17 N act at a point in the directions shown in the diagram. The system is in equilibrium. Find the...
A car moves in a straight line with initial speed u m s⁻¹ and constant acceleration a m s⁻². The car takes 5 s to travel the first 80 m and it take...
A particle of mass 13 kg is on a rough plane inclined at an angle of θ to the horizontal, where tan θ = 5/12. The coefficient of friction between t...
A constant resistance to motion of magnitude 350 N acts on a car of mass 1250 kg. The engine of the car exerts a constant driving force of 1200 N. ...
A car has mass 1000 kg. When the car is travelling at a steady speed of v m s⁻¹, where v > 2, the resistance to motion of the car is (Av + B) N, wh...
Particles P and Q leave a fixed point A at the same time and travel in the same straight line. The velocity of P after t seconds is 6t(t − 3) m s⁻¹...
A bus moves in a straight line between two bus stops. The bus starts from rest and accelerates at 2.1 m s⁻² for 5 s. The bus then travels for 24 s ...
Coplanar forces of magnitudes 12 N, 24 N and 30 N act at a point in the directions shown in the diagram. [Figure X.X]
A car of mass 1400kg is travelling up a hill inclined at an angle of 4° to the horizontal. There is a constant resistance to motion of magnitude 15...
Two particles A and B, of masses 1.3 kg and 0.7 kg respectively, are connected by a light inextensible string which passes over a smooth fixed pull...
A particle of mass 18 kg is on a plane inclined at an angle of 30° to the horizontal. The particle is projected up a line of greatest slope of the ...
A particle P moves in a straight line. The acceleration a m s⁻² of P at time t s is given by a = 6t – 12. The displacement of P from a fixed point ...
A particle P of mass 0.3 kg is attached to a fixed point A by a light inextensible string of length 0.8 m. The fixed point O is 0.15 m vertically b...
A particle is projected with speed V m s¯¹ at an angle of 0° above the horizontal. At the instant 4 s after projection the speed of the particle is...
The diagram shows the cross-section through the centre of mass of a uniform solid object. The object is a cylinder of radius 0.2 m and length 0.7m,...
A small ball is projected with speed 25 m s¯¹ at an angle of 30° above the horizontal from a point O on horizontal ground. At time t s after projec...
A particle P of mass 0.4 kg is attached to one end of a light elastic string of natural length 0.5 m and modulus of elasticity 6 N. The other end o...
ABC is a uniform lamina in the form of a triangle with AB = 0.3 m, BC = 0.6 m and a right angle at B [Figure 6.1].
A particle P of mass 0.5 kg is attached to a fixed point O by a light elastic string of natural length 1 m and modulus of elasticity 16N. The parti...
A small ball is projected from a point O on horizontal ground at an angle of 30° above the horizontal. At time t s after projection the vertically ...
A uniform lamina ABCEFG is formed from a square ABDG by removing a smaller square CDFE from one corner. AB = 0.7 m and DF = 0.3 m (see diagram). Fi...
A particle P of mass 0.4 kg is attached to a fixed point A by a light inextensible string of length 0.5 m. The point A is 0.3 m above a smooth hori...
A particle P of mass 0.5 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 16 N. The other end ...
A light elastic string has natural length a m and modulus of elasticity λ N. When the length of the string is 1.6 m the tension is 4 N. When the le...
A particle is projected with speed 15 m s⁻¹ at an angle of θ° above the horizontal. At the instant 4 s after projection the speed of the particle i...
Fig. 1 shows an object made from a uniform wire of length 0.8 m. The object consists of a straight part AB, and a semicircular part BC such that A,...
A particle is projected with speed V m s⁻¹ at an angle of θ° above the horizontal. At the instant 4 s after projection the speed of the particle is...
A small ball is projected with speed 25 m s⁻¹ at an angle of 30° above the horizontal from a point O on horizontal ground. At time t s after projec...
The times, t seconds, taken to swim 100m were recorded for a group of 9 swimmers and were found to be as follows. 95 126 117 135 120 125 114 119 136
Jameel has 5 plums and 3 apricots in a box. Rosa has x plums and 6 apricots in a box. One fruit is chosen at random from Jameel's box and one fruit...
A fair six-sided die is thrown twice and the scores are noted. Event X is defined as 'The total of the two scores is 4'. Event Y is defined as ‘The...
The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both ...
In a certain country the probability that a child owns a bicycle is 0.65.
At a funfair, Amy pays $1 for two attempts to make a bell ring by shooting at it with a water pistol. • If she makes the bell ring on her first att...
The weight of adult female giraffes has a normal distribution with mean 830 kg and standard deviation 120 kg.
Freddie has 6 toy cars and 3 toy buses, all different. He chooses 4 toys to take on holiday with him.
Two ordinary fair dice are thrown and the numbers obtained are noted. Event S is 'The sum of the numbers is even'. Event T is 'The sum of the numbe...
The volume of ink in a certain type of ink cartridge has a normal distribution with mean 30 ml and standard deviation 1.5 ml. People in an office u...
The probability that Janice will buy an item online in any week is 0.35. Janice does not buy more than one item online in any week.
It is known that 20% of male giant pandas in a certain area weigh more than 121 kg and 71.9% weigh more than 102 kg. Weights of male giant pandas i...
Maryam has 7 sweets in a tin; 6 are toffees and 1 is a chocolate. She chooses one sweet at random and takes it out. Her friend adds 3 chocolates to...