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.
Two particles A and B, of masses 0.8 kg and 1.6 kg respectively, are connected by a light inextensible string. Particle A is placed on a smooth pla...
A particle of mass 3 kg is on a rough plane inclined at an angle of 20° to the horizontal. A force of magnitude P N acting parallel to a line of gr...
A car of mass 1400 kg travelling at a speed of v m s⁻¹ experiences a resistive force of magnitude 40v N. The greatest possible constant speed of th...
A particle P moves in a straight line starting from a point O. The velocity v m s⁻¹ of P at time t s is given by v = 12t - 4t² for 0 ≤ t ≤ 2, v = 1...
A small ball B is projected from a point O on horizontal ground. The initial velocity of B has horizontal and vertically upwards components of 18ms...
A non-uniform rod AB of length 0.5 m and weight 8 N is freely hinged to a fixed point at A. The rod makes an angle of 30° with the horizontal with ...
A particle P of mass 0.4 kg is projected horizontally along a smooth horizontal plane from a point O. At time t s after projection the velocity of ...
A small object is projected from a point O with speed V m s¯¹ at an angle of 45° above the horizontal. At time t s after projection, the horizontal...
A particle P of mass 0.7 kg is attached by a light elastic string to a fixed point O on a smooth plane inclined at an angle of 30° to the horizonta...
A particle P of mass 0.2 kg is attached to one end of a light inextensible string of length 0.6 m. The other end of the string is attached to a par...
A uniform solid cone has height 1.2 m and base radius 0.5 m. A uniform object is made by drilling a cylindrical hole of radius 0.2 m through the co...
A small ball B is projected from a point O on horizontal ground towards a point A 12m above the ground. 0.9 s after projection B has travelled a ho...
One end of a light elastic string is attached to a fixed point O. The other end of the string is attached to a particle P of mass 0.4 kg. The strin...
ABC is an object made from a uniform wire consisting of two straight portions AB and BC, in which AB = a, BC = x and angle ABC = 90°. When the obje...
A particle P is projected from a point O on horizontal ground with initial speed 20 m s⁻¹ and angle of projection 30°. At the instant t s after pro...
A uniform object is made by joining a solid cone of height 0.8 m and base radius 0.6 m and a cylinder. The cylinder has length 0.4 m and radius 0.5...
A particle P of mass 0.2 kg is released from rest at a point O above horizontal ground. At time t s after its release the velocity of P is v m s⁻¹ ...
A small object is projected from a point O with speed V m s⁻¹ at an angle of 45° above the horizontal. At time t s after projection, the horizontal...
In a statistics lesson 12 people were asked to think of a number, x, between 1 and 20 inclusive. From the results Tom found that Σx = 186 and that ...
In a survey 55 students were asked to record, to the nearest kilometre, the total number of kilometres they travelled to school in a particular wee...
Andy has 4 red socks and 8 black socks in his drawer. He takes 2 socks at random from his drawer.
The distance that car tyres of a certain make can travel before they need to be replaced has a normal distribution. A survey of a large number of t...
In Pelmerdon 22% of families own a dishwasher.
Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of th...
Find the number of different ways in which all 9 letters of the word MINCEMEAT can be arranged in each of the following cases. (A, E, I are vowels)
Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows. 37 40 45 38 36 38 42 38 40 39
In a group of students, ¾ are male. The proportion of male students who like their curry hot is ⅗ and the proportion of female students who like th...
(i) The volume of soup in Super Soup cartons has a normal distribution with mean μ millilitres and standard deviation 9 millilitres. Tests have sho...
Mrs Rupal chooses 3 animals at random from 5 dogs and 2 cats. The random variable X is the number of cats chosen.
The lengths, t minutes, of 242 phone calls made by a family over a period of 1 week are summarised in the frequency table below. Length of phone ca...
(a) Find the number of ways in which all 9 letters of the word AUSTRALIA can be arranged in each of the following cases. (i) All the vowels (A, I, ...
In a certain country, 60% of mobile phones sold are made by Company A, 35% are made by Company B and 5% are made by other companies.
The masses in kilograms of 50 children having a medical check-up were recorded correct to the nearest kilogram. The results are shown in the table....
The random variable X has the distribution N(−3, σ²). The probability that a randomly chosen value of X is positive is 0.25.
The members of a swimming club are classified either as 'Advanced swimmers' or 'Beginners'. The proportion of members who are male is x, and the pr...
Farfield Travel and Lacket Travel are two travel companies which arrange tours abroad. The numbers of holidays arranged in a certain week are recor...
A game is played with 3 coins, A, B and C. Coins A and B are biased so that the probability of obtaining a head is 0.4 for coin A and 0.75 for coin...
The diameters of apples in an orchard have a normal distribution with mean 5.7cm and standard deviation 0.8 cm. Apples with diameters between 4.1 c...
Find the number of ways the 9 letters of the word SEVENTEEN can be arranged in each of the following cases. 5 letters are chosen from the 9 letters...
Find the coefficient of x in the expansion of (2/x - 3x)^5
Two points A and B have coordinates (1, 3) and (9, –1) respectively. The perpendicular bisector of AB intersects the y-axis at the point C. Find th...
A curve is such that dy/dx = x^3 - 4/x^2. The point P (2, 9) lies on the curve.
Angle x is such that sinx = a + b and cos x = a – b, where a and b are constants.
The diagram shows a semicircle with diameter AB, centre O and radius r. The point C lies on the circumference and angle AOC = θ radians. The perime...
The equation of a curve is y = 3 cos 2x and the equation of a line is 2y + 3x/π = 5.
Functions f and g are defined by f : x ↦ 3x – 2, x ∈ R, g : x ↦ (2x + 3)/(x – 1), x ∈ R, x ≠ 1.
The position vectors of points A and B, relative to an origin O, are given by OA = (6, -2, -6) and OB = (3, k, -3), where k is a constant.
The curve C₁ has equation y = x² – 4x + 7. The curve C₂ has equation y² = 4x + k, where k is a constant. The tangent to C₁ at the point where x = 3...
(a) In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five terms. The first term is a. (b) The sum to in...
The diagram shows part of the curve y = √(4x + 1) + 9/√(4x + 1) and the minimum point M. [Figure 11.1]