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.
A particle of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus of elasticity 9N. The other end of t...
A particle P of mass 0.5 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus of elasticity 12N. The other end o...
A particle is projected from a point O on horizontal ground with speed Vms¯¹ at an angle of 60° above the horizontal. At the instant 3 s after proj...
A and B are two fixed points on a vertical axis with A above B. A particle P of mass 0.4 kg is attached to A by a light inextensible string of leng...
A particle P of mass 0.2kg is projected horizontally from a fixed point O on a smooth horizontal surface. When the displacement of P from O is xm t...
ABCD is a uniform lamina in the shape of a trapezium which has centre of mass G. The sides AD and BC are parallel and 1.8 m apart, with AD = 2.4 m ...
A particle is projected from a point on horizontal ground with speed 15 m s⁻¹ at an angle of θ° above the horizontal. The particle strikes the grou...
A small ball B is projected with speed 30 m s⁻¹ at an angle of 60° above the horizontal from a point O. At time t s after projection the horizontal...
When Shona goes to college she either catches the bus with probability 0.8 or she cycles with probability 0.2. If she catches the bus, the probabil...
Annan has designed a new logo for a sportswear company. A survey of a large number of customers found that 42% of customers rated the logo as good.
The mean and standard deviation of 20 values of x are 60 and 4 respectively.
In a probability distribution the random variable X takes the values −1, 0, 1, 2, 4. The probability distribution table for X is as follows. X -1 0...
Ransha measured the lengths, in centimetres, of 160 palm leaves. His results are illustrated in the cumulative frequency graph below. [Figure with ...
The word STEEPLECHASE has 12 letters.
The shortest time recorded by an athlete in a 400 m race is called their personal best (PB). The PBs of the athletes in a large athletics club are ...
Twelve tourists were asked to estimate the height, in metres, of a new building. Their estimates were as follows. 50 45 62 30 40 55 110 38 52 60 55 40
Benju cycles to work each morning and he has two possible routes. He chooses the hilly route with probability 0.4 and the busy route with probabili...
The speeds, in kmh⁻¹, of 90 cars as they passed a certain marker on a road were recorded, correct to the nearest kmh⁻¹. The results are summarised ...
In Quarendon, 66% of households are satisfied with the speed of their wifi connection.
A fair red spinner has four sides, numbered 1, 2, 3, 3. A fair blue spinner has three sides, numbered −1, 0, 2. When a spinner is spun, the score i...
The heights, in metres, of fir trees in a large forest have a normal distribution with mean 40 and standard deviation 8.
The word TOADSTOOL has 9 letters.
There are 300 students at a music college. All students play exactly one of the guitar, the piano or the flute. The numbers of male and female stud...
How many different arrangements are there of the 9 letters in the word CORRIDORS?
A sports team of 7 people is to be chosen from 6 attackers, 5 defenders and 4 midfielders. The team must include at least 3 attackers, at least 2 d...
The heights of students at the Mainland college are normally distributed with mean 148 cm and standard deviation 8 cm.
Last Saturday, 200 drivers entering a car park were asked the time, in minutes, that it had taken them to travel from home to the car park. The res...
A box contains 3 red balls and 5 white balls. One ball is chosen at random from the box and is not returned to the box. A second ball is now chosen...
A competition is taking place between two choirs, the Notes and the Classics. There is a large audience for the competition. * 30% of the audienc...
The coefficient of x³ in the expansion of (1 + kx)(1 – 2x)⁵ is 20. Find the value of the constant k.
The first, second and third terms of a geometric progression are 2p + 6, −2p and p + 2 respectively, where p is positive. Find the sum to infinity ...
The equation of a curve is y = 2x² + m(2x + 1), where m is a constant, and the equation of a line is y = 6x + 4. Show that, for all values of m, th...
The sum, Sₙ, of the first n terms of an arithmetic progression is given by Sₙ = n² + 4n. The kth term in the progression is greater than 200. Find ...
Functions f and g are defined by f(x) = 4x – 2, for x ∈ R, g(x) = 4/(x+1), for x ∈ R, x ≠ −1.
Prove the identity ( 1 COS X – tan x )( 1 sin x + 1 ) ≡ 1 tan x
The point (4, 7) lies on the curve y = f(x) and it is given that f'(x) = 6x⁻½ – 4x⁻³/₂.
In the diagram, ABC is an isosceles triangle with AB = BC = r cm and angle BAC = θ radians. The point D lies on AC and ABD is a sector of a circle ...
A circle has centre at the point B (5, 1). The point A (−1, –2) lies on the circle.
The diagram shows part of the curve y = 2/(3-2x)² - x and its minimum point M, which lies on the x-axis. [Figure 10.1]
A curve has equation y = 3 cos 2x + 2 for 0 ≤ x ≤ π.
Given that ln(2x + 1) – ln(x − 3) = 2, find x in terms of e.
The polynomial p(x) is defined by p(x) = x³ + ax² + bx + 16, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the...
The diagram shows the curve y = 2 + e⁻²ˣ. The curve crosses the y-axis at the point A, and the point B on the curve has x-coordinate 1. The shaded ...
Solve the equation |2x – 5| = |x + 6|.
The sequence of values given by the iterative formula xn+1 = (6+8xn) / (8+xn²) with initial value x₁ = 2 converges to α.
It is given that 3 sin 2θ = cos θ where θ is an angle such that 0° < θ < 90°.
A curve is defined by the parametric equations x = 3t - 2 sin t, y = 5t + 4 cos t, where 0 ≤ t ≤ 2π. At each of the points P and Q on the curve, th...
A curve has equation y = f(x) where f(x) = (4x³ + 8x - 4) / (2x - 1)
Solve the equation 7 cot θ = 3 cosec θ for 0° < θ < 90°.
Given that 2³ˣ⁺² + 8 2³ˣ - 7 to 4 significant figures. = 5, find the value of 2³ˣ and hence, using logarithms, find the value of x correct