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.
Prove that cosec 2θ − cot 2θ = tan θ.
A curve is such that the gradient at a general point with coordinates (x, y) is proportional to y / √(x + 1). The curve passes through the points w...
The equation of a curve is y = e⁻⁵ˣ tan²x for −π/2 < x < π/2. Find the x-coordinates of the stationary points of the curve. Give your answers corre...
Let f(x) = (14 - 3x + 2x²) / ((2 + x)(3 + x²))
The diagram shows a trapezium ABCD in which AD = BC = r and AB = 2r. The acute angles BAD and ABC are both equal to x radians. Circular arcs of rad...
With respect to the origin O, the points A and B have position vectors given by OA = 2i – j and OB = j – 2k.
Expand (1 + 3x)⁻² in ascending powers of x, up to and including the term in x³, simplifying the coefficients.
Solve the equation 4ˣ = 3 + 4⁻ˣ. Give your answer correct to 3 decimal places.
The parametric equations of a curve are x = t + ln(t + 2), y = (t − 1)e⁻²ᵗ, where t > -2.
Let f(x) = (15-6x) / ((1+2x)(4-x))
By first expanding tan(2θ + 2θ), show that the equation tan 4θ = ½ tan θ may be expressed as tan⁴θ + 2 tan²θ – 7 = 0.
By sketching a suitable pair of graphs, show that the equation cot ½x = 1 + e⁻ˣ has exactly one root in the interval 0 < x < π.
For the curve shown in the diagram, the normal to the curve at the point P with coordinates (x, y) meets the x-axis at N. The point M is the foot o...
The diagram shows the curve y = (ln x) / x³ and its maximum point M. [Figure X.X]
The quadrilateral ABCD is a trapezium in which AB and DC are parallel. With respect to the origin O, the position vectors of A, B and C are given b...
Verify that −1 + √2i is a root of the equation z⁴ + 3z² + 2z + 12 = 0.
A winch operates by means of a force applied by a rope. The winch is used to pull a load of mass 50 kg up a line of greatest slope of a plane incli...
Two particles A and B have masses mkg and 0.1 kg respectively, where m > 0.1. The particles are attached to the ends of a light inextensible string...
Three particles P, Q and R, of masses 0.1 kg, 0.2 kg and 0.5 kg respectively, are at rest in a straight line on a smooth horizontal plane. Particle...
Two cyclists, Isabella and Maria, are having a race. They both travel along a straight road with constant acceleration, starting from rest at point...
A particle moving in a straight line starts from rest at a point A and comes instantaneously to rest at a point B. The acceleration of the particle...
Three coplanar forces of magnitudes 10N, 25 N and 20 N act at a point O in the directions shown in the diagram.
A slide in a playground descends at a constant angle of 30° for 2.5 m. It then has a horizontal section in the same vertical plane as the sloping s...
A particle of mass 0.6 kg is projected with a speed of 4 m s⁻¹ down a line of greatest slope of a smooth plane inclined at 10° to the horizontal.
Coplanar forces of magnitudes 34 N, 30N and 26 N act at a point in the directions shown in the diagram.
A ring of mass 0.3 kg is threaded on a horizontal rough rod. The coefficient of friction between the ring and the rod is 0.8. A force of magnitude ...
A particle of mass 12 kg is stationary on a rough plane inclined at an angle of 25° to the horizontal. A pulling force of magnitude P N acts at an ...
A car of mass 1250 kg is pulling a caravan of mass 800 kg along a straight road. The resistances to the motion of the car and caravan are 440 N and...
A particle A is projected vertically upwards from level ground with an initial speed of 30 m s⁻¹. At the same instant a particle B is released from...
A particle P moving in a straight line starts from rest at a point O and comes to rest 16 s later. At time t s after leaving O, the acceleration a ...
Particles P of mass 0.4 kg and Q of mass 0.5 kg are free to move on a smooth horizontal plane. P and Q are moving directly towards each other with ...
A cyclist is travelling along a straight horizontal road. She is working at a constant rate of 150 W. At an instant when her speed is 4 m s⁻¹, her ...
Four coplanar forces act at a point. The magnitudes of the forces are 20 N, 30 N, 40 N and F N. The directions of the forces are as shown in the di...
A particle is projected vertically upwards with speed u m s⁻¹ from a point on horizontal ground. After 2 seconds, the height of the particle above ...
A car of mass 1400 kg is towing a trailer of mass 500 kg down a straight hill inclined at an angle of 5° to the horizontal. The car and trailer are...
A particle moves in a straight line and passes through the point A at time t = 0. The velocity of the particle at time t s after leaving A is v m s...
A particle P of mass 0.3 kg rests on a rough plane inclined at an angle θ to the horizontal, where sin θ = 7/25. A horizontal force of magnitude 4 ...
A bag contains 12 marbles, each of a different size. 8 of the marbles are red and 4 of the marbles are blue.
A company produces a particular type of metal rod. The lengths of these rods are normally distributed with mean 25.2 cm and standard deviation 0.4 ...
How many different arrangements are there of the 8 letters in the word RELEASED?
To gain a place at a science college, students first have to pass a written test and then a practical test. Each student is allowed a maximum of tw...
The times taken by 200 players to solve a computer puzzle are summarised in the following table. Time (t seconds) 0 ≤ t < 10 10 ≤ t < 20 20 ≤ t < 4...
In Questa, 60% of the adults travel to work by car.
Sharma knows that she has 3 tins of carrots, 2 tins of peas and 2 tins of sweetcorn in her cupboard. All the tins are the same shape and size, but ...
An ordinary fair die is thrown repeatedly until a 5 is obtained. The number of throws taken is denoted by the random variable X.
The weights of bags of sugar are normally distributed with mean 1.04 kg and standard deviation σ kg. In a random sample of 2000 bags of sugar, 72 w...
On each day that Alexa goes to work, the probabilities that she travels by bus, by train or by car are 0.4, 0.35 and 0.25 respectively. When she tr...
A fair spinner has sides numbered 1, 2, 2. Another fair spinner has sides numbered –2, 0, 1. Each spinner is spun. The number on the side on which ...
Every day Richard takes a flight between Astan and Bejin. On any day, the probability that the flight arrives early is 0.15, the probability that i...
Find the total number of different arrangements of the 8 letters in the word TOMORROW.