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.
Expand (9-3x)¹ᐟ² in ascending powers of x, up to and including the term in x², simplifying the coefficients.
By sketching a suitable pair of graphs, show that the equation cot2x = secx has exactly one root in the interval 0 < x < ½π.
The square roots of 6-8i can be expressed in the Cartesian form x+iy, where x and y are real and exact. By first forming a quartic equation in x or...
Solve the equation 5ˣ = 5ˣ⁺² – 10. Give your answer correct to 3 decimal places.
The complex number u is given by u = (cos(⅓π) + i sin(⅓π))⁴ / (cos(½π) - i sin(½π)). Find the exact value of arg u.
The variables x and y satisfy the equation ay = bˣ, where a and b are constants. The graph of lny against x is a straight line passing through the ...
Show that the equation tan³x+2 tan2x-tanx = 0 may be expressed as tan⁴x-2 tan²x-3 = 0 for tanx ≠ 0.
The parametric equations of a curve are x = tan²2t, y = cos 2t, for 0 < t < ¼π.
With respect to the origin O, the points A, B and C have position vectors given by OA = (2, 1, -3), OB = (0, 4, 1), and OC = (-3, -2, 2).
A balloon in the shape of a sphere has volume V and radius r. Air is pumped into the balloon at a constant rate of 40π starting when time t = 0 and...
Let f(x) = 2e²ˣ / (e²ˣ - 3eˣ + 2)
The complex number z satisfies |z|= 2 and 0 ≤ argz <¦π.
Let f(x) = 2x³ - 5x² +4. Show that if a sequence of values given by the iterative formula xn+1=√4/(5-2xn), converges, then it converges to a root o...
The number of bacteria in a population, P, at time t hours is modelled by the equation P = aekt, where a and k are constants. The graph of InP agai...
Find the complex number z satisfying the equation (z-3i)/(z+3i) = (2-9i)/5. Give your answer in the form x+ iy, where x and y are real.
Show that cos⁴θ - sin⁴θ - 4 sin²θcos²θ ≡ cos²2θ + cos 2θ - 1.
The lines l and m have vector equations l: r = 2i+j-3k+λ(-i+2k) and m: r = 2i+j-3k+µ(2i−j+5k). Lines l and m intersect at the point P.
The parametric equations of a curve are x = 3 sin 2t, y = tan t + cot t, for 0 < t < ¦π.
Let f(x) = 7a² / ((a-2x)(3a+x)), where a is a positive constant.
Find the quotient and remainder when x⁴ + 16 is divided by x² + 4.
A water tank is in the shape of a cuboid with base area 40000 cm². At time t minutes the depth of water in the tank is h cm. Water is pumped into t...
The diagram shows the curve y = 2sinx√2+cosx, for 0 ≤ x ≤ 2π, and its minimum point M, where x = a. [Figure 11.1]
Two particles, of masses 1.8 kg and 1.2kg, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang ...
A particle of mass 7.5kg, starting from rest at A, slides down an inclined plane AB. The point B is 12.5 metres vertically below the level of A, as...
Coplanar forces of magnitudes 52N, 39N and PN act at a point in the directions shown in [Figure 3.1]. The system is in equilibrium. Find the values...
A bus travels between two stops, A and B. The bus starts from rest at A and accelerates at a constant rate of a ms⁻² until it reaches a speed of 16...
A particle, A, is projected vertically upwards from a point O with a speed of 80 ms⁻¹. One second later a second particle, B, with the same mass as...
A particle of mass 1.2kg is placed on a rough plane which is inclined at an angle θ to the horizontal, where sin θ = 3/25. The particle is kept in ...
A car has mass 1200kg. When the car is travelling at a speed of vms⁻¹, there is a resistive force of magnitude kv N. The maximum power of the car’s...
A particle P moves in a straight line, passing through a point O with velocity 4.2 ms⁻¹. At time t s after P passes O, the acceleration, a ms⁻², of...
The velocity of a particle moving in a straight line at time t seconds after leaving a fixed point O is vms⁻¹. The diagram shows a velocity-time gr...
A block of mass 20kg is held at rest at the top of a plane inclined at 30° to the horizontal. The block is projected with speed 5ms⁻¹ down a line o...
A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is 90kg. The power exerted by the cyclist is 25...
The diagram shows two particles, A and B, of masses 0.2kg and 0.1 kg respectively. The particles are suspended below a horizontal ceiling by two st...
Two particles, P and Q, of masses 2mkg and mkg respectively, are held at rest in the same vertical line. The heights of P and Q above horizontal gr...
A particle, P, travels in a straight line, starting from a point O with velocity 6 ms⁻¹. The acceleration of P at time t s after leaving O is a ms⁻...
Two particles, A and B, of masses 0.2kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...
An athlete has mass mkg. The athlete runs along a horizontal road against a constant resistance force of magnitude 24 N. The total work done by the...
Coplanar forces of magnitudes 16N, 12N, 24N and 8N act at a point in the directions shown in the diagram. [Figure 2]
A car of mass 1600kg travels up a slope inclined at an angle of sin⁻¹0.08 to the horizontal. There is a constant resistance of magnitude 240N actin...
Two particles, A and B, of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially, B is at rest and A is moving towards B w...
A particle of mass 12kg is going to be pulled across a rough horizontal plane by a light inextensible string. The string is at an angle of 30° abov...
A particle moves in a straight line. It starts from rest, at time t = 0, and accelerates at 0.6tms⁻² for 4s, reaching a speed of Ums⁻¹. The particl...
Two particles, A and B, of masses 3 kg and 5 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulley. ...
Nicola throws an ordinary fair six-sided dice. The random variable X is the number of throws that she takes to obtain a 6.
The random variable X takes the values -2, -1, 0, 2, 3. It is given that P(X = x) = k(x² + 2), where k is a positive constant.
The time taken, in minutes, to walk to school was recorded for 200 pupils at a certain school. These times are summarised in the following table. T...
Rahul has two bags, X and Y. Bag X contains 4 red marbles and 2 blue marbles. Bag Y contains 3 red marbles and 4 blue marbles. Rahul also has a coi...
The weights of the green apples sold by a shop are normally distributed with mean 90 grams and standard deviation 8 grams.
The heights of the female students at Breven college are normally distributed: • 90% of the female students have heights less than 182.7 cm. • 40% ...