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.
Solve the equation z² – 6iz – 12 = 0, giving the answers in the form x + iy, where x and y are real and exact.
Relative to the origin O, the points A, B and C have position vectors given by OA = (1, 1, 1), OB = (3, 1, 2) and OC = (5, -2, -2).
The variables x and θ satisfy the differential equation x sin² θ (dx/dθ) = tan² θ – 2 cot θ, for 0 < θ < ½π and x > 0. It is given that x = 2 when ...
The diagram shows part of the curve y = sin √x. This part of the curve intersects the x-axis at the point where x = a. [Figure 8.1]
The diagram shows a semicircle with diameter AB, centre O and radius r. The shaded region is the minor segment on the chord AC and its area is one ...
Let f(x) = (4 – x + x²) / ((1+x)(2 + x²))
Solve the equation ln(2x – 1) = 2ln(x + 1) – lnx. Give your answer correct to 3 decimal places.
Expand √(1 + 2x)/(1 - 2x) in ascending powers of x, up to and including the term in x², simplifying the coefficients.
Find the exact value of ∫(from 0 to π/4) x sec²x dx.
The parametric equations of a curve are x = 2t - tan t, y = ln(sin 2t), for 0 < t < ½π. Show that dy/dx = cot t.
Solve the quadratic equation (1 – 3i)z² – (2 + i)z + i = 0, giving your answers in the form x + iy, where x and y are real.
Show that the equation √5 secx + tanx = 4 can be expressed as Rcos(x + α) = √5, where R > 0 and 0° < α < 90°. Give the exact value of R and the val...
The curve with equation y = x³/(eˣ - 1) has a stationary point at x = p, where p > 0.
With respect to the origin O, the position vectors of the points A, B and C are given by OA = (0, 5, 2), OB = (1, 0, 1) and OC = (4, -3, -2). The m...
A gardener is filling an ornamental pool with water, using a hose that delivers 30 litres of water per minute. Initially the pool is empty. At time...
Let f(x) = (5 - x + 6x²)/((3 - x)(1 + 3x²)).
Coplanar forces of magnitudes PN, QN, 16N and 22N act at a point in the directions shown in the diagram. The forces are in equilibrium.
Small smooth spheres A and B, of equal radii and of masses 6 kg and 2 kg respectively, lie on a smooth horizontal plane. Initially A is moving towa...
A constant resistance of magnitude 1400N acts on a car of mass 1250kg.
A block of mass 8 kg is placed on a rough plane which is inclined at an angle of 18° to the horizontal. The block is pulled up the plane by a light...
A particle P moves on the x-axis from the origin O with an initial velocity of −20ms⁻¹. The acceleration a ms⁻² at time ts after leaving O is given...
Fig. 6.1 shows particles A and B, of masses 4kg and 3kg respectively, attached to the ends of a light inextensible string that passes over a small ...
A cyclist is riding a bicycle along a straight horizontal road AB of length 50m. The cyclist starts from rest at A and reaches a speed of 6ms⁻¹ at ...
A particle P of mass 0.4kg is in limiting equilibrium on a plane inclined at 30° to the horizontal.
A particle of mass 0.3 kg is held at rest by two light inextensible strings. One string is attached at an angle of 60° to a horizontal ceiling. The...
A car of mass 1200kg is travelling along a straight horizontal road AB. There is a constant resistance force of magnitude 500N. When the car passes...
A block A of mass 80kg is connected by a light, inextensible rope to a block B of mass 40kg. The rope joining the two blocks is taut and is paralle...
Three particles A, B and C of masses 0.3 kg, 0.4kg and mkg respectively lie at rest in a straight line on a smooth horizontal plane. The distance b...
A particle P travels in a straight line, starting at rest from a point O. The acceleration of P at time t s after leaving O is denoted by a ms⁻², w...
A particle P is projected vertically upwards with speed ums¯¹ from a point on the ground. P reaches its greatest height after 3 s.
A box of mass 5kg is pulled at a constant speed of 1.8 ms¯¹ for 15s up a rough plane inclined at an angle of 20° to the horizontal. The box moves a...
A ring of mass 4kg is threaded on a smooth circular rigid wire with centre C. The wire is fixed in a vertical plane and the ring is kept at rest by...
A particle P travels in the positive direction along a straight line with constant acceleration. P travels a distance of 52 m during the 2nd second...
Particles X and Y move in a straight line through points A and B. Particle X starts from rest at A and moves towards B. At the same instant, Y star...
A car of mass 1750kg is pulling a caravan of mass 500kg. The car and the caravan are connected by a light rigid tow-bar. The resistances to the mot...
Particles of masses 1.5kg and 3kg lie on a plane which is inclined at an angle of α to the horizontal, where tan α = 3/4. The section of the plane ...
The probability distribution table for a random variable X is shown below. x -2 -1 0.5 1 2 P(X = x) 0.12 p q 0.16 0.3 Give...
The residents of Persham were surveyed about the reliability of their internet service. 12% rated the service as 'poor', 36% rated it as 'satisfact...
The Lions and the Tigers are two basketball clubs. The heights, in cm, of the 11 players in each of their first team squads are given in the table....
In a large population, the systolic blood pressure (SBP) of adults is normally distributed with mean 125.4 and standard deviation 18.6. Three adult...
A game is played with an ordinary fair 6-sided die. A player throws the die once. If the result is 2, 3, 4 or 5, that result is the player's score ...
A Social Club has 15 members, of whom 8 are men and 7 are women. The committee of the club consists of 5 of its members. The 15 members are having ...
On any day, Kino travels to school by bus, by car or on foot with probabilities 0.2, 0.1 and 0.7 respectively. The probability that he is late when...
The lengths of the rods produced by a company are normally distributed with mean 55.6mm and standard deviation 1.2 mm.
Three fair 6-sided dice, each with faces marked 1, 2, 3, 4, 5, 6, are thrown at the same time repeatedly. The score on each throw is the sum of the...
The times taken, in minutes, to complete a word processing task by 250 employees at a particular company are summarised in the table. Time taken (t...
Eric has three coins. One of the coins is fair. The other two coins are each biased so that the probability of obtaining a head on any throw is 1/4...
At a company’s call centre, 90% of callers are connected immediately to a representative. A random sample of 12 callers is chosen.
Find the number of different arrangements of the 9 letters in the word ALLIGATOR in which the two As are together and the two Ls are together.
50 values of the variable x are summarised by Σ(x – 20) = 35 and Σχ² = 25 036. Find the variance of these 50 values.