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.
Find the exact value of ∫(from 0 to 1) x tan⁻¹x dx.
It is given that f(x) = (x−a)²g(x), where f(x) and g(x) are polynomials. Show that (x-a) is a factor of f'(x) .
By sketching a suitable pair of graphs, show that the equation cot2x = 2 sin 2x-1 has exactly one root in the interval 0 < x < π.
The equation of a curve is 2y³ – 3x²y-x³ = 16.
Prove the identity sin 4x = 4 sinx(2 cos³x-cosx).
Let f(x) = (x²+4ax+6a²) / ((x+2a)(x+3a)), where a is a positive constant.
The diagram shows a tank for holding water. The tank is in the shape of a cube of side 50 cm. At time t seconds, the depth of water in the tank is ...
Relative to the origin O, the position vectors of the points A, B and C are OA = 4i−2j, OB = 2i+8j+4k, and OC = -2i+6k. The midpoint of AB is M, as...
Solve the inequality | 3x+2|<3|2x-1|.
Find the quotient and the remainder when 3x⁴ – 2x² is divided by x + 1.
Solve the equation 2^(3x-4) = 3/5^x. Give your answer in the form (ln m)/(ln n), where m and n are integers.
Show that cos4x+2sin²x-1 = 8sin⁴x-6 sin²x.
Find the exact value of ∫(from 0 to π/2) x² sin 2x dx.
Solve the equation (5z)/(2-i) - zz* + 20+8i = 0. Give your answers in the form x+iy, where x and y are real.
The curve with equation y = e⁻⁵ˣln 5x has a stationary point at x = p.
The line l₁ passes through the point (3, 1, −6) and is parallel to the vector 2i+j+4k. The line l₂ passes through the point (−1, 3, −6) and is perp...
Express 2/(1-9y²) in partial fractions.
The diagram shows the graph of y = sec²x√(3+2 tanx) for -¼π ≤ x ≤ ¼π, and its minimum point M. [Figure 11.1]
A car of mass 900kg is moving along a straight horizontal road against a constant resistance to motion of 350N. At an instant when the car is movin...
Two particles, P and Q, of masses 3 kg and 5kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4 ms⁻¹ directly...
Coplanar forces of magnitudes 45N, 28N, 72N and 35N act at a point in the directions shown in the diagram. [Figure 3.1] Find, in either order, the ...
Two particles, A and B, of masses mkg and 3kg respectively, are connected by a light inextensible string. Particle B is on a fixed plane which is a...
A particle P of mass mkg is in equilibrium on a rough plane inclined at an angle θ° to the horizontal. The equilibrium of P is maintained by a forc...
A particle A of mass 2.5kg is released from rest from the top of a smooth plane, which makes an angle of sin⁻¹ 0.2 with the horizontal. The particl...
A particle P starts from a point O and moves in a straight line. The velocity v ms⁻¹ of P, at time t s after leaving O, is given by v = ¹/₃(2t-3)(t...
A block A of mass 2kg and a particle B of mass 0.5kg are connected by a light inextensible string inclined at 15° to the horizontal. They are pulle...
The diagram shows the displacement-time graph for the motion of a particle. The particle starts from rest at a point O and travels with constant ac...
A railway locomotive of mass 240000 kg is towing a coach of mass 36000 kg down a hill inclined at an angle of sin⁻¹ 0.04 to the horizontal. The dri...
A car of mass 1400 kg travelling on a straight horizontal road accelerates uniformly from a speed of 15 m s⁻¹ to 20 m s⁻¹ over a distance of 175 m.
A particle P of mass 0.1 kg is projected vertically upwards with speed 30 m s⁻¹ from horizontal ground. At the same instant a particle Q of mass 0....
A block of mass 5 kg is being pulled straight down a line of greatest slope of a rough plane by a force of magnitude 20 N. The plane is inclined at...
A particle starts from rest at a point O. The acceleration of the particle at time t s after leaving O is a m s⁻², where a = 2(t+1)⁻½ - 1 for t ≥ 0...
Four coplanar forces of magnitudes 20 N, 30 N, 15 N and 25 N act at a point P in the directions shown in Fig. 7.1. The forces act in a vertical pla...
The diagram shows the velocity-time graph for the motion of an athlete. The athlete runs in a straight line from point A to point B, runs back to p...
The engine of a motorcycle can generate a maximum power of 105kW. The mass of the motorcycle and its rider is 400kg. The total resistance to the mo...
A block of mass 4kg is pulled along a rough horizontal road by a constant force of magnitude 25 N acting at an angle of 36° above the horizontal. T...
A particle P moves in a straight line. At time ts after passing through a point O on the line, the displacement of P from O is sm, where s = 0.01t³...
Particles A and B, of masses 2kg and 6kg respectively, are attached to the ends of a light inextensible string. The string passes over a smooth fix...
Particle P of mass m kg and particle Q of mass 2 kg are free to move on a smooth horizontal plane. P and Q are moving directly towards each other w...
A particle P of mass 6 kg lies on a rough plane inclined at an acute angle θ to the horizontal. A horizontal force of magnitude 12N acts on P as sh...
The random variable X takes the value x with probability kx², where k is a constant and x takes the values -2, 1, 2, 3 only.
A fair six-sided dice with faces labelled 1, 2, 3, 4, 5, 6 is thrown repeatedly until a 6 is obtained.
The back-to-back stem-and-leaf diagram shows the annual salaries, in dollars, of 27 employees at each of two companies, Browns and Greens. Browns ...
Bag A contains 8 red marbles and 3 blue marbles. Bag B contains 4 red marbles and 1 blue marble. A marble is chosen at random from bag A. If the ma...
On any given day, Cooper either wears a blue jumper or he wears a green jumper or he does not wear a jumper. The probability that he wears a blue j...
A factory produces chocolate bars. The weights of the bars are normally distributed with mean 155 g and standard deviation 6 g. A random sample of ...
How many different arrangements are there of the 10 letters in the word SEYCHELLES?
A coin is biased so that the probability of obtaining a head when it is thrown is 0.4. The coin is thrown repeatedly until the first head is obtained.
Kayla has a bag containing 3 red marbles, 1 blue marble and 2 green marbles. She selects one marble from the bag at random and does not replace it ...
The heights of the 124 Senior members of the Giraffes basketball club are normally distributed with mean 187.4 cm and standard deviation 6.4 cm. Th...