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.
Showing all necessary working, solve the equation 9ˣ = 3ˣ + 12. Give your answer correct to 2 decimal places.
Showing all necessary working, solve the equation cot 2θ = 2 tan θ for 0° < θ < 180°.
Find the exact coordinates of the point on the curve y = x / (1 + ln x) at which the gradient of the tangent is equal to ¼.
Throughout this question the use of a calculator is not permitted. It is given that the complex number −1 + (√3)i is a root of the equation kx³ + 5...
In the diagram, A is the mid-point of the semicircle with centre O and radius r. A circular arc with centre A meets the semicircle at B and C. The ...
The variables x and y satisfy the differential equation dy/dx = x e^(x+y). It is given that y = 0 when x = 0.
Let f(x) = (10x + 9) / ((2x + 1)(2x + 3)²).
The points A and B have position vectors i + 2j – k and 3i + j + k respectively. The line l has equation r = 2i + j + k + μ(i + j + 2k).
The diagram shows the curve y = sin 3x cos x for 0 ≤ x ≤ ½π and its minimum point M. The shaded region R is bounded by the curve and the x-axis. [F...
Use logarithms to solve the equation 53−2x = 4(7x), giving your answer correct to 3 decimal places.
Show that ∫₀^(1/4 π) x² cos 2x dx = (1/8)(π² – 8).
Let f(θ) = (1 - cos 2θ + sin 2θ) / (1 + cos 2θ + sin 2θ)
The equation of a curve is y = (1 + e⁻ˣ) / (1 - e⁻ˣ), for x > 0.
The variables x and y satisfy the differential equation (x + 1)y dy/dx = y² + 5. It is given that y = 2 when x = 0. Solve the differential equation...
The diagram shows the curve y = x⁴ – 2x³ – 7x − 6. The curve intersects the x-axis at the points (a, 0) and (b, 0), where a < b. It is given that b...
The curve y = sin(x + (1/3)π) cos x has two stationary points in the interval 0 ≤ x ≤ π.
Throughout this question the use of a calculator is not permitted. The complex number u is defined by u = 4i / (1-(√3)i)
Let f(x) = 2x(5 – x) / ((3+x)(1-x)²)
The line l has equation r = i + 2j + 3k + μ(2i – j – 2k).
Given that tan α = 12/5 and tan θ = 4/3, show that the coplanar forces shown in the diagram are in equilibrium. [Figure 1.1]
A particle P is projected vertically upwards with speed 25 m s⁻¹ from a point 3 m above horizontal ground.
A lorry has mass 12000 kg.
A particle of mass 1.3 kg rests on a rough plane inclined at an angle θ to the horizontal, where tan θ = 12/5. The coefficient of friction between ...
A particle P moves in a straight line from a fixed point O. The velocity v m s⁻¹ of P at time t s is given by v = t² – 8t + 12 for 0 ≤ t ≤ 8.
Two particles A and B, of masses 0.4 kg and 0.2 kg respectively, are connected by a light inextensible string. Particle A is held on a smooth plane...
Coplanar forces of magnitudes 40 N, 32 N, PN and 17 N act at a point in the directions shown in the diagram. The system is in equilibrium. Find the...
A car moves in a straight line with initial speed u m s⁻¹ and constant acceleration a m s⁻². The car takes 5 s to travel the first 80 m and it take...
A particle of mass 13 kg is on a rough plane inclined at an angle of θ to the horizontal, where tan θ = 5/12. The coefficient of friction between t...
A constant resistance to motion of magnitude 350 N acts on a car of mass 1250 kg. The engine of the car exerts a constant driving force of 1200 N. ...
A car has mass 1000 kg. When the car is travelling at a steady speed of v m s⁻¹, where v > 2, the resistance to motion of the car is (Av + B) N, wh...
Particles P and Q leave a fixed point A at the same time and travel in the same straight line. The velocity of P after t seconds is 6t(t − 3) m s⁻¹...
A bus moves in a straight line between two bus stops. The bus starts from rest and accelerates at 2.1 m s⁻² for 5 s. The bus then travels for 24 s ...
Coplanar forces of magnitudes 12 N, 24 N and 30 N act at a point in the directions shown in the diagram. [Figure X.X]
A car of mass 1400kg is travelling up a hill inclined at an angle of 4° to the horizontal. There is a constant resistance to motion of magnitude 15...
Two particles A and B, of masses 1.3 kg and 0.7 kg respectively, are connected by a light inextensible string which passes over a smooth fixed pull...
A particle of mass 18 kg is on a plane inclined at an angle of 30° to the horizontal. The particle is projected up a line of greatest slope of the ...
A particle P moves in a straight line. The acceleration a m s⁻² of P at time t s is given by a = 6t – 12. The displacement of P from a fixed point ...
A particle P of mass 0.3 kg is attached to a fixed point A by a light inextensible string of length 0.8 m. The fixed point O is 0.15 m vertically b...
A particle is projected with speed V m s¯¹ at an angle of 0° above the horizontal. At the instant 4 s after projection the speed of the particle is...
The diagram shows the cross-section through the centre of mass of a uniform solid object. The object is a cylinder of radius 0.2 m and length 0.7m,...
A small ball is projected with speed 25 m s¯¹ at an angle of 30° above the horizontal from a point O on horizontal ground. At time t s after projec...
A particle P of mass 0.4 kg is attached to one end of a light elastic string of natural length 0.5 m and modulus of elasticity 6 N. The other end o...
ABC is a uniform lamina in the form of a triangle with AB = 0.3 m, BC = 0.6 m and a right angle at B [Figure 6.1].
A particle P of mass 0.5 kg is attached to a fixed point O by a light elastic string of natural length 1 m and modulus of elasticity 16N. The parti...
A small ball is projected from a point O on horizontal ground at an angle of 30° above the horizontal. At time t s after projection the vertically ...
A uniform lamina ABCEFG is formed from a square ABDG by removing a smaller square CDFE from one corner. AB = 0.7 m and DF = 0.3 m (see diagram). Fi...
A particle P of mass 0.4 kg is attached to a fixed point A by a light inextensible string of length 0.5 m. The point A is 0.3 m above a smooth hori...
A particle P of mass 0.5 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 16 N. The other end ...
A light elastic string has natural length a m and modulus of elasticity λ N. When the length of the string is 1.6 m the tension is 4 N. When the le...
A particle is projected with speed 15 m s⁻¹ at an angle of θ° above the horizontal. At the instant 4 s after projection the speed of the particle i...