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.
The diagram shows the curve with equation y = e⁻½ˣ(x² – 5x + 4). The curve crosses the x-axis at the points A and B, and has a maximum at the point C.
Show that 4 sin(θ + π/6) cos(θ – π/6) = √3 + 2 sin 2θ.
Solve the equation 3e²ˣ - 4e⁻²ˣ = 5. Give the answer correct to 3 decimal places.
Sketch the graph of y = |2x + 3|.
Find the coefficient of x³ in the binomial expansion of (3 + x)√1 + 4x.
Show that the equation sin 2θ + cos 2θ = 2 sin² θ can be expressed in the form cos² θ + 2 sin θ cos θ – 3 sin² θ = 0.
The equation of a curve is x²y – ay² = 4a³, where a is a non-zero constant.
Relative to the origin O, the points A, B and C have position vectors given by OA = (2 3 3), OB = (4 1 2) and OC = (3 -2 -4). The quadrilateral ABC...
The variables x and y satisfy the differential equation cos 2x dy/dx = 4 tan 2x / sin² 3y, where 0 ≤ x < π/4. It is given that y = 0 when x = π/6. ...
Let f(x) = (3-3x²) / ((2x + 1)(x + 2)²).
The constant a is such that ∫₀ᵃ xe⁻²ˣ dx = 1/8.
The polynomial x³ + 5x² + 31x + 75 is denoted by p(x).
Solve the inequality |5x-3| < 2|3x – 7|.
Solve the equation ln(2x² – 3) = 2 ln x – ln 2, giving your answer in an exact form.
On an Argand diagram, sketch the locus of points representing complex numbers z satisfying |z + 3 – 2i| = 2.
Solve the equation 2 cos x – cos (x/2) = 1 for 0 ≤ x ≤ 2π.
The complex number 2 + yi is denoted by a, where y is a real number and y < 0. It is given that f(a) = a³ – a² – 2a.
The equation cot (x/2) = 3x has one root in the interval 0 < x < π, denoted by α.
The equation of a curve is 3x² + 4xy + 3y² = 5.
(a) The variables x and y satisfy the differential equation (dy/dx) = (4 + 9y²)/e^(2x+1). It is given that y = 0 when x = 1.
Let f(x) = (2x² + 17x - 17) / ((1 + 2x)(2-x)²).
The diagram shows the curve y = (x + 5)√3 – 2x and its maximum point M. [Figure 10.1]
The points A and B have position vectors i + 2j – 2k and 2i – j + k respectively. The line l has equation r = i − j + 3k + μ(2i – 3j + 4k).
Solve the equation ln(x + 5) = 5 + lnx. Give your answer correct to 3 decimal places.
Find the quotient and remainder when 2x⁴ – 27 is divided by x² + x + 3.
The parametric equations of a curve are x = (cos θ) / (2 - sin θ), y = θ + 2 cos θ. Show that dy/dx = (2 − sin θ)².
The diagram shows the part of the curve y = x² cos 3x for 0 ≤ x ≤ π/6, and its maximum point M, where x = a. [Figure 5.1]
Express 3 cos x + 2cos(x – 60°) in the form Rcos(x – α), where R > 0 and 0° < α < 90°. State the exact value of R and give α correct to 2 decimal p...
Use the substitution u = cosx to show that ∫(from 0 to π/2) sin 2x e^(2 cos x) dx = ∫(from 1 to -1) 2u e^(2u) du.
The variables x and y satisfy the differential equation dy/dx = (y² + 4)/(x(y + 4)) for x > 0. It is given that x = 4 when y = 2√3. Solve the diffe...
The lines l and m have equations l: r = ai + 3j + bk + λ(ci – 2j + 4k), m: r = i +2j + 3k + μ(2i – 3j + k). Relative to the origin O, the position ...
Let f(x) = (21 – 8x – 2x²) / ((1 + 2x)(3−x)²).
The complex number z is defined by z = (5a - 2i) / (3 + ai), where a is an integer. It is given that arg z = –π/4.
Two particles P and Q, of masses mkg and 0.3kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 5ms¯¹ directly ...
A particle P of mass 0.4 kg is projected vertically upwards from horizontal ground with speed 10ms-1.
A particle moves in a straight line starting from rest. The displacement s m of the particle from a fixed point O on the line at time t s is given ...
The velocity of a particle at time t s after leaving a fixed point O is vms¯¹. The diagram shows a velocity-time graph which models the motion of t...
Four coplanar forces act at a point. The magnitudes of the forces are F N, 10 N, 50 N and 40 N. The directions of the forces are as shown in the di...
Two particles P and Q, of masses 0.2kg and 0.1 kg respectively, are attached to the ends of a light inextensible string. The string passes over a f...
A car of mass 1200kg is travelling along a straight horizontal road. The power of the car's engine is constant and is equal to 16kW. There is a con...
A particle of mass 1.6kg is dropped from a height of 9 m above horizontal ground. The speed of the particle at the instant before hitting the groun...
Two particles A and B, of masses 3.2kg and 2.4kg respectively, lie on a smooth horizontal table. A moves towards B with a speed of vms¯¹ and collid...
Coplanar forces of magnitudes 30N, 15N, 33N and PN act at a point in the directions shown in the diagram, where tan α = 4/3. The system is in equil...
An athlete of mass 84kg is running along a straight road.
A particle of mass 0.6kg is placed on a rough plane which is inclined at an angle of 35° to the horizontal. The particle is kept in equilibrium by ...
A particle P starts at rest and moves in a straight line from a point O. At time ts after leaving O, the velocity of P, vms¯¹, is given by v = bt +...
Two particles P and Q, of masses 2kg and 0.25 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulley....
Two particles P and Q, of masses 0.1kg and 0.4kg respectively, are free to move on a smooth horizontal plane. Particle P is projected with speed 4m...
A car of mass 1500kg is towing a trailer of mass mkg along a straight horizontal road. The car and the trailer are connected by a tow-bar which is ...
A smooth ring R of mass 0.2kg is threaded on a light string ARB. The ends of the string are attached to fixed points A and B with A vertically abov...