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 [Figure 7.1] y = x² + 3x + 1 + 5 cos ½x. The curve crosses the y-axis at the point P and the gradient of the curve at P...
Find the quotient and remainder when x⁴ is divided by x² + 2x – 1.
Two variable quantities x and y are believed to satisfy an equation of the form y = C(aˣ), where C and a are constants. An experiment produced four...
The equation x³ = 3x + 7 has one real root, denoted by α.
Prove the identity tan(45° + x) + tan(45° – x) = 2 sec 2x.
The equation of a curve is 2x⁴ + xy³ + y⁴ = 10.
The variables x and y satisfy the differential equation dy/dx = 4 cos² y tan x, for 0 ≤ x < ½π, and x = 0 when y = ¼π. Solve this differential equa...
The complex number u is given by u = 8 – 15i. Showing all necessary working, find the two square roots of u. Give answers in the form a + ib, where...
Let f(x) = (4x² + 9x - 8) / ((x + 2)(2x - 1))
The diagram shows the curve y = (1 + x²)e⁻ˣ/² for x ≥ 0. The shaded region R is enclosed by the curve, the x-axis and the lines x = 0 and x = 2. [F...
The equations of two lines l and m are r = 3i − j − 2k + λ(−i + j + 4k) and r = 4i + 4j – 3k + μ(2i + j − 2k) respectively.
The diagram shows a sketch of the curve y = 3 / √(9-x³) for values of x from -1.2 to 1.2. [Figure 1.1]
Showing all necessary working, solve the equation 2log₂ x = 3 + log₂ (x + 1), giving your answer correct to 3 significant figures.
By expressing the equation tan(θ + 60°) + tan(θ – 60°) = cot θ in terms of tan θ only, solve the equation for 0° < θ < 90°.
The curve with equation y = (2 – sin x) / cos x has one stationary point in the interval -π/2 < x < π/2.
The variables x and y satisfy the differential equation (x + 1) dy/dx = y(x + 2), and it is given that y = 2 when x = 1. Solve the differential equ...
The equation of a curve is x³y – 3xy³ = 2a⁴, where a is a non-zero constant.
Throughout this question the use of a calculator is not permitted. The complex number 1 – (√3)i is denoted by u.
Let f(x) = (8x² + 9x + 8) / ((1-x)(2x + 3)²).
It is given that ∫(1 to a) x² ln x dx = 2, where a > 1.
Two planes p and q have equations x + y + 3z = 8 and 2x – 2y + z = 3 respectively.
Let f(x) = (4x² + 9x - 8) / ((x + 2)(2x−1)).
The diagram shows the curve y = (1 + x²)e⁻½ˣ for x ≥ 0. The shaded region R is enclosed by the curve, the x-axis and the lines x = 0 and x = 2. [Fi...
A block of mass 3 kg is initially at rest on a smooth horizontal floor. A force of 12 N, acting at an angle of 25° above the horizontal, is applied...
A tractor of mass 3700 kg is travelling along a straight horizontal road at a constant speed of 12 m s⁻¹. The total resistance to motion is 1150 N.
A roller-coaster car (including passengers) has a mass of 840 kg. The roller-coaster ride includes a section where the car climbs a straight ramp o...
The diagram shows the velocity-time graph of a particle which moves in a straight line. The graph consists of 5 straight line segments. The particl...
A particle starts from a point O and moves in a straight line. The velocity of the particle at time t s after leaving O is v m s⁻¹, where v = 1.5 +...
Coplanar forces, of magnitudes F N, 3F N, G N and 50 N, act at a point P, as shown in the diagram. [Figure 6.1]
Two particles A and B of masses 0.9 kg and 0.4 kg respectively are attached to the ends of a light inextensible string. The string passes over a fi...
A particle of mass 0.2 kg is resting in equilibrium on a rough plane inclined at 20° to the horizontal.
A block of mass 15 kg hangs in equilibrium below a horizontal ceiling attached to two strings as shown in the diagram. One of the strings is inclin...
A car travels along a straight road with constant acceleration. It passes through points A, B and C. The car passes point A with velocity 14 m s⁻¹....
A particle P is projected vertically upwards from horizontal ground with speed 12 m s⁻¹.
A cyclist is riding up a straight hill inclined at an angle α to the horizontal, where sin α = 0.04. The total mass of the bicycle and rider is 80 ...
Two particles P and Q, each of mass m kg, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley whi...
A particle starts from rest and moves in a straight line. The velocity of the particle at time t s after the start is v m s⁻¹, where v = −0.01t³ + ...
Three coplanar forces of magnitudes FN, 20 N and 30 N act at a point P, as shown in the diagram. The resultant of the three forces acts in a direct...
A lorry of mass 7850 kg travels on a straight hill which is inclined at an angle of 3° to the horizontal. There is a constant resistance to motion ...
A particle is released from rest and slides down a line of greatest slope of a rough plane which is inclined at 25° to the horizontal. The coeffici...
Two particles A and B have masses 0.35 kg and 0.45 kg respectively. The particles are attached to the ends of a light inextensible string which pas...
A particle starts from a fixed origin with velocity 0.4 m s⁻¹ and moves in a straight line. The acceleration a m s⁻² of the particle t s after it l...
The diagram shows the velocity-time graphs for two particles, P and Q, which are moving in the same straight line. The graph for P consists of four...
A particle P of mass 0.2 kg rests on a rough plane inclined at 30° to the horizontal. The coefficient of friction between the particle and the plan...
A hollow cylinder with a rough inner surface has radius 0.5 m. A particle P of mass 0.4kg is in contact with the inner surface of the cylinder. The...
A small ball is projected from a point 1.5 m above horizontal ground. At a point 9 m above the ground the ball is travelling at 45° above the horiz...
One end of a light inextensible string of length 0.4 m is attached to a fixed point A which is above a smooth horizontal surface. A particle P of m...
A particle P 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...
One end of a light elastic string of natural length 0.8 m and modulus of elasticity 24 N is attached to a fixed point O. The other end of the strin...
A solid object consists of a uniform hemisphere of radius 0.4m attached to a uniform cylinder of radius 0.4 m so that the circumferences of their c...