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 ∫₀² 6e²ˣ⁺¹ dx.
Find the quotient when x⁴ – 32x + 55 is divided by (x – 2)² and show that the remainder is 7.
The diagram shows the curve with equation y = (ln x)² – 2 ln x. The curve crosses the x-axis at the points A and B, and has a minimum point M.
The diagram shows the curve with parametric equations x = 4t + e²ᵗ, y = 6t sin 2t, for 0 ≤ t ≤ 1. The point P on the curve has parameter p and y-co...
Solve the equation In(2 + x) – lnx = 2 ln 3.
Find the exact value of ∫₀² 6e^(2x+1) dx.
The diagram shows the curve with equation y = (lnx)² – 2 lnx. The curve crosses the x-axis at the points A and B, and has a minimum point M. [Figur...
The diagram shows the curve with parametric equations x = 4t + e^(2t), y = 6t sin 2t, for 0 ≤ t ≤ 1. The point P on the curve has parameter p and y...
Solve the inequality 2|3x – 1| < |x + 1|.
Find the real root of the equation (2eˣ + e⁻ˣ) / (2 + eˣ) = 3, giving your answer correct to 3 decimal places. Your working should show clearly tha...
Given that cos(x – 30°) = 2 sin(x + 30°), show that tan x = (2-√3) / (1-2√3)
Prove that (1 - cos 2θ) / (1 + cos 2θ) = tan² θ.
Solve the equation z² – 2piz – q = 0, where p and q are real constants.
The parametric equations of a curve are x = ln(2 + 3t), y = t / (2 + 3t)
The diagram shows the curve y = (tan⁻¹ x) / √x and its maximum point M where x = a. [Figure 7.1]
With respect to the origin O, the points A and B have position vectors given by OA = (1, 2, 1) and OB = (3, 1, -2). The line l has equation r = (2,...
The equation of a curve is y = x⁻² ln x for x > 0. The curve has one stationary point.
The variables x and t satisfy the differential equation dx/dt = x²(1 + 2x), and x = 1 when t = 0. Using partial fractions, solve the differential e...
Solve the inequality |2x – 1| < 3|x + 1|.
The variables x and y satisfy the equation x = A(3⁻ʸ), where A is a constant.
Using integration by parts, find the exact value of ∫₀² tan⁻¹(½x)dx.
The complex number u is given by u = 10 – 4√6i. Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and ...
Prove that cosec 2θ − cot 2θ = tan θ.
A curve is such that the gradient at a general point with coordinates (x, y) is proportional to y / √(x + 1). The curve passes through the points w...
The equation of a curve is y = e⁻⁵ˣ tan²x for −π/2 < x < π/2. Find the x-coordinates of the stationary points of the curve. Give your answers corre...
Let f(x) = (14 - 3x + 2x²) / ((2 + x)(3 + x²))
The diagram shows a trapezium ABCD in which AD = BC = r and AB = 2r. The acute angles BAD and ABC are both equal to x radians. Circular arcs of rad...
With respect to the origin O, the points A and B have position vectors given by OA = 2i – j and OB = j – 2k.
Expand (1 + 3x)⁻² in ascending powers of x, up to and including the term in x³, simplifying the coefficients.
Solve the equation 4ˣ = 3 + 4⁻ˣ. Give your answer correct to 3 decimal places.
The parametric equations of a curve are x = t + ln(t + 2), y = (t − 1)e⁻²ᵗ, where t > -2.
Let f(x) = (15-6x) / ((1+2x)(4-x))
By first expanding tan(2θ + 2θ), show that the equation tan 4θ = ½ tan θ may be expressed as tan⁴θ + 2 tan²θ – 7 = 0.
By sketching a suitable pair of graphs, show that the equation cot ½x = 1 + e⁻ˣ has exactly one root in the interval 0 < x < π.
For the curve shown in the diagram, the normal to the curve at the point P with coordinates (x, y) meets the x-axis at N. The point M is the foot o...
The diagram shows the curve y = (ln x) / x³ and its maximum point M. [Figure X.X]
The quadrilateral ABCD is a trapezium in which AB and DC are parallel. With respect to the origin O, the position vectors of A, B and C are given b...
Verify that −1 + √2i is a root of the equation z⁴ + 3z² + 2z + 12 = 0.
A winch operates by means of a force applied by a rope. The winch is used to pull a load of mass 50 kg up a line of greatest slope of a plane incli...
Two particles A and B have masses mkg and 0.1 kg respectively, where m > 0.1. The particles are attached to the ends of a light inextensible string...
Three particles P, Q and R, of masses 0.1 kg, 0.2 kg and 0.5 kg respectively, are at rest in a straight line on a smooth horizontal plane. Particle...
Two cyclists, Isabella and Maria, are having a race. They both travel along a straight road with constant acceleration, starting from rest at point...
A particle moving in a straight line starts from rest at a point A and comes instantaneously to rest at a point B. The acceleration of the particle...
Three coplanar forces of magnitudes 10N, 25 N and 20 N act at a point O in the directions shown in the diagram.
A slide in a playground descends at a constant angle of 30° for 2.5 m. It then has a horizontal section in the same vertical plane as the sloping s...
A particle of mass 0.6 kg is projected with a speed of 4 m s⁻¹ down a line of greatest slope of a smooth plane inclined at 10° to the horizontal.
Coplanar forces of magnitudes 34 N, 30N and 26 N act at a point in the directions shown in the diagram.
A ring of mass 0.3 kg is threaded on a horizontal rough rod. The coefficient of friction between the ring and the rod is 0.8. A force of magnitude ...
A particle of mass 12 kg is stationary on a rough plane inclined at an angle of 25° to the horizontal. A pulling force of magnitude P N acts at an ...
A car of mass 1250 kg is pulling a caravan of mass 800 kg along a straight road. The resistances to the motion of the car and caravan are 440 N and...