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.
A solid rectangular block has a square base of side x cm. The height of the block is h cm and the total surface area of the block is 96 cm². (i) Ex...
The diagram shows the curve y = (x – 2)² and the line y + 2x = 7, which intersect at points A and B. Find the area of the shaded region.
The equation of a curve is y = ½(2x – 3)³ – 4x. (i) Find dy/dx. (ii) Find the equation of the tangent to the curve at the point where the curve int...
The function f: x → 4-3 sin x is defined for the domain 0 ≤ x ≤ 2π. (i) Solve the equation f(x) = 2. (ii) Sketch the graph of y = f(x). (iii) Find ...
Find ∫(x³ + 1/x²) dx.
Find the terms in x² and x³ in the expansion of (1 – ½x)⁶.
The equation x² + px + q = 0, where p and q are constants, has roots –3 and 5.
A curve has equation y = 4/(3x-4) and P (2, 2) is a point on the curve.
Prove the identity cos θ / (tan θ(1 – sin θ)) = 1 + 1/sin θ
The function f is defined by f : x → (x+3)/(2x-1), x ∈ R, x ≠ 1/2.
The line L₁ passes through the points A (2, 5) and B (10, 9). The line L₂ is parallel to L₁ and passes through the origin. The point C lies on L₂ s...
Relative to the origin O, the position vectors of the points A, B and C are given by `OA = (2 5)`, `OB = (4 3)`, `OC = (10 6)`. The point D is such...
The function f is such that f(x) = 3 – 4 cosᵏx, for 0 ≤ x ≤ π, where k is a constant.
A circle is divided into 6 sectors in such a way that the angles of the sectors are in arithmetic progression. The angle of the largest sector is 4...
The diagram shows part of the curve y = 4√x – x. The curve has a maximum point at M and meets the x-axis at O and A. [Figure X.X]
The diagram shows the region enclosed by the curve y = 6/(2x-3), the x-axis and the lines x = 2 and x = 3. Find, in terms of π, the volume obtained...
The equation of a curve is y = 4√x + 2/√x
The coefficient of x³ in the expansion of (a + x)⁵ + (2 – x)⁶ is 90. Find the value of the positive constant a.
The point A has coordinates (−1, −5) and the point B has coordinates (7, 1). The perpendicular bisector of AB meets the x-axis at C and the y-axis ...
Prove the identity tan x + 1/tan x = 1/(sin x cos x)
The diagram shows a metal plate made by removing a segment from a circle with centre O and radius 8 cm. The line AB is a chord of the circle and an...
In an arithmetic progression, the sum of the first n terms, denoted by Sn, is given by Sn = n² + 8n. Find the first term and the common difference.
The vector OA has a magnitude of 15 units and is in the same direction as the vector 3i – 4k. The vector OB has a magnitude of 14 units and is in t...
The diagram shows part of the curve y = −x² + 8x – 10 which passes through the points A and B. The curve has a maximum point at A and the gradient ...
Functions f and g are defined by f: x → 2x + 5 for x ∈ R, g: x → 8/(x-3) for x ∈ R, x ≠ 3.
A curve is such that dy/dx = 6/x² and (2, 9) is a point on the curve. Find the equation of the curve.
Find the coefficient of x² in the expansion of
The straight line y = mx + 14 is a tangent to the curve y = 12/x + 2 at the point P. Find the value of the constant m and the coordinates of P.
The diagram shows a square ABCD of side 10 cm. The mid-point of AD is O and BXC is an arc of a circle with centre O. [Figure 4.1]
It is given that a = sin θ – 3 cos θ and b = 3 sin θ + cos θ, where 0° ≤ θ ≤ 360°.
Relative to an origin O, the position vectors of points A and B are given by OA = i - 2j + 2k and OB = 3i + pj + qk, where p and q are constants.
The point R is the reflection of the point (−1, 3) in the line 3y + 2x = 33. Find by calculation the coordinates of R.
The volume of a solid circular cylinder of radius r cm is 250π cm³.
A function f is defined by f(x) = 5/(1-3x) for x ≥ 1.
The first and last terms of an arithmetic progression are 12 and 48 respectively. The sum of the first four terms is 57. Find the number of terms i...
The diagram shows the curve y = √(1 + 4x), which intersects the x-axis at A and the y-axis at B. The normal to the curve at B meets the x-axis at C...
Find the coordinates of the point at which the perpendicular bisector of the line joining (2, 7) to (10, 3) meets the x-axis.
Find the coefficient of x² in the expansion of (1 + x²)((x/2) - (4/x))⁶
The reflex angle θ is such that cos θ = k, where 0 < k < 1.
The diagram shows a sector of a circle with radius r cm and centre O. The chord AB divides the sector into a triangle AOB and a segment AXB. Angle ...
Prove the identity 1/cos θ - cos θ/(1 + sin θ) = tan θ.
The 1st, 2nd and 3rd terms of a geometric progression are the 1st, 9th and 21st terms respectively of an arithmetic progression. The 1st term of ea...
The diagram shows a trapezium ABCD in which BA is parallel to CD. The position vectors of A, B and C relative to an origin O are given by O A = (3/...
The equation of a curve is such that d²y/dx² = 2x – 1. Given that the curve has a minimum point at (3, –10), find the coordinates of the maximum po...
The diagram shows part of the curve y = 8 – √(4 – x) and the tangent to the curve at P (3, 7). [Figure 9.1]
Functions f and g are defined by f : x → 2x – 3, x ∈ R, g : x → x² + 4x, x ∈ R. Function h is defined by h : x → x² + 4x for x ≥ k, and it is given...
The function f is such that f'(x) = 5 – 2x² and (3, 5) is a point on the curve y = f(x). Find f(x).
In the diagram, AYB is a semicircle with AB as diameter and OAXB is a sector of a circle with centre O and radius r. Angle AOB = 2θ radians. Find a...
Find the coefficients of x² and x³ in the expansion of (2 – x)⁶.
Variables u, x and y are such that u = 2x(y – x) and x + 3y = 12. Express u in terms of x and hence find the stationary value of u.