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 first 3 terms in the expansion, in ascending powers of x, of (1 – 2x²)⁸.
Prove the identity tan²x - sin²x = tan²x sin²x.
The length, x metres, of a Green Anaconda snake which is t years old is given approximately by the formula x = 0.7 √(2t – 1), where 1 ≤ t ≤ 10. Usi...
The diagram shows points A, C, B, P on the circumference of a circle with centre O and radius 3 cm. Angle AOC = angle BOC = 2.3 radians. [Figure 4.1]
The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum of the first m terms is zero. Find the value of m.
A curve has equation y = kx² + 1 and a line has equation y = kx, where k is a non-zero constant.
The function f is defined by f(x) = x² – 4x +7 for x > 2.
The diagram shows part of the curve y = 2/(1-x) and the line y = 3x + 4. The curve and the line meet at points A and B. [Figure 8.1]
The diagram shows a pyramid OABCP in which the horizontal base OABC is a square of side 10 cm and the vertex P is 10cm vertically above O. The poin...
The diagram shows an open rectangular tank of height h metres covered with a lid. The base of the tank has sides of length x metres and 5/4x metres...
The diagram shows part of the curve y = 1/(3x + 1)⁴. The curve cuts the y-axis at A and the line x = 5 at B. [Figure 11.1]
Find the first 3 terms in the expansion of (2 – y)⁵ in ascending powers of y.
The functions f and g are defined for x ∈ R by f: x → 3x + a, g: x → b - 2x, where a and b are constants. Given that ff(2) = 10 and g⁻¹(2) = 3, find
Relative to an origin O, the position vectors of points A and B are given by OĀ = 5i + j + 2k and OB = 2i + 7j + pk, where p is a constant.
The equation of a curve is y² + 2x = 13 and the equation of a line is 2y + x = k, where k is a constant.
Sketch, on the same diagram, the graphs of y = sinx and y = cos 2x for 0° ≤ x ≤ 180°.
The diagram shows a circle C₁ touching a circle C₂ at a point X. Circle C₁ has centre A and radius 6 cm, and circle C₂ has centre B and radius 10 c...
A curve is such that dy/dx = 5 - 8/x². The line 3y + x = 17 is the normal to the curve at the point P on the curve. Given that the x-coordinate of ...
The equation of a curve is y = √(8x – x²). Find
The diagram shows a quadrilateral ABCD in which the point A is (-1, -1), the point B is (3, 6) and the point C is (9, 4). The diagonals AC and BD i...
(a) An arithmetic progression contains 25 terms and the first term is –15. The sum of all the terms in the progression is 525. Calculate (b) A coll...
In the expansion of (x² - a/x)⁷, the coefficient of x⁵ is –280. Find the value of the constant a.
A function f is such that f(x) = (√(x + 3) / 2) + 1, for x ≥ −3.
The diagram shows a plan for a rectangular park ABCD, in which AB = 40 m and AD = 60 m. Points X and Y lie on BC and CD respectively and AX, XY and...
The line y = x/k + k, where k is a constant, is a tangent to the curve 4y = x² at the point P.
The diagram shows a triangle ABC in which A has coordinates (1, 3), B has coordinates (5, 11) and angle ABC is 90°. The point X (4, 4) lies on AC. ...
Show that the equation 2 cos x = 3 tan x can be written as a quadratic equation in sin x.
The position vectors of the points A and B, relative to an origin O, are given by OA = (1, 0, 2) and OB = (k, -k, 2k), where k is a constant.
In a geometric progression, all the terms are positive, the second term is 24 and the fourth term is 13½. Find the first term,
The diagram shows part of the curve y = 9/(2x + 3), crossing the y-axis at the point B (0, 3). The point A on the curve has coordinates (3, 1) and ...
A curve is defined for x > 0 and is such that dy/dx = x + 4/x². The point P (4, 8) lies on the curve.
The diagram shows a sector of a circle with centre O and radius 20 cm. A circle with centre C and radius x cm lies within the sector and touches it...
Given that cosx = p, where x is an acute angle in degrees, find, in terms of p,
Fig. 1 shows a hollow cone with no base, made of paper. The radius of the cone is 6 cm and the height is 8 cm. The paper is cut from A to O and ope...
The equation of a curve is y = 2 / √(5x-6)
Relative to an origin O, the position vectors of points A and B are given by OA = i + 2j and OB = 4i + pk.
The diagram shows a rectangle ABCD in which point A is (0, 8) and point B is (4, 0). The diagonal AC has equation 8y + x = 64. Find, by calculation...
In the diagram, S is the point (0, 12) and T is the point (16, 0). The point Q lies on ST, between S and T, and has coordinates (x, y). The points ...
An athlete runs the first mile of a marathon in 5 minutes. His speed reduces in such a way that each mile takes 12 seconds longer than the precedin...
A function f is defined by f : x → 3 cos x − 2 for 0 ≤ x ≤ 2π.
The diagram shows part of the curve y = 8/x + 2x and three points A, B and C on the curve with x-coordinates 1, 2 and 5 respectively.
A curve has equation y = 2x² – 3x.
The diagram shows part of the curve y = x² + 1. Find the volume obtained when the shaded region is rotated through 360° about the y-axis. [Figure w...
The diagram shows a triangle AOB in which OA is 12 cm, OB is 5 cm and angle AOB is a right angle. Point P lies on AB and OP is an arc of a circle w...
Find the first 3 terms, in ascending powers of x, in the expansion of (1 + x)⁵.
A curve has equation y = 12 / (3-2x)
Show that the equation 1 + sin x tan x = 5 cos x can be expressed as 6 cos²x - cos x − 1 = 0.
The equation of a curve is y = x³ + ax² + bx, where a and b are constants.
The diagram shows a pyramid OABCX. The horizontal square base OABC has side 8 units and the centre of the base is D. The top of the pyramid, X, is ...
The sum, Sₙ, of the first n terms of an arithmetic progression is given by Sₙ = 32n – n². Find the first term and the common difference.