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.
Using an appropriate quadratic factorisation, find the first three terms in the binomial expansion of (9x²+12x+4)⁵, in ascending powers of x. You m...
The function f is defined by f(x) = 2e⁻ˣ +3 for x ∈ R. On the axes, sketch the graph of y = f(x) and hence, on the same axes, sketch the graph of y...
Solve the equation (2-3 cotx) cosx = 0 for 0 < x ≤ π/2.
In this question, all lengths are in centimetres and all angles are in radians. [Figure showing a sector AOB of a circle and a cone formed from it]...
A particle P moves in a straight line. t seconds after passing a fixed point, O, the acceleration of P, a m s⁻², is given by a = t²-2 for 0 ≤ t ≤ 4...
A geometric progression has first term a and common ratio r, where r > 0. The sum of the 2nd and 3rd terms of the progression is 168. The sum of th...
Solve the inequality |5x+2|≥3.
In this question, all lengths are in metres and time is in seconds. A particle P moves in a straight line such that its displacement s from a fixed...
Functions f and g are such that f(x) = 3x / (x+4) for x > 0 g(x)=√(x+2) for x >-2. Solve the equation fg(x) = 1.
Given that y = 4 sin 2x cos 2x, find the value of dy/dx when x = π/6.
A 4-digit number is to be formed using the digits 0, 2, 4, 5, 6 and 8. The 4-digit number must not start with 0. Any digit may be used at most once...
The volume, V, of a sphere is increasing at the constant rate of 2π cm³ s⁻¹. Find the rate of change of the surface area, S, of this sphere when th...
The first three terms of an arithmetic progression can be written as 2ln(x³), 51n(x²), 2ln(x⁷).
The diagram shows part of the curve y = 15/x - 5/x². The curve meets the x-axis at the point A. The curve has a maximum at the point B. Find the ar...
Solve the equation 3 sec 3x = √3 cosec 3x for -120° ≤ x ≤ 120°.
The first three terms, in descending powers of x, in the expansion of (3x²-a)ⁿ (1+2/x²)² can be written as 729x¹² - 972x¹⁰ + bx⁸, where a, b and n ...
The equation of a curve is given by y = 2x² + ax + 14, where a is a constant. Given that this equation can also be written as y = 2(x – 3)² + b, wh...
Sketch, on the same set of axes, the graphs of y = cos x and y = sin 2x for 0° ≤ x ≤ 180°.
Show that `cos x / (1 - sin x) + cos x / (1 + sin x) = 2 sec x.`
Factorise completely the expression 2x³ – 11x² – 20x – 7.
A curve has the equation y = 2x sin x + π/3. The curve passes through the point P(π/2, a).
Find, in ascending powers of x, the first 3 terms in the expansion of (2 – 5x)⁶, giving your answer in the form a + bx + cx², where a, b and c are ...
(a) Sets A and B are such that A = {x : sin x = 0.5 for 0° ≤ x ≤ 360°}, B = {x : cos (x − 30°) = − 0.5 for 0° ≤ x ≤ 360°}. Find the elements of
The figure shows a rectangular metal block of length 4x cm, with a cross-section which is a square of side xcm and area Acm². The block is heated a...
The diagram shows a circle, centre O, radius 4 cm, enclosed within a sector PBCDP of a circle, centre P. The circle centre O touches the sector at ...
Find `∫ (1/√(1 + x)) dx`.
Answer only one of the following two alternatives. EITHER
OR A curve has the equation `y = Ae^(2x) + Be⁻ˣ` where `x ≥ 0`. At the point where `x = 0`, `y = 50` and `dy/dx = -20`.
Show that COS X + COS X = 2 sec x. 1 - sin x 1 + sin x
A curve has the equation y = 2x sin x + π/3. The curve passes through the point P (π/2, a).
Sets A and B are such that A = {x : sin x = 0.5 for 0° ≤ x ≤ 360°}, B = {x : cos (x − 30°) = − 0.5 for 0° ≤ x ≤ 360°}. Find the elements of (i) A,
Find ∫ 1/(√1 + x) dx.
EITHER: A curve is such that dy/dx = 4x² – 9. The curve passes through the point (3, 1).
OR: A curve has the equation y = Ae²ˣ + Be⁻ˣ where x ≥ 0. At the point where x = 0, y = 50 and dy/dx = -20.
Solve the equation |2x + 10| = 7.
The expression x³ + ax² – 15x + b has a factor x – 2 and leaves a remainder of 75 when divided by x + 3. Find the value of a and of b.
A number, N₀, of fish of a particular species are introduced to a lake. The number, N, of these fish in the lake, t weeks after their introduction,...
Students take three multiple-choice tests, each with ten questions. A correct answer earns 5 marks. If no answer is given 1 mark is scored. An inco...
Find the set of values of m for which the line y = mx – 2 cuts the curve y = x² + 8x + 7 in two distinct points.
A 4-digit number is formed by using four of the seven digits 1, 3, 4, 5, 7, 8 and 9. No digit can be used more than once in any one number. Find ho...
A rectangular sheet of metal measures 60 cm by 45 cm. A scoop is made by cutting out squares, of side x cm, from two corners of the sheet and foldi...
Solve the equation lg(5x + 10) + 2 lg 3 = 1 + lg(4x + 12),
A plane, whose speed in still air is 250 kmh⁻¹, flies directly from A to B, where B is 500 km from A on a bearing of 060°. There is a constant wind...
Solutions to this question by accurate drawing will not be accepted. The diagram shows a quadrilateral ABCD in which A is the point (1, 4) and B is...
Solve the equation 5 sin x – 3 cos x = 0, for 0° ≤ x ≤ 360°,
Answer only one of the following two alternatives. EITHER The functions f and g are defined, for x > 1, by f(x) = (x + 1)² - 4, g(x) = (3x + 5) / (...
OR A particle moves in a straight line so that, at time t s after passing a fixed point O, its velocity is v m s⁻¹, where v = 6t + 4 cos 2t. Find
Solve the equation lg(5x + 10) + 2lg3 = 1 + lg(4x + 12),
A plane, whose speed in still air is 250kmh⁻¹, flies directly from A to B, where B is 500km from A on a bearing of 060°. There is a constant wind o...
Solutions to this question by accurate drawing will not be accepted. [Figure showing a quadrilateral ABCD on a Cartesian plane. Point A is (1,4), P...