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.
Fig. 1 shows an object made from a uniform wire of length 0.8 m. The object consists of a straight part AB, and a semicircular part BC such that A,...
A particle is projected with speed V m s⁻¹ at an angle of θ° above the horizontal. At the instant 4 s after projection the speed of the particle is...
A small ball 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...
The times, t seconds, taken to swim 100m were recorded for a group of 9 swimmers and were found to be as follows. 95 126 117 135 120 125 114 119 136
Jameel has 5 plums and 3 apricots in a box. Rosa has x plums and 6 apricots in a box. One fruit is chosen at random from Jameel's box and one fruit...
A fair six-sided die is thrown twice and the scores are noted. Event X is defined as 'The total of the two scores is 4'. Event Y is defined as ‘The...
The Mathematics and English A-level marks of 1400 pupils all taking the same examinations are shown in the cumulative frequency graphs below. Both ...
In a certain country the probability that a child owns a bicycle is 0.65.
At a funfair, Amy pays $1 for two attempts to make a bell ring by shooting at it with a water pistol. • If she makes the bell ring on her first att...
The weight of adult female giraffes has a normal distribution with mean 830 kg and standard deviation 120 kg.
Freddie has 6 toy cars and 3 toy buses, all different. He chooses 4 toys to take on holiday with him.
Two ordinary fair dice are thrown and the numbers obtained are noted. Event S is 'The sum of the numbers is even'. Event T is 'The sum of the numbe...
The volume of ink in a certain type of ink cartridge has a normal distribution with mean 30 ml and standard deviation 1.5 ml. People in an office u...
The probability that Janice will buy an item online in any week is 0.35. Janice does not buy more than one item online in any week.
It is known that 20% of male giant pandas in a certain area weigh more than 121 kg and 71.9% weigh more than 102 kg. Weights of male giant pandas i...
Maryam has 7 sweets in a tin; 6 are toffees and 1 is a chocolate. She chooses one sweet at random and takes it out. Her friend adds 3 chocolates to...
Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.
A group of 6 teenagers go boating. There are three boats available. One boat has room for 3 people, one has room for 2 people and one has room for ...
The time taken, in minutes, by a ferry to cross a lake has a normal distribution with mean 85 and standard deviation 6.8.
Megan sends messages to her friends in one of 3 different ways: text, email or social media. For each message, the probability that she uses text i...
Mr and Mrs Keene and their 5 children all go to watch a football match, together with their friends Mr and Mrs Uzuma and their 2 children. Find the...
Find the number of ways a committee of 6 people can be chosen from 8 men and 4 women if there must be at least twice as many men as there are women...
On average, 34% of the people who go to a particular theatre are men.
A fair five-sided spinner has sides numbered 1, 1, 1, 2, 3. A fair three-sided spinner has sides numbered 1, 2, 3. Both spinners are spun once and ...
The times in minutes taken by 13 pupils at each of two schools in a cross-country race are recorded in the table below. Thaters School 38 43 48 52 ...
The following parts relate to binomial expansions.
The following parts relate to trigonometric equations.
A weather balloon in the shape of a sphere is being inflated by a pump. The volume of the balloon is increasing at a constant rate of 600 cm³ per s...
The nth term of an arithmetic progression is (1/2)(3n – 15). Find the value of n for which the sum of the first n terms is 84.
The function f is defined for x ∈ R by f: x ↦ a - 2x, where a is a constant.
The equation of a curve is y = 2x² + kx + k − 1, where k is a constant.
In the diagram, OAB is a sector of a circle with centre O and radius 2r, and angle AOB = π/6 radians. The point C is the midpoint of OA. [Figure 7.1]
The diagram shows part of the curve y = 6/x. The points (1, 6) and (3, 2) lie on the curve. The shaded region is bounded by the curve and the lines...
Functions f and g are such that f(x) = 2 - 3 sin 2x for 0 ≤ x ≤ π, g(x) = -2f(x) for 0 ≤ x ≤ π. The diagram below shows the graph of y = f(x). [Fig...
The equation of a curve is y = 54x – (2x – 7)³.
The equation of a circle with centre C is x² + y² – 8x + 4y − 5 = 0.
Given that 2^y = 9^3x, use logarithms to show that y = kx and find the value of k correct to 3 significant figures.
Find the exact coordinates of the stationary point on the curve with equation y = 5xex^(1/2)x.
The equation of a curve is cos 3x + 5 sin y = 3. Find the gradient of the curve at the point (1/3 π, 1/6 π).
The variables x and y satisfy the equation y = Ax^(-2p), where A and p are constants. The graph of ln y against ln x is a straight line passing thr...
Sketch, on the same diagram, the graphs of y = |2x – 3| and y = 3x + 5.
The polynomial p(x) is defined by p(x) = 6x³ + ax² - 4x – 3, where a is a constant. It is given that (x + 3) is a factor of p(x).
It is given that ∫[from 0 to a] (4/(2x+1) + 8x) dx = 10, where a is a positive constant.
Show that 3 sin 2θ cot θ = 6 cos² θ.
Given that 2ʸ = 9³ˣ, use logarithms to show that y = kx and find the value of k correct to 3 significant figures.
Find the exact coordinates of the stationary point on the curve with equation y = 5xe½ˣ.
The equation of a curve is cos 3x + 5 sin y = 3. Find the gradient of the curve at the point (¹⁄₆π, ¹⁄₆π).
The variables x and y satisfy the equation y = Ax⁻²ᵖ, where A and p are constants. The graph of ln y against ln x is a straight line passing throug...
Sketch, on the same diagram, the graphs of y = |2x – 3| and y = 3x + 5.
It is given that ∫₀ᵃ ( 4/(2x + 1) + 8x) dx = 10, where a is a positive constant.