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.
Two particles P and Q of masses 0.2 kg and 0.3 kg respectively are free to move in a horizontal straight line on a smooth horizontal plane. P is pr...
A car of mass 1400 kg is travelling at constant speed up a straight hill inclined at α to the horizontal, where sin α = 0.1. There is a constant re...
A particle Q of mass 0.2 kg is held in equilibrium by two light inextensible strings PQ and QR. P is a fixed point on a vertical wall and R is a fi...
An elevator moves vertically, supported by a cable. The diagram shows a velocity-time graph which models the motion of the elevator. The graph cons...
A block of mass 5 kg is being pulled along a rough horizontal floor by a force of magnitude X N acting at 30° above the horizontal (see diagram). T...
A particle moves in a straight line. It starts from rest from a fixed point O on the line. Its velocity at time t s after leaving O is v m s⁻¹, whe...
Two particles P and Q of masses 0.5 kg and mkg respectively are attached to the ends of a light inextensible string. The string passes over a fixed...
A fair spinner with 5 sides numbered 1, 2, 3, 4, 5 is spun repeatedly. The score on each spin is the number on the side on which the spinner lands.
Georgie has a red scarf, a blue scarf and a yellow scarf. Each day she wears exactly one of these scarves. The probabilities for the three colours ...
The time spent by shoppers in a large shopping centre has a normal distribution with mean 96 minutes and standard deviation 18 minutes.
The random variable X takes the values 1, 2, 3, 4 only. The probability that X takes the value x is kx(5-x), where k is a constant.
A driver records the distance travelled in each of 150 journeys. These distances, correct to the nearest km, are summarised in the following table....
Find the total number of different arrangements of the 11 letters in the word CATERPILLAR.
There are 400 students at a school in a certain country. Each student was asked whether they preferred swimming, cycling or running and the results...
A construction company notes the time, t days, that it takes to build each house of a certain design. The results for a random sample of 60 such ho...
The diagram shows the graph of the probability density function, f, of a random variable X. [Figure 2.1]
An architect wishes to investigate whether the buildings in a certain city are higher, on average, than buildings in other cities. He takes a large...
On average, 1 in 400 microchips made at a certain factory are faulty. The number of faulty microchips in a random sample of 1000 is denoted by X.
The volumes, in litres, of juice in large and small bottles have the distributions N(5.10, 0.0102) and N(2.51, 0.0036) respectively.
It is known that 8% of adults in a certain town own a Chantor car. After an advertising campaign, a car dealer wishes to investigate whether this p...
A curve with equation y = f(x) is such that f'(x) = 2x^3 - x3. 1 - x3. It is given that f(8) = 5.
A curve has equation y = x² + 2cx + 4 and a straight line has equation y = 4x + c, where c is a constant. Find the set of values of c for which the...
Find the term independent of x in each of the following expansions.
The first term of a geometric progression and the first term of an arithmetic progression are both equal to a. The third term of the geometric prog...
The functions f and g are defined by f(x) = x² for x ∈ R, g(x) = 2x² - 8x + 14 for x ∈ R.
The circle with equation (x + 1)² + (y − 2)² = 85 and the straight line with equation y = 3x – 20 are shown in the diagram. The line intersects the...
Show that (sin θ + 2 cos θ)/(cos θ - 2 sin θ) - (sin θ - 2 cos θ)/(cos θ + 2 sin θ) = 4/(5 cos² θ - 4)
The diagram shows the circle with equation (x – 2)² + y² = 8. The chord AB of the circle intersects the positive y-axis at A and is parallel to the...
Functions f, g and h are defined as follows: f : x ↦ x - 4x^(1/2) + 1 for x ≥ 0, g : x ↦ mx² + n for x ≥ −2, where m and n are constants, h : x ↦ x...
The diagram shows a circle with centre A of radius 5cm and a circle with centre B of radius 8cm. The circles touch at the point C so that ACB is a ...
It is given that a curve has equation y = k(3x – k)⁻¹ + 3x, where k is a constant.
Solve the equation |5x-2| = |4x + 9|.
A curve has equation y = 7 + 4 ln(2x + 5). Find the equation of the tangent to the curve at the point (−2, 7), giving your answer in the form y = m...
The variables x and y satisfy the equation y = 3^(2a)a^x, where a is a constant. The graph of ln y against x is a straight line with gradient 0.239.
Show that sin 2θ cot θ – cos 2θ = 1.
Given that y = tan²x, show that dy/dx = 2 tan x + 2 tan³ x.
The polynomial p(x) is defined by p(x) = 4x³ + 16x² + 9x – 15.
A curve has equation e^(2xy) – e^y = 100.
Solve the inequality |2x + 3| > 3|x + 2|.
On a sketch of an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities |z + 2 - 3i| ≤ 2 and arg z ...
The variables x and y satisfy the equation xⁿy² = C, where n and C are constants. The graph of ln y against ln x is a straight line passing through...
The parametric equations of a curve are x = 1 – cos θ, y = cos θ – ½ cos 2θ.
The angles α and β lie between 0° and 180° and are such that tan(α + β) = 2 and tan α = 3 tan β.
Find the complex numbers w which satisfy the equation w² + 2iw* = 1 and are such that Re w ≤ 0. Give your answers in the form x + iy, where x and y...
By sketching a suitable pair of graphs, show that the equation 4 – x² = sec ½x has exactly one root in the interval 0 < x < π.
Find the quotient and remainder when 8x³ + 4x² + 2x + 7 is divided by 4x² + 1.
The variables x and y satisfy the differential equation (x + 1)(3x + 1) dy/dx = y, and it is given that y = 1 when x = 1.
The points A and B have position vectors 2i + j + k and i – 2j + 2k respectively. The line l has vector equation r = i + 2j – 3k + μ(i – 3j – 2k).
The diagram shows the curve y = sin x cos 2x for 0 ≤ x ≤ ½π, and its maximum point M. [Figure 11.1]
A crane is used to raise a block of mass 600kg vertically upwards at a constant speed through a height of 15 m. There is a resistance to the motion...