Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
A car of mass 1200 kg is travelling along a horizontal road.
Two particles A and B of masses m kg and 4 kg respectively are connected by a light inextensible string that passes over a fixed smooth pulley. Par...
One end of a light inextensible string is attached to a fixed point A. The other end of the string is attached to a particle P of mass m kg which h...
An object is made from a uniform solid hemisphere of radius 0.56m and centre O by removing a hemisphere of radius 0.28 m and centre O. The diagram ...
A particle is projected from a point O on horizontal ground. The initial components of the velocity of the particle are 10 m s⁻¹ horizontally and 1...
A uniform semicircular lamina of radius 0.7 m and weight 14 N has diameter AB. The lamina is in a vertical plane with A freely pivoted at a fixed p...
A particle P of mass 0.15 kg is attached to one end of a light elastic string of natural length 0.4 m and modulus of elasticity 12 N. The other end...
A particle P of mass 0.5 kg is at rest at a point O on a rough horizontal surface. At time t = 0, where t is in seconds, a horizontal force acting ...
A particle P of mass 0.2 kg moves with speed 4 m s¯¹ and angular speed 5 rad s¯¹ in a horizontal circle on a smooth surface. P is attached to one e...
The ends of two light inextensible strings of length 0.7 m are attached to a particle P. The other ends of the strings are attached to two fixed po...
An open box in the shape of a cube with edges of length 0.2 m is placed with its base horizontal and its four sides vertical. The four sides and ba...
A small object of mass 0.4 kg is released from rest at a point 8 m above the ground. The object descends vertically and when its downwards displace...
A particle of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 6 N. The other end of ...
The end A of a non-uniform rod AB of length 0.6 m and weight 8 N rests on a rough horizontal plane, with AB inclined at 60° to the horizontal. Equi...
A particle P is projected from a point O with speed V ms¯¹. At time t s after projection the horizontal and vertically upwards displacements of P f...
Kadijat noted the weights, x grams, of 30 chocolate buns. Her results are summarised by Σ(x − k) = 315, Σ(x − k)² = 4022, where k is a constant. Th...
Ashfaq throws two fair dice and notes the numbers obtained. R is the event ‘The product of the two numbers is 12'. T is the event ‘One of the numbe...
Redbury United soccer team play a match every week. Each match can be won, drawn or lost. At the beginning of the soccer season the probability tha...
The times taken, t seconds, by 1140 people to solve a puzzle are summarised in the table. Time (t seconds): 0 < t < 20, 20 < t < 40, 40 < t < 60, 6...
Eggs are sold in boxes of 20. Cracked eggs occur independently and the mean number of cracked eggs in a box is 1.4.
(a) The random variable X has a normal distribution with mean μ and standard deviation σ. You are given that σ = 0.25μ and P(X < 6.8) = 0.75. (b) T...
(a) Eight children of different ages stand in a random order in a line. Find the number of different ways this can be done if none of the three you...
Rani and Diksha go shopping for clothes.
Anabel measured the lengths, in centimetres, of 200 caterpillars. Her results are illustrated in the cumulative frequency graph below. [Figure below]
In a probability distribution the random variable X takes the value x with probability kx², where k is a constant and x takes values −2, −1, 2, 4 o...
Two identical biased triangular spinners with sides marked 1, 2 and 3 are spun. For each spinner, the probabilities of landing on the sides marked ...
The lengths of videos of a certain popular song have a normal distribution with mean 3.9 minutes. 18% of these videos last for longer than 4.2 minu...
A library contains 4 identical copies of book A, 2 identical copies of book B and 5 identical copies of book C. These 11 books are arranged on a sh...
During the school holidays, each day Khalid either rides on his bicycle with probability 0.6, or on his skateboard with probability 0.4. Khalid doe...
A biased die has faces numbered 1 to 6. The probabilities of the die landing on 1, 3 or 5 are each equal to 0.1. The probabilities of the die landi...
The probability that George goes swimming on any day is 1/3. Use an approximation to calculate the probability that in 270 days George goes swimmin...
A shop sells two makes of coffee, Café Premium and Café Standard. Both coffees come in two sizes, large jars and small jars. Of the jars on sale, 6...
Hebe attempts a crossword puzzle every day. The number of puzzles she completes in a week (7 days) is denoted by X.
The following histogram represents the lengths of worms in a garden. [Figure X.X]
The coefficient of x² in the expansion of (2 + x/2)⁶ + (a + x)⁵ is 330. Find the value of the constant a.
The equation of a curve is y = x² – 6x + k, where k is a constant.
A company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by 2% of the amount obtained in t...
The function f is such that f(x) = a + b cos x for 0 ≤ x ≤ 2π. It is given that f(π/3) = 5 and f(π) = 11.
The diagram shows a three-dimensional shape. The base OAB is a horizontal triangle in which angle AOB is 90°. The side OBCD is a rectangle and the ...
The diagram shows points A and B on a circle with centre O and radius r. The tangents to the circle at A and B meet at T. The shaded region is boun...
The function f is defined by f : x → 7 – 2x² – 12x for x ∈ R.
Points A and B have coordinates (h, h) and (4h + 6, 5h) respectively. The equation of the perpendicular bisector of AB is 3x + 2y = k. Find the val...
A curve is such that dy/dx = √(4x + 1) and (2, 5) is a point on the curve.
The diagram shows part of the curve y = x/2 + 6/x. The line y = 4 intersects the curve at the points P and Q. [Figure 18]
Solve the equation 3e2x – 82ex + 27 = 0, giving your answers in the form k ln 3.
The variables x and y satisfy the equation y = A × Blnx, where A and B are constants. The graph of In y against Inx is a straight line passing thro...