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.
A particle P of mass 0.2 kg is released from rest at a point O on a rough plane inclined at 60° to the horizontal, and travels down a line of great...
A particle P of mass 0.2kg is released from rest at a point O on a smooth horizontal surface. A horizontal force of magnitude te⁻ᵛ N directed away ...
A uniform solid cone has height 0.6 m and base radius 0.2 m. A uniform hollow cylinder, open at both ends, has the same dimensions. An object is ma...
A particle P of mass 0.4 kg is released from rest at a point O on a smooth plane inclined at 30° to the horizontal. P moves down the line of greate...
A light elastic string has natural length 2 m and modulus of elasticity 39 N. The ends of the string are attached to fixed points A and B which are...
OAB is a uniform lamina in the shape of a quadrant of a circle with centre O and radius 0.8 m which has its centre of mass at G. The lamina is smoo...
One end of a light elastic string of natural length 0.4 m and modulus of elasticity 8 N is attached to a fixed point O on a smooth horizontal plane...
A small ball B is projected from a point O which is h m above a horizontal plane. At time 2s after projection B has speed 18 m s⁻¹ and is moving in...
A hollow cylinder with a rough inner surface has radius 0.5 m. A particle P of mass 0.4 kg is in contact with the inner surface of the cylinder. Th...
A solid object consists of a uniform hemisphere of radius 0.4 m attached to a uniform cylinder of radius 0.4 m so that the circumferences of their ...
The discrete random variable X has the following probability distribution. x | 1 | 2 | 3 | 6 P(X = x) | 0.15 | p | 0.4 | q Given that E(X) = 3.05, ...
The time taken by a car to accelerate from 0 to 30 metres per second was measured correct to the nearest second. The results from 48 cars are summa...
An experiment consists of throwing a biased die 30 times and noting the number of 4s obtained. This experiment was repeated many times and the aver...
The ages of a group of 12 people at an Art class have mean 48.7 years and standard deviation 7.65 years. The ages of a group of 7 people at another...
Over a period of time Julian finds that on long-distance flights he flies economy class on 82% of flights. On the rest of the flights he flies firs...
A village hall has seats for 40 people, consisting of 8 rows with 5 seats in each row. Mary, Ahmad, Wayne, Elsie and John are the first to arrive i...
The weight, in grams, of pineapples is denoted by the random variable X which has a normal distribution with mean 500 and standard deviation 91.5. ...
Andy counts the number of emails, x, he receives each day and notes that, over a period of n days, Σ(x – 10) = 27 and the mean number of emails is ...
The circumferences, ccm, of some trees in a wood were measured. The results are summarised in the table. Circumference (c cm) 40 < c ≤ 50 | 50 < c ...
A box contains 6 identical-sized discs, of which 4 are blue and 2 are red. Discs are taken at random from the box in turn and not replaced. Let X b...
A fair tetrahedral die has faces numbered 1, 2, 3, 4. A coin is biased so that the probability of showing a head when thrown is 1/3. The die is thr...
Blank CDs are packed in boxes of 30. The probability that a blank CD is faulty is 0.04. A box is rejected if more than 2 of the blank CDs are faulty.
(a) Find the number of different 3-digit numbers greater than 300 that can be made from the digits 1, 2, 3, 4, 6, 8 if (b) A team of 5 is chosen fr...
In Jimpuri the weights, in kilograms, of boys aged 16 years have a normal distribution with mean 61.4 and standard deviation 12.3. In Brigville the...
A statistics student asks people to complete a survey. The probability that a randomly chosen person agrees to complete the survey is 0.2. Find the...
Tien measured the arm lengths, x cm, of 20 people in his class. He found that Σx = 1218 and the standard deviation of x was 4.2. Calculate Σ(x – 45...
At the end of a revision course in mathematics, students have to pass a test to gain a certificate. The probability of any student passing the test...
A fair die with faces numbered 1, 2, 2, 2, 3, 6 is thrown. The score, X, is found by squaring the number on the face the die shows and then subtrac...
The number of Olympic medals won in the 2012 Olympic Games by the top 27 countries is shown below. 104 88 82 65 44 38 35 34 28 28 18 18 17 17 14 13...
A car park has spaces for 18 cars, arranged in a line. On one day there are 5 cars, of different makes, parked in randomly chosen positions and 13 ...
Josie aims to catch a bus which departs at a fixed time every day. Josie arrives at the bus stop T minutes before the bus departs, where T ~ N(5.3,...
Find the coefficient of 1/x² in the expansion of (3x + 2/(3x²))⁷.
Showing all necessary working, find ∫₁⁴ (√x + 2/√x) dx.
The diagram shows part of the curve y = x(9 – x²) and the line y = 5x, intersecting at the origin O and the point R. Point P lies on the line y = 5...
Functions f and g are defined by f: x → 2 – 3 cos x for 0 ≤ x ≤ 2π, g: x → ½x for 0 ≤ x ≤ 2π.
The first three terms of an arithmetic progression are 4, x and y respectively. The first three terms of a geometric progression are x, y and 18 re...
The diagram shows a triangle ABC in which BC = 20 cm and angle ABC = 90°. The perpendicular from B to AC meets AC at D and AD = 9 cm. Angle BCA = θ°.
The diagram shows a solid cylinder standing on a horizontal circular base with centre O and radius 4 units. Points A, B and C lie on the circumfere...
The diagram shows an isosceles triangle ACB in which AB = BC = 8 cm and AC = 12 cm. The arc XC is part of a circle with centre A and radius 12 cm, ...
The function f is defined by f : x → 2x² – 12x + 7 for x ∈ R.
The equation of a curve is y = 2x + 12/x and the equation of a line is y + x = k, where k is a constant.
The diagram shows part of the curve y = 3√(4x + 1) – 2x. The curve crosses the y-axis at A and the stationary point on the curve is M.
Solve the equation |9x – 2| = |3x + 2|.
Show that ∫₁⁷ (6 / (2x + 1)) dx = ln 125.
Solve the equation sec² θ = 3 cosec θ for 0° < θ < 180°.
The diagram shows the curve with equation y = x⁴ + 2x³ + 2x² – 12x – 32. The curve crosses the x-axis at points with coordinates (α, 0) and (β, 0)....
A curve has parametric equations x = t + ln(t + 1), y = 3te²ᵗ.
The diagram shows the curve with equation y = √(1 + 3cos²(x)) for 0 ≤ x ≤ π. The region R is bounded by the curve, the axes and the line x = π. [Fi...
The diagram shows the curve with equation y = sin 2x + 3 cos 2x for 0 ≤ x ≤ π. At the points P and Q on the curve, the gradient of the curve is 3. ...
Solve the inequality |3x – 5| < 2|x|.