Cambridge & Pearson Edexcel Past Paper Questions

The lengths of female snakes of a particular species are normally distributed with mean 54 cm and standard deviation 6.1 cm.

The numbers of chocolate bars sold per day in a cinema over a period of 100 days are summarised in the following table. Number of chocolate bars so...

For n values of the variable x, it is given that Σ(x – 50) = 144 and Σx = 944. Find the value of n.

A total of 500 students were asked which one of four colleges they attended and whether they preferred soccer or hockey. The numbers of students in...

Two machines, A and B, produce metal rods of a certain type. The lengths, in metres, of 19 rods produced by machine A and 19 rods produced by machi...

Trees in the Redian forest are classified as tall, medium or short, according to their height. The heights can be modelled by a normal distribution...

A fair three-sided spinner has sides numbered 1, 2, 3. A fair five-sided spinner has sides numbered 1, 1, 2, 2, 3. Both spinners are spun once. For...

Find the number of different ways in which the 10 letters of the word SUMMERTIME can be arranged...

On any given day, the probability that Moena messages her friend Pasha is 0.72.

Juan goes to college each day by any one of car or bus or walking. The probability that he goes by car is 0.2, the probability that he goes by bus ...

In a certain large college, 22% of students own a car.

In a certain town, the time, X hours, for which people watch television in a week has a normal distribution with mean 15.8 hours and standard devia...

A fair four-sided spinner has edges numbered 1, 2, 2, 3. A fair three-sided spinner has edges numbered -2, -1, 1. Each spinner is spun and the numb...

A pair of fair coins is thrown repeatedly until a pair of tails is obtained. The random variable X denotes the number of throws required to obtain ...

The annual salaries, in thousands of dollars, for 11 employees at each of two companies A and B are shown below. Company A 30 32 35 41 41 42 47 49 ...

Find the number of different possible arrangements of the 9 letters in the word CELESTIAL.

The lengths, X centimetres, of a random sample of 7 leaves from a certain variety of tree are as follows. 5.2 4.8 5.5 6.1 4.8 3.9 4.4 It is now giv...

In the past the yield of a certain crop, in tonnes per hectare, had mean 0.56 and standard deviation 0.08. Following the introduction of a new fert...

The masses, in kilograms, of large sacks of flour and small sacks of flour have the independent distributions N(40, 1.5²) and N(12, 0.7²) respectiv...

A fair spinner has five sides numbered 1, 2, 3, 4, 5. The score on one spin is denoted by X. Fiona has another spinner, also with five sides number...

Each week a sports team plays one home match and one away match. In their home matches they score goals at a constant average rate of 2.1 goals per...

The length of time, T minutes, that a passenger has to wait for a bus at a certain bus stop is modelled by the probability density function given b...

The masses, in grams, of plums of a certain type have the distribution N(40.4, 5.2²). The plums are packed in bags, with each bag containing 6 rand...

A shop obtains apples from a certain farm. It has been found that 5% of apples from this farm are Grade A. Following a change in growing conditions...

In the data-entry department of a certain firm, it is known that 0.12% of data items are entered incorrectly, and that these errors occur randomly ...

The score on one spin of a 5-sided spinner is denoted by the random variable X with probability distribution as shown in the table. x | 0 | 1 | 2 |...

The random variable X has the distribution Po(λ).

A random variable X has probability density function given by f(x) = { k/x² 1 ≤ x ≤ a, 0 otherwise, where k and a are positive constants.

A random sample of 100 values of a variable X is taken. These values are summarised below. n = 100 Σχ = 1556 Σχ² = 29004 Calculate unbiased estimat...

Each day at the gym, Sarah completes three runs. The distances, in metres, that she completes in the three runs have the independent distributions ...

The number of customers who visit a particular shop between 9.00 am and 10.00 am has the distribution Po(λ). In the past the value of λ was 5.2. Fo...

The random variable A has the distribution Po(1.5). A₁ and A₂ are independent values of A.

Sunita has a six-sided die with faces marked 1, 2, 3, 4, 5, 6. The probability that the die shows a six on any throw is p. Sunita throws the die 50...

The length, X centimetres, of worms of a certain type is modelled by the probability density function f(x) = { (1/125)(10-x)(x - 5) 5 ≤ x ≤ 10,...

A market researcher is investigating the length of time that customers spend at an information desk. He plans to choose a sample of 50 customers on...

Express 16x² – 24x + 10 in the form (4x + a)² + b.

The graph of y = f(x) is transformed to the graph of y = 2f(x – 1). Describe fully the two single transformations which have been combined to give ...

The equation of a curve is y = (x − 3)√x + 1 + 3. The following points lie on the curve. Non-exact values are rounded to 4 decimal places. A (2, k)...

The coefficient of x in the expansion of (4x + 10/x)³ is p. The coefficient of 1/x in the expansion of (2x + k/x)⁵ is q. Given that p = 6q, find th...

The function f is defined by f(x) = 2x² + 3 for x ≥ 0.

Points A and B have coordinates (8, 3) and (p, q) respectively. The equation of the perpendicular bisector of AB is y = −2x + 4. Find the values of...

The point A has coordinates (1, 5) and the line l has gradient −2/3 and passes through A. A circle has centre (5, 11) and radius √52.

The first, second and third terms of an arithmetic progression are a, 3/2a and b respectively, where a and b are positive constants. The first, sec...

The diagram shows part of the curve with equation y² = x – 2 and the lines x = 5 and y = 1. The shaded region enclosed by the curve and the lines i...

Prove the identity (1 + sin x) / (1 - sin x) - (1 - sin x) / (1 + sin x) = 4 tan x / cos x

The gradient of a curve is given by dy/dx = 6(3x – 5)³ – kx², where k is a constant. The curve has a stationary point at (2, -3.5).

The diagram shows a cross-section of seven cylindrical pipes, each of radius 20 cm, held together by a thin rope which is wrapped tightly around th...

Solve the equation ln(2 + x) – ln x = 2 ln 3.

The solutions of the equation 5|x| = 5 – 2x are x = a and x = b, where a < b. Find the value of |3a – 1| + |7b – 1|.

Solve the equation sin(2θ + 30°) = 5 cos(2θ + 60°) for 0° < θ < 180°.