Cambridge & Pearson Edexcel Past Paper Questions

Farmer Jones grows apples. The weights, in grams, of the apples grown this year are normally distributed with mean 170 and standard deviation 25. A...

Sajid is practising for a long jump competition. He counts any jump that is longer than 6 m as a success. On any day, the probability that he has a...

A group of 15 friends visit an adventure park. The group consists of four families. • Mr and Mrs Kenny and their four children • Mr and Mrs Lizo an...

The diameters, x millimetres, of a random sample of 200 discs made by a certain machine were recorded. The results are summarised below. n = 200 Σx...

Arvind uses an ordinary fair 6-sided die to play a game. He believes he has a system to predict the score when the die is thrown. Before each throw...

The lengths, in centimetres, of two types of insect, A and B, are modelled by the random variables X ~ N(6.2, 0.36) and Y ~ N(2.4, 0.25) respectively.

The independent random variables X and Y have distributions Po(2) and B(20, ¹/₄) respectively.

Cars arrive at a fuel station at random and at a constant average rate of 13.5 per hour.

A random variable X has probability density function f. The graph of f(x) is a straight line segment parallel to the x-axis from x = 0 to x = a, wh...

In the past, the mean time for Jenny's morning run was 28.2 minutes. She does some extra training and she wishes to test whether her mean time has ...

A javelin thrower noted the lengths of a random sample of 50 of her throws. The sample mean was 72.3 m and an unbiased estimate of the population v...

In the past, the mean height of plants of a particular species has been 2.3m. A random sample of 60 plants of this species was treated with fertili...

It is known that 1.8% of children in a certain country have not been vaccinated against measles. A random sample of 200 children in this country is...

The number of cars arriving at a certain road junction on a weekday morning has a Poisson distribution with mean 4.6 per minute. Traffic lights are...

A random variable X has probability density function given by f(x) = {1/16 (4x-x²) for 2 ≤ x ≤ 4, 0 otherwise.

The masses, in kilograms, of large and small sacks of grain have the distributions N(53, 11) and N(14, 3) respectively.

X is a random variable with distribution Po(2.90). A random sample of 100 values of X is taken.

The number of characters in emails sent by a particular company is modelled by the distribution N(1250, 480²).

Anton believes that 10% of students at his college are left-handed. Aliya believes that this is an under-estimate. She plans to carry out a hypothe...

Batteries of type A are known to have a mean life of 150 hours. It is required to test whether a new type of battery, type B, has a shorter mean li...

Each box of Seeds & Raisins contains S grams of seeds and R grams of raisins. The weight of a box, when empty, is B grams. S, R and B are independe...

The number of clients who arrive at an information desk has a Poisson distribution with mean 2.2 per 5-minute period.

A random sample of 5 values of a variable X is given below. 2 3 3 5 a

The random variables X and W have probability density functions f and g defined as follows: f(x) = { p(a²-x²) for 0 ≤ x ≤ a, 0 otherwise, g(w) = {...

The equation of a curve is such that dy/dx = 4/(x-3)³ for x > 3. The curve passes through the point (4, 5). Find the equation of the curve.

The coefficient of x⁴ in the expansion of (x + a)⁶ is p and the coefficient of x² in the expansion of (ax + 3)⁴ is q. It is given that p + q = 276....

Express 4x² – 24x + p in the form a(x + b)² + c, where a and b are integers and c is to be given in terms of the constant p.

Solve the equation 8x⁶ + 215x³ – 27 = 0.

The diagram shows the curve with equation y = 10x^(1/2) - (5/2)x^(3/2) for x > 0. The curve meets the x-axis at the points (0, 0) and (4, 0). [Figu...

The diagram shows a sector OAB of a circle with centre O. Angle AOB = θ radians and OP = AP = x. [Figure 6.1]

By first expanding (cos θ + sin θ)², find the three solutions of the equation (cos θ + sin θ)² = 1 for 0 ≤ θ < π.

The diagram shows the graph of y = f(x) where the function f is defined by f(x) = 3 + 2 sin(1/4 x) for 0 ≤ x ≤ 2π. [Figure 8.1]

The second term of a geometric progression is 16 and the sum to infinity is 100.

The equation of a circle is (x − a)² + (y − 3)² = 20. The line y = (1/2)x + 6 is a tangent to the circle at the point P.

The equation of a curve is y = k√(4x + 1) − x + 5, where k is a positive constant.

Use logarithms to solve the equation 12x = 32x+1. Give your answer correct to 3 significant figures.

A curve has equation y = (2 + 3 ln x) / (1 + 2x) Find the equation of the tangent to the curve at the point (1, ⅔). Give your answer in the form ax...

It is given that ∫[from 0 to a] (3e^(2x) - 1) dx = 12, where a is a positive constant.

The polynomial p(x) is defined by p(x) = 2x³ + 3x² + kx − 30, where k is a constant. It is given that (x – 3) is a factor of p(x).

The diagram shows the curve with parametric equations x = 4e^(2t), y = 5e^(-t) cos 2t, for -¼π ≤ t ≤ ¼π. The curve has a maximum point M.

Show that ∫[from ¼π to ½π] (4 cos² 2x + 1/cos² x) dx = ¾√3 + ⅙π - 1.

Express 7 cos θ + 24 sin θ in the form Rcos(θ – α), where R > 0 and 0° < α < 90°. Give the value of α correct to 2 decimal places.

Solve the equation sec² θ + 5 tan² θ = 9 + 17 sec θ for 0° < θ < 360°.

The variables x and y satisfy the equation y = Ae^(A-B)x, where A and B are constants. The graph of ln y against x is a straight line passing throu...

The diagram shows part of the curve y = 6/(2x + 3). The shaded region is bounded by the curve and the lines x = 6 and y = 2.

The diagram shows the graph of y = 3 – e^(-½x). It is given that the two roots of 3 – e^(-½x) = |5x – 4| are denoted by α and β, where α < β.

The diagram shows the curve with equation y = e^(–½x)(x² – 5x + 4). The curve crosses the x-axis at the points A and B, and has a maximum at the po...

Show that 4 sin(θ + ¼π) cos(θ – ¼π) = √3 + 2 sin 2θ.

A curve has parametric equations x = (2t + 3)/(t + 2), y = t² + at + 1, where a is a constant. It is given that, at the point P on the curve, the g...

The diagram shows the graph of y = 3 – e⁻½ˣ. It is given that the two roots of 3 – e⁻½ˣ = |5x – 4| are denoted by α and β, where α < β.