Cambridge & Pearson Edexcel Past Paper Questions

The word INTELLECT has 9 letters.

At a college, the students choose exactly one of tennis, hockey or netball to play. The table shows the numbers of students in Year 1 and Year 2 at...

Find the number of different arrangements of the 9 letters in the word ALGEBRAIC.

A fair coin and an ordinary fair six-sided dice are thrown at the same time. The random variable X is defined as follows. • If the coin shows a tai...

The heights, in metres, of white pine trees are normally distributed with mean 19.8 and standard deviation 2.4. In a certain forest there are 450 w...

In a class of 21 students, there are 10 violinists, 6 guitarists and 5 pianists. A group of 7 is to be chosen from these 21 students. The group wil...

Teams of 15 runners took part in a charity run last Saturday. The times taken, in minutes, to complete the course by the runners from the Falcons a...

In a game, players attempt to score a goal by kicking a ball into a net. The probability that Leno scores a goal is 0.4 on any attempt, independent...

30% of the residents of Wimfield own an electric car. Three residents are chosen at random.

A red fair six-sided dice has faces labelled 1, 1, 1, 2, 2, 2. A blue fair six-sided dice has faces labelled 1, 1, 2, 2, 3, 3. Both dice are thrown...

In Molimba, the heights, in cm, of adult males are normally distributed with mean 176cm and standard deviation 4.8 cm.

On a certain day, the heights of 150 sunflower plants grown by children at a local school are measured, correct to the nearest cm. These heights ar...

A factory produces chocolates. 30% of the chocolates are wrapped in gold foil, 25% are wrapped in red foil and the remainder are unwrapped. Indigo ...

The 9 letters in the word HAPPINESS are divided at random into a group of 5 and a group of 4.

The heights of a certain species of deer are known to have standard deviation 0.35 m. A zoologist takes a random sample of 150 of these deer and fi...

The masses, in kilograms, of small and large bags of wheat have the independent distributions N(16.0,0.4) and N(51.0,0.9) respectively. Find the pr...

The times, T minutes, taken by a random sample of 75 students to complete a test were noted. The results were summarised by Σt = 230 and Σt² = 930....

A random variable X has probability density function f defined by f(x) = { a/x² - 18/x³, 2 ≤ x ≤ 3 { 0, otherwise, where a i...

The lengths, in centimetres, of worms of a certain kind are normally distributed with mean μ and standard deviation 2.3. An article in a magazine s...

The numbers of customers arriving at service desks A and B during a 10-minute period have the independent distributions Po(1.8) and Po(2.1) respect...

The number of accidents per year on a certain road has the distribution Po(λ). In the past the value of λ was 3.3. Recently, a new speed limit was ...

A random variable X has the distribution B(4500000, 1000000). Use a Poisson distribution to calculate an estimate of P(X≥ 4).

The lengths of a random sample of 50 roads in a certain region were measured. Using the results, a 95% confidence interval for the mean length, in ...

A factory owner models the number of employees who use the factory canteen on any day by the distribution B(25, p). In the past the value of p was ...

A population is normally distributed with mean 35 and standard deviation 8.1 . A random sample of size 140 is chosen from this population and the s...

A machine puts sweets into bags at random. The numbers of lemon and orange sweets in a bag have the independent distributions Po(3.7) and Po(2.6) r...

The time, X hours, taken by a large number of people to complete a challenge is modelled by the probability density function given by f(x) = { 2/...

The heights of one-year-old trees of a certain variety are known to have mean 2.3 m. A scientist believes that, on average, trees of this age and v...

A random variable X has probability density function f defined by f(x) = { a/x² - 18/x³ for 2 ≤ x ≤ 3, 0 otherwise, where a is a constant.

Express 9x²-36x+8 in the form p(x+q)²+r, where p, q and r are constants.

Find the term independent of x in the expansion of (2x² - 3/x)⁶

The graph of y = f(x) is transformed to the graph of y = f(3x) +2. Describe fully the two transformations which have been combined to give the resu...

The equation of a curve is such that dy/dx = kx³ + 2/x², where k is a constant. The curve passes through the point S (2, 20) and the gradient of th...

The equation of a curve is y = 4x^(1/2) - x. The curve has a maximum point when x = a and crosses the x-axis at the point with coordinates (b, 0), ...

Sketch the graph of y = 3 sinx+2 for 0 ≤ x ≤ 2π.

The coordinates of the points P and Q are (1, 1) and (7, 11) respectively. The line segment PQ forms a diameter of a circle.

The first three terms of a geometric progression are a, b and c respectively, where a, b and c are positive constants. The first three terms of an ...

The function f is defined by f(x) = 4/(3x-6)² + 1/(3x-6)³ for x > 2. The function g is defined by g(x) = 4x-3 for x > a.

The diagram shows a circle with centre A and radius r passing through points B, C and D. A larger circle of radius s has centre C and passes throug...

Find ∫ 6 sin²x dx.

Solve the equation e²ˣ (e²ˣ – 8) = 48.

Solve the equation |2x-3|=|5x+2|.

Solve the equation cotθ tan(θ+45°) = 7 for 0° < θ < 90°.

The diagram shows the curve with equation y = 8e⁻¹/²ˣ - 1. The curve meets the axes at the points A and B. The shaded region is bounded by the curv...

A curve has parametric equations x = tan θ, y = sin θ – 2 sin³θ, for 0 < θ < ½π.

The polynomial p(x) is defined by p(x) = 2x⁴ + kx³ + kx² + 17x + 18, where k is a constant. It is given that (x+2) is a factor of p(x).

The equation of a curve is y = 4e¹⁻²ˣ √(3x-1).

Solve the equation ln(3x+5) – ln(x - 2) = 4. Give your answer in an exact form.

Solve the equation 2tan²θ+3 secθ = 18 for −180° < θ < 180°.

Solve the inequality | 3x-4|<|2x+5|.