Cambridge Past Paper Questions

Anil is a candidate in an election. He received 40% of the votes. A random sample of 120 voters is chosen. Use an approximation to find the probabi...

The random variable X takes the values 1, 2, 3, 4. It is given that P(X = x) = kx(x + a), where k and a are constants.

The times taken, in minutes, to complete a cycle race by 19 cyclists from each of two clubs, the Cheetahs and the Panthers, are represented in the ...

Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events A and B are defined as foll...

The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg. On 10% of days less than 16kg of grapes a...

Find the number of different arrangements of the 10 letters in the word CASABLANCA in which the two Cs are not together.

In a certain country, 20540 adults out of a population of 6012300 have a degree in medicine.

The graph of the function f is a straight line segment from (0, 0) to (2, 1). [Figure for part (a)] The graph of the function g is a semicircle, ce...

In the past, the annual amount of wheat produced per farm by a large number of similar sized farms in a certain region had mean 24.0 tonnes and sta...

A certain train journey takes place every day throughout the year. The time taken, in minutes, for the journey is normally distributed with varianc...

Large packets of rice are packed in cartons, each containing 20 randomly chosen packets. The masses of these packets are normally distributed with ...

A sample of 5 randomly selected values of a variable X is as follows: 1 2 6 1 a where a > 0. Given that an unbiased estimate of the varianc...

The number of accidents per week at a certain factory has a Poisson distribution. In the past the mean has been 1.9 accidents per week. Last year, ...

In a survey of 200 randomly chosen students from a certain college, 23% of the students said that they owned a car. Calculate an approximate 93% co...

The masses, in kilograms, of newborn babies in country A are represented by the random variable X, with mean u and variance σ². The masses of a ran...

The number, X, of books received at a charity shop has a constant mean of 5.1 per day.

When a child completes an online exercise called a Mathlit, they might be awarded a medal. The publishers claim that the probability that a randoml...

A random variable X has probability density function f, where f(x) = { (3/2)(1-x²) 0 ≤ x ≤ 1, 0 otherwise. } Find E(X).

A club has 264 members, numbered from 1 to 264. Donash wants to choose a random sample of members for a survey. In order to choose the members for ...

In a random sample of 100 students at Luciana's college, x students said that they liked exams. Luciana used this result to find an approximate 90%...

The mass, in tonnes, of steel produced per day at a factory is normally distributed with mean 65.2 and standard deviation 3.6. It can be assumed th...

Last year the mean time for pizza deliveries from Pete's Pizza Pit was 32.4 minutes. This year the time, t minutes, for pizza deliveries from Pete'...

It is known that 1 in 5000 people in Atalia have a certain condition. A random sample of 12500 people from Atalia is chosen for a medical trial. Th...

A random variable X has probability density function f, where the graph of y = f(x) is a semicircle with centre (0, 0) and radius √(2/π), entirely ...

A new light was installed on a certain footpath. A town councillor decided to use a hypothesis test to investigate whether the number of people usi...

The coefficient of x² in the expansion of (1 – 4x)⁶ is 12 times the coefficient of x² in the expansion of (2+ax)⁵. Find the value of the positive c...

The curve y = x² is transformed to the curve y = 4(x-3)²-8. Describe fully a sequence of transformations that have been combined, making clear the ...

The function f is defined as follows: f(x) = √x−1 for x > 1. The diagram shows the graph of y = g(x) where g(x) = 1/(x²+2) for x ∈ R. The function ...

The first and second terms of an arithmetic progression are tanθ and sinθ respectively, where 0 < θ < ½π. For parts (b)(i) and (b)(ii), the first a...

The curve with equation y = 2x – 8x¹⁄² has a minimum point at A and intersects the positive x-axis at B. The diagram shows the curve with equation ...

The equation of a circle is (x−6)² + (y+a)² = 18. The line with equation y = 2a−x is a tangent to the circle.

The diagram shows a symmetrical plate ABCDEF. The line ABCD is straight and the length of BC is 2 cm. Each of the two sectors ABF and DCE is of rad...

A function f is such that f'(x) = 6(2x−3)² − 6x for x ∈ R.

The equation of a curve is y = (5−2x)³/² + 5 for x < 5/2.

A curve has equation y = 2 tanx-5 sin x for 0 < x < π. Find the x-coordinate of the stationary point of the curve. Give your answer correct to 3 si...

A curve has equation x²lny+y² + 4x = 9. Find the gradient of the curve at the point (2, 1).

A curve has equation y = 1+e2x 1+3x . The curve has exactly one stationary point P.

The diagram shows the curve with equation y = √sin2x+sin²2x for 0 < x < π. The shaded region is bounded by the curve and the straight lines x = π a...

The polynomial p(x) is defined by p(x) = 9x³ + 6x² +12x+k, where k is a constant.

Solve the inequality |5x+7|>|2x-3|.

Use logarithms to solve the equation 6^(2x−1) = 5e^(3x+2). Give your answer correct to 4 significant figures.

The diagram shows the curve with equation y = 8e¯ˣ – e^(2x). The curve crosses the y-axis at the point A and the x-axis at the point B. The shaded ...

A curve is defined by the parametric equations x = 4 cos²t, y = √3 sin 2t, for values of t such that 0 < t < π/2. Find the equation of the normal t...

The polynomial p(x) is defined by p(x) = 9x³ +18x² +5x+4.