Cambridge Past Paper Questions

Solve the equation (n-4) n+1C5 = n+2C7.

A curve has equation y = e^(x²)/(x-2) for x < 2.

For –1 ≤ x ≤ 1 it is given that x = 2−3sinθ and y = 3cot²θ. Find y in terms of x.

The line y = 4x-3 meets the curve y = 3+5x-2x² at the points A and B.

The diagram shows the shaded region ABCD. The lines AC and BD each have a length of 12 cm. The lines AC and BD bisect each other at the point O. Th...

Find the exact value of the term independent of x in the expansion of (2+3/x)¹⁰ (1-4x²)².

Variables x and y are such that when eʸ is plotted against x³, a straight-line graph is obtained. This line passes through the points (1, 13.5) and...

A 6-character password is to be formed from the following characters. Letters b f g k m (5 characters) Numbers 3 5 7 9 (4 characters) Symbols * ! @...

In this question lengths are in centimetres and time, t, is in seconds. A particle P is moving in a straight line with a speed of 26 in the directi...

An arithmetic progression has first term t and common difference 1.5. The 4th, 8th and 20th terms of this arithmetic progression form the 1st, 2nd ...

It is given that f(x) = ln(2x+5) for x > a, where a is a constant. It is also given that g(x) = x² +1 for x ∈ R.

The diagram shows parts of the graphs of y = 2+5eˣ and y = 4-3e²ˣ. Find the area of the shaded region. Give your answer in the form a+b ln3, where ...

Study Fig. 1, which shows information about the birth and death rates of Eritrea (an LEDC) and Denmark (an MEDC). Country Birth Rate (per 1000 popu...

Study Photographs A and B (Insert), which were taken in the CBD of Bangalore, a large city in India (an LEDC). [Photograph A, Photograph B] Study F...

Study Photographs C and D (Insert), which show part of a meander on a river. Photograph D shows a student carrying out fieldwork at the area marked...

Study Fig. 5, which shows an area before and after a volcanic eruption. [Figure 5]

Study Fig. 7, which shows the amount of money spent by tourists visiting North Carolina, along with Photographs E and F (Insert) which were taken i...

Study Fig. 9, which shows the percentage use of water in different parts of the world. [Figure 9] Study Fig. 10, which shows information about acce...

(a) Study Fig. 1, which shows information about the birth and death rates of Nigeria (an LEDC) and Ireland (an MEDC). Country Birth Rate (per 1000...

(a) Study Fig. 3, a map which shows the location of one shopping area in an MEDC and a possible site for another. Key urban area motorway main roa...

(a) Study Fig. 4, which shows a cross section of a river meander. Key P 20 cm/sec 60 cm/sec 40 cm/sec S Q R Lines joining points of equal velocity...

(a) Study Fig. 5, which shows information about an earthquake in Sichuan province, China, which occurred in May 2008. [Figure 5] (b) Study Fig. 6...

(a) Study Fig. 7, which shows the percentage of the world's high technology exports from selected countries. [Figure 7] (b) Study Fig. 8, which s...

(a) Study Fig. 9, which shows the percentage use of water in selected world regions. [Figure 9] (b) Study Fig. 10, which shows information about ...

(a) Study Fig. 1, a graph which shows average population density by continent. [Fig. 1 is a bar chart showing average population density (per sq k...

(a) Study Fig. 3, a map showing the population of the largest cities in India in 2008. [Fig. 3 is a map of India with various cities marked (New D...

(a) Study Fig. 5, which is a cross section of a cliff and beach. [Fig. 5 is a cross section showing a cliff and beach. The vertical axis represent...

(a) Study Fig. 6, which shows the global distribution of areas with tropical rainforest and tropical desert climates. [Fig. 6 is a world map showi...

(a) Study Fig. 7, which shows information about coal. [Fig. 7 displays three separate charts providing information about coal. Top-right chart: "C...

(a) Study Fig. 8, a map showing pollution of a river in an MEDC. [Fig. 8 is a map of a river showing its direction of flow (north to south then ea...

Study the 1:50000 map of Bindura, Zimbabwe.

Study Fig. 3, a climate graph for the city of Arica. Arica is in the Atacama Desert in Chile, South America. [Figure 3]

Study Photograph A (Insert), of a river and its surroundings, and Fig. 6, which is a field sketch of the same area. [Photograph A] [Figure 6]

Study Fig. 7, which shows the main urban areas in Zambia, an LEDC in Africa. [Figure 7]

Study Fig. 9, which shows world car production. [Figure 9]

Study Fig. 11, which shows the amount of food aid received by several countries. [Figure 11]

A group of students was investigating the effects of groynes on a beach. Groynes are structures built out into the sea to stop or slow down longsho...

Students wanted to investigate some characteristics of the CBD (Central Business District) of a town. Fig. 17 (Insert) shows the centre of the town...

Study the 1:50000 map of Port Antonio, Jamaica.

Study Fig. 1, which shows natural hazards occurring in India. [Figure 1]

Study Photograph A (Insert) of Lahore, a city in Pakistan, and Photograph B (Insert) of a town in the United Kingdom. [Photograph A] [Photograph B]

Study Fig. 3, which shows a section of coastline. Samples of beach material were taken at points A, B and C. [Figure 3]

Study Fig. 5, which shows where tourists to Australia came from in 2005. [Figure 5]

Study Fig. 6, which shows population density in Brazil. [Figure 6]

Eight students wanted to find out more about people who lived in a squatter settlement which was near to their school in a city in Uttar Pradesh, I...

A student was studying weather measurement in her lesson. She decided to do some fieldwork to measure and record rainfall and wind direction at her...

Study the 1:25000 map of Curepipe, Mauritius.

Study Fig. 2, which shows data for a hydro-electric power station in northern Europe. [Figure 2]