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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,045

1. The angles of elevation and depression of the top and bottom of a light-house from the top of a building 60 meters high are 30° and 60° respectively.

(i) Find the difference between the heights of the light-house and the building.

(ii) Find the distance between the light-house and the building.

2. Find the mean of the first n natural numbers.

3. Find the median of the following data:

71, 72, 73, 75, 76, 80, 134.

4. All aces, jacks and queens are removed from the deck of playing cards. One card is drawn at random from the remaining cards. Find the probability that the card is a king.

5. If the diameter of cross-section of a wire is decreased by 5%, how much percent would the length have to be increased so that the volume remains the same?

6. The radii of two circles are 19 centimeters and 9 centimeters respectively. Find the radius of the circle which has its circumference equal to the sum of the circumferences of the two circles.

7. (i) Using cos(A-B) = cosA cosB + sinA sinB, find the value of cos 15° .

(ii) Evaluate : cosec² 67° - tan² 23°

8. Find the area of a quadrant of a circle whose circumference is 22 centimeters.

9. Express cos 75° + cot 75° in terms of trignometric ratios of angle between 0° and 45°.

10. The length of a minute hand of a clock is 14 centimeters. Find the area swept by the minute hand in 15 minutes.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Are these questions also for teenagers?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,045

Oh yes, the title says so! I don't know the UK equivalent of Matriculation ( I guess GCSE). Students aged 14-16 normally appear for the examination.

For real challenges, I shall post them separately and name the topic accordingly!

You may test your skills there

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Daniel123****Member**- Registered: 2007-05-23
- Posts: 663

If this is equivalent to GCSE, the British education system is rubbish. Here, the trig questions wouldn't be encountered (usually) until AS/A level (16-18).

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,045

I remember we were asked to make a clinometer (an inclinometer), a simple one, to measure the angle of elevation and hence find the height knowing the base distance. I guess I was 13 then. Soon, I shall post topics in Exercies which 16-18 year olds are expected to know thoroughly to do fairly well in Mathematics!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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