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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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.

Character is who you are when no one is looking.

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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: 12,919

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

Character is who you are when no one is looking.

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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: 12,919

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!

Character is who you are when no one is looking.

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