Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

Matriculation level - #n+4

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.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Matriculation level - #n+4

Are these questions also for teenagers?

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

Re: Matriculation level - #n+4

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

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Matriculation level - #n+4

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).

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

Re: Matriculation level - #n+4

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!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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