Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,230

High School Mathematics - III

1. What is the maximum value of sinθ+cosθ?

2. Simplify:-

3.If

,
the value of tan²θ is equal to _______________.

4. The value of

is equal to ____________________.

5. If tanθ+sinθ=m and tanθ-sinθ=n, then what is m² - n² equal to?

6. If sinA=5/13, what is tanA equal to?

7. What is the value of sin30° x sin45° x sin60° ?

8. What is the value of sin15°/cos75° ?

9. What is the value of sin²π - cos²π?

10. If A+B=180°, what is the value of sin²A+sin²B?

11. The value of 4sin²30°-tan²60°+sec²45° is equal to  ______________.

12. In a class of 100 students, 20 know English, 20 do not know French, and 10 know neither English nor French. How many students know both English and French?

13. Find the quadratic equation whose roots are 1/2 and 1/3.

14. What is the product of the reciprocal of the roots of the quadratic equation 2x² + x + 1 = 0.

15. In the equation ax² + 3x + 5 = 0, one root is the reciprocal of the other. What is the value of a?

16. The quadratic equation whose one root is 3+2√3 is ________________.

17. If x+1/y=5 and 2x+3/y=13, what is the value of (2x-3y)?

18. If 2x-y=4 and x+y=5, then what is the value of xy?

19. The sum of two numbers is 100 and the greater exceeds three times the less by 4. What is the value of the greater number?

20. The equation whose roots are squares of the roots of
x²+x+2=0 is _________________.

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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.