## Friday, October 3, 2008

## Tuesday, September 30, 2008

### Class XI Mathematics Marking Scheme

**10 questions of 1 mark each**

12 questions of 4 mark each

7 questions of 6 marks each

Total - 29 questiions

Total Marks = 100 marks

Sets 7 marks

Relation and Functions 9 marks

Trigonometry 22 marks

Mathematical Induction 5 marks

Complex Numbers 15 marks

Linear Inequalites 10 marks

Straight Lines 16 marks

Conic Sections 16 marks

12 questions of 4 mark each

7 questions of 6 marks each

Total - 29 questiions

Total Marks = 100 marks

Sets 7 marks

Relation and Functions 9 marks

Trigonometry 22 marks

Mathematical Induction 5 marks

Complex Numbers 15 marks

Linear Inequalites 10 marks

Straight Lines 16 marks

Conic Sections 16 marks

### Class XI ( 1 Marks Questions)

**( Note : a^2 means a raise to the power of 2)**

1. Let A = {1,2,3,4,5}. Define a relation R from A to A by R ={(x,y): y = x + 3 }

2. Write the general solution of cos x = 1/2

3. Express (-5i)(i/8) in the form a + i b

4. Find the slope of the lines passing through the points (3,-2) and (-1,4)

5. Write the value of sin 75

6. Write the domain of the function f(x) = (x^2 + 2x + 3)/ (x^2 -5x + 6)

7. Express i^9 + i^19 in the form a+ib

8. If tan x = tan y , then find x

9. Check whether P(n) : n^3 + n is divisible by 3 is true for all n belonging to N.

Give reason also.

10. If x is an integer, find the smallest value of x which satisfies the inequality

2x +(5/2) > (5x/3) +2

11. Write the principal solution of sin x = 1/2

12. Write the equation of a line parallel to x-axis and passing through (-2,3)

13. Find the value of sin 15

14. Determine the range of the relation R defined by

R = { (x,x+5): x belongs to {0,1,2,3,4,5} }

15. If A and B are two sets such that n(A) = 15, n(B) = 25 and

n(A intersection B ) = 5, find n(AUB)

16. Solve x^2 + 2 = 0

17. If (x/3 + 2, y -1/3) = (7/3, 2/3) find the values of x and y.

18. Evaluate sin(40+x)cos(10+x) - cos(40+x)sin(10+x)

19. Write the equation of a line passing through (-2,3) and slope is -4.

20 Find the value of sin 150 + cos 300

21 Examine the relation : R ={ (2,2), (2,4), (3,3) (4,4) }

State whether it is a function or not?

22 Find the multiplicative inverse of z = -1 + i3

23. Find the additive inverse of z = 1 + i2

24. Find the equation of the straight line which makes an angle of 60 degrees with

the x-axis and cuts of an intercept -2 on the y-axis.

25. If cot 2A = tan (n-2)A, then what is A?

26. If tan A = square root(3), the what is tan 2A ?

27. Find the equation of the straight line which cuts off intercept 3 and -4 along

the axes of x and y respecttively.

28. Find the value of cos 35 + cos 145 + cos 330

29. If f(x) = x^2 , find {f(1.2)- f(1)} / (1.2 -1)

30. Write the equation of the line for which tan x = 1/2 , where x is the

inclination of the line with x-axis and y-intercept is -3/2.

31. If f(x) = [x^2 + 1/x^2] then find the value of f(x) + 1/f(x)

32. If sin A = 1/2, then what is sin 3A ?

33. Find the slope and y-intercept of the line 5x + 7y = 28.

34. Write the domain of the function f(x) = (3x+4)/(x^2 -3x +2)

35. Write the equation of the straight line which cuts off an intercept 2 from y

axis and makes an angle of 135 with the x-axis.

36. Express (3+5i)(7-3i) in the form of a +i b

37. If A = {p,q,r} and B = {l,m,n} find AxB

38. Find the power set of A where A = {1,{1,2}}.

39. If A = {1,2} and B = {x,y,z}. Find the number of relations from A to B.

40. Find the radius of the circle in which a central angle of 60 intersects an arc

of length 44cm

41. Find cot 510

42. Write the equation of a straight line passing through the points (3,5) and (7,11)

43. If x = 15 then what is the value of (3tan x - tan^3 x)/(1- 3 tan^2 x)

44. Solve x^2 + x +1 = 0

45. If x = 30 then find the value of [ 2 tan x/1-tan^2 x) ]

46. If f(x) = 3x -2 when x <>= 0

find f(-1) and f(0)

47. Write the equation of the straight line passing through the point (5,6) and

has intercept on the axes equal in magnitude and both positive.

48. What is the value of tan 225 cot 405 + tan 405 cot 675

49. If tan x = 2/3 and tan y = 1/5 the what is the value of x + y .

50. Express i + i^2 + i^3 + i^4 + i^5 + i^6 + i^7 in the form of a+ib

For any query mail at : aarti_elearning@yahoo.com

1. Let A = {1,2,3,4,5}. Define a relation R from A to A by R ={(x,y): y = x + 3 }

2. Write the general solution of cos x = 1/2

3. Express (-5i)(i/8) in the form a + i b

4. Find the slope of the lines passing through the points (3,-2) and (-1,4)

5. Write the value of sin 75

6. Write the domain of the function f(x) = (x^2 + 2x + 3)/ (x^2 -5x + 6)

7. Express i^9 + i^19 in the form a+ib

8. If tan x = tan y , then find x

9. Check whether P(n) : n^3 + n is divisible by 3 is true for all n belonging to N.

Give reason also.

10. If x is an integer, find the smallest value of x which satisfies the inequality

2x +(5/2) > (5x/3) +2

11. Write the principal solution of sin x = 1/2

12. Write the equation of a line parallel to x-axis and passing through (-2,3)

13. Find the value of sin 15

14. Determine the range of the relation R defined by

R = { (x,x+5): x belongs to {0,1,2,3,4,5} }

15. If A and B are two sets such that n(A) = 15, n(B) = 25 and

n(A intersection B ) = 5, find n(AUB)

16. Solve x^2 + 2 = 0

17. If (x/3 + 2, y -1/3) = (7/3, 2/3) find the values of x and y.

18. Evaluate sin(40+x)cos(10+x) - cos(40+x)sin(10+x)

19. Write the equation of a line passing through (-2,3) and slope is -4.

20 Find the value of sin 150 + cos 300

21 Examine the relation : R ={ (2,2), (2,4), (3,3) (4,4) }

State whether it is a function or not?

22 Find the multiplicative inverse of z = -1 + i3

23. Find the additive inverse of z = 1 + i2

24. Find the equation of the straight line which makes an angle of 60 degrees with

the x-axis and cuts of an intercept -2 on the y-axis.

25. If cot 2A = tan (n-2)A, then what is A?

26. If tan A = square root(3), the what is tan 2A ?

27. Find the equation of the straight line which cuts off intercept 3 and -4 along

the axes of x and y respecttively.

28. Find the value of cos 35 + cos 145 + cos 330

29. If f(x) = x^2 , find {f(1.2)- f(1)} / (1.2 -1)

30. Write the equation of the line for which tan x = 1/2 , where x is the

inclination of the line with x-axis and y-intercept is -3/2.

31. If f(x) = [x^2 + 1/x^2] then find the value of f(x) + 1/f(x)

32. If sin A = 1/2, then what is sin 3A ?

33. Find the slope and y-intercept of the line 5x + 7y = 28.

34. Write the domain of the function f(x) = (3x+4)/(x^2 -3x +2)

35. Write the equation of the straight line which cuts off an intercept 2 from y

axis and makes an angle of 135 with the x-axis.

36. Express (3+5i)(7-3i) in the form of a +i b

37. If A = {p,q,r} and B = {l,m,n} find AxB

38. Find the power set of A where A = {1,{1,2}}.

39. If A = {1,2} and B = {x,y,z}. Find the number of relations from A to B.

40. Find the radius of the circle in which a central angle of 60 intersects an arc

of length 44cm

41. Find cot 510

42. Write the equation of a straight line passing through the points (3,5) and (7,11)

43. If x = 15 then what is the value of (3tan x - tan^3 x)/(1- 3 tan^2 x)

44. Solve x^2 + x +1 = 0

45. If x = 30 then find the value of [ 2 tan x/1-tan^2 x) ]

46. If f(x) = 3x -2 when x <>= 0

find f(-1) and f(0)

47. Write the equation of the straight line passing through the point (5,6) and

has intercept on the axes equal in magnitude and both positive.

48. What is the value of tan 225 cot 405 + tan 405 cot 675

49. If tan x = 2/3 and tan y = 1/5 the what is the value of x + y .

50. Express i + i^2 + i^3 + i^4 + i^5 + i^6 + i^7 in the form of a+ib

For any query mail at : aarti_elearning@yahoo.com

## Monday, May 5, 2008

### Activity

Aim :

To interpret the factors of a quadratic polynomial of the type x^2 + bx + c using paper grids, strips and slips

Material Required :

Coloured Paper, Geometry Box, Fevistick

Procedure:

Given Equation x^2 + 5x + 6

To represent this we need 1 square tile representing x^2, 5 tiles representing x and 6tiles representing 1.

By spliting the middle term of the equation we get the expression x^2 + 3x + 2x + 6

Place a square tile of dimension 10 x 10 representing x^2

Add 3 tiles of dimension 10 x 1 to any side of the tile x^2 . The area of the new shape formed x^2 + 3x

Add 2 tiles of dimension 10 x 1 to any side of the previous shape obtained in the previous step . The area of the new shape formed x^2 + 3x + 2x

Add 6 tiles of dimension 1 x 1 to any side of the previous shape obtained in the previous step . The area of the new shape formed x^2 + 3x + 2x + 6

Observation

A rectangle is formed whose length and breadth are x+2 and x+3.

Result

The length and breadth of the rectangle so formed represents the factors of the given polynomial.

To interpret the factors of a quadratic polynomial of the type x^2 + bx + c using paper grids, strips and slips

Material Required :

Coloured Paper, Geometry Box, Fevistick

Procedure:

Given Equation x^2 + 5x + 6

To represent this we need 1 square tile representing x^2, 5 tiles representing x and 6tiles representing 1.

By spliting the middle term of the equation we get the expression x^2 + 3x + 2x + 6

Place a square tile of dimension 10 x 10 representing x^2

Add 3 tiles of dimension 10 x 1 to any side of the tile x^2 . The area of the new shape formed x^2 + 3x

Add 2 tiles of dimension 10 x 1 to any side of the previous shape obtained in the previous step . The area of the new shape formed x^2 + 3x + 2x

Add 6 tiles of dimension 1 x 1 to any side of the previous shape obtained in the previous step . The area of the new shape formed x^2 + 3x + 2x + 6

Observation

A rectangle is formed whose length and breadth are x+2 and x+3.

Result

The length and breadth of the rectangle so formed represents the factors of the given polynomial.

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