Opt Maths

Subject: Opt  Maths                                                          Full Mark:50

Class: VIII                     Time: 1.5 Hrs.                         Pass Mark:  20

Group 'A'

1.     Fill in the blanks. [6]

a.     The angle taken into consideration before finding perpendicular and base is called …………..

b.     The distance between (x,y) and (0,0) is ………….

c.      If a point divides the line within the line it is called ………..  division.

d.     In case of internal and external division the formula is same but only ………… alters.

e.      The columns are ………. Lines and rows are ………. Lines.

f.       The matrices can be added or subtracted if their ………….. is same.

Group 'B' 2x8=16

2.     a)  Find the distance between the points (4,3) and (-2,-5)

       b)  Find the Coordinate of the point which divides the line joining the point (-3,9) and (1,-3). Externally in the ratio 3:1

       c)  Simplify:   - 

          d) Show that  = sec A + tan A

        e)    Find the value of 'x'  If, tan30^o + sin30^o + x = cos60^o

        f)     Construct  i) B_2×3   and  ii)  P_3×3 Matrix

        g)    Define a equal matrix, with one example.

        h)    Find the mid-point of the line joining A(4,8) and B(0,2)

Group 'C' 4x7=28

3.     Prove that the point (1,3) ,(1,2), (3,2) and (3,3) are the vertices of a rectangle.

4.     In what ratio does the point P( x, -9) divide the line joining the points A(1,3) and B(2,7) . Hence  find the value of x.

5.     If A(x,3) and B(7,-1) and AB=5 units. Find all the possible values of x.

6.     Prove that :

        3sin²  + cot²  - 2 cosec²  - tan²  =

7.     If A= 0, B= 30^o, C=45^o, D= 60^o and E=90^o verify

         sin²A + sin² B + sin² C + sin² D =  sin²E

8.     Prove that  :

            = sec A – tan A

9.     If A = and B= verify that

        (A + B) ^T = A^T +B^T

The End