OBJECTIVES OF LINES AND ANGLES

LINES AND ANGLES

SRINIVASA RAMANUJAN, MAN WHO KNEW INFINITY

TRUE OR FALSE

a) Pairs of vertically opposite angles is always equal
b) The sum of all the interior angles of a triangle is 360
c) If the sum of two adjacent angles is 45, then two adjacent angles are acute angles
d) If a line is perpendicular is one of two parallel lines, then it is also perpendicular to the other
e) Two lines are intersected by any transversal, and then their corresponding angles formed are equal
f) Can we have a triangle where all the interior angles are more than 60
g) Sum of two complimentary angles is equal to 90
h) Sum of all the exterior angles of any polygon is always equal to 360

Fill in the blanks 

1. Sum of two supplementary angles is ______
2. Two lines parallel to the same line is ____  each other
3. An acute angle is always less than _____
4. Angles forming a linear pair are ______
5. If one angle of triangle is equal to the sum of other two angles, then the triangle is_____
6. if two straight lines intersect ,the adjacent angles are ______
7. Two angles whose sum is equal to 360 are known as _________
8. The median of an equilateral triangles are ____________
9. Two angles whose sum is equal to 90 are known as _________
10. The angle comes from the latin word ___________, meaning a ____________
11. Cointerior angles are known as ________________ and _________________
12.   Two angles whose sum is equal to 180 are known as _________
13.  Two angles whose sum is equal to  360 are known as _________
14. COMPLETE TH TABLE
Angle                                          30 80 11 87
Complementary angle

       Supplementary angle

13. The median of an equilateral triangles are ____________
14. A triangle is  isosceles if and only iff two altitudes are ______
15. A triangle is  isosceles if and only if any two altitudes are ______
16. Lines which are parallel to the same line are ¬¬¬¬¬¬¬¬¬_____________ to each other.

MULTIPLE CHOICE QUESTION:

1. A pair of adjacent angles is called linear pair if the sum of two adjacent angles is?
a)180          b)90         c)270           d)360

2. An exterior angle of the triangle is 110. And its two opposite interior angles are in the ratio 3:4. What are the values of those angles?
a) 50,60             b) 25,30             c) 30,40           d) 40,48

3. If the ll lines are intersected by a transversal, then each pair of corresponding angles so formed is
a)  Equal        b) complementary          c) supplementary     d) none of these

4. An angle is 140 more than its complementary angle, then angle is
a) 30                      b) 53                   c) 50                  d) none of these

5. If the supplementary of an angle is three times its complement, then angle is
a) 40                      b) 35                   c) 50                 d) 45

6. An angle is 18 less than its complementary angle. Then measure of this angle is
a) 36                      b) 48                   c) 83                  d) 81

7. Supplement of an angle is one fourth to itself. The measure of the angle is :
a) 18                     b) 36                     c) 144               d) 81

MATCH THE FOLLOWING:

                    LIST-A                                      LIST-B
              P) corresponding angles             1) ∠1=∠7
                Q) alternate interior angles       2) ∠4+∠5=180
                R) alternate exterior angles       3) ∠1=∠5
               S) co-interior angles                  4) ∠4=∠6

 CODE:        
               P      Q       R      S
a)        4         1        2      3
b)        3         2        4      1
c)        4         2        1      3
d)           3         4        1      2

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OBJECTIVES OF POLYNOMIAL, CLASS: IX

POLYNOMIAL

FATHER OF MODERN MATHEMATICS RENE DESCARTES

FILL IN THE BLANKS

1.The word polynomial comes from ________________

2.The word polynomial was introduced in latin by _______________________

3.Polynomial with one term is known as_______________

4.Polynomial with two term is known as_______________

5.Polynomial with three term is known as______________

6.Polynomial with four term is known as_______________

7.Polynomial with five term is known as _______________

8.Polynomial of degree 1 is known as _________________

9.Polynomial of degree 2 is known as _________________

10.Polynomial of degree 3 is known as _________________

11.Polynomial of degree 4 is known as ___________________ polynomial

12.Polynomial of degree 5 is known as ___________________ polynomial

13.________________  in 1637 introduced the graph of a polynomial equation

14.If the leading coefficient of a univariate polynomial is one , then it is called ______________

15.A polynomial in one variable is called a ___________________polynomial

16.When P(x) is divided by ( x – a), then P(a)represents ________________

17.If P(c) =  0, then ( x - c ) is a __________ of P(x)

18.X^3 + Y^3 + Z^3 = _________ ,if X + Y + Z is zero.

19.X^3 + Y^3 +Z^3 – 3XYZ = K(X+Y+Z){(X-Y)^2 + (Y-Z)^2 + (Z-X)^2}, then k = _______

20.Every ____________ polynomial has zero.

21.The degree of zero polynomial is __________________

22.The value of 3y^3 – 4y + √11 at y = 2 is _______________

23.If x + y = 4 and xy = 6, then the value of x^3 + y^3 = _______

24.A constant polynomial have  _____________ zero

25.A quadratic polynomial have almost _______ zeros

26.A polynomial of degree n have almost ___________ zeroes

27.A constant polynomial zero is known as ___________ polynomial

28.A zero polynomial have ______________ zeros

29.Every real number is a zero/es of the ________ polynomial

30.A zero of a polynomial ______________ be zero

31.A polynomial can have more than _______ zero

32.Every linear polynomial has _______ and only _______ zero

33.Exponent of every polynomial is _______________ number

34.Degree of x^2 + 3x^4 + 66 is _________________

35.Degree of x^2y^2 + x^3y^2 – 2x^3 is ______________

36.Remainder theorem is also known as ___________

TRUE OR FALSE

1.A polynomial have more than one zero.

2.The zero of the polynomial p(x) = 2x – 1 is ½.

3.The remainder when p(x) = 2x^3 – 2x^2 + x – 1 is divided by x + 1 is -12.

4.( x + 1) and ( 2x – 3) are factor of polynomial 2x^2 – 9x + 12.

5.2x+ √2is polynomial.

6.X^2 – x^1/2 is polynomial.

7.Y^2 – 1/y - 2 is polynomial.

8.Is x^4 + 4 = (a^2 + a + 2)(a^2 – a + 2) ?

9.Quadratic polynomial is univariate

10.x^2 + x^3 – 4x^4 is monic.

MULTIPLE CHOICE QUESTIONS

1.  Which one is not a polynomial

      (a)   4x^2 + 2x – 1(b)   y + 3/y(c)   x^3 – 1(d)   y^2 + 5y + 1

2.  The polynomial ax^2 + bx + cx^4 + 5 is 

      (a)   linear           (b) quadratic          (c) cubic            (d)  Biquadratic

3.  Identify the polynomial

      (a)   x^–2 + x^–1 + 5     b) x^1/2 -1/2    (c)  1/x  + (- x)  (d)   3x^2 + 7

4.  The zero of the polynomial p(x) = 2x + 5 is

      (a)   2        (b)   5      (c)   2/5        (d)   -5/2

5.  The number of zeros of x^2 + 4x + 2

      (a)   1      (b)   2      (c)   3      (d)   none of these

6.  The polynomial of type px^2 + qx + r, a = 0 is of type

      (a)   linear      (b)   quadratic     (c)   cubic       (d)   Biquadratic

7.  The value of k, if (x – 1) is a factor of 4x^3 + 3x^2 – 4x + k, is

      (a)   1     (b)   2      (c)   –3       (d)   3

8.  The degree of polynomial p(x) = x+√(x^2+1)  is

      (a)   0     (b)   2      (c)   1       (d)   3

9.  If 3 + 6 – 9 = 0, then the value of (3)3 + (6)3 – (9)3 is

      (a)   260       (b)  –360        (c)  –486   (d)   486

10.  If value of 104 × 96 is

      (a)   9984   (b)   9469      (c)   10234     (d)   11324

11.  The value of 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37 is

      (a)   237      (b)   126     (c)   56        (d)   64

12.  The value of [(361)^3 (+139)^3)]/[(361)^2-361*139+(139)^2 ] is

      (a)   300  (b)   500   (c)   400     (d)   600

13.  If x + y = 2, x^2 + y^2 = 5 then xy is

      (a)   1    (b)   3      (c)   2       (d)  None of these

14.  If x + 2 is a factor of x^3 – 2ax^2 + 16, then value of a is

      (a)   3    (b)   1    (c)   4   (d)   2

15.  If one of the factor of x^2 + x – 20 is (x - 4). Find the other

      (a)   x – 4   (b)   x + 2      (c)   x + 5        (d)   x – 5

16. which one of the following algebraic expressions is a polynomial in variable x ?

(a)  x2 + 1/x^2             (b) √x+1⁄(√x)               (c) x^2+ (3x)^(3⁄2)/√x    (d) none of these

17. Degree of the polynomial p(x) = ( x + 2 )( x – 2 ) is 

(a) not define            (b) 1                             (c) 0                         (d) 2 

18. If x^3 + y^3 + z^3 = 2k[ ( x – y)^2 + ( y – z)^2 + ( z – x)^2 ] then k is

(a) 1/4                         (b) 1/2                          (c) any real number      (d) not define

19. If both x = 2 and x = ½ are factors of px^2 + 5x + r, then p = 

(a) ¾ r                       (b) 2r                           (c) r/2                         (d) r 

20. Who is the father of polynomials ?

(a) Diophantus           (b) Newton                  (c) Euclid                      (d) Aryabhatta

MATCH THE FOLLOWING

Match or Choices for the correct combination of elements from List-A and list – B are given as options (a), (b), (c) & (d) out of which one is correct.

1. List- B shows the degree of polynomials given in List- A.

                                                                

          List-A                                       List- B

p) 2 – y^2 – y^3 + 2y^8                1) 2

q) 2                                                2) 1

r) 5X - √7                                      3) 0

s) 4 – X^2                                      4) 8         

CODE

                p q r s

            a) 1 3 2 4

            b) 4 3 2 1

            c) 4 2 3 1

            d) 2 3 4 1

2. List – B gives the values of k for polynomials given in List-B when it divided by x – 1

             LIST-A                                LIST – B

p) Kx2 – 3x – 2k                        1)  0

q) X^2 – x + k                            2) -3

r) 2x^2 + kx + 3                      3) (√2-1)/3

s) 3kx^2 - √2x + 1                     4)  -5

CODE

p q r s

a) 2 1 4 3

b) 4 1 3 2

c) 1 4 3 2

d) 2 2 4 1

3. List-B gives value of the polynomials given in List – A at the given points.

            LIST-A                                      LIST-B

p) 3t^3 – 2t^2 + t at t = ½                    1) 2

q) 3x^3 + x^2 – 20x +12 at x = 2/3     2) -1

r) 7u^5-4u^3 + 2 at u = 0                    3) 3/8

s) (3s – 1)(2s-3) at s = 1/2                   4) 0

CODE

    p q r s

a) 1 2 3 4

b) 4 2 1 3

c) 4 3 2 1

d) 3 4 1 2

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OBJECTIVES OF EUCLID GEOMETRY - CLASS: IX

EUCLID GEOMETRY

FATHER OF GEOMETRY - EUCLID

MULTIPLE CHOICE QUESTIONS

1. How many straight lines can pass  through two given lines?
  a)  None       b).  Only one         c).  Two              d).  Three

2.  What is the least number of lines required to make a closed figure?
           a)  One         b) Two                  c).  Three           d)  Four

3.  Which of the following is an axiom?
           a) Theorem    b) Definitions   c)  The universal truth in all branches of Mathematics
       d) Universal truth specific to geometry

4.  How many dimension does a surface has?
           a).  One         b) Two               c)  Three              d)  Four

5.  A solid has how many dimensions?
           a).  One         b) Two               c)  Three              d) Four

6.  The figure formed by two straight lines having a common point between them is known as
           a)  Angle        b)  Triangle       c)  Rhombus          d).  Kite

7.  How many lines can passes through one common point?
           a)  One          b) Two               c).  Three             d).  Four

8.  Which of the following are boundaries of a surface?
           a)  Lines        b) Curves           c).  Surfaces        d).  Points

9. . Euclid belongs to
a) Greece                 b) Italy              c) Germany           d) Egypt

10 . The total number of propositions in the elements is?
a) 20                         b) 7                    c)13                      d) 465

11. Ram salary is equal to Mohan salary, Due to recession, the salaries of ram and Mohan are made half. The final salary of Ram will still be equal to Mohan. This is are per
a) Ist  axiom             b) 7th  axiom       c) 6th axiom          d) 2nd axiom

12 . Which of these statements are false?
a)The number of dimensions in the solid is 3
b) The number of dimensions in the surface is 2
c) The number of dimensions of a point is 1
d) None of these

13. The number of line segments determined by the three non collinear points is
a) one                          b) two                  c) three                          d) four

14. Boundaries of the solid are
a) lines                       b) points                c) surface                      d) curves

15. It is known that if p+q=11 then p+q+r=11+r. The Euclid axioms that illustrates this statement is
a) Ist axiom               b)3Th  axiom           c) 4th axiom                    d) 2nd axiom

16. which of the following is not an undefined term?
a) line            b) angle             c) plane            d) point

17. Which of the following needs a proof?
a) postulates       b) Definitions         c) Propositions         d) Axioms

True or False statement

a) In geometry, we take point, line and plane as defined term
b) Two lines drawn in a plane always intersect at a point
c) Only one line can pass through the two points X and Y
d) If two circle are equal, then there radii is also equal
e) Three points are concurrent if they have only one common point between them
f) The statements that are proved are called postulates
g) The whole is greater than the part is a postulate
h) If the area of square X equals to the area of rectangle Y and the area of rectangle Y is equal to area of circle Z,then area of square X equals to area of circle Z

MATCH THE FOLLOWING

1.                  LIST – A                                  LIST- B 
A) Who gave the proof that circle can be     1)  Brahagupta
          bisected  into two equal parts by
           its diameter 
B) Who derived the value for area of            2) Aryabatta
        isosceles triangle
C) Who derived the value for                        3) Bhaskara –II
       volume of pyramid       
D) Who  discovered the formula                   4) Thales
      for the finding the area of
       cyclic quadrilateral     
                                                                        5) Pythagoras

2.               LIST- A                                LIST-B

 P)  only one line can pass through                     1) One point
Q)  infinite number of lines can pass through     2) common
R)  two distinct lines can’t have more than
        one point in                                                  3) two point
S)  two distinct points always determines           4) a line

CODE:     P        Q           R         S

A)          1          4           3          2
B)          3          1           2          4
C)          3          2           1          4
D)          4          2           1          3

 

3.         LIST-A                LIST-B

P)   a point                         1)  has length and breadth
Q) a line                             2) has no part
R) a surface                       3) has breadthless length
S) ends of a line                4) points

CODE:         P      Q    R    S

A)                4     2     3     1
B)                2     4     3     1
C)                1     4     3     2
D)                2    3      1     4

4.              LIST-A                  LIST-B 

P) POSTULATE 1         1) A TERMINATED LINE CAN  BE PRODUCED                                                                                                     INDEFINITELY

Q) POSTULATES 2     2) ALL RIGHT ANGLES ARE EQUAL TO ONE                                                                                                      ANOTHER

R) POSTULATS 3       3) A STRAIGHT LINE MAY BE BE DRAWN FROM                                                                                            ONE POINT TO ANY OTHER POINTS

Q) POSTULATES 4      4) A CIRCLE CAN BE DRAWN WITH ANY                                                                                                           CENTRE AND RADIUS

CODE :        P    Q    R    S

A)              1     3     2    4
B)              4     3     2    1
C)              3     1     4    2
D)              3     4     1    2

FILL UPS:

1. The assumptions which are obvious universal truths is known as _________.
2. Things which are equal to the same things _________ to one another.
3. If equal are subtracted from equals, then remaining things are _______
4. Things  which are double of the same things are _____ to one another.
5. Two distinct intersecting lines cannot be ________ one anther.
6. All right angles are ________
7. The whole is greater than its ________________
8. Euclid’s is also known as ____________________
9. Point has ____________ dimensions
10. Line has ____________  dimensions
11. Surface has _________ dimensions
12. Solids has ___________ dimensions
13. Boundaries of a solid are called _____________
14. Boundaries of a surfaces are called __________
15. Lines end in ________________
16. Geometry is derived from __________ and _________ ( word)
17. Euclid was a students of ____________

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