I Am Sharing 'IX CH 2and 3 Assignment' With You

Class: IX Subject : Mathematics Polynomials and coordinate geometry
1. If 5 is a zero of x³ + kx² + 2x +8 find k.

2. If (x-2) is a zero of of x³- 4x² + kx -8 find k.
2
3. Expand by using Identity a) (-2x-3y-z)² b) (1- 𝑦)²
4. Evaluate using identities:- (a) 103 x 97 (b) (0.99)2 (c) 1053
5. Show that (x – 1) is a factor of x – 1
10
6. Find the value of a, if (x – a) is a factor of x3 – a2x + x + 2.

7. Determine the value of a for which the polynomial 2x4 – ax3 + 4x2 + 2x + 1 is divisible by (1 – 2x).
8. Factorise the polynomials:-
a. x3 – 6x2 + 11x – 6 b) x3 + 13x2 + 31x – 45 given that x + 9 is a factor
c) x³-6x²+11x-6
9. Factorize:-
a) a3 – 0.216 (b) (x + 1)3 + (x – 1)3
10. Give possible expressions for the length and breadth of a rectangle having A = 35y2 + 13y – 12
(Area).
11. Factorise by splitting the middle term :
(a)9x2 – 3x—9 (b) x2 - 14x +40 (c) 5x2+ 16x+3
1. On which axes do the given points lie?

2. (i) (7, 0) (ii) (0, -3) (iii) (0, 6) (iv) (-5, 0)
3. In which quadrants do the given points lie?
(i) (4, -2) (ii) (-3, 7) (iii) (-1, -2) (iv) (3, 6)
4. In which quadrant or on which axes do each point lies
a) The ordinate is 3 and abscissa is – 4
b) The abscissa is – 2 and ordinate is – 3
5. Given point P (3, 4). What is the distance of point P from (a) x axis (b) y axis?
6. Plot the points A (4, 0), B (4, 4) and C (0, 4) on the graph. Join OA, AB, BC, and CO. Name the
figure so
formed and measure its sides
7. How many axes and quadrants are there in a Cartesian plane?
8. Plot the points on a graph paper:
(a) (3, 4) (b) (-2, 3) (c) (-1,-2) (d) (5,-1)
9. Find the area of the triangle whose vertices are (0, 4), (0, 0) and (2, 0) by plotting them on graph
10. Write the coordinates of a point which:-
a. Lies on the x-axis and is at a distance of 4 units to the right of the origin.
b. Lies on the y-axis and is at a distance of y units below the x-axis.
c. Is at a distance of 3 units from the x-axis and 7 units from the y-axis. [there would be four
such points]
d. The coordinates of the origin 0 are ………………………
e. The y coordinate of every point on the x-axis is ……………
f. Distance along the x-axis is called ……………………
a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) The assertion is true but the reason is false.
d.) Both assertion and reason are false.
1. Assertion: every integer is a rational number

Reason: every integer is expressed in the form of m/1 so it is rational number
2. Assertion: √5 is an irrational number.
Reason: A number is called irrational, if it cannot be written in the
form p/q, where p and q are integers and q≠0
3. Assertion: 0.468 is a terminating decimal.
Reason: A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or
a recurring decimal.
4. Assertion: 7 is rational number

Reason: square root of all rational numbers is irrational.
5. Assertion: 1/7 and 2/7 in between only five irrational numbers are present.
Reason: Every rational number between limited irrational numbers is present.
6. Assertion: degree of non zero constant polynomial is zero

Reason: polynomials having two terms are called binomial.
7. Assertion: 2x-1 is the linear polynomial.

Reason: A polynomial of degree 1 is called a linear polynomial.
8. Assertion: the degree of zero polynomial is not defined.

Reason : Each term of the polynomial has a coefficient.
9. Assertion: a polynomial can have more than one zero.

Reason: every real number is zero of zero polynomial.
10. Assertion: The polynomial 3x4-4x-3/2+x2 is not a polynomial

Reason: because the power in the term 4x3/2 which is not a whole number.
11. Assertion: p(x) = x5 degree=5

Reason: 4√t+t6degree is 6
12. Assertion: Point A(-7, -9) lies on III quadrant
Reason: A point both of whose coordinates are negative lies in III quadrant
13. Assertion: : A point whose abscissa is 2 and ordinate is -3 lies in fourth quadrant
Reason: Points of the type (- ; +) lie in the second quadrant
14. Assertion: The perpendicular distance of a point from the y-axis is called its x-coordinate.
Reason: The x coordinate of the point on the y-axis is zero.
15. Assertion: Point (4, -2) lies in IV quadrant.
Reason:Point (-1,2) lies in Il-quadrant and (2,- 1) lies in IV quadrant
16. Assertion: the coordinate of origin are (0,0)
Reason : the distance from the y-axis is called y coordinate
CASE STUDY 1
There is a square park ABCD in the middle of Saket colony in Delhi.

Four children Deepak, Ashok, Arjun and Deepa went to play with their
balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are
red, blue, yellow and green respectively.
All four children roll their ball from centre point O in the direction
of XOY, X’OY, X’OY’ and XOY’. Their balls stopped as shown in
the above image.
I. What is the distance between Deepak and Ashok’s ball?
II. Find the coordinates of each ball
III. in which quadrant Arjun’s ball lies?
IV. if Arjun throw his ball 6 units in East then what is distance between Ashok and Arjun’s ball?l
CASE STUDY 2
The Class IX students of a secondary school in

Krishinagar have been allotted a rectangular plot of land
for their gardening activity. Saplings of Gulmohar are
planted on the boundary at a distance of 1m from each
other. There is a lawn PQRS in the ground as shown in the
figure below.
I. What are the coordinates of C, taking A as origin?
II. Which type of parallelogram PQRS?
III. find the area of parallelogram PQRS
IV. If we join RP line then what is area of 𝛥 SPR
CASE STUDY 3
Students of class IX are on a visit to Sansad Bhawan. Teacher

assigns them the activity of observing and takes some pictures to
analyse the seating arrangement between various MP and speaker
based on coordinate geometry. The staff tour guide explained various
facts related to Math's of Sansad Bhawan to the students. Students
were surprised when the teacher asked them if they needed to apply
coordinate geometry on the seating arrangement of MP's and
speakers.
Calculate the following refer to the below image and graph. Answer
the following questions:
Answer the following refer to the above image and graph:
I. What is the shortest distance between OF ?
II. Is the C Mirror image of D along y axis?
III. What is the abscissa of point C ?
IV. what is perpendicular distance of point H from x-axis
V. is CDBF a parallelogram

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Class: IX Subject : Mathematics Polynomials and coordinate geometry

1. If 5 is a zero of x³ + kx² + 2x +8 find k.

6. Find the value of a, if (x – a) is a factor of x3 – a2x + x + 2.

a) a3 – 0.216 (b) (x + 1)3 + (x – 1)3

1. On which axes do the given points lie?

1. Assertion: every integer is a rational number

4. Assertion: 7 is rational number

6. Assertion: degree of non zero constant polynomial is zero

7. Assertion: 2x-1 is the linear polynomial.

8. Assertion: the degree of zero polynomial is not defined.

9. Assertion: a polynomial can have more than one zero.

10. Assertion: The polynomial 3x4-4x-3/2+x2 is not a polynomial

11. Assertion: p(x) = x5 degree=5

There is a square park ABCD in the middle of Saket colony in Delhi.

The Class IX students of a secondary school in

Students of class IX are on a visit to Sansad Bhawan. Teacher

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