### CBSE Half Yearly Sample Paper 2020-21 Mathematics for class 9

Time: 3:00 hour Subject- Mathematics M.M.-80

General Instructions:

- This question paper contains 37 questions.
- All questions are compulsory.
- Question 1 to 16 are very short answer type questions. Each question carries 1 mark.
- Question 17 to 23 are short answer type questions. Each question carries 2 mark.
- Question 24 to 33 are long answer type questions. Each question carries 3 mark.
- Question 34 to 37 are very long answer type questions. Each question carries 5 mark.

**(1 mark questions)**

1- Write the co-efficient of x^{3} in x+3x^{2}-5x^{3}+x^{4}.

2- Write the constant term in ᴨ/2x^{2}+7x-2/5ᴨ.

3- Determine the degree of y^{2}(y-y^{3}).

4- Give an example of a monomial of degree 5.

5- Rewrite x-2x^{2}+8+5x^{3 }in standard form.

6- If a+b+c=0,then find a^{3}+b^{3}+c^{3}

7- How many linear equations can be satisfied by x=2 and y=3?

8- If which quadrant does the point(-7,-4)lie?

9- In ΔABC,it is given that base=12cm and height=5cm,find its area?

10- Each side of an equilateral triangle is 8cm.find its area?

11- If the point(3,4)lies on the graph of 3y=ax+7,then find the value of a?

12- Find the class mark of the class 100-120.

13- Find the mode of the data 15,17,15,19,14,18,15,14,16,15,14,20,19,14,15

14- What is the probability of an impossible event?

15- Let E be an event ,then find P(not E)

16- Find the supplement of 134^{0}.

**(2 marks questions)**

17- Find the value of the polynomial 5x-4x^{2}+3 at x=0

18- Using suitable identity to find (x+4)(x+10)

19- The cost of a notebook is twice the cost of a pen.write a linear equation in two variables to represent this statement.

20- The blood groups of 30 students of class VIII are recorded follows: A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O,A,AB,O,A,A,O,O,AB,B,A,0,B,A,B,O

Represent this data in the form of frequency distribution table.

21- In a cricket match, a batswoman hits a boundary 6 times out of 30 balls. Find the probability that she did not hit a boundary.

22- Find the zero of the polynomial in P(x)=x+5

23- Find the value of K, if x=2,y=1 is a solution of the equation 2x+3y=k.

**(3 marks questions)**

24- Find p(0), P(1) and P(2) for P(y) =y^{2}-y+1

25- Find the remainder when x^{3}-ax^{2}+6x-a, is divided by x-a.

26- Evaluate the product without multiplying directly of (103×107).

27- Express: 2x+3y=9.3 5⎺ the linear equation in the form of ax+by+c=0and indicate the values and a, b and c.

28- Give the equations of two lines passing through (2,14).how many more such lines are there and why?

29- In the figure ,if AB‖CD,EF⏊ CD and ang GED=126^{0}, Find * / *AGE,

*GEF and*

__/__*FGE.*

__/__30- Find the value of K, if x-1 is a factor of p(x)= x^{2}+x+k

31- Factorise: 12x^{2}-7x+1

32- Without actually calculating the cubes, find the value of (-12)^{3}+(7)^{3}+(5)^{3}

33- Give the geometric representations of y=3 as an equation.

i) in one variable

ii) in two variable

**(5 marks Questions)**

34- Factorize: x^{3}-3x^{2}-9x-5

35- In which quadrant or on which axis do each of points (-2,-4),(3,-1),(-1,0), (1,2) and (-3,-5)lie? Verify your answer by locating them on the Cartesian plane.

36- Sides of a triangle are in the ratio of 12:17:25and its perimeter is 540cm.Find its area.

37- The following numbers of goals were scored by a team in a series of 10 matches: 2,3,4,5,0,1,3,3,4,3. Find the mean, median and mode of these scores.