### CBSE Class 9 Mathematics Sample Paper

Annual Examination (2020-21)

Class-IX

Time: 3:00 hour/M.M -80

All questions are compulsory.

(1 mark questions)

1- Give one example of a monomial of degree 35.

2- Write a name of property of congruency of triangle.

3- What is the sum of angle of a quadrilateral?

4- Draw different pairs of circles, how many points do each pair have common, what is the maximum number of common points?

5- Construct an angle of 60 with the help of compass.

6- Find the volume of cuboid whose dimension are l= 20cm, b= 15cm, h=10 cm.

7- If a coin tossed once what is the probability of getting head?

8-Find the median of first five natural numbers?

9- What is the mode of given data? 25, 30,15, 40, 30, 50, 60, 30.

10- What is the c. s. a. of cylinder whose radius is r and height is h.

(2 marks questions)

11- Find p(0) and p(1) for p(x) = (x-1) (x+1).

12- Write the statement of “S. A. S” rule of congruency of triangle.

13- Find the volume of right circular cone whose radius and height are 6cm and 7cm respectively.

14- Give two examples of data that you can collect from your day to day life.

15- In an experiment probability of happening of an event P (E) = 0.6 what is the probability of not happening of an event P(not E)?

16- A matchbox measures 4cm x 2.5cm x 1.5cm. What will be the volume of a packet containing 12 such boxes

17- Construct an equilateral triangle with side 5cm.

18- Draw a circle with radius 5cm. and locate its centre, radius, diameter and circumference.

19- Verify that x= -1/3 is the zero of following polynomial. P(x) = 3x+1

20- Find the zero of the polynomial P(x)= 2x+5.

(3 marks questions)

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

OR

If X+Y+Z = 0, show that X^{3}+Y^{3}+Z^{3 }= 3 X Y Z

22- Find the value of k if x-1 is the factor of P(x) = x^{2} + x + k.

23- ABC is a right angled triangle in which < A = 90◦ and AB = AC find <B and < C.

OR

Show that the angles of an equilateral triangle are 60◦ each.

24- ABC is an isosceles triangle with AB = AC. draw AP perpendicular to BC then to show that < B = < C

25- The angles of a quadrilateral are in ratio 3:5:9:13. Find all the angles of the quadrilateral.

26- Prove that the line segment joining the mid points of two sides of a triangle is parallel to third side.

OR

ABC is a triangle right at C. A line through the mid points M of hypotenuse AB and parallel to BC intersect AC at D. Show that-

i) D is the mid- point of AC

ii) MD perpendicular to AC

iii) CM = MA = ½ AB

27- Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

OR

Prove that a cyclic parallelogram is a rectangle.

28- Find the total surface area of a hemisphere of radius 10cm. (use Π =3.14)

29- The blood groups of thirty students of class ix are recorded as follows…

A, B ,O, O, AB, O, A, O , B, A, O, B, A, O, O, AB, A, O, A, A, O, O, AB, B, A, O, B, A, B, O

30- Three coins are tossed simultaneously 200times with the following frequencies of different outcomes.

outcomes | 3heads | 2 heads | 1 head | no head |

frequency | 23 | 72 | 77 | 28 |

Compute the probability (i) 2 head (ii) 1 head (iii) 3 tail

(4 marks questions)

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

OR

The following observations have been arranged in ascending order. If the median og the data is 63. Find value of X.

29, 32, 48, 50, X, X+2, 72, 78, 84, 95.

32- What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (use Π =3.14).

OR

The diameter of the moon is approximately one fourth of the diameter of the earth; find the ratio of their surface areas.

33- Construct a triangle XYZ in which <Y= 30◦, and < Z= 90◦ and XY + YZ +ZX = 11cm.

OR

Construct a triangle ABC in which BC=7cm, < B = 75◦ and AB + AC = 13cm.

34- Fill in the blank.

i) surface area of cuboid = ______

ii) total surface area of a cylinder = ______

iii) Volume of a cone = ______

iv) volume of hemisphere = _______

35- Suitable match the following.

Column I |
Column II |

( x + y )^{2} |
x^{2} + y^{2} + z^{2} + 2xy +2yz + 2 z x |

(x + y + z )^{2} |
x^{2} + y^{2} + 2x y |

(X + Y )^{3} |
X^{3}+Y^{3}+ 3XY (X+Y) |

X^{3} + Y^{3} + Z^{3} – 3 X Y Z |
(X+Y+Z) ( X^{2 }+ Y^{2 }+ Z^{2 }– X Y – Y Z – Z X ) |