SA2MAT002Q

CBSE Sample Paper-02
SUMMATIVE ASSESSMENT –II

MATHEMATICS
Class – IX

Time allowed: 3 hours Maximum Marks: 90

General Instructions:

a) All questions are compulsory.
b) The question paper consists of 31 questions divided into five sections – A, B, C, D and E.
c) Section A contains 4 questions of 1 mark each which are multiple choice questions, Section B

contains 6 questions of 2 marks each, Section C contains 8 questions of 3 marks each, Section
D contains 10 questions of 4 marks each and Section E contains three OTBA questions of 3
mark, 3 mark and 4 mark.
d) Use of calculator is not permitted.

Section A

1. If the perimeter of one of the faces of a cube is 40 cm , them its volume is
2. What is the upper limit of the interval: 20 – 23?
3. Out of 35 students Participating in a debate 10 are girls. The Probability that winner is a boy is
4. A triangle has an area of 45 square foot. Base of the triangle is 9 foot. What is corresponding

height of triangle.

Section B

5. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top.
Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1m2 cost Rs.20.

6. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of
white washing the walls of the room and the ceiling at the rate of Rs. 7.50 per m2.

7. In figure, ∠ PQR = 100°, where P, Q, R are points on a circle with centre O. Find ∠ OPR.
8. In figure, PQRS and ABRS are parallelograms and X is any point on the side BR. Show that:

(i) ar (PQRS) = ar (ABRS)
(ii) ar (AXS) = 1 ar (PQRS)

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9. The class marks of the observations are 17, 21, 25, 29, 33, 37, 41, 45. Find the class intervals.
10. The average mark of boys in an examination is 68 & that of girls in 89. If the average mark of all

candidates in that examination is 80, find the ratio of the no. of boys to the number of girls that
appeared in the examinations.

Section C

11. ABCD is a rhombus and P, Q, R, S are mid-points of AB, BC, CD and DA respectively. Prove that
quadrilateral PQRS is a rectangle.

12. ABCD is a rectangle and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA
respectively. Show that the quadrilateral PQRS is a rhombus.

13. Recall that two circles are congruent if they have the same radii. Prove that equal chords of
congruent circles subtend equal angles at their centres.

14. A conical tent is 10 m high and the radius of its base is 24 m. Find:
(i) slant height of the tent.
(ii) cost of the canvas required to make the tent, if the cost of a m2 canvas is Rs. 70.

15. 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)

16. A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of
recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of
each of the cones is to be painted and the cost of painting is Rs. 12 per m2, what will be the cost

( )of painting all these cones? Use π = 3.14 and take 1.04 = 1.02

17. The following is the monthly expenditure (Rs.) of ten families of the particular area:
145, 115, 129, 135, 139, 158, 170, 175, 188, 163
(a) Make a frequency distribution table by using the following class interval:
100 – 120, 120 – 140, 140 – 160, 160 – 180, 180 – 200.
(b) Construct a frequency polygon for the above frequency distribution.

18. The marks obtained by 30 students is given in the following table:

Marks 70 58 60 52 65 75 68

No. of Students 3 5 4 7 6 2 3

Find the Probability that a student secures

(i) 60 marks (ii) 75 marks (iii) Less than 60 marks

Section D

19. Construct a triangle ABC in which BC = 7cm ∠B = 75° and AB+AC=9cm
20. Construct a triangle XYZ in which ∠y = 30° ∠Z = 90° and XY + YZ + ZX = 11cm

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21. A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are
sitting at equal distance on its boundary each having a toy telephone in his hands to talk each
other. Find the length of the string of each phone.

22. Prove that the parallelogram which is a rectangle has the greatest area.
23. ABCD is a trapezium, in which AB DC, BD is a diagonal and E is the mid-point of AD. A line is

drawn through E, parallel to AB intersecting BC at F (See figure). Show that F is the mid-point of
BC.

24. D, E and F are respectively the mid-points of the sides BC, CA and AB of a ∆ ABC. Show that:
(i) BDEF is a parallelogram.
(ii) ar (DEF) = 1 ar (ABC)
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(iii) ar (BDEF) = 1 ar (ABC)
2

25. Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets.
Two sizes of boxes were required. The bigger of dimensions 25 cm by 20 cm by 5 cm and the
smaller of dimensions 15 cm by 12 cm by 5 cm. 5% of the total surface area is required extra, for
all the overlaps. If the cost of the card board is Rs. 4 for 1000 cm2, find the cost of cardboard
required for supplying 250 boxes of each kind.

26. Find:
(i) the lateral or curved surface area of a petrol storage tank that is 4.2 m in diameter and
4.5 m high.
(ii) how much steel was actually used if 1 of the steel actually used was wasted in making
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the tank?

27. Draw a histogram with frequency polygon for the following data:

Class Interval 25-29 30-34 35-39 40-44 45-49 50-54

Frequency 5 15 23 20 10 7

28. An insurance company selected 2000 drivers at random in a particular city to find a relationship

between age and accidents. The data obtained are given below:

Age of drivers Accident in one year.

(in yrs) 0 1 2 3 Over 3

18-29 440 160 110 61 35

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30-50 505 125 60 22 18

Above 50 360 45 35 15 9

Find the probability of the following events for a driver chosen at random from a city :
(i) Being 18-29 years of age and having exactly 3 accidents in a year.
(ii) Being 30-50 years of age and having one or more accidents in a year.
(iii) Having no. accidents in a year.

29. OTBA Question for 3 marks from Algebra. Material will be supplied later.
30. OTBA Question for 3 marks from Algebra. Material will be supplied later.
31. OTBA Question for 4 marks from Algebra. Material will be supplied later.

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