9 CBSE (SA-II) - Pioneer Mathematics

L.K. Gupta (Mathematics Classes)

www.pioneermathematics.com MOBILE: 9815527721, 4617721

PIONEER GUESS PAPER th

9 CBSE (SA-II) MATHEMATICS TIME: 2:30 HOURS

MAX. MARKS: 80

GENERAL INSTRUCTIONS & MARKING SCHEME All questions are compulsory. The questions paper consists of 34 questions divided into four sections A, B, C and D. Section A contains 10 questions of 1 mark each, which are multiple choice type questions, Section B contains 8 questions of 2 mark each, Section C contains 10 questions of 3 marks each, Section D contains 6 questions of 4 marks each. • There is no overall choice in the paper. However, internal choice is provided in one question of 2 marks, 3 questions of 3 marks and two questions of 4 marks. • Use of calculators is not permitted. • • •

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PHONE NUMBER


FOR SOLUTIONS KINDLY VISIT

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www.pioneermathematics.com MOBILE: 9815527721, 4617721 Section− −A Question numbers 1 to carry 1 mark each. For each of the questions 1-10, four alternative choices have been provided of which only one is correct. You have to select the correct choice. L.K. Gupta (Mathematics Classes)

1.

The graph of the linear equation y = x passes through the point

(A)

 3 −3  2 , 2   

2.

The graph of y = 6 is a line

(A)

parallel to x-axis at a distance 6 units from the origin

(B)

parallel to y-axis at distance 6 units from the origin

(C)

making an intercept 6 on the x-axis.

(D)

making an intercept 6 on both the axes.

3.

In Fig. 1 , if AOB is a diameter of the circle and AC = BC then ∠ CAB is equal to:

(A)

300

4.

In Fig.2, AB and CD are two equal chords of a circle with centre O. OP and OQ are

(B)

(B)

 3  0, 2   

600

(C)

(C)

(1, 1)

900

(D)

(D)

 −1 1   2 , 2  

450

perpendiculars on chords AB and CD, respectively. If ∠ POQ = 1500 , then ∠ APQ is equal to (A)

300

5.

In Fig. 3 , the area of parallelogram ABCD is :

(A) AB × BM

6.

(B)

750

(B) BC × BN

(C)

150

(C) DC × DL

(D)

600

(D) AD × DL

A coin is tossed 1000 times with following frequencies Head : 455, Tail : 545, then

probability of a head is (A) 0.455

(B) 0.547

(C) 0.545

(D) 0.575

PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 320, SECTOR 40–D, CHANDIGARH SOLUTIONS ON www.pioneermathematics.com → latest updates

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www.pioneermathematics.com MOBILE: 9815527721, 4617721 In the given Fig. 4 , if ∠P = 400 , then value of x is :


7.

(A) 400

(B) 500

(C) 600

(D) 300

If ∠N = 330 , then the value of ∠ LOM (Fig. 5) is

8.

(A) 570

(B) 330

(C) 900

(D) 660

9.

The total surface area of a cube is 96 cm2. The volume of the cube is :

(A)

8 cm3

(B)

512 cm3

(C)

64 cm3

(D)

27 cm3

10. The marks obtained by 17 students in a mathematics test (out of 100) are given below: 91, 82, 100, 100, 96, 65, 82, 76, 79, 90, 46, 64, 72, 68, 66, 48, 49. The range of data is: (A)

46

(B)

54

(C)

90

(D)

100

Section B Question numbers 11 to 18 carry 2 marks each.

11. The cost of a Video game is Rs 50 more than the twice the cost of a calculator write a linear equation in two variables to represent this statement

12. Diagonal AC of a parallelogram ABCD bisects ∠ A (See fig. ) show that : (i) it bisects ∠C (ii) ABCD is a rhombus

13. Let ABCD be a parallelogram of area 124 cm2. If E and F are the mid-points of sides AB and CD respectively, then find the area of parallelogram AFED.


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14. Find the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.

15. In Fig., O is the centre of the circle. Find ∠ BAC . 16. The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2 = xyz.

17. In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

18. In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays, Find the probability that on a ball played: (i) he hits boundary

(ii) he does not hit a boundary

Section−C Question numbers 19 to 28 carry 3 marks each.

19. Draw a graph of each of the following equations : (i) −3x + 4y = 12

(ii) 3x − 2y = 0

20. The taxi fare in a city is as follows : For the first kilometer, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and fare as Rs y, write a linear equation for this information and draw its graph ?

21. ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC.

22. In Fig. PQRS is a square and T and U are, respectively, the mid-points of PS and QR. Find the area of ∆ OTS if PQ = 8 cm.

23. An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle. 24. A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe PIONEER EDUCATION (THE BEST WAY TO SUCCESS): S.C.O. 320, SECTOR 40–D, CHANDIGARH SOLUTIONS ON www.pioneermathematics.com → latest updates

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whose cross-section is 25

cm2,

www.pioneermathematics.com MOBILE: 9815527721, 4617721 at the rate of 16 km per hour. How much the level of the water

rises in the tank in 45 minutes.

25. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

26. The following table shows the daily production of T.V. sets in an industry for 7 days of a week: Day

Mon

Tue

Wed

Thu

Fri

Sat

Sun

Number of T.V. Sets

300

400

150

250

100

350

200

Represent the above information by a pictograph.

27. A die was rolled 10500 times the frequency of each outcome is shown in the table. What was the empirical probability of each outcome?

28. The following table gives the life time of 400 neon lamps: Life time

300−400

400−500

500−600 600−700 700−800 800−900

900−1000

14

56

60

48

(in hours) Number

86

74

62

of lamps: A bulb is selected at random. Find the probability that the life time of the selected bulb is: (i) less than 400

(ii) between 300 to 800 hours

(iii) at least 700 hours.


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www.pioneermathematics.com MOBILE: 9815527721, 4617721 Section−D Question numbers 29 to 34 carry 4 marks each 29. The parking charges of a car on Mumbai Railway station for first two hours is Rs 50 and L.K. Gupta (Mathematics Classes)

Rs 10 for subsequent hours. Write down an equation and draw the graph of this. Read the charges from the graph : (i) for one hour

(ii) for three hours

(iii) for five hours

30. In Fig. , O is the centre of the circle, prove that ∠ x = ∠ y + ∠ z .

31. ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F. (i)

Prove that ar ( ∆ ADF ) = ar ( ∆ ECF )

(ii)

If the area of ∆ DFB = 3 cm2, find the area of gm ABCD.

32. Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 600 and 450. 33. A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs 7per 100 cm2.

34. The monthly profits (in Rs.) of 100 shops are distributed as follows: Profits per shop : 0−50 50−100 100−50 150−200 200−250 250−300 No. of shops: 12 18 27 20 17 6 Draw a histogram for the data and show the frequency polygon for it.


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