Aakash institute subjective math paper

19/01/2018

G1_FDN-IX CODE-A

Regd. Office : Aakash Tower ower 8 Pusa Road New DelhiDelhi- 0005 Ph.: 0 0-47 -476245 62456 6

TERM TEST-2 (MATHEMATICS) MM : 80

Integrated Classroom Course for Olympiads and Class-IX (2017-2018)

Time : 3 Hrs.

COMPLETE SYLLABUS OF MODULE-II

GENERAL INSTRUCTIONS : .

Alll que Al quest stio ions ns ar are e com compu puls lsor ory y.

2.

The Th e ques questi tion on pap paper er con consi sist sts s of 30 questions divided questions divided into four sections A, B, C and D. D.

.

Section A comprises A comprises of 6 questions of questions of 1 mark each. mark each. Section B comprises B comprises of 6 questions of questions of 2 marks each. Section C C comprises 10 questions of 3 marks marks each. Section D D comprises of 8 questions of 4 marks. marks. (Including one value based question)

4.

There is no overall There overall choice choice in the the paper paper.. However However internal internal choice choice is provided provided in in 2 questions questions of  marks marks and and 2 questions of 4 marks.

5.

Use Us e of of calc calcul ulat ator or is not not pe perm rmit itte ted. d.

6.

It is man mandat datory ory to use use Blue Blue/Bla /Black ck Pen Pen to write write the ans answer wer..

FOR OFFICE USE ONLY

Name

: __ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ___ _

Sec ecti tion on : __ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ___ _

Marks obtained in : Mathematics Total

Roll No.

(To (T o be filled by the t he Examiner) (1)

C l a ss - I X

Term Test - Mathematics (G_FDN-TT2A)

MATHEMATICS

SECTION-A Very Short Answer Type Questions : Q1.. Q1

[6×1 = 6]

Express the linear equation  x – – 4y 4y = = 7 in the form ax + + by + + c = = 0 and determine the values of a b and c. [1]

Ans.

Q2.

If PQRS is PQRS is a parallelogram then compute the values of x and and y. P 24° 56°

Q

[1]] [1

7y S

3 x R

Ans.

Q3.

In a ∆ C    is is a median on side C . If area of ∆  =  = 24 cm2 then find the area of ∆ C and C and area of [1] [1] ∆ C .

Ans.

(2)


Q4.

Class-IX

If the difference between the total surface area and lateral surface area of a cube is 72 cm 2 then find the volume of the cube. [1]

Ans.

Q5.

Find the mode of 2 5 6 8 2 4  22 2 5.

[1]

Ans.

Q6.

In a society of 00 people 0 persons like to eat “Pizza” and rest of the persons like to eat “Burger”. Find the probability that a person selected at random from the people who like to eat “Burger” [1]

Ans.

(3)

Class-IX


SECTION-B Short Answer Type Questions : Q7.

[6×2 = 12]

Determine any two solutions of the equation 4 x – y + 6 = 0.

[2]

Ans.

Q8.

In a rhombus C. If ∠  : ∠ =  : 2 and  = 5 cm then find all angles of C and perimeter of C [2]

Ans.

(4)


Class-IX

Q9. PQRS is a cyclic quadrilateral whose diagonals intersect at point T . If find ∠QRS and ∠SPQ.

∠SQR =

80° and

∠RPQ =

0° then [2]

Ans.

Q10. The paint in a box is sufficient to paint an area equal to 9.4 m 2. How many cuboidal boxes of dimensions  cm × 4 cm × 5 cm can be painted out of this box? [2] Ans.

(5)

Class-IX


Q11. The percentage of marks obtained by a student in the monthly tests are given below: Tests Percentage of marks

I

II

III

IV

V

VI

VII

VIII

IX

X

67

84

62

74

55

58

79

64

68

72

Based on this data find the probability that the student gets more than 68% and less than 82% marks in a test. [2] Ans.

Q12. Find the length of chord which is at a distance of 6 cm from the centre of a circle of radius 0 cm. Ans.

(6)

[2]


Class-IX

SECTION-C Short Answer Type Questions : Q13. (i)

[10×3 = 30]

Determine the point of the linear equation  x + 7y = 20 whose ordinate is equal to its abscissa.

(ii) Write a linear equation such that each point on its graph has an ordinate 5 times its abscissa. Ans.

(7)

[1½] [1½]

Class-IX


Q14. PQRS is a parallelogram such that the bisectors of show that QX = SY .

∠P and ∠R intersect

sides QR at X and PS at Y . Then [3]

Ans.

Q15. A cylindrical container opened at both the ends is made of aluminium sheet which is 2 cm thick. If the inner diameter is 4 cm and its length is 50 cm then find how many cubic centimeters of aluminium has been used in making the container [Take π = .4] [3] OR A shopkeeper used semicircular sheet of paper of radius 4 cm to form an open cone for bhelpuri . Find the height and slant height of the cone so formed. [3] (8)


Class-IX

Ans.

Q16. Prove that the angle in a semicircle is a right angle. Ans.

(9)

[3]

Class-IX


Q17. Construct a right triangle where one side is 8 cm and the sum of the other side and hypotenuse is 6 cm

[3]

Ans.

Q18. Find the amount of water (in litres) displaced by a solid spherical ball of diameter .5 cm when it is completely immersed in water. [3] Ans.

(10)


Class-IX

1 Q19. Find the missing frequency if the mean of given frequency distribution is 13 . 3 x i

4

8

12

16

20

f i

3

5

x

9

6

[3]

Ans.

(11)

Class-IX


Q20. In a parallelogram PQRS diagonals of PQRS bisect each other at right angle. If a perpendicular is drawn from point P which bisects side SR at point T . Then find all the angles of PQRS. [3] Ans.

Q21. Solid spheres each of radius  cm are packed into a rectangular box of internal dimensions 8 cm × 2 cm × 0 cm. When 5 spheres are packed in the box and also filled with some preservative liquid. Find the volume of this liquid. [Use π = .4 ] [3] OR A right triangle with sides 2 cm 9 cm and 5 cm is revolved about the side 2 cm. Find the volume of the solid so formed. [3] Ans.

(12)


Class-IX

Q22. PQRS is a square. If T and U are the mid-points of QR and PQ respectively then find the ratio of area of [3] ∆SUT to the area of ∆TUQ Ans.

(13)

Class-IX


SECTION-D Long Answer Type Questions :

[8×4 = 32]

Q23. Let the cost of a chocolate and a sweet be ` x and `y respectively. A boy pays `0 for 2 chocolates and 5 sweets. Write the given data in the form of a linear equation in two variables. Also represent it graphically. [4] OR Draw the graph of the linear equation  x – 4y – 24 = 0 and hence find the area of triangle formed by the line and coordinate axis [4] Ans.

(14)


Class-IX

Q24. In the given figure  || C  C is one-third of  and AD =

BE , then find the ratio of ar ( ∆  ) to the 3

ar(∆ O). A

B

O D

C [4] E

Ans.

(15)

Class-IX


Q25. Prove that chords equidistant from the centre of a circle are equal in length. Ans.

(16)

[4]


Class-IX

Q26. Construct a triangle C in which  + C + C = 2 cm construction Ans.

(17)

∠ =

60°

∠C =

45°. Also write the steps of [4]

Class-IX


Q27. A cubical storage tank when it is full of liquid the volume of liquid is 5625 liters. If the present depth of liquid is .6 m then find the volume of liquid already used from the tank [4] OR (i) Two solid spheres made up of same metal having weights 500 g and 500 g respectively determine the radius of larger sphere if half the radius of smaller sphere is 6 cm. [2] (ii) A cloth having an area of 660 m 2 is shaped into the form of a conical tent of radius 4 m then find the slant height of the tent. [2] Ans.

(18)


Class-IX

Q28. In a city the weekly observation made in a study on the cost of living index are given in the following table Cost of living index

Number of weeks

160 – 170 170 – 180 180 – 190 190 – 200 200 – 210 210 – 220

6 12 18 9 4 3

Total

52

Draw a frequency polygon for the data above (without constructing a histogram) Ans.

(19)

[4]

Class-IX

Term

Test - Mathematics (G_FDN-TT2A)

Q29. A die is thrown 600 times with the frequencies for the outcomes  2  4 5 and 6 as given in the following table : Outcome Frequency

1

2

3

4

5

6

70

90

124

56

120

140

Observe the outcomes and frequencies carefully. Find the probability of (i)

Getting an outcome which is a composite number.

(ii) Getting an outcome which is divisor of 6.

[2] [2]

Ans.

(20)

Term


Class-IX

Value Based Question : Q30. Rajeev has a triangular field C as shown in the given figure. He constructed a hospital in field MNC for poor people of his society to provide cheap and best medical facilities. If M and N are the mid-points of side  and C respectively C = 200 m and height of ∆ C is 50 m then find A

M

(i)

N

C B The area of field left with Rajeev after the construction of the hospital.

(ii) What value is being depicted by Mr. Rajeev?

[3] [1]

Ans.

(21)

Class-IX

Term



 (22)




Aakash institute subjective math paper

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