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II, 2016-17

SUMMATIVE ASSESSMENT – II, 2016-17 / MATHEMATICS

IX / Class – IX : 3 hours 90

Time Allowed : 3 hours Maximum Marks: 90

1.

2. 31 4

1 6 2 10

3 11 4

3.

4.

General Instructions:

1. All questions are compulsory. 2. The question paper consists of 31 questions divided into four sections A, B, C and D.

Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11 questions of 4 marks each.

3. There is no overall choice in this question paper. 4. Use of calculator is not permitted.

/ SECTION-A

1 4 1

Question numbers 1 to 4 carry one mark each.

1 a 3 6x ay

Find a, if linear equation 3 6x ay has one solution as (4, 3).

1

2 3x 70,

A linear equation in one variable given by 3x 70 has how many solution (s)?

1

3

Construct an acute angle and draw its bisector.

1

4

The volume of a cube is numerically equal to its surface area. Find the length of its edge.

1

/ SECTION-B

5 10 2

Question numbers 5 to 10 carry two marks each.

5 D C BAD85 2

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x y

In the given figure, two circles intersect at D and C. If BAD85, find x and y.

6 DEFG GHDE GH10 cm GF12 cm ar (GEF)

ar (DEFG)

DEFG is a parallelogram with GHDE. If GH10 cm and GF12 cm, find ar (GEF) and ar (DEFG).

2

7 MON80 2MON

Using protractor, draw MON80. Construct 2MON using compass and ruler.

2

8 8.4 cm 2.1 cm

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of sphere.

2

9 500

2 1

150 210 140

(a)

(b)

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes :

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Outcomes 2 heads 1 head No head

Frequency 150 210 140

If two coins are tossed again, then find the probability of getting : (a) one head and one tail. (b) two tails.

10 53%

Probability of success of an event is 53%. Find the probability of failure of this event.

2

/ SECTION-C

11 20 3

Question numbers 11 to 20 carry three marks each.

11 4 13y x x y

In the linear equation 4 13,y x if x is the number of hours a labourer is on work and y are

his wages in rupees then draw the graph. Also find the wage when work is done for 6 hours.

3

12 ABCD A C (– 1, – 1) (1, 1) B D

ABCD is a square. Coordinates of A and C are (–1, –1) and (1, 1) respectively. Write coordinates of B and D. Also write equations of all the sides of the square.

3

13 PQ12 cm R RQ3

cm

Draw a line segment PQ12 cm and by ruler and compasses, obtain a point R on it such that RQ3 cm. Write steps of construction.

3

14 AB CD O P

MPNP OM AB ON DC ABCD

In the figure, AB and CD are two chords of a circle with centre O, intersecting each other at P

when produced such that MPNP. If OM AB and ON DC, show that ABCD.

3

15 PQRS PR QS A

ar (PSA)ar (QAR)ar (PAQ)ar (SAR)

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Diagonals PR and QS of quadrilateral PQRS interact each other at A. Show that ar (PSA)ar

(QAR)ar (PAQ)ar (SAR).

16 2 cm 352 cm2

If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm2. Find the radius of the sphere before the increase.

3

17 40

48 (8 )

3, 16, 20, 12, 19, 1, 23, 17, 8, 24, 21, 5, 13, 14, 15, 12, 6, 4, 2, 3, 7, 9, 26 21, 22, 19, 15, 16, 2, 4, 12, 14, 16, 5, 9, 8, 6, 15, 18, 25. Construct a frequency table for the following marks obtained by 40 students in a test using equal class intervals, one of them being 48 (8 not included). 3, 16, 20, 12, 19, 1, 23, 17, 8, 24, 21, 5, 13, 14, 15, 12, 6, 4, 2, 3, 7, 9, 26 21, 22, 19, 15, 16, 2, 4, 12, 14, 16, 5, 9, 8, 6, 15, 18, 25.

3

18 21 2 3 4

The mean age of 3 students is 21 yrs. If the ratio of their ages is 2 : 3 : 4, then find the ages of the students.

3

/ SECTION-D

21 31 4

Question numbers 21 to 31 carry four marks each.

19 xy0, xy0, y3.

Draw the graphs of the following equations on the same graph sheet : xy0, xy0, y3. Also, find the area enclosed between these lines.

4

20 ` x ` y 2 ` 600

Cost of 1 bat is ` x and that of 1 ball is ` y. Cost of 1 bat and 2 balls together is ` 600. Write a linear equation which satisfies this data. Draw the graph for the same.

4

21

Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

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22 MNOP MO X

RQ MN BS PM ar(PSXR) ar(BNQX)

MNOP is a parallelogram as shown in figure. X is any point on MO. RQMN and BSPM. Show that ar(PSXR)ar(BNQX).

4

23 LXY X60, Y105 11 cm

Construct LXY, if base angles X60, Y105 and its perimeter is 11 cm.

4

24 4000 150

2000

cm15 m 16 m

(a)

(b)

A village having a population of 4000 requires 150 litres of water per head per day. Due to lack of sources of water, they collect the water into a tank measuring 2000 cm15 m 16 m from a river using a long pipe. (a) Find for how many days will the water of this tank last ? (b) Which message is conveyed by the people of village ?

4

25 30 m , 24 m 18 m :

(a)

(b)

(c)

A room is 30 m long, 24 m broad and 18 m high. Find : (a) length of longest rod that can be placed in the room. (b) its total surface area. (c) its volume.

4

26

20 cm 18 km 4

Water is supplied to a city population from a river through a cylindrical pipe. The diameter of the cross section of pipe is 20 cm, the speed of water through the pipe is 18 km per hour. Find the quantity of water in litres which is supplied to the city in 4 hours.

4

27 14

100

10 – 11 11 – 12 12 – 13

12 18 10

18 12 11

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13 - 14 10 9

(a) 11

(b) 14 12

(c) 12

(d) 12

For selection of “under 14 team for swimming”, a competition is organized in a school. 100 students are selected and the details are as under :

Age Group (in years) Number of girls Number of boys

10 – 11 11 – 12 12 – 13 13 - 14

12 18 10 10

18 12 11 9

(a) Find the probability of selecting a girl with age 11 years or more. (b) Find the probability of selecting a boy under 14 years but more than or equal to 12 years. (c) Find the probability of selecting a student in 12 years or more age group. (d) Find the probability of selecting a student under 12 years of age.

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A B

0-10 4 0-10 6

10-20 10 10-20 20

20-30 18 20-30 16

30-40 13 30-40 11

40-50 10 40-50 2

The following two tables give the distribution of students of two sections according to the marks obtained by them :

Section A Section B

Marks Frequency Marks Frequency

0-10 4 0-10 6

10-20 10 10-20 20

20-30 18 20-30 16

30-40 13 30-40 11

40-50 10 40-50 2

Represent the marks of the students of both the sections on the same graph by two frequency polygons.

4

य/SECTION-E ( /Open Text)

(* Please ensure that open text of the given theme is supplied with this question paper.)

Theme : Solving Mystery of messed up fields.

29

In Dorjee’s fields if adjacent angles are in the ratio 1:3, then find all the angles of his field.

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30

Prove that some of angles of Krishna’s field are 360 .

3

31 ABCD AB, BC, CD DA P, Q, R

S PQRS

Let Krishna’s Field is ABCD and P, Q, R and S are mid-points of sides AB, BC, CD and DA. Prove that PQRS is a parallelogram.

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