Salwan Public School
Sector-15 (II), Gurgaon
Holiday Homework (Winter Break)
Class – IX
Social Science
Dear Students,
“New Year arrives with hopes and it gives us new courage and belief for a very new start.
Wish you and your family a very Happy New Year”.
An investment in knowledge pays the best interest. Let’s begin the year 2016 with new
learning.
Our project for winter break is United Nation Sustainable development. To begin with, all
the Students to imagine themselves as researchers, and prepare a dossiers for LEVEL - I.
They are also required to present the work in a class discussion.
What are the Sustainable Development Goals?
The Sustainable Development Goals, otherwise known as the Global Goals, build on the
Millennium Development Goals (MDGs), eight anti-poverty targets that the world
committed to achieving by 2015. The MDGs, adopted in 2000, aimed at an array of issues
that included slashing poverty, hunger, disease, gender inequality, and access to water and
sanitation. Enormous progress has been made on the MDGs, showing the value of a unifying
agenda underpinned by goals and targets. Despite this success, the indignity of poverty has
not been ended for all.
The new SDGs, and the broader sustainability agenda, go much further than the MDGs,
addressing the root causes of poverty and the universal need for development that works for
all people.
The Project Comprises Of Seventeen UN SUSTAINABLE DEVELOPMENT GOALS
BEYOND 2015.
All students to read the subject matter attached in the booklet “The world we want”.
(Click on the link given below)
http://www.unicef.org/post2015/files/TWWW_A4_Single_Page_LowRes_English.pdf
The project comprises of seventeen UN SUSTAINANLE DEVELOPMENT GOALS
BEYOND 2015for all the sections of classes IX and X.
The project comprises of five levels. To begin with, all the students will prepare a dossier for
level I of the project based on the following guidelines:
 The students will thoroughly read the attached booklet ‘The World we want’ and
answer the questions given with each goal.
 The students will understand the effect of the themes/goals and link the cause of the
theme to human activities.
 The students to kindly follow the procedure mentioned below for the same.
 Roll nos. 1-10 to work on goals/themes 1 to 4
 Roll nos. 11-20 to work on goals/themes 5 to 8
 Roll nos. 21-30 to work on goals/themes 9 to 12
 Roll nos. 31- last to work on goals/themes 13 to 17
 Research any efforts made by the private sector through planned interventions or CSR
(corporate social responsibility) activities to combat the threat of the appropriate
theme.
 Suggest measures to be adopted to counter the effects of the theme or prevent the
causes of the theme.
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Mathematics
(To be done in Maths note book)
1.
In the figure, ABCD is a trapezium with AB||DC. Diagonals AC and BD intersect at O.
Prove that ar (ΔAOD) = ar (ΔBOC)
D
C
O
A
B
2.
Draw the graphs of the equations 3x – 2y = 4 and x + y – 3 = 0 on the same graph paper.
Hence, find the point where the two graphs intersect.
3.
Find the values of RTQ and RQT from the figure.
S
P
4.
1400
450
T
O
R
Q
ABCD is a quadrilateral. A line through D parallel to AC meets BC produced in P.
Prove that ar (ΔABP) = ar (quad ABCD)
P
D
C
A
5.
B
In the following figure, AP||BQ||CR, Prove that ar(ΔAQC) = ar(ΔPBR)
A
P
Q
B
C
6.
R
Draw the graph of the equation 2x – 3y =5. From the graph, find the value of y when
(i) x = 4 and (ii) x = 3
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7.
In the figure, O is the centre of the circle. Calculate the magnitudes of APC and AOC.
P
O
320 470
A
8.
C
In the figure, PT touches the circle whose centre is O at R. Diameter SQ when produced
meets PT at P. Given SPR =x, QRP=y, then show that x+2y = 900.
S
O
y0
Q
x0
P
9.
y0
T
R
A man purchased x no of electric bulb and p no of switches. 7 electric bulbs were fused.
2 switches were defected. If he sold each non defective bulb and switch is Rs.10 and
Rs. 4.50 respectively. Total cost getting is Rs.170. Write linear equation by using above
information.
10. ABC=690, ACB=310,
A
D
Find BDC.
690
310
B
C
11. If the no of hours for which a labourer works is x and y are his wages (in rupees) and
y=2x-1, draw the graph of work wages equation. From the graph. Find the wages of the
labourer if he works for 6 hours.
D
12. In the given figure, AB
C
Is a diameter of a circle
With centre O and CD||BA.
If  BAC=200, find
A
i)  BOC
ii) COD
iii) CAD
iv) ADC
Page 3 of 5
200
O
B
13. Four years before, age of a mother was 3 times the age of the age of her daughter.
Write a linear equation to represent this situation and draw its graph.
14. ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F.
Show that
(i) Area ACB=Area ACF
(ii) Area AEDF=area ACDE
15. Two congruent circles intersect each other at a points A and B. through A any line
segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.
16. In the given figure, O is the centre of a circle. Prove that (i) x + y = z.
(ii) PQ and RS are two parallel chords of a circle whose centre is O and radius is 10 cm.
If PQ =16 cm and RS = 12 cm find the distance between PQ and RS, if they lie: (a) on
the same side of the centre O (b) on opposite side of the centre O.
17. BC is a chord of a circle with centre O. A is a point on an arc BC. Prove that
(i) BAC + OBC =90°, if A is the point on the major arc.
(ii) BAC - OBC = 90°, if A is the point on the minor arc.
18. The bisectors of the opposite angles A and C of a cyclic quadrilateral ABCD intersect the
circle at the points E and F, respectively (Fig.). Prove that EF is a diameter of the circle.
(ii) Prove that sum of opposite angles of a cyclic quadrilateral is 1800
19. Diagonals AC and BD of a cyclic quadrilateral ABCD intersect at right angles at M.
Prove that a line drawn through M to bisect any side of the quadrilateral is perpendicular
to the opposite side.
(ii) AB is the chord of a circle with centre O and AB is produced to C such that BO = BC.
CO produced meets the circle at D. If ACD = y and AOD = x prove that x = 3y.
Page 4 of 5
20. O is any point on the diagonal PR of a parallelogram PQRS. Prove that
ar(PSO) = ar(PQO)
21. ABC and BDE are two equilateral triangles such that D is the mid point of BC. Then
1
prove that ar(BDE)= ar(ABC)
4
22. Draw the graph of 2x+5y=13.Find the points where the line meets
the X-axis and Y-axis.
23. A railway half ticket costs half the full fare. The reservation charges are the same for both
half and full tickets. A family of three adults and five children pay Rs 1200 for their
travel from Hyderabad to Bengaluru. If the basic fare is Rs x and reservation charge is
Rs y, then find the linear equation that represents the given information.
24. A shopkeeper makes a profit of 20 per cent on selling a children’s umbrella, and a loss of
10 per cent on selling a normal umbrella, but gains Rs. 10 on selling one of each. If the
cost of a children’s umbrella is Rs. x, and that of a normal umbrella is Rs. y, then frame a
linear equation that represents the information given.
25. A man purchased x no of electric bulb and p no of switches. 7 electric bulbs were fused.
2 switches were defected. If he sold each non defective bulb and switch is Rs.10 and
Rs. 4.50 respectively. Total cost getting is Rs.170. Write linear equation by using above
information.
26. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal
areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.
27. In Fig. 9.34, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are
squares on the sides BC, CA and AB respectively. Line segment AX. DE meets BC at Y.
Show that:
a) ar (CYXE) = 2 ar (FCB)
b)
MBC  ABD
c) ar (BCED) = ar (ABMN) + ar (ACFG)
28. In Fig bellow, BC||XY, BX||CA and AB||YC. Prove that: ar ( ABX )  ar ( ACY ) .
29. In parallelogram ABCD, E and F are two points on side AB and BC respectively. Show
that ar ( ADF )  ar ( DCE ) .
30. If O is the centre of the circle, the angle subtended by the arc BCD at the centre is 140º. BC is
produced to P. Determine BCD and DCP.
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