BHARATIYA VIDYA BHAVAh{, KOCHI
FINAL EXAMII{ATI ON 202 4-2825
MATHEMATTCS (041)
Class: IX Marks:80
xTime:3 Hours
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Read the following instructions carefully and follow them:
1 This question paper contains 38 questions.
2 This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (1\4CQt and questions no. 19
and 20 are Assertion- Reason based questions of 1 mark each",,,
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02
marks each.
5. In Section C, Questions no. 26-3I are short answer (SA) type questions, carrying 03 marks
each.
6. In Section D, Questions no. 32-35 are long answer OA) Epe questions, carrying 05 marks
each.
7. In Section E" Questions no. 36-38 are case study based questions carrying 4 marks each with
sub parts of the values of 1, 1 and2 marks each respectively
8 All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has
been provided in all the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10 Take n:+wherever required if not stated.
7
11. Use of calculators is not allowed.
Section A
Section A consists of 20 ions of I mark each.
Which of the follora,ing is an irrational number?
a) s3
4 b) 7.ssss..... c) n d)Y,
The value of p for which x + p is a factor of
x2 +px+3 -p is------------
a) 1 b)-1 c)3 d)-3
The distance of a chord I cm long from the centre of a circle of radius 5 cm is
a) 4cm
The value of (216)2ls - (125)2/z ig
a)7 b) 10
The zero of the polynomial 3x - 5 is
Atra{fic signal board is equilateral in shape, with words 'SCHOOLAHEAD'
with on it. The perimeter of the board is 30 cm, then the area of the signal board
is
$25..13 cm2 b)100y'3 cmz c)30r8 cm2 d) 5{1 cmz
7 Total Surface area of hemisphere of diameter 2r is I
a)3 nf bi1zid c) nf d)anf
8 Class mark of the class 70-80 is 1
a) 65 b)85 c)75 d)1 so
9 If the area of the base of a conical tent is 154 m2 and its volume is 1232 m3 I
"then
the height of the tent is
a) 12m b)18m c)25m -d)24m
10 Degree of a zero polynomial is 1
a) 0 b)1 c) any natural number d) not defined
11 Ag and CD are t*o .q*t tttotOt of u tittt. *ittt centre O such that ZAOB:800. I
Then zCOD: -----
a) 1000
b) 4oo
c) 20o
d) 800
l2 a sphere is numerically equal, then its radius is I
a)2 units b)3 units c)4 units d) 5 units
l3 The linear equation 3x - 7y = 0,represented as 1
ax*by*c=0,has
a) a unique solution
b) infinitely many solutions
c) two solutions
d) no solution
l4 The coefiicient of x in the expansion of (r - 3)3 is I
a)1 b)e c) 18 d)27
l5 A ltnear equation in two variables is of the form ax * by * c: 0, where a, 1
b" c are real numbers and
a) a*0,b10 b) a:0, blO c) al0, b:0 d) a:0, c:0
t6 The value of x in the figure is I
a) 50o
b) 4oo
'c) 180
d) 1oo
t7 tn triangle PQ& zR: zP andQR:4 cm and PR:5 cm. Then the length of PQ is I
a) 4cm b) 5 cm. c)2cm d)25cm
18 ftre of a quadrilateral are in the tatio 2'.3'.6'.7. The largest angle pf the
ar gles 1
quadrilateral is
a) +oo b) 1209 c) l4oo d) 1600
DIRECTION: the question number 19 and 20, a statement of Assertion (A) is
It
followed by a statement of Reason {R).
Choose the correct option
A) Both assertion (A) and reason (R) are true and reason (R) is the correct
explanation of assertion (A)
B) Both assertion (A) and reason (R) are true and reason (R) is not the correct
explanation of assertion (A)
C)Assertion (A) is true but reason (R) is false.
D)Assertion (A) is false but reason (R) is true.
19 Assertion(A): An angle is 14o more than its complementary angle, theflangle I
is 52o
Reason(R): Two angles are said to be supplementary if their sum of measure of
angles is 180"
20 Assertion (A): If the diagonals of a parallelogram ABCD are equal, then I
zABC:900
Reason (R): If the diagonals of a parallelogram are equal, it becomes a rectangle.
Section B
Section B consists of 5 questions of 2 marks each.
21 Ifp (r) = 2x3 r3xz * L7x + rz,findp (t) +p (0)
- 2
OR
Findthevalueof k,if x-- l isafactor of 4x3 *3x2 - 4x*k
22 If AB ll CD, zAPQ : 50o and zPRD : 127o, find x and y 2
ZJ Expand (3x + 4y - 5z)z 2
24 In a parallelogram ABCD, zD:L150,determine the measure of zA and 2ts. 2
25 Find the curved surface area of a cone, if its slant height is 14 m and the radius of 2
its base is 12 m.
OR
Find thd volume of a sphere whose surface area is 154 cm2,
Section C
Section C consists of 6 questions of 3 marks each
26 Locate € on the number line.
1
J
27 Factorise a) 125 + b3 )
.,'
b)6x2 * 5x -^6
28 Find 3 solutions for the following linear equation in two variables: J
2x*3y -tZ
29 Prove.that in an isosceles triangle, the angles opposite to equal sides are equal. J
-) t, In the below figure, Xand Y are respectively the mid-points of the opposite sides J
AD and BC of a parallelogram ABCD. Also, BX and DY intersect AC at P and Q,
respectively. Show that AP: PQ : QC.
OR
Show that the bisectors ofangles ofa parallelogram form a rectangle
31 The perimeter of a tdangular field is 450 m and its sides' lre in the raldo 13:12:5 . 3
Find the area of the triangle.
OR
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its
base 3:2. Find the area of the triangle.
Section I)
Section D consists of 4 ouestions of 5 marks each
J,/. Prove that the angle subtended by an arc at the centre is double the angle 5
subtended by it at any point on the remaining part of the circle.
-1 l
Find the value of a and b if ;# : 3+ fo{3
5
OR
rf x =w andy =fif,findxz * y'.
34 For the following data, draw a histogram and a frequency polygon on the same
Marks Number of students
0-10 5
t0-20 10
2A30 4
5
30-40 6
40-50 7
50-60 J
60-70 2
70-80 2
80-90 3
90-100 9
35 A ABC and A DBC are two isosceles triangles on the same base gC and ue.tices
A and D are on the same side of BC. If AD is extended to intersect BC at B
show that
(i) AABD = AACD
(ii)AABP=AACP
(iii) AP bisects z Aas well as z D
OR
P, Q, R and s are respectively the midpoints of the sides AB, BC, cD and DA of
:
a quadrilateral ABCD in which AC BD. prove that
. (i) PQRS is a rhombus
(ii) PQRS is a square ifAC I BD. i F
Section E
section E consists of 3 case study based questions of 4 marks each.
36
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There is a square park ABCD in the middle of Saket colony in Delhi. Four
children Deepak, Ashok, Arjun and Deepa went to play with their balls. The
colour of the ball ofAshok, Deepak, Arjun and Deepa are red, blue, yeilow and
green respectively.
All four children roll their ball from centre point o to Xol', x'o\', x'o}'' and
XOY' regions. Their balls stopped as shown in the abdve image.
Answer the following questions:
(i) What are the coordinates of the ball of Ashok? 1
- (ii) What are the coordinates of the ball of Deepa? 1
(iii) What is the distance between Arjun's ball and Deepa,s ball?
OR
Name the quadrants in which the following points lie? 2
(i) (-3,2) (ii)
{4,-4)
Once.four friends Rahui, Arun, Ajay and \tjay went for a picnic at a hiil station"
Due to peak season, they did not get a proper hotel in the city. The weather was
fine so they decided to make a conical tent at a park.
They were carrying 300 m2 cloth with them. As shown in the figure they made
the tent with height 12 m and diameter 10 m. The remaining cloth was used for
the floor.
Find the slant height of the tent?
How much cloth was used for the floor?
What was the total surface area of the tent?
OR
Find the volume of the tent.
Riya goes to a stationery shop to buy school supplies. The shop is filled with
neatly arranged shelves displaying a variety of school supplies-colourful pens,
stacks of notebooks, art materials, and other essentials. She picks up a pen and a
notebook, examining their quality and price. She checks the prices and notices
that the cost of a notebook is twice the cost of a pen.
(i)
{f
Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be x and that of a pen to be y)
(ii) Riya buys 3 pens and 2 notebooks. lf the cost of one pen is tl0, how
much does she spend in total?
(iii) Find the values of k, if x : 1" y : 2 is a solution of the equation
kzx +ky =Z n
.oR
If x = 2k - 1, and y
- k is a solution olthe equation
3x - 5y - 7 - 0, find the value of k.
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