ICSE Class 10 Sample Paper 2027 Mathematics

FOR ICSE CLASS 10 EXAM PREPARATION

ICSE Class 10 2027
Sample Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

ICSE Class 10 2027 Sample Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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a

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m ICSE 2027 EXAMINATION .co
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g l a SPECIMEN QUESTION PAPER a
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MATHEMATICS

Maximum Marks: 80

Time allowed: Three hours

1.
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Answers to this Paper must be written on the paper provided separately.
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2.
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epaper.
You will not be allowed to write during first 15 minutes.

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3. This time is to be spent in reading the question

4. a
The time given at the head of this Paper is the time allowed for writing the answers.

5. Attempt all questions from Section A and any four questions from Section B.

6. All working, including rough work, must be clearly shown, and must be done on the same sheet as the
rest of the answer.

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7. Omission of essential working will result in loss of marks.
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c. o The intended marks for questions or parts of questions are given in brackets [s].em
8.

s em9. Mathematical tables are provided. g l a
la a
ag Instruction for the Supervising Examiner

Kindly read aloud the Instructions given above to all the candidates present in the Examination Hall.

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s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 24

NOTE:

The Specimen Question Paper in the subject provides a realistic
format of the Board Examination Question Paper and should be used
as a practice tool. The questions for the Board Examination can be set
from any part of the syllabus. However, the format of the Board
Examination Question Paper will remain the same as that of the
Specimen Question Paper.

T27 511 – SPECIMEN 2 of 14

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SECTION A (40 Marks)a

(Attempt all questions from this Section.)

Question 1
Choose the correct answers to the questions from the given options. [15]
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(Do not copy the question, write the correct answers only.)

(i) .co
A customer pays a total GST of ₹ 600 on an article in an intra-state sale,
m s e m
s e g l a
a
and the tax rate is 12%. The price of the article is:

(a) ag
l
₹ 2,000
a
(b) ₹ 3,000

(c) ₹ 5,000
[Understanding
(d) ₹ 7,200 & Evaluation]

(ii) Assertion (A): In a recurring deposit account, a man deposits ₹ 1000 per month
m
.co
for 1 year. On maturity he receives ₹ 13500. The amount of
interest he earns is ₹1500.
e m
Reason (R):
l as
Interest earned = Maturity value − Total amount deposited.

ag
(a) (A) is true and (R) is false.

(b) (A) is false and (R) is true.

(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).

m
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A). [Application]

mA man buys 50, ₹ 100 shares of a company at ₹ 125 paying 6% dividend . c o
c. o per annum. At the end of the year, the company will pay a total dividend
(iii)

e m
e m l a s
las on:
a g
ag (a) ₹ 100

(b) ₹ 125

(c) ₹ 5000
[Understanding
(d) ₹ 6250 & Analysis]

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s e m
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g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 24

(iv) If the roots of the quadratic equation 끫룊 2 − 8끫룊 + 끫뢌2 = 0 are equal, then the
positive value of p is:

(a) 16

(b) 8

(c) 4
[Understanding
(d) 2
& Application]

(v) 12, 18 and 끫뤲 are in continued proportion. The value of 끫뤲 is:

(a) 24

(b) 27

(c) 30
[Understanding
(d) 36 & Evaluation]

(vi) (끫룊 + 2) 끫뢜끫뢶끫뢺 (끫룊 + 3) are the factors of 끫룊 3 + 4끫룊 2 + 끫룊 − 6. The third factor
of the given polynomial is:

(a) (끫룊 − 1)

(b) (끫룊 − 4)

(c) (끫룊 + 1)
[Understanding
(d) (끫룊 + 4)
& Application]

(vii) 3
Given two matrices A and B, where A= [−1 2] and B= � � then
4
product AB is:

−3
(a) � �
8

(b) 5

(c) [5]
[Understanding
(d) [−3 8] & Evaluation]

T27 511 – SPECIMEN 4 of 14

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se g la
th a by 5 × 2 then
(viii) If the n term of a Geometric Progression (G.P.) is given 끫뢶

the common ratio is:
(a) 2

(b) 5

(c) 10
[Analysis &
m
(d) 20
c o m Application]
m .co
The line 끫료 = 2끫룊 .passes through which pair of coordinates? s e
em a
(ix)

(a) (0,la
s g l
g 0) and (2, 2) a
a
(b) (0, 2) and (2, 4)

(c) (1, 2) and (-1, -2)

(d) (2, 2) and (-2, -2) [Application]

(x) On a map of scale 1: 50,000, a rectangular plot has sides 4 cm by 3 cm. The actual
area of the plot on ground is:
m
(a) 3 끫뢰끫뢰 2

m .co
s e
(b) 9 끫뢰끫뢰2
l a
(c) 12 끫뢰끫뢰2 ag [Application &
(d) 16 끫뢰끫뢰2 Evaluation]

(xi) In the given diagram, the radius of the circle with centre O is 3 cm. PA and PB
are the tangents to the circle which are at right angle to each other. The length of
OP is:

m
m .co
m .co s e m
s e g la
g la 3 a
a (a)
√2
끫뢠

(b) 3 cm

(c) 3√2 cm [Analysis &
Evaluation]
(d) 6√2 cm

m .
T27 511 – SPECIMEN
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s e m
s em l a
g la ag
a
𝑐𝑐

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 24

3 2
(xii) A conical tent with a capacity of 616 has a base area 154 . The
height of the tent is:

(a) 3m

(b) 4m
[Understanding,
(c) 7m
Analysis &
(d) 12 m Evaluation]

(xiii) Assertion (A): If 끫뢜끫뢌 끫븆 + 끫룂 = 끫뢜 and 끫뢜끫뢌 끫븆 − 끫룂 = 끫뢞, then ab = 1.

Reason (R): 끫뢜끫뢌 2 − 끫룂 2
=1

(a) (A) is true and (R) is false.

(b) (A) is false and (R) is true.

(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).

(d) Both (A) and (R) are true, but (R) is not the correct explanation for [Understanding
(A). & Analysis]

(xiv) Consider the following distribution 30, 34, 35, 36, 37, 38, 39, 40. If the
value 35 is removed from the given data, then the median changes by:

(a) 0.5

(b) 1.0

(c) 1.5
[Analysis &
(d) 2.0 Evaluation]

(xv) A game of chance consists of spinning an arrow which is equally likely to
come to rest pointing to one of the numbers 1, 2, 3……12. The probability
that it will point to an odd number is:

1
(a)
6
1
(b)
12
1
(c)
2
[Understanding
5
(d) & Analysis]
12
𝑚𝑚

𝑚𝑚

T27 511 – SPECIMEN 6 of 14
𝑠𝑠

𝑡𝑡𝑡𝑡𝑡𝑡

𝑠𝑠

𝑡𝑡𝑡𝑡𝑡𝑡
𝑠𝑠

𝜃𝜃

𝑡𝑡𝑡𝑡

𝜃𝜃

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Question 2 a
(i) Three students A, B and C of Class 10 are each given an equal amount of [4]
Play- Dough to form different shaped solids for a mathematics project. A
forms a cone of radius 7 cm and height 28 cm. B forms a sphere of radius
r and C forms a cylinder of radius 14 cm. Find the:

m
.co
(a) radius r of the sphere so formed.
m
(b) .co
height of the cylinder so formed.
s e m
s em g l a
la a
(c) Volume of the dough given to each of them.
g
[Analysis,
a your answers to (b) and (c) correct to the nearest whole number.
Give Application &
22 Evaluation]
(Use 끫븖 = )
7

(ii) Solve the quadratic equation (끫룊 − 2)2 + 11끫룊 − 7 = 0 and give your [4]

answer correct to 3 significant figures. [Application]

A line is formed joining the two points P(−끫뾤, 끫뾞) and Q(끫뾞끫뾞, −끫뾠). Straight
m
(iii) [4]

line PQ intersects the 끫뤲 − 끫뤄 끫뤄끫뤄 at R. Find the:co
m .
s e
(a) ratio PR : RQ.
l a
(b) coordinates of the point R. ag
[Analysis &
(c) equation of the line perpendicular to PQ at R. Evaluation]

Question 3

(i) A shopkeeper marked an article at ₹ 2000. The rate of GST on the article [4]
is 18%. The customer has only ₹ 1888 with him and he requests the
m
m shopkeeper to reduce the price so that he can buy the article at ₹ 1888 c. o [Analysis &
c. o including GST. What percent discount must the shopkeeper give to doseso?m Evaluation]

s em(ii) An Arithmetic Progression (A.P.) consists of all whole numbers
g l awhich
la a [4]

ag are divisible by 3 and 5.

(a) Write its first term and the common difference.

(b) Find the 10th term of the A.P. [Application &
Evaluation]
(c) Find the sum of the first 10 terms of the A.P.

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T27 511 – SPECIMEN
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s e m
s em l a
la ag
𝒂𝒂

ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 24

(iii) Study the graph and answer the given questions: [5]

(a) Write down the coordinates of A, B, C, D and E.

(b) Write down the image of A under reflection on the y- axis.

(c) Name the point, with its coordinates, which is the image of C under
reflection through the origin.

(d) What is the image of the polygon ABCDEFGHI when reflected on
the y-axis? [Analysis &
Creativity]
(e) Write down the equation of the line joining the points N and D.

T27 511 – SPECIMEN 8 of 14

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SECTION B (40 Marks)a

(Attempt any four questions from this Section.)

Question 4

(i) A man opened a recurring deposit account in a bank. He deposits ₹ 1000 [3]
m
c o m
per month for 2 years. The matured value is equal to 26 times the amount
m .co
he pays per month.. Find the: e
e m l as
s
la paid by the bank.
(a) interest ag
g
(b) arate of interest per annum that the bank was paying for the recurring [Application &
deposit account. Evaluation]

(ii) 끫룊 1 끫룊 [3]
Given, matrix A = � � and B =� �, such that AB is a null matrix. Find the:
2 2 끫룊 − 2

(a) order of the null matrix.

om
[Analysis &
(b) value of 끫룊, given that 끫룊 > 0.
. c Evaluation]

e m
(iii) Prove the following trigonometric identity:
l as [4]

끫뢠끫뢌 2
1 − 끫룂
+
끫뢜끫뢲 2
1 − 끫뢠끫뢌
= 1 + 끫뢠끫뢌 ag [Application &
Analysis]

Question 5

(i) Ms. Kaur invested ₹ 8000 in buying ₹ 100 shares of a company paying 6% [3]
dividend at ₹ 80. After a year, she sold these shares at ₹ 75 each and invested
m
m
c. o ₹ 20 shares paying 15% dividend at ₹ 27 each. Find the:
the proceeds including the dividend received during the first year in buying
m.co
m s e
s e g la
g la (a) dividend received by her during the first year.
a
a (b) number of shares she purchased using the total proceeds including the
[Understanding,
Application &
dividend. Evaluation]

m .
T27 511 – SPECIMEN
.co 9 of 14
s e m
s em l a
la ag
𝑐𝑐

𝜃𝜃

𝑠𝑠

𝜃𝜃

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝑡𝑡𝑡𝑡𝑡𝑡

𝑐𝑐𝑐𝑐

ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 24

(ii) Solve the following inequation, write the solution set and represent it on the [3]
real number line. [Application,
12x 7x 2
−6 + ≤ − 3 < + 2끫룊, 끫룊 ∈ R. Evaluation &
5 5 5
Creativity]

(iii) In the given figure, O is the centre of the circle and 끫롨끫롮 = 끫롨끫롪. If ∠끫롨끫롪끫롬 = [4]

32° , find the angles 끫룊, 끫료, 끫룎, 끫롮 and 끫룈.

[Application,
Analysis &
Evaluation]

Question 6

(i) Using Remainder and Factor Theorem, factorise the following polynomial: [3]

2끫룊 3 + 5끫룊 2 − 28끫룊 − 15. [Analysis &
Application]

(ii) In the given diagram, AD ∥ GE ∥ BC, DE = 18 cm, EC = 3 cm, AD = 35 cm. [3]
D
E
C
F

A G B

Find:
(a) AF: FC and AG: GB

(b) length of EF [Analysis &
Application]
(c) area (trapezium ADEF): area (Δ EFC)

T27 511 – SPECIMEN 10 of 14

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(iii) Use ruler and compass for this question: a [4]

(a) Draw line segment 끫롨끫롪 of length 6 cm.

(b) Construct the locus of points which are equidistant from A and B. Mark
a point on the locus which is 4.5 cm from A. Name this point as O.

m
(c) Construct the locus of all points which are 4.5 cm from O.

(d)
c o m
Mark the point of intersection of loci (b) and (c) as P, which is on the
m .co
same side of .AB as O. s e
em a
[Analysis &
s g l
la the locus of points which are equidistant from AP and AB. a
Creativity]
g
(e) Construct
a
Question 7
(i) A bag contains identical cards numbered 1 to 50. A card is selected [3]
randomly. Find the probability that the card selected, is:

(a) divisible by 6. [Application &
m
.co
Evaluation]
(b) not divisible by 2 and 3.

e m
(ii)
l as
In the given figure, the parallelogram ABCD circumscribes a circle, touching the [3]

ag
circle at P, Q, R and S. Prove that:

m
m .co
m .co s e m
s e (a) AB = BC
g la
la
[Analysis &

g a
a
(b) diagonals AC and BD bisect each other at right angles. Application]

(iii) 끫뤄 + 끫뾠끫뾠 + 끫뤲 (끫뤄 + )끫뾠 [4]
Given, = 끫뢜 ≠ 0
끫뤄 − 끫뾠끫뾠 + 끫뤲 (끫뤄 − )끫뾠
[Understanding
Using properties of proportion, find the value of 끫룊. & Application]

m .
T27 511 – SPECIMEN
.co 11 of 14
s e m
s em l a
g la ag
a
𝒃𝒃
𝒃𝒃

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 11 of 24

Question 8
(i) The mean of the following distribution is 27 and the sum of all the [3]
frequencies is 50. Find the missing frequencies 끫룊 and 끫료.

끫뢌 0 − 10 10 − 20 20 − 30 30 − 40 40 − 50

끫롲끫뢾 끫뢊끫뢺 8 끫룊 12 13 끫료 [Application &
Evaluation]

(ii) 2 [3]
In the given diagram, the area of the shaded region is 57 . Form an
equation in 끫룊 and solve it to find the possible value of 끫룊.

12 m

끫룊
10 m
[Application,
Analysis &
끫룊
Evaluation]

(iii) Two beakers (drinking glasses) are cylindrical in shape having diameter and [4]
height 7 cm and 10 cm respectively. Glass A has hemispherical raised
bottom, and glass B has a conical raised bottom of height 3.5 cm.

Determine which glass has a greater capacity and calculate the difference in
their capacities. Give your answer correct to 2 decimal places.
22
(Use 끫븖 = )
7

A 10 cm B 10 cm
[Analysis,
3.5 cm Application &
Evaluation]
7 cm 7 cm

T27 511 – SPECIMEN 12 of 14
𝐶𝐶

𝐶𝐶𝐶𝐶𝐶𝐶
𝐹𝐹

𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹

𝑚𝑚

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Question 9 a
(i) The distribution given below represents marks obtained by 200 students in [5]
a Mathematics Examination with maximum marks 80.

Marks No. of students
0 − 10 8

m
.co
10 − 20 12

o m 16
m
c
20 − 30
.
30m− 40 s e
s e 24
g l a
g a
l − 50
40 29 a
a 50 − 60 38
60 − 70 42
70 − 80 31

Using graph paper draw an ogive for the given distribution. Along one axis
take 2 cm equal to 10 marks and along the other axis take 1cm equal to 10
m
.co
students.

Use your graph to find the following:
e m
l as
(a) Median
ag [Understanding,
Application &
(b) Number of students who scored above 75 marks
Creativity]
(c) If the pass percentage is 35%, find the number of students who scored
35% and below.

m
c. o[Understanding,
(ii) Draw the necessary diagram for this question. [5]
m
c. o A man on the top of a lighthouse observes the angle of depression ofstwo e m
s em ships on the opposite sides of the lighthouse as 32° and 58° respectively.
g l a If Creativity,

la the height of the lighthouse is 120 m, find the distance between theatwo ships.
ag
Application &
Evaluation]
Give your answer correct to the nearest meter.

m .
T27 511 – SPECIMEN
.co 13 of 14
s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 24

Question 10

(i) A finite Geometric Proportion (G.P.) series contains 10 terms. The sum of [3]
the first three terms is 7 and that of the last three terms is 896. Find the first [Application &
term and the common ratio. Evaluation]

(ii) In a circle with centre O, PA and PB are tangents drawn from an external [3]

point P. If PA = 9 cm and ∠끫롨끫뢆끫롪 = 60° , find the:

(a) length of PB.

(b) radius of the circle.

[Application &
Evaluation]

(iii) The table given below shows a record of the weight in kilogram of 100 [4]
students of a school.

Weight(kg) No. of Students
30 − 35 5
35 − 40 7
40 − 45 14
45 − 50 21
50 − 55 25
55 − 60 15
60 − 65 7
65 − 70 6
[Understanding,
Draw a histogram and find the modal weight. Application &

[Take 2 cm = 5 kg along one axis and 2 cm = 5 students along the other Creativity]

axis]

T27 511 – SPECIMEN 14 of 14

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a
ICSE 2027 SPECIMEN
DRAFT MARKING SCHEME – MATHEMATICS

Question 1
(i) (c) ₹ 5000 [15]

(ii) (c) Both (A) and (R) are true and (R) is the correct explanation for (A).
m
(c) ₹ 5000
m .co
.co
(iii)
e m
(iv) (c) 4
em l as
la s ag
(v)
g
(b) 27
a
(vi) (a) (끫룊 − 1)

(vii) (c) [5]

(viii) (a) 2

(ix) (c) (1, 2) and (- 1, - 2)

m
.co
(x) (a) 3 끫뢰끫뢰2

(xi)
e m
s
(c) 3√2 cm

g la
a
(xii) (d) 12 m

(xiii) (c) Both (A) and (R) are true and (R) is the correct explanation for (A).

(xiv) (a) 0.5

(xv) 1
(c)
2

m
m .co
.co
Question 2

m
(i) 4 3 1 2 4 1
s em [4]
la
끫븖끫뢾 = 끫븖끫뢊 끫롶 → 끫븖끫뢾 3 = 끫븖72 . 28 → 끫뢾 3 = 73 → 끫뢾 = 7끫뢠
e
(끫뢜)

las 3 3 3 3
a g
ag (끫뢞)
4 3
4 2 ′
7
끫븖끫뢾 = 끫븖끫뢊′ 끫롶 → × 끫븖 × 7 × 7 × 7 = 끫븖 × 14 × 끫롶 → 끫롶 = 끫뢠
3 3
2 ′ ′
3
= 2.33끫뢠 = 2끫뢠

1 2 1 22
(끫뢠) 끫븖끫뢊 끫롶 = × × 72 × 28 = 1437.33 = 1437끫뢠 3
3 3 7

m .
.co s e m
s em l a
la ag
T27 511 - SPECIMEN Page 1 of 10

ag
𝑐𝑐

𝑐𝑐
𝑐𝑐

𝑐𝑐

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 24
𝑐𝑐

(ii) (끫룊 − 2)2 + 11끫룊 − 7 = 0 [4]

끫룊 2 + 4 − 4끫룊 + 11끫룊 − 7 = 0

끫룊 2 + 7끫룊 − 3 = 0

−7 ± �49 − 4(1)(−3) −7 ± √61 −7 ± 7.8102
끫룊 = = =
2×1 2 2

끫룊 = 0.4051, 끫룊 = −7.4051

끫룊 = 0.405, 끫룊 = −7.41

(iii) 끫뢴(−2)+끫뢶(1) [4]
(a) R (끫룊, 0), 끫뢴+끫뢶
= 0 → −2 + 끫뢶 = 0 → : 끫뢶 = 1: 2

∴ 끫뢆 : 끫뢊끫뢊 = 1: 2
1(11)+2(−4)
(b) 끫룊 = → 끫룊 = 1,
1+2

끫뢊(1, 0)
−2−1 1
(c) 끫뢆끫뢆 = 11 + 4 = − 5

끫뢌끫뢌끫뢌끫뢌끫뢌 끫뢸 끫뢲 끫뢺 끫뢺 끫룂 끫뢆 = 5

끫뢊 끫뢊 , 끫료 − 0 = 5(끫룊 − 1)

5끫룊 − 끫료 = 5

Question 3
(i) Let the reduced price be x [4]
끫룊 + 18% 끫뢸 끫룊 = 1888 → 끫룊 = ₹ 1600

Reduction in price = ₹ 2000 − ₹1600 = ₹400
400
Percentage reduction = 2000 × 100 = 20%

(ii) (끫뢜) 끫뢜 = 15 끫뢜 = 15 [4]

(끫뢞) 끫뢎10 = 끫뢜 + (10 − 1) = 15 + 9 × 15 = 150
10
(c) 끫뢌10 = 2 [2 × 15 + 9 × 15] = 825

(iii) (a) 끫롨(0, 3), 끫롪(1, 2), 끫롬(2, 2), 끫롮(2, 1)끫뢜 끫롰(3, 0) [5]

(b) 끫뢬 끫뢸 끫롨 끫뢾 끫룂ℎ 끫료 − 끫뢜 끫뢜 끫롨(0, 3)
𝑚𝑚

𝑚𝑚
𝑃𝑃
𝑚𝑚

T27 511 - SPECIMEN Page 2 of 10
𝑜𝑜

𝑙𝑙

𝑙𝑙𝑙𝑙

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝑝𝑝𝑝𝑝

𝑝𝑝𝑝𝑝𝑝𝑝

𝑡𝑡

𝑃𝑃
𝑅𝑅

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅

𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

𝑜𝑜
𝑎𝑎𝑎𝑎

𝑑𝑑

𝑑𝑑

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 16 of 24
𝑎𝑎𝑎𝑎
𝑖𝑖𝑖𝑖𝑖𝑖

𝑖𝑖

𝑜𝑜

𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢

𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑜𝑜𝑜𝑜

𝑒𝑒

𝑎𝑎𝑎𝑎

𝑖𝑖𝑖𝑖

m
m .co
m .co s e m
se (c) 끫롼(−2, −2)
g l a
a
(d) 끫롨 끫롨끫롨끫롨끫롨 끫롨끫롨

(e) 끫료 = 1
SECTION − B

Question 4

m
.co
(i) P = ₹ 1000, n = 2 yrs, MV = 26 P ∴ MV = ₹ 26000 [3]
m
.co
(a) I = ₹ 26000 - ₹ 24000 = ₹ 2000
m s e m
s e l a
(b) a
ag
1000×24×25 끫뢾 1
l = × 100 × 12 = 2000
ag끫뢾 = 8% p.a.
2

(ii) (끫뢜) 끫뢸 끫롨 (2 × 1) = 끫뢸 끫뢶 [3]

(b)

끫룊 1 끫룊
끫롨 = � �� �
2 2 끫룊 − 2
m
2
AB= �끫룊 + 끫룊 − 2� = � �
0
.co
4끫룊 − 4
s em0

4끫룊la
g −4=0
a 끫룊 = 1
(iii) 끫뢠 2 끫븆 2
끫븆 [4]
끫롶 끫뢌 = +
1 − 끫룂 1 − 끫뢠
2 2
끫뢠 끫븆 끫븆
= +
끫뢠
1 − 끫뢠 1−
m
m .co
.co
3 3
끫뢠 끫븆 끫븆
em
s
= +
e m 끫뢠 − − 끫뢠
l a
las 끫뢠 3
끫븆 3
끫븆
ag
ag =
끫뢠 −
−
끫뢠 −
1 3 3
= [끫뢠 끫븆 − 끫븆]
(끫뢠 − )
2 2
(끫뢠 − )(끫뢠 끫븆 + 끫븆 + 끫뢠 )
= = 1 + 끫뢠 = 끫뢊
(끫뢠 − )

m .
.co e m
𝐴𝐴

𝐴𝐴

em as
𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼

s l
𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

𝑜𝑜

𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

𝐴𝐴

𝑖𝑖𝑖𝑖

𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

𝑜𝑜

𝑛𝑛𝑛𝑛𝑛𝑛

𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

ag
𝐴𝐴

la
T27 511 - SPECIMEN Page 3 of 10
𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠

g
𝐿𝐿

𝑡𝑡𝑡𝑡𝑡𝑡

𝑐𝑐𝑐𝑐𝑐𝑐
𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑐𝑐𝑐𝑐𝑐𝑐
𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

a
𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠
𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑐𝑐𝑐𝑐𝑐𝑐
𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠
𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠
𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

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𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠

𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑅𝑅𝑅𝑅
𝑐𝑐𝑐𝑐𝑐𝑐

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

Question 5
8000
(i) (a) . 끫뢸 ℎ끫뢜 끫뢜 = = 100 [3]
80

6 × 100 × 100
끫롨 끫롮 끫롮 = = ₹600
100

(b) 끫뢌 끫뢌끫뢌 끫뢺 = ₹75 × 100 = ₹7500

끫뢜 끫뢎 끫뢺 = ₹7500 + ₹600 = ₹8100

8100
. 끫뢸 ℎ끫뢜 끫뢜 = = 300
27

(ii) 12끫룊 7끫룊 2 [3]
−6 + ≤ − 3 < + 2끫룊, 끫룊 ∈ 끫뢊
5 5 5
12끫룊 7끫룊 7끫룊 2
−6 + ≤ −3 − 3 < + 2끫룊
5 5 5 5
12끫룊 7끫룊 7끫룊 2
− ≤6−3 − 2끫룊 < + 3
5 5 5 5
5끫룊 3끫룊 17
≤3 − <
5 5 5

끫룊 ≤ 3 17
끫룊 > −
3
2
끫룊 > −5
3
2
끫뢌끫뢌끫뢌 끫뢌 : �끫룊: − 5 < 끫룊 ≤ 3, 끫룊 ∈ 끫뢊�
3

(iii) (a) ∆끫롨 , ∠끫롪 = 90° (∠ 끫뢜 − 끫뢠 끫뢠 ) [4]

∴ 끫룊 + 90° + 32° = 180°,

끫룊 = 58°

끫료 = 끫룊 = 58° (끫뢜 . . 끫룂ℎ .)

끫룎 = 끫룊 = 58° (∠ )
𝑁𝑁𝑁𝑁

𝑜𝑜

𝑠𝑠

𝑎𝑎𝑎𝑎
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴

𝐷𝐷

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
𝑆𝑆

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝑝𝑝
𝑎𝑎𝑎𝑎

𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝑝𝑝
𝑁𝑁𝑁𝑁

𝑜𝑜

𝑠𝑠

𝑎𝑎𝑎𝑎

T27 511 - SPECIMEN Page 4 of 10
𝑆𝑆𝑆𝑆𝑆𝑆

𝑆𝑆
𝐼𝐼𝐼𝐼

𝐴𝐴𝐴𝐴

𝐵𝐵𝐵𝐵

𝑠𝑠

𝑖𝑖𝑖𝑖

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑐𝑐𝑐𝑐

𝑐𝑐𝑐𝑐

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𝑎𝑎𝑎𝑎

𝑠𝑠𝑠𝑠𝑠𝑠

𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
𝑠𝑠

𝑜𝑜𝑜𝑜

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

m
m .co
m .co s e m
se ) l a
ag
∆끫롨 , 끫롨 = 끫롨 (

∠끫롨 = ∠끫롨 = 끫룎 = 58°

+ 끫룎 + 끫룎 = 180° → = 180° − 116°

= 64°

끫롨 , + 끫룈 = 180° ( .∠ 끫뢸 끫뢠 끫뢠 끫뢠 . 끫뢜 )
m
m 끫룈 = 180° − 64°, 끫룈 = 116°
.co
m .co s e m
a
Question 6
s e l
(i)
g l a (끫룊) = 2끫룊 3 + 5끫룊 2 − 28끫룊 − 15 ag [3]
a (3) = 2(3)3 + 5(3)2 − 28(3) − 15

= 54 + 45 − 84 − 15 = 99 − 99 = 0

∴ (끫룊 − 3) 끫뢜 끫뢸 (끫룊).

2끫룊 2 + 11끫룊 + 5

m
.co
끫룊 − 3 2끫룊 3 + 5끫룊 2 − 28끫룊 − 15

em
2끫룊 3 − 6끫룊 2
s
g la − 28끫룊
2
a11끫룊

11끫룊 2 − 33끫룊

5끫룊 − 15

5끫룊 − 15

××
m
m (끫룊) = (끫룊 − 3)(2끫룊 2 + 11끫룊 + 5)
.co
.co s e m
em a
(끫룊) = (끫룊 − 3)(끫룊 + 5)(2끫룊 + 1)
s g l
g la a
a (ii) (a) ∆끫롨 , 끫롲 끫룂 끫롨 , [3]

끫롨 끫롮 18 6
∴ = = = (끫롪. 끫뢆. 끫뢎. )
끫롲 끫롰 3 1

끫롨 : 끫롲 = 6: 1

끫롨끫롨 끫롨 6
m 끫롨끫롨: =6∶1
.
c. o
, = = ,
끫롲
m
𝐼𝐼𝐼𝐼

𝐴𝐴𝐴𝐴

𝐴𝐴

𝐴𝐴

𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔

1
e
𝐴𝐴𝐴𝐴

𝐴𝐴𝐴𝐴
𝑣𝑣

𝑣𝑣
𝑣𝑣

s
𝐼𝐼𝐼𝐼

𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞

𝐴𝐴𝐴𝐴𝐴𝐴

𝑣𝑣

𝑜𝑜𝑜𝑜𝑜𝑜

𝑠𝑠

𝑜𝑜

𝑐𝑐

𝑐𝑐𝑐𝑐

𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞

𝑎𝑎𝑎𝑎

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

em a
𝑓𝑓

l
𝑓𝑓

s
𝑖𝑖𝑖𝑖

𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

𝑜𝑜

𝑓𝑓

la ag
T27 511 - SPECIMEN Page 5 of 10

ag
𝑓𝑓

𝑓𝑓
𝐼𝐼𝐼𝐼

𝐴𝐴𝐴𝐴

𝐹𝐹

𝑖𝑖𝑖𝑖

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝑡𝑡

𝐴𝐴

𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔
𝐴𝐴

𝐷𝐷


𝐹𝐹

𝐸𝐸

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𝐴𝐴

𝐹𝐹
𝐴𝐴
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝐺𝐺𝐺𝐺
𝐺𝐺𝐺𝐺

𝐹𝐹

끫롰끫롰 끫롰끫롰 끫롰끫롰 3
(b) ∆끫롨 ~∆끫롲 , ∴ = → = ∴ 끫롰 = 5 끫뢠
끫롨끫롨 35 21

끫뢜 끫뢜끫뢜 끫룂 끫룂.끫롨끫롨 끫롨끫롨 2 −끫롰끫롰2 352 −52 40×30
(c) = = = → 끫뾤끫뾤 ∶ 끫뾞
끫뢜 끫뢜끫뢜 ∆끫롰끫롰끫롰 끫롰끫롰2 52 25

(iii) [4]

Question 7
8 4
(i) (a) {6,12,18,24,30,36,42,48}, P(divisible by 6) = = [3]
50 25

4 21
(b) P (not divisible by 2 and 3) = 1 − 25 = 25

(ii) (a) Given, ABCD is a parallelogram, [3]

AP = AS (tangents drawn from an external point are equal)

BP = BQ (tangents drawn from an external point are equal)

CR = CQ (tangents drawn from an external point are equal)

DR = DS (tangents drawn from an external point are equal)

Adding, (AP+BP) + (CR + DR) = (AS + DS) + (BQ + CQ)

AB + CD = AD + BC

AB + AB = BC + BC (opp. Sides of parallelogram are equal)

2AB = 2 BC

AB = BC
𝐴𝐴𝐴𝐴

𝐹𝐹𝐹𝐹

𝐸𝐸

𝑐𝑐
𝐷𝐷𝐷𝐷
𝑎𝑎

𝑡𝑡𝑡𝑡

𝐴𝐴𝐴𝐴
𝑎𝑎

T27 511 - SPECIMEN Page 6 of 10

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 20 of 24

m
m .co
m .co s e m
se (b) In quad ABCD, AB = BC= CD = DA
g l a
a
∴ 끫롨 끫뢜 끫뢾ℎ

∴ 끫롨 끫뢜 끫롪 끫뢞 ℎ ℎ 끫뢜 끫뢾 . 끫뢜 끫뢜 ( 끫뢸 끫뢾ℎ )

(iii) 끫뢜 + 2끫뢞 + 끫룊 (끫뢜 + 끫뢞)2 [4]
=
끫뢜 − 2끫뢞 + 끫룊 (끫뢜 − 끫뢞)2

(끫뢜+끫뢞)2 +(끫뢜−끫뢞)2
m
.co
끫뢜+2끫뢞+끫룊+끫뢜−2끫뢞+끫룊
Applying C & D, = (끫뢜+끫뢞)2 − (끫뢜−끫뢞)2
m 끫뢜+2끫뢞+끫룊−끫뢜+2끫뢞−끫룊

m .co 2(끫뢜 + 끫룊) 2 (끫뢜2 + 끫뢞 2 )
s e m
s e =
l a
a ag
4끫뢞 4끫뢜
g l
a (끫뢜 + 끫룊) =
(끫뢜2 + 끫뢞 2 )
끫뢜

끫뢞 2
끫룊 =
끫뢜

Question 8

om
(i) 끫롬lass 끫룊 [3]

8. c
0 – 10 5
e 끫룊 m 40

10 – 20 15
las 15 끫룊
ag
20 – 30 25 12 300

30 – 40 35 13 455

40 – 50 45 y 45 y

x+y+33=50 795+15 x+45 y

m
.co
∑ 795 + 15끫룊 + 45끫료
m = = = 27

.co
∑ 50
e m
e m 끫뢜 끫룊 + 끫료 = 17
l as
s
3끫룊 + 9끫료 = 111

la ag
ag 끫룊 = 7 끫뢜 끫료 = 10

(ii) 12 × 10 − (12 − 끫룊)(10 − 끫룊) = 57 [3]

120 − 120 + 22끫룊 − 끫룊 2 = 57

끫룊 2 − 22끫룊 + 57 = 0 → (끫룊 − 19)(끫룊 − 3) = 0

끫룊 = 19 끫뢶 , ∴ 끫룊 = 3
m .
.co e m
𝐴𝐴𝐴𝐴𝐴𝐴

𝑖𝑖𝑖𝑖

𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
𝐴𝐴

𝑎𝑎𝑎𝑎

𝐵𝐵

𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

𝑒𝑒𝑒𝑒𝑒𝑒

𝑜𝑜𝑜𝑜

𝑒𝑒𝑒𝑒

𝑎𝑎

𝑟𝑟

𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

𝑜𝑜

𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

em as
𝑎𝑎

s l
la ag
𝑓𝑓

𝑓𝑓𝑓𝑓

T27 511 - SPECIMEN Page 7 of 10

ag
𝑓𝑓𝑓𝑓
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑓𝑓

𝑎𝑎𝑎𝑎
𝑎𝑎𝑎𝑎

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𝑖𝑖𝑖𝑖

𝑛𝑛𝑛𝑛

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝑚𝑚

(iii) 2 2 [4]
끫뢒끫롨 = 끫븖끫뢾 2 ℎ − 끫븖끫뢾 3 = 끫븖. 3.52 . 10 − . 끫븖. 3.53
3 3

1 1
끫뢒끫롪 = 끫븖끫뢾 2 ℎ − 끫븖끫뢾 2 ℎ′ = 끫븖. 3.52 . 10 − . 끫븖. 3.53
3 3
∴ 끫뢒끫롪 > 끫뢒끫롨
1 2
끫뢒끫롪 − 끫뢒끫롨 = �끫븖끫뢾 2 ℎ − 3 끫븖끫뢾 2 ℎ′� − �끫븖끫뢾 2 ℎ − 3 끫븖끫뢾 3 �
1 2
= 끫븖끫뢾 2 ℎ − 3 끫븖끫뢾 2 ℎ′ − 끫븖끫뢾 2 ℎ + 3 끫븖끫뢾 3
2 1
끫뢒끫롪 − 끫뢒끫롨 = 3 끫븖끫뢾 3 − 3 끫븖끫뢾 2 ℎ′
2 22 1 22
= 3 × 7 × 3.53 − 3 × 7 × 3.52 × 3.5

1 22
= 3 × 7 × 3.53

= 44.916
3
Difference in the capacity of Glass A and Glass B = 44.92 끫뢠

Also, Glass B has greater capacity than Glass A as 끫뢒끫롪 − 끫뢒끫롨 > 0

Question 9

(i) Marks 끫뢠 [5]

0 − 10 8 8 (a) = 53 ± 1

10 − 20 12 20 (b) 끫룂ℎ끫뢜 75

20 − 30 16 36 = 200 − 186 = 14

30 − 40 24 60 (c) number of students who
scored 35% and below.
40 − 50 29 89
= 33 ± 2
50 − 60 38 127

60 − 70 42 169

70 − 80 31 200
𝑐𝑐

T27 511 - SPECIMEN Page 8 of 10
𝑓𝑓

𝑐𝑐

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑎𝑎

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

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m
m .co
m .co s e m
se g l a
a

m
m .co
m .co s e m
s e l a
g l a ag
a

m
m .co
s e
la
0

ag
(ii) 끫롪 [5]
∆끫롨 , = tan(90° − 32°)
끫롨

끫롪 = 120 × 끫룂 58° = 120 × 1.600 = 192

끫롬
∆끫롨 , = tan(90° − 58°)
끫롨
m
m 끫롬 = 120 × 끫룂 .co
.co
32° = 120 × 0.6249 = 74.988
e m
e m 끫롪 = 끫롪 + 끫롬 = 120 × 1.600 + 120 × 0.6249 = 120 × 2.2249
l as
las = 266.988 = 267
ag
ag A
58° 32°
120m

58° 32°
C
o mD B
m .
.c s e
s em l a
la ag
T27 511 - SPECIMEN Page 9 of 10
𝐵𝐵
𝐼𝐼𝐼𝐼

𝐴𝐴𝐴𝐴

𝐴𝐴

g
𝐵𝐵

𝑡𝑡𝑡𝑡

𝐶𝐶
𝐼𝐼𝐼𝐼

𝐴𝐴𝐴𝐴

𝐴𝐴

a
𝐶𝐶

𝑡𝑡𝑡𝑡

𝑚𝑚
𝐵𝐵

𝐵𝐵

𝐶𝐶

𝑚𝑚

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Question 10

(i) 끫룂ℎ 끫룂 끫뢞 끫뢜, 끫뢜 , 끫뢜끫뢾 2 , … … … . . 끫뢜끫뢾 9 [3]

, 끫뢜 + 끫뢜 + 끫뢜끫뢾 2 = 7 끫뢜 끫뢜끫뢾 7 + 끫뢜끫뢾 8 + 끫뢜끫뢾 9 = 896

끫뢜끫뢾 7 + 끫뢜끫뢾 8 + 끫뢜끫뢾 9 896
=
끫뢜 + 끫뢜 + 끫뢜끫뢾 2 7

끫뢜끫뢾 7 (1 + 끫뢾 + 끫뢾 2 )
= 128
끫뢜(1 + 끫뢾 + 끫뢾 2 )

끫뢾 7 = 128 → 끫뢾 = 2

끫뢜(1 + 2 + 22 ) = 7 → 끫뢜 = 1

(ii) PA = PB = 9 cm (tangents from the same point) [3]

1
∆ , = 끫룂 30° =
끫뢆 √3
1
끫뢾 = =9× = 3√3 = 3 × 1.7321
√3

= 5.1963

= 5.2 끫뢠

(iii) [4]

0

Mode: 51.5kg.
𝐿𝐿𝐿𝐿𝐿𝐿

𝑒𝑒

𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

𝑏𝑏

𝑎𝑎
𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺

𝑎𝑎

𝑎𝑎𝑎𝑎

𝑎𝑎
𝑂𝑂𝑂𝑂
𝐼𝐼𝐼𝐼

𝑂𝑂𝑂𝑂𝑂𝑂

𝑡𝑡𝑡𝑡
𝑃𝑃
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑂𝑂𝑂𝑂

T27 511 - SPECIMEN Page 10 of 10
𝑐𝑐

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