Here are the clues solved across: 2. 100 (Sum is a square) 5. 27 (A cube) 6. 125 (The fifth power of a prime number 5) 9. 1729 (First three digits are cube of a cube 12^3 and last two digits are square of second digit in 1-down 4^2) 10. 777 (A palindrome of odd numbers starting from 7) 13. 256 (The fourth power of a square 16^4) 14. A

2. 1
CLASS - 8
Hi ! Welcome to the world of Mathematics. Here you will come across
everything that a Math Champ should know — facts, logic, reasoning and
lots of fun. And I’m sure, you will also enrich your knowledge of Maths.
What is Mathematics ?
Mathematics is a language that makes use of symbols and notations
for describing numerical, geometric and graphical relationships. It
helps enhance one’s logical & critical thinking, accuracy and problem-
solving that reflects in decision-making. Solving mathematical
problems, imparts us the ability to understand the world (physical,
social and economic) better; and most of all, to think creatively.
Problem-solving is one of the features that makes mathematics an
important subject. Problem-solving abilities are not built in a day.
Trying to solve more difficult problems and watching others do the
same, are the key ingredients of this process.
How to study Maths ?
Mathematics is a subject which you may spend hours studying, and
still not get any wiser. However much you have studied, if you cannot
solve the problem on day of the test, you are lost. Thankfully, there are
some techniques for studying maths, that you can try regardless of
your level. And trust me, you may end up loving mathematics.
Here are some tips to conquer the subject :
1. Enjoy doing math !
People usually do things that they enjoy doing. So if you enjoy math,
you will like to do it more and more, and as you do more, you will
become better at it, which in turn will compel you to continue doing
it. This creates a virtuous circle, which results in excellence. Remember
to enjoy the math itself, not the contest winnings or recognitions.
While some people enjoy winning contests and getting recognized,
they get discouraged if they don’t get those. However, if you enjoy the
math itself, your motivation is not the recognition, so you will continue
doing it irrespective of the result.
2. Work on examples
In math, practice helps one understand why & how a technique works,
and what ‘shortcuts’ should be used, when. Studying worked
examples, taking on additional examples, and constructing new
examples, makes one discover different relationships between
mathematical objects.
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3. Excelling in Math
Excelling in mathematics, just like excelling in a sport or music, needs
deeper involvment and regular training, followed by a regular practice
of your own. To develop mathematical skills, students must strive hard
in problem-solving on their own and not just watch teachers solve
problems.
4. Work on your weaknesses
To achieve good skills in math, it is essential to find out your
weaknesses first. Then you need to take efforts to transform your
weaknesses into your strengths first, and later hone your strengths in
order to excel.
5. Always understand first and then memorize
There are a lot of formulae and shortcuts in math. It is important to
understand where & why they are applied and how they work bringing
out the correct results; rather than simply memorizing them by
cramming. This understanding makes their recalling easier and use,
correct.
6. Imagine yourself explaining the problem
The best way, to study math is to pretend to be a teacher explaining
the concept to a group of students. That answers all the ‘whys’ of it
including those that come to your mind first. If you are able to deliver
the lesson by explaining in such a way, then you clearly understand
what you are saying. This, by far, is the best way of mastering what you
are studying.
7. Always write down your solutions, clearly.
Even though a proof may seem crystal clear in your head, there might
be some details and loopholes that you might have missed. Always
write down a complete and clear solution to make sure that you do
have it right. Write in a way not just to convince yourself, but other
readers too.
8. Never give up until you crack a math problem
Many problems will eventually yield to your persistence. The
exhilaration and confidence that come with this experience are
definitely worth all your time and effort.

3. 3
CLASS - 8
SYLLABUS - UIMO
Mathematics - 1: Rational Numbers, Linear Equations in One
Variable, Understanding Quadrilaterals, Data Handling, Squares
and Square Roots, Cubes and Cube Roots, Comparing Quantities,
Algebraic Expressions and Identities, Visualizing Solid Shapes,
Mensuration, Exponents and Powers, Direct and Inverse
Proportions, Factorization.
Mathematics - 2: Syllabus as per Mathematics – 1. This section
includes multiple choice questions which have more than one
option as correct answers.
Reasoning : Analogy, Series, Coding-decoding, Mirror image, Paper
cutting, Odd one out, Analytical reasoning, Direction sense,
Mathematicalreasoning, Cube and dice, Clocks, Calendar, Logical
venn diagrams.
Critical Thinking : Syllabus as per mathematics and reasoning.
This section includes a combination of skills like conscious
application in real life, Logical & Inductive Reasoning, Tactics &
Strategies in decision making, higher order thinking.
EXAMINATION PATTERN
All questions are objective-type with no negative marking for
wrong answers.
S.No
1
2
3
4
Section
Mathematics - 1
Mathematics - 2
Logical Reasoning
Critical Thinking
No. of Questions
30
15
10
05
Marks
30
15
10
05
60 M
Total
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Born: 17 January 1905 (Dahanu, Maharashtra)
Died : 1986 (aged 80–81) (Devlali, Maharashtra)
Nationality : Indian
Occupation : School teacher
Known for : Results in recreational mathematics
Discoveries
Working largely alone, Kaprekar discovered a number of results in
number theory and described various properties of numbers. In
addition to the Kaprekar constant and the Kaprekar numbers which
were named after him, he also described self numbers or Devlali
numbers, the Harshad numbers and Demlo numbers.
Kaprekar constant
Main article : Kaprekar constant
In 1949, Kaprekar discovered an interesting property of the number
6174, which was subsequently named the Kaprekar constant. He
showed that 6174 is reached in the limit as one repeatedly subtracts
the highest and lowest numbers that can be constructed from a set of
four digits that are not all identical. Thus, starting with 1234, we have:
4321 – 1234 = 3087, then
8730 – 0378 = 8352, and 8532 – 2358 = 6174.
Repeating from this point onward leaves the same number (7641 –
1467 = 6174). In general, when the operation converges it does so in at
most seven iterations.
Kaprekar Number : Another class of numbers Kaprekar described are
the Kaprekar numbers.[8] A Kaprekar number is a positive integer with
the property that if it is squared, then its representation can be
partitioned into two positive integer parts whose sum is equal to the
original number (e.g. 45, since 452=2025, and 20+25=45, also 9, 55, 99
etc.) However, note the restriction that the two numbers are positive;
for example, 100 is not a Kaprekar number even though 1002=10000,
and 100+00 = 100. This operation, of taking the rightmost digits of a
square, and adding it to the integer formed by the leftmost digits, is
known as the Kaprekar operation.

4. 5
CLASS - 8
Pair up the given items which look a like, by
passing through all the hexagons.
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6 6 6 6 = 0
6 6 6 6 = 1
6 6 6 6 = 2
6 6 6 6 = 3
6 6 6 6 = 4
6 6 6 6 = 5
6 6 6 6 = 6
6 6 6 6 = 7
Insert the mathematical signs (+, –, ×, ÷, and brackets)
between the numbers given below to make the relation true.
Sign of decimal may also be used.

5. 7
CLASS - 8
Reasoning and Logic are two very important characteristics of
intelligence. With these two characteristics you can predict
what will be the outcome of a certain situation without actually
waiting for it to happen. For example, you may sometimes be
knowing about the anger of your mother before she is angry
or know before hand that your teacher will praise you on seeing
your work. In such situations you know the ‘cause’ and ’effect’
of the situations. This can be called as ‘logic and reasoning’.
Non verbal reasoning enables students to analyze and solve
complex problems without relying upon or being limited by
language abilities. Many mathematical concepts, science
problems and computer science tasks require strong reasoning
skills.
WHICH ONE IS DIFFERENT ?
The objective of this chapter is to assort the items of a given
group on the basis of a certain common quality they posses
and then identify the stranger or odd one out.
Example 1: Find the one that does not belong to the group.
(A) FEB (B) UTQ (C) ZYV (D) SRN
Answer: (D)
Explanation : In all other groups, there is a gap of two letters
as in the alphabet between second and third letters.
DIRECTION SENSE
The objective of this chapter is to judge the student’s ability to
trace and follow correctly and also to sense correct direction.
Example 1: Lenin went 15 km to the West from his house, then
turned left and walked 20 km. He then turned east and walked
25 km and finally turning left covered 20 km. How far is he
now from his house ?
(A) 15 km (B) 20 km (C) 25 km (D) 10 km
Answer: (D)
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Explanation: Points A and E show the starting and end positions
respectively of Lenin. It is clear that E is 10 km away from A.
Hence option (D) is the correct answer.
North
West
South
East
B A E
D
C
15km
x x
x
20km
20km
10km
WHAT COMES NEXT ?
This chapter deals with questions in Number series, Letter
series and series based on continuation of figures. Even though
there are various types of problems on series but the
fundamental concept for each type is the same.
Example 1: What will be the next term in the series below ?
BDF, CFI, DHL, ?
(A) CJM (B) EIM (C) EJO (D) EMI
Answer: (C)
Explanation: Clearly first, second, third letters of each term
are respectively moved one, two and three steps forward to
obtain the corresponding letters of the next term.
MIRROR IMAGES AND WATER IMAGES
The image of an object as seen in a mirror is known as Mirror
image and the Reflection of an object as seen in water is known
as Water image. In a mirror image of an object, right side of
the object appears at left side and vice versa and in the water
images the upper part of the object is seen down ward and
vice – versa.

6. 9
CLASS - 8
Example 1: Looking into a mirror, the clock shows 9:30 as the
time. What is the actual time ?
(A) 2:30 (B) 3:30 (C) 4:30 (D) 6:30
Answer: (A)
Explanation: In the mirror (1) clock appears as time = 9 : 30
(1) (2)
This is the mirror (2) image of the clock shown time = 2:30
Clearly, this clock shows the time 2:30. Therefore, the actual
time is 2:30. Hence the answer is (A).
PAPER FOLDING
The problems on paper folding involve the process of selecting
a figure which would most nearly match the pattern that would
be formed when a transparent sheet carrying designs on either
side of a dotted line is folded along this line. The figure has to
be selected from a set of four alternatives.
Example 1: In the following question, a transparent sheet
having some design on either side of a dotted line is given.
The figure is followed by four answer figures marked (A), (B),
(C) and (D). One out of these four alternatives is obtained by
folding the transparent sheet along the dotted line. You have
to choose the correct option.
(A) (B) (C) (D)
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Answer: (A)
Explanation : Here the sheet has been folded from bottom and
designs on the either side of the dotted line combinetoform fig (A).
ANALOGY
Analogy means “Similar item”. In this chapter, questions
demand you to determine the relationship between two
numbers or words in pair and then to identify a similar
relationship between the members of a different pair of words.
Analogy tests are therefore, meant to test student’s overall
knowledge, power of reasoning and ability to think accurately.
Outofthefourchoicesgivenforeachexample,youhavetoselect
one that will maintain the relationship on the two sides of the
sign : : the same if it is substituted for the question mark ‘?’
Example 1: Which pattern below completes the second pair in
the same way as the first pair ?
FLO : MOC : : RDP : ?
(A) NGO (B) GMP (C) MGP (D) MPG
Answer: (A)
Explanation: The first and third letters are moved two and three
step backwards respectively and the second letter three steps
forwards.
F L O : M O C R D P N G O
+3
–2
–3
:
+3
–2
–3
::
INSERTING MISSING NUMBERS
In these type of questions, a figure, a set of figures, an
arrangement or a matrix is given, each of which bears certain
characters, be it numbers, letters, following a certain pattern.
The candidate is required to identify this pattern and
accordingly find the missing character in the figure.

7. 11
CLASS - 8
Example 1: What number should replace the question mark ?
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(A) 12 (B) 18 (C) 25 (D) 30
Answer: (D)
Explanation:
7× 4 ×3 9 2×6
= 14; = 18
6 6
×
12 ×2× 4 9× 4 × 5
= 16; = 30
6 6
ANALYTICAL REASONING
This chapter of Analytical Reasoning involves the problems
relating to the counting of geometrical figures in a given
complex figure. The systematic method for determining the
number of any particular type of figure by the analysis of the
complex figure would be clear from the examples that follow.
Example 1: Count the number of triangles in the figure given
below.
(A) 17 (B) 13 (C) 15 (D) 16
Answer: (D)
Explanation : After labelling the figure in the question, it looks
as shown.
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B
A
N
P Q
C
S
D
R
M
O
E
F H G
There are sixteen triangles in this figure namely:
AMN, AMB, ABN, ACD, ACO, AOD, OSR, OSE, OER, OFG, OFH,
OHG, PMC, NQD, COS and ODR.
Since there are sixteen triangles the correr answer is (D).
CUBES AND DICE
When the number of cubes in a figure are to be counted, the
procedure to be adopted is as described in the following
example.
Example 1: Count the number of cubes in the given figure.
(A) 14 (B) 12 (C) 10 (D) 8
Answer: (C)
Explanation : Clearly, in the figure there is 1 column containing
3 cubes, 2 columns containing 2 cubes each and 3 columns
containing 1 cube each.
Number of cubes in columns of 3 cubes = 1 × 3 = 3;
Number of cubes in columns of 2 cubes = 2 × 2 = 4;
Number of cubes in columns of 1 cube = 3 × 1 = 3;
Therefore, total number of cubes = 3 + 4 + 3 = 10.

8. 13
CLASS - 8
1
2 3
4 5
6 7 8
9
10 11 12
13 14
ACROSS
2 Sum is a square
5 A cube
6 The fifth power of a prime
number
9 First three digits are cube of a
cube and last two digits are
square of second digit in 1-
down
10 A palindrome of odd numbers
starting from 7
13 The fourth power of a square
14 A square
DOWN
1 A square
3 The fourth power of a prime
number (palindrome)
4 A palindrome
7 The second digit is three
times of first and last two
digits are three times of second
8 Consecutive natural numbers
starting from 4
11 Consecutive natural numbers
in descending order
12 The fourth power of a square
14 Unified Council
Fun with series is a reasoning based mathematical game in which we
need to select a right pattern that shows the relation between the given
series of numbers.
For example: In this example, there is no simple
or transparent relationship between the individual
numbers. But if we group some of the numbers
into two digit pairs, we will get a pattern as follows:
68 + 5 = 73 35 + 7 = 42 13 + 4 = 17 25 + 6 = 31
So the missing number on the fourth line is 1.
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Below, there is a random arrangement of numbers.
Find the pattern and fill in the empty square.
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9. 15
CLASS - 8
Fill in the numbers from 4 to 15 in the given circles so that the sum of
each line joining their circles equals to 38. No number should be filled
more than once.
16 Unified Council
Search out the mathematical terms with the help of given clues. Write
them and fill them in the given circular puzzle.
• Space occupied by a substance • A measure in C.G.S. system
• A general expression • Placed in the middle
• A meeting point of two lines • Distance
• A proposition to be proved • Figure remains after division
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10. 17
CLASS - 8
The ability to think clearly and rationally is important
whatever we choose to do. Systematic thoughts can
improve the way we express and evaluate creative ideas.
Critical thinking can also play an important role in
cooperative reasoning and constructive tasks, acquire
knowledge, improve our theories, and strengthen
arguments.
The future of critical thinking includes developments in
fields such as artificial intelligence and machine-learning,
robotics, nanotechnology, 3-D printing, and genetics and
biotechnology, will cause widespread disruption not only
to business models but also to labor markets over the
next five years, with enormous change predicted in the
skill sets needed to thrive in the new landscape.
Unified council is committed in developing students'
critical thinking skills for better grades, higher test scores,
and success in life. Our efforts are to empower the mind
and encourage you to meet learning needs.
18 Unified Council
Try These
1. Shown here are different types of leaves. Count how
many types of leaves there are.
(A) 5 (B) 6 (C) 7 (D) 8
2. Assertion (A) : A little gap is left between iron rails.
Reason (R) : Iron expands in summer.
(A) Both A and R are true and R is the correct explanation
of A.
(B) Both A and R are true but R is NOT the correct
explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

11. 19
CLASS - 8
SOLUTIONS
PAIRING FUN WITH SERIE
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%
GAME OF SIGNS
6 – 6 + 6 – 6 = 0; 6 ÷ 6 × 6 ÷ 6 = 1
6 ÷ 6 + 6 ÷ 6 = 2; (6 + 6 + 6) ÷ 6 = 3
6 – (6 + 6) ÷ 6 = 4; $ $
× – 6 ÷ 6 = 5
$ $
× + 6 – 6 = 6; $ $
× + 6 ÷ 6 = 7
CROSSWORD
! $ # '
$
!
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% # ! ! # %
#
$ # $ ' $
$
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$ %
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20 Unified Council
MAGIC SQUARES
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CHAIN QUIZ
1
2
3
4
5
6
7
8
V O L
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T
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E
D
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A
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G
L
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N
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T
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O
R
E
M
A
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N
D E R
CRITICAL THINKING
(1) D (2) A

12. 21
CLASS - 8
Life is an exciting journey with a new lesson around every corner. Happi-
ness comes after hardwork and sorrow, pleasure is often accompained by pain. One
never knows what tomorrow will be like. But, what is important, is to live life to the
fullest; enjoy the happy moments, fight the hard ones and keep on learning all the
time. Like in journeys, life too is better enjoyed if it is planned. Knowing the direc-
tion, stations, co-travellers and destinations helps one to be calm, strong, depend-
able and successful in the journey of life.
How to rate one’s life?
How to plan one’s life?
You and your life are unique. You are the only person responsible for what
happens to your life. You are also responsible towards your family, friends, school,
town, country and the whole mankind. Always keep these things in mind while you
plan your life. Set goals-both short term and long term, and analyse and renew your
goals once you reach them. The Life Planner provided in the next page will help you
in this journey.
How to use Life Planner ?
This is your life planner. First, find out what you would like to do when you
grow up. You could be a teacher, astronaut, painter, inventor, archaeologist, innovator,
or anything you wish. Write it down in the box and then cut a photograph of such a
person from a magazine (newspaper) and paste it in the space provided. There is
also a table with yearly targets. Fill it up keeping your aim in mind and then follow it
with determination. All the best.
Give yourself a mark after each birthday or new year. And make this
interesting graph of your life.
LIFE PLANNER
ITS MY LIFE
Quality
of
life
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
LIFE RATINGS
8 9
Age in years
10 11 12 13 14 15 16 17 18
It’s my life
22 Unified Council
Paste
the
picture
of
your
hero
here
Year
Most
Your
What
Who
you
think
Did
you
achieve
Who
helped
How
can
important
target
is
required
will
help
you?
your
target?
you?
you
event
of
you?
Date?
improve?
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
Note:
You
can
make
another
table
like
this
and
start
again
with
fresh
goals.
Life
Planner
I
will
be
a
/
an
Paste
your
photograph
here
like
GOAL
!

13. 23
CLASS - 8 24 Unified Council