( i )

By

Sanjay Gupta

Upkar Prakashan, Agra-2

(For Class VIII)

( ii )

© Publishers

Publishers

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( iii )

Contents

Mathematics

● ● ● ● ● Rational Numbers ..................... 3–5

● ● ● ● ● Linear Equations in One

Variable ................................... 6–10

● ● ● ● ● Understanding Quadrilaterals .... 11–13

● ● ● ● ● Practical Geometry ................... 14–15

● ● ● ● ● Data Handling .......................... 16–18

● ● ● ● ● Squares and Square Roots ........ 19–25

● ● ● ● ● Cubes and Cube Roots .............. 26–30

● ● ● ● ● Comparing Quantities ................ 31–34

● ● ● ● ● Algebraic Expressions and

Identities .................................. 35–38

● ● ● ● ● Visualising Solid Shapes ............ 39–40

● ● ● ● ● Mensuration ............................. 41–47

● ● ● ● ● Exponents and Powers ............. 48–53

● ● ● ● ● Direct and Inverse Proportions .. 54–58

● ● ● ● ● Factorisation ............................. 59–65

● ● ● ● ● Introduction to Graphs ............... 66–69

● ● ● ● ● Playing with Numbers ............... 70–71

Science

Physics

● ● ● ● ● Force and Pressure ................... 3–6

● ● ● ● ● Friction .................................... 7–8

● ● ● ● ● Sound ...................................... 9–11

● ● ● ● ● Chemical Effects of Electric

Current .................................... 12–13

● ● ● ● ● Some Natural Phenomena ......... 14–16

● ● ● ● ● Light ........................................ 17–20

● ● ● ● ● Stars and the Solar System ........ 21–24

Chemistry

● ● ● ● ● Synthetic Fibres and Plastics ..... 25–26

● ● ● ● ● Materials : Metal and

Non-Metals ............................. 27–29

● ● ● ● ● Coal and Petroleum .................. 30–32

● ● ● ● ● Combustion and Flame .............. 33–36

● ● ● ● ● Pollution of Air and Water ......... 37–38

Biology

● ● ● ● ● Food Production and

Management ............................ 39–42

● ● ● ● ● Micro-Organisms : Friend

and Foe ................................... 43–45

● ● ● ● ● Conservation of Plants and

Animals ................................... 46–47

● ● ● ● ● Cell : Structure and Functions .... 48–50

● ● ● ● ● Reproduction in Animals ............ 51–53

● ● ● ● ● Reaching the Age of

Adolescence ............................ 54–56

( iv )

National Level Science Talent Search Examination

Introduction

It’s indubitable that our children are living in the era of information technology. They aresurrounded by not only condusive environment but myriads of information are poured incessantly,into their fertile mind. But sky is the limit. They need rigorous workout to cleave the chest of thesky to show their worth. Success emerges out of salubrious guidance and industry. UnifiedCouncil has designed such a competitive examination that will bring the hidden talent to thesurface, through National Level Science Talent Search Examination.

Unified Council is India’s first ISO 9001 certified organization that put the student to educa-tional testing and assessment, through inculcating basic concepts of Maths and Science. A ros-trum of eminent professionals and academicians, Unified Council is inclined to find out the subter-ranean water beneath the ruffled surface. It is decidedly committed to make the younger genera-tion fundamentally strong.

Upkar is proud to present the book to enable the students to face the challenge. Everymeticulous care has been taken to make the book outstanding in its contents and lucrative in itsnature. The book inculcates an interesting methodology to impart logical and analytical skills.Besides, hints for the difficult questions would definitely develop the confidence, to solve thequestion.

Who is Eligible—All the students of Classes 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 are fully eligibleto participate in the competition.

Syllabus—CBSE/ICSE/State Board Syllabi.

Medium—Only in English.

Design—For each class there will be separate question paper of objective nature. There willbe 75 questions of 75 marks for class III and 100 questions of 100 marks (for IV of XII). Theduration of examination will be 90 minutes in every case.

Test Centres and Date of Examination—The test centres are spread all across the coun-try and the examination is being conducted on the last Sunday of January.

Besides, top 100 student will be honoured with scholarship, cash awards and rewards whichwill be presented by eminent scholars at a grandeur function in Hyderabad.

MATHEMATICS

Rational Numbers

Points to Remember1. Whole numbers are closed under addition and

multiplication but not under subtraction anddivision. However, integers are closed underaddition, subtraction and multiplication butnot under division.

2. A number which can be written in the Formpq, where p and q are integers and q ≠ 0 is

called a rational number, for example, –23

, 67

are all rational numbers. Since the numbers 0,

–2, 4 can be written in the form pq, they are

also rational numbers.3. Rational numbers are closed under multipli-

cation. That is, for any two rational numbers aand b, a × b is also a rational number.

4. For any rational number a , a ÷ 0 is notdefined. So rational numbers are not closedunder division. However, if we exclude zerothen the collection of, all other rationalnumbers is closed under division.

5. Two rational numbers can be added in anyorder. We say that addition is commutativefor rational numbers. That is, for any tworational numbers a and b, a + b = b + a

6. Subtraction is not commutative for rationalnumbers.

7. Multiplication is commutative for rationalnumbers. In general, a × b = b × a a for anytwo rational numbers a and b.

8. Expressions on both sides are not equal. Sodivision is not commutative for rationalnumbers.

9. Addition is associative for rational numbers.That is, for any three rational numbers a , band c, a + (b + c ) = (a + b ) + c.

10. Subtraction is not associative for rationalnumbers.

11. Multiplication is associative for rationalnumbers. That is for any three rationalnumbers, a, b and c, a × (b × c) = (a × b) × c.

12. When you add 0 to a whole numbers, the sumis again that whole number. This happens forintegers and rational numbers also.In general, a + 0 = 0 + a = a, where a is a

whole numberb + 0 = 0 + b = b, where b is an

integerc + 0 = 0 + c = c, where is

rational numberZero is called the identity for the addition ofrational numbers. It is the additive identity forintegers and whole numbers as well.

13. a × 1 = 1 × a = a for any rational number a. 1is the multiplicative identity for rationalnumbers.

14. A rational number cd is called the reciprocal or

multiplicative inverse of another rational

number ab if

ab ×

cd = 1.

EXAMPLES

Example 1. Find 24 + ( )–3

8 + ( )–6

12 + ( )2

16

Solution : 24 + ( )–3

8 + ( )–6

12 + ( )2

16

=2448

+ ( )–1848

+ ( )–2448

+ ( )648

(Note that 48 is the LCM of 7, 8, 12 and 16)

=24 – 18 – 24 + 6

48

=–1248

=–14

Ans.

4G | Mathematics

Example 2. Find –68

× 212

× 1416

× ( )–169

.

Solution : we have –68

× 212

× 1416

× ( )–169

= ( )–6 × 28 × 12

× ( )14 × (–16)16 × 9

= – 18 × ( )–14

9 =

–1 × (–14)8 × 9

= 736

Ans.

Example 3. Write any 3 rational numbersbetween – 2 and 0.

Solution : 2 can be written as –2010

and 0 as 010

,

Thus we have –1910

, –1810

, –1710

, –1610

, –1510

, …, –110

between –2 and 0.

You can take any three of these. Ans.

Multiple Choice Questions

01.34 +

24 –

14 is equal to—

(A) 0 (B) 1

(C) 4 (D)14

02. Find the value of | –1330

|—

(A)1330

(B)–1330

(C) 2 (D) 30

03. Evaluate 25 +

25 + … up to fifteen times—

(A) 2 (B) 12(C) 14 (D) 6

04. Simplify : | 24 | – | – 24 |—(A) 1 (B) 0(C) 48 (D) 30

05. Sum of first three prime numbers which end—(A) 39 (B) 14(C) 24 (D) 30

06. Which statement is not true for the system ofintegers ?(A) 0 is additive identity integers(B) Division of two integers is an integer(C) Sum of two integers is an integer(D) None of these

07. How many rational numbers lie between – 1and + 1 ?

(A) Many rational numbers(B) No rational number(C) Only one rational number(D) None of these

08. Which statement is not true for the system ofrational numbers ?(A) x + (y + z) = (x + y) + z(B) x + (y + z) = (x × y) × z(C) x – x = 1(D) None of these

09. Which statement is true ?

(A) √⎯ 3 is not a real number(B) Additive identity of 5 is –5

(C)–812

=–1510

(D)–45

<25

10. Difference between two even numbers afterand before 2n, where n is positive number—(A) 0 (B) 4(C) 2 (D) 6

11. Which of the following is not an integer ?(A) –7 × 9 (B) –13 + 23(C) 2 ÷ 7 (D) 2 – 0

12. Which of the following is in the lowest term ?

(A)424

(B)12123

(C)16128

(D)67

13. Which number is divisible by 12 ?(A) 2449 (B) 1680(C) 3642 (D) 5662

14. The three consecutive natural numbers whosesum of squares is 110 are—(A) 9, 10, 11 (B) 6, 7, 8(C) 4, 5 6 (D) 5, 6, 7

Mathematics | 5G

15. Express 4·08 in the form of pq—

(A)40499

(B)899

(C)39699

(D)39899

16. Simplify : 10 14 of

410

× 108

of 416

—

(A) 1 1032

(B) 1 1132

(C) 1 329

(D) 1 932

17. The additive inverse of – ab

is—

(A)ba

(B)ab

(C)– ab

(D) None of these

18. Multiplicative inverse of ‘0’ is—(A) Does not exist

(B)10

(C) 0(D) None of these

19. Express 0·78 as a rational number—

(A)5078

(B)7850

(C)3950

(D) None of these

20. Express 0·—70 as rational number—

(A)7090

(B)7099

(C)710

(D) None of these

21. Which step in the following problem iswrong ?

x = y = 1x = y

Step 1 : x 2 = xy

Step 2 : x2 – y2 = xy – y 2

Step 3 : (x + y) (x – y) = y (x – y)

Step 4 : x + y =y (x – y)

x – yx + y = y1 + 1 = 1

2 = 1(A) Step 3 (B) Step 4(C) Step 1 (D) Step 2

22. The value of 3 – 4

1 + 1

2 + 1

1 + 13

(A)115

(B)215

(C)13

(D)152

Answers with Hints1. (B) 2. (A) 3. (D) 4. (C) 5. (A)6. (B) 7. (A) 8. (C) 9. (A) 10. (B)

11. (C) 12. (D) 13. (B) 14. (D) 15. (A)16. (D)17. (B)

∴ P + (–P) = (–P) + P = 0 is the additive

inverse property.

So additive inverse of – ab

is ab .

18. (A) Does not exist since division by zero isnot defined.

19. (C) 0·78 =78100

= 3950

.

20. (B) 0·—70 =

7099

.

21. (B) ·.· x = y = 1⇒ x – y = 0Division by zero is not defined.So we cannot divide by (x – y)

22. (A)

Science Talent & Olympiad Exam. (ForClass VIII)

Publisher : Upkar Prakashan ISBN : 9789350133439 Author : Sanjay Gupta

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