International Mathematics Olympiad Work Book Class 8 IIT JEE Foundation Mahabir Singh MTG

97 Pages·09.517 MB·English

by  Mahabir Singh

8
By
Mahabir Singh
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Chapter 1 : Rational Numbers 5
Chapter 2 : Linear Equations In One Variable 8
Chapter 3 : Understanding Quadrilaterals 11
Chapter 4 : Practical Geometry 14
Chapter 5 : Data Handling 17
Chapter 6 : Squares and Square Roots 21
Chapter 7 : Cubes and Cube Roots 24
Chapter 8 : Comparing Quantities 27
Chapter 9 : Algebraic Expressions and Identities 30
Chapter 10 : Visualising Solid Shapes 33
Chapter 11 : Mensuration 36
Chapter 12 : Exponents and Powers 40
Chapter 13 : Direct and Inverse Proportions 43
Chapter 14 : Factorisation 46
Chapter 15 : Introduction to Graphs 49
Chapter 16 : Playing with Numbers 53
Chapter 17 : Logical Reasoning 56
Hints & Explanations 60
S F International Mathematics Olympiad - 2017 84
(with Hints & Explanations)

CHAPTER
1 RATIONAL NUMBERS
MATHEMATICAL REASONING
65 12 a b
1. Divide the sum of and by their (A) (B)
12 7 b a
difference.
b
599 680 642 501 (C) − (D) None of these
(A) (B) (C) (D) a
311 216 133 301
7. Which of the following properties of rational
2. The sum of the additive inverse and numbers is given below?
1
multiplicative inverse of is ________. 7 −8 −13 7 −8 7 −13
5 ×  +  = × + × .
4  3 12  4 3 4 12
24 24
(A) (B) − (C) 25 (D) –25 (A) Commutativity of addition
5 5
(B) Associativity of multiplication
−28
3. The product of two rational numbers is . (C) Distributivity of multiplication over
81
14 addition
If one of the numbers is , then find the
(D) Distributivity of addition over multipli-
27
other number. cation
2 8 2 4 2+3×2
(A) (B) (C) − (D) − 8. If x = , then |–x| is equal to ________.
5 17 3 3 −5
8 8
1−2a (A) (B) − (C) 0 (D) 1
4. If a = 7, then the value of −  5 5
 a−5
is _________.
9. Which of the following options is true ?
13 15 13 15 5 7 9 11 11 9 7 5
(A) − (B) − (C) (D) (A) < < < (B) < < <
2 2 2 2 7 9 11 13 13 11 9 7
5. Which of the following statements is 5 11 7 9 5 9 11 7
(C) < < < (D) < < <
TRUE? 7 13 9 11 7 11 13 9
(A) Every point on the number line 10. The rational number which is not lying
represents a rational number. 5 1
between and is _________.
(B) The product of a rational number 16 2
and its reciprocal is 0. 3 7 1 13
(A) (B) (C) (D)
(C) (17 × 12)–1 = 17–1 × 12 8 16 4 32
1  3 5  9 4  5 6 
(D) Reciprocal of , a ≠ 0 is a. 11. Simplify :  ×  − ×  + × 
a 11 6  12 3 13 15
a
6. The multiplicative inverse of − 177 303 289 17
b (A) − (B) − (C) (D)
is _________. 286 40 492 24
5
CLASS 8
3 2 2 3
12. What should be subtracted from  −  14. If x = andy = , then find the value of
4 3 3 2
−1
to get ? (x + y) ÷ (x – y).
6
15 13 17 11
6 1 2 1 (A) (B) − (C) (D) −
(A) − (B) (C) (D) − 2 5 6 6
13 4 7 8
4
15. If x=− , then which of the following
3 7 −3 9 −3 6 11
13. Simplify : + +  + +  + .
8 2  5 8  2 5 rational number lies between x and |x|?
−2 −41 39 41 7 11 2 5
(A) (B) (C) (D) (A) (B) − (C) − (D)
3 10 5 10 13 15 11 8
EVERYDAY MATHEMATICS
16. There are 42 students in a class. Out 3 5
(C) cup (D) cup
3 2 8 8
of these, of the boys and of the
4 3 19. The wingspans of different species of
girls come to school by bus. The total birds is given below.
number of boys and girls of the same
class who come to school by bus is 30. Species Blue Golden Seagull Albatross
How many boys are there in the class? of birds jay eagle
(A) 20 (B) 24 (C) 26 (D) 16
Length
41 1 7 3
17. Mrs Priya earns ` 18000 per month. She of 100m 22m 110m 35m
7 1 wingspans
spends on household items and on
12 8 How much longer is the wingspan of a Golden
rest of the things. The amount she saves eagle than the wingspan of a Blue jay?
is ________. 209 209
(A) cm (B) m
(A) ` 7120 (B) ` 5250 100 100
(C) ` 5520 (D) ` 6562.50 9 215
(C) m (D) cm
1 100 100
18. One fruit salad recipe requires cup of
2
20. There are few adults and children in a
sugar. Another recipe for the same fruit
3
salad requires 2 tablespoons of sugar. If restaurant. If of the people in the restaurant
1 8
1 tablespoon is equivalent to cup, then
are adults and there are 90 more children
16
how much more sugar does the first recipe than adults, then how many children are
require? there in the restaurant?
4 6
(A) cup (B) cup (A) 180 (B) 200 (C) 225 (D) 230
5 5
ACHIEVERS SECTION (HOTS)
21. Which of the following options is (C) Rational numbers are closed
INCORRECT? under the operations of subtraction,
(A) The rational number 0 is the additive multiplication and division.
identity for rational numbers.
(B) The additive inverse of the rational (D) There are infinite rational numbers
number a/b is –a/b and vice-versa.
between any two rational numbers.
6
IMO WORKBOOK
22. Match the following. 24. Which of the following options holds?
Column-I Column-II Statement - 1 : Rational numbers are
closed under division.
(P) Product of a rational (i) –1
number and its reciprocal Statement - 2 : The value of
is −7 15  1 1 1 17
 ×  −1×  + ×  is .
12 x 18 −7  4 2 4 24
(Q) If and are (ii) 0
30 5 (A) Both Statement - 1 and Statement - 2
equivalent, then x = are true.
(B) Statement - 1 is true and Statement - 2
 8 −32 16 7
(R)  ÷ ÷ × = (iii) 2 is false.
21  39 13 4 (C) Statement - 1 is false but Statement - 2
(S) Sum of a rational (iv) 1 is true.
(D) Both Statement - 1 and Statement - 2
number and its additive
are false.
inverse is
(A) (P) → (iv); (Q) → (iii); (R) → (i); (S) → (ii) 25. State ‘T’ for true and ‘F’ for false.
−8
(B) (P) → (i); (Q) → (iii); (R) → (iv); (S) → (ii) (i) The rational number lies neither to
−3
(C) (P) → (iv); (Q) → (iii); (R) → (ii); (S) → (i)
the right nor to the left of zero on the
(D) (P) → (i); (Q) → (iv); (R) → (iii); (S) → (ii)
number line.
1 5
23. Fill in the blanks. (ii) The rational numbers and− are
(i) 0 is neither P nor Q . 2 2
on the opposite sides of 0 on the
(ii) R has/have no reciprocal.
number line.
(iii) The rational numbers S and T are
(iii) 0 is the smallest rational number.
equal to their reciprocal.
(iv) For every rational number x, x + 1 = x.
P Q R S T
(i) (ii) (iii) (iv)
(A) Positive negative 1 1/2 –1/2
(A) F T T F
(B) Integer rational 0 –1 0 (B) T F F F
(C) Positive negative 0 1 –1 (C) F T F F
(D) Natural integer –1 1 –1 (D) T T F F
JJJ
Darken your choice with HB Pencil
7
CLASS 8
CHAPTER LINEAR EQUATIONS
2
IN ONE VARIABLE
MATHEMATICAL REASONING
1. Solve for x : 11 22
(A) cm (B) cm
(3x+1) (2x−3) (x+3) (3x−1) 3 3
+ = +
16 7 8 14
(C) 11 cm (D) 10 cm
(A) 5 (B) 10 (C) –14 (D) 12
8. A number whose seventh part exceeds its
2. A number is 56 greater than the average
of its third, quarter and one-twelfth. Find eighth part by 1, is ________.
the number. (A) 58 (B) 56 (C) 64 (D) 68
(A) 85 (B) 64 (C) 72 (D) 40
9. A number consists of two digits whose sum
1
3. If of a number is 10 less than the original is 9. If 27 is subtracted from the original
3
number, its digits are interchanged. Then
number, then the number is________.
(A) 30 (B) 15 (C) 10 (D) 27 the original number is ________.
(A) 53 (B) 45 (C) 92 (D) 63
4. Solve for x: 6(3x + 2) – 5(6x – 1) = 6(x – 3)
– 5(7x – 6) + 12x 10. The denominator of a rational number is
(A) – 1 (B) 1 (C) 0 (D) 2 greater than its numerator by 3. If 3 is
subtracted from the numerator and 2 is
5. The number 299 is divided into two parts in
added to its denominator, then the new
the ratio 5 : 8. The product of the numbers
number becomes 1/5. The original rational
is ________.
number is ______.
(A) 21140 (B) 21294
5 5 3 3
(C) 21160 (D) 31294 (A) − (B) (C) (D) −
8 8 8 8
rd
2
6. If   of a number is 20 less than  5x−1 x−1 1
3 11. If x−2x−  = + then, x is
 3  3 2
the original number, then the number
equal to ______.
is________.
3 4 7 9
(A) 60 (B) 40 (C) 80 (D) 120 (A) (B) (C) (D)
2 7 3 2
7. The perimeter of a rectangle is numerically
12. A two digit number is less than 20. The
equal to the area of rectangle. If width
sum of the digits is double that of their
3
of rectangle is 2 cm, then its length product. What is the number?
4
is________. (A) 12 (B) 15 (C) 13 (D) 11
8
IMO WORKBOOK
th 14. If the angles of a triangle are in the ratio
4
13. Find two parts of 34 such that   of one 2 : 3 : 4, then the difference between the
7
greatest and the smallest angle is ______.
2th (A) 10° (B) 20° (C) 30° (D) 40°
part is equal to   of the other.
5 15. One-sixth of a number when subtracted from
the number itself gives 25. The number is
(A) 16, 18 (B) 14, 20
_______ .
(C) 15, 19 (D) None of these (A) 30 (B) 32 (C) 35 (D) 28
EVERYDAY MATHEMATICS
16. There were only two candidates in an did not drink anything. How many guests
election. One got 62% votes and was were there in all?
elected by a margin of 144 votes. The total (A) 240 (B) 180 (C) 144 (D) 190
number of voters were ________. 19. Two years ago, Mohit was three times as
(A) 500 (B) 600 (C) 700 (D) 800 old as his son and two years hence, twice
of Mohit’s age will be equal to five times
17. Sunita is twice as old as Ashima. If six years
that of his son. Then the present age of
is subtracted from Ashima’s age and four Mohit is ________.
years added to Sunita’s age, then Sunita (A) 14 years (B) 38 years
will be four times that of Ashima’s age. Find (C) 32 years (D) 34 years
the sum of their ages two years ago. 20. A steamer goes downstream and covers
(A) 40 years (B) 42 years the distance between two ports in 5 hours
(C) 36 years (D) 38 years while it covers the same distance upstream
in 6 hours. If the speed of the stream is
18. At a party, colas, squash and fruit juice 1 km/hr, find the speed of the steamer in
were offered to guests. One-fourth of the still water.
guests drank colas, One-third drank squash, (A) 12 km/hr (B) 11 km/hr
two-fifths drank fruit juice and just three (C) 13 km/hr (D) 14 km/hr
ACHIEVERS SECTION (HOTS)
21. Fill in the blanks. 22. Which of the following statements is
(i) The solution of the equation ax + b = 0 CORRECT?
is_______. 1
Statement - 1 : x = is the solution of
(ii) The shifting of a number from one side 2
of an equation to other is _______. (2x−3)−(2x−1)= x−2.
(iii) If a and b are positive integers then 4 2 3
the solution of the equation ax = b has 63
Statement - 2 : x = is the solution of
to be always _______. 2
(iv) Linear equation in one variable has 2x−17  x−1
−x−  =12.
only one variable with power _______. 2  3 

(i) (ii) (iii) (iv) (A) Only Statement - 1
(A) x = b/a commutativity positive 1
(B) Only Statement - 2
(B) x = –b/a commutativity negative 2
(C) Both Statement - 1 and Statement - 2
(C) x = b/a transposition negative 2
(D) x = –b/a transposition positive 1 (D) Neither Statement - 1 nor Statement - 2
9
CLASS 8