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, TABLE OF CONTENTS
1. REAL NUMBERS .............................................................................................................................. 7
2. POLYNOMIALS ............................................................................................................................. 14
3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES .......................................................... 21
4. QUADRATIC EQUATIONS......................................................................................................... 30
5. ARITHMETIC PROGRESSION .................................................................................................... 39
6. TRIANGLES .................................................................................................................................... 47
7. COORDINATE GEOMETRY ........................................................................................................ 57
8. INTRODUCTION TO TRIGONOMETRY ................................................................................. 64
9. APPLICATIONS OF TRIGONOMETRY ...................................................................................... 9
10. CIRCLES .......................................................................................................................................... 16
11. CONSTRUCTIONS ....................................................................................................................... 23
12. AREAS RELATED TO CIRCLES.................................................................................................. 29
13. SURFACE AREAS AND VOLUMES............................................................................................ 37
14. STATISTICS ................................................................................................................................... 46
15. PROBABILITY ................................................................................................................................ 55
6
, 1. REAL NUMBERS
QR Code:
Learning outcome and Learning Objectives:
Content area /
Learning Objectives Learning Outcome
Concept
Apply Euclid Division Algorithm in order to obtain
HCF of 2 positive integers in the context of the
given problem
Euclid's Division
Apply Euclid Division Algorithm in order to prove
results of positive integers in the form of ax+b
where a and b are integers
Generalises properties of numbers and
Fundamental Use the Fundamental Theorem of Arithmetic in
relations among them studied earlier,
Theorem of order to calculate HCF and LCM of the given
to evolve results, such as, Euclid’s
Arithmetic numbers in the context of the given problem
division algorithm, fundamental
Recall the properties of irrational number in order
theorem of arithmetic in order to apply
to prove that whether the
them to solve problems related to real
sum/difference/product/quotient of 2 numbers is
Irrational Numbers life contexts
irrational or not
Apply theorems of irrational number in order to
prove whether a given number is irrational or not
Decimal Apply theorems of rational numbers in order to
Representation of find out about the nature of their decimal
Irrational Numbers representation and their factors
7
, Test items
LOB: Apply Euclid Division Algorithm in order to obtain HCF of 2 given numbers in the context of the given
problem
1. A worker needs to pack 350 kg of rice and 150 kg of wheat in bags such that each bag weighs the same.
Each bag should either contain rice or wheat. Which option shows the correct steps to find the greatest
amount of rice/wheat the worker can pack in each bag?
Option 1: Step 1: 350 = 2(150) + 50
Step 2: 150 = 3(50) + 0
Step 3: Greatest amount: 50 kg
Option 2: Step 1: 350 = 2(150) + 50
Step 2: 150 = 2(50) + 0
Step 3: Greatest amount: 50 kg
Option 3: Step 1: 350 = 2(150) + 50
Step 2: 150 = 3(50) + 0
Step 3: Greatest amount: 150 kg
Option 4: Step 1: 350 = 2(150) + 50
Step 2: 150 = 2(50) + 0
Step 3: Greatest amount: 150 kg
Correct Answer: Option 1
2. Pranay wants to stack few one-rupee coins and some five-rupee coins in such a way that:
a. Each stack has the same number of coins.
b. There is least number of stacks.
c. Each stack either has one rupee or five-rupee coins.
d. No coins are left over after creating stacks.
His first step to find the number of coins that should be in each stack is 195=1(180) +15. Given that he
has more of five-rupee coins than one-rupee coins, how many one-rupee coins stack can he make?
Option 1: 12
Option 2: 13
Option 3: 15
Option 4: 25
Correct Answer: Option 1
LOB: Apply Euclid Division Algorithm in order to prove results of positive integers in the form of ax+b where a
and b are constants
1. Given that p is a non-negative integer, which of these gives positive integers that are multiple of 5?
Option 1: 10p and 10p+2.
Option 2: 10p and 10p+3.
Option 3: 10p and 10p+4.
Option 4: 10p and 10p+5.
Correct Answer: Option 4
2. In the equation below, a, b, q, r are integers, 0≤r<b, a is a multiple of 3 and b=9.
a=bq+r
Which of the following forms represent a?
Option 1: Only 9q and 9q+3, as only these forms when divided by 3 gives r=0.
Option 2: Only 9q+1and 9q+4, as only these forms when divided by 3 gives r=1.
Option 3: Only 9q, 9q+3, and 9q+6, as only these forms when divided by 3 gives r=0.
Option 4: Only 9q+1, 9q+4, and 9q+7, as only these forms when divided by 3 gives r=1.
Correct Answer: Option 3
LOB: Use the Fundamental Theorem of Arithmetic in order to calculate HCF and LCM of the given numbers in
the context of the given problem
8
, TABLE OF CONTENTS
1. REAL NUMBERS .............................................................................................................................. 7
2. POLYNOMIALS ............................................................................................................................. 14
3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES .......................................................... 21
4. QUADRATIC EQUATIONS......................................................................................................... 30
5. ARITHMETIC PROGRESSION .................................................................................................... 39
6. TRIANGLES .................................................................................................................................... 47
7. COORDINATE GEOMETRY ........................................................................................................ 57
8. INTRODUCTION TO TRIGONOMETRY ................................................................................. 64
9. APPLICATIONS OF TRIGONOMETRY ...................................................................................... 9
10. CIRCLES .......................................................................................................................................... 16
11. CONSTRUCTIONS ....................................................................................................................... 23
12. AREAS RELATED TO CIRCLES.................................................................................................. 29
13. SURFACE AREAS AND VOLUMES............................................................................................ 37
14. STATISTICS ................................................................................................................................... 46
15. PROBABILITY ................................................................................................................................ 55
6
, 1. REAL NUMBERS
QR Code:
Learning outcome and Learning Objectives:
Content area /
Learning Objectives Learning Outcome
Concept
Apply Euclid Division Algorithm in order to obtain
HCF of 2 positive integers in the context of the
given problem
Euclid's Division
Apply Euclid Division Algorithm in order to prove
results of positive integers in the form of ax+b
where a and b are integers
Generalises properties of numbers and
Fundamental Use the Fundamental Theorem of Arithmetic in
relations among them studied earlier,
Theorem of order to calculate HCF and LCM of the given
to evolve results, such as, Euclid’s
Arithmetic numbers in the context of the given problem
division algorithm, fundamental
Recall the properties of irrational number in order
theorem of arithmetic in order to apply
to prove that whether the
them to solve problems related to real
sum/difference/product/quotient of 2 numbers is
Irrational Numbers life contexts
irrational or not
Apply theorems of irrational number in order to
prove whether a given number is irrational or not
Decimal Apply theorems of rational numbers in order to
Representation of find out about the nature of their decimal
Irrational Numbers representation and their factors
7
, Test items
LOB: Apply Euclid Division Algorithm in order to obtain HCF of 2 given numbers in the context of the given
problem
1. A worker needs to pack 350 kg of rice and 150 kg of wheat in bags such that each bag weighs the same.
Each bag should either contain rice or wheat. Which option shows the correct steps to find the greatest
amount of rice/wheat the worker can pack in each bag?
Option 1: Step 1: 350 = 2(150) + 50
Step 2: 150 = 3(50) + 0
Step 3: Greatest amount: 50 kg
Option 2: Step 1: 350 = 2(150) + 50
Step 2: 150 = 2(50) + 0
Step 3: Greatest amount: 50 kg
Option 3: Step 1: 350 = 2(150) + 50
Step 2: 150 = 3(50) + 0
Step 3: Greatest amount: 150 kg
Option 4: Step 1: 350 = 2(150) + 50
Step 2: 150 = 2(50) + 0
Step 3: Greatest amount: 150 kg
Correct Answer: Option 1
2. Pranay wants to stack few one-rupee coins and some five-rupee coins in such a way that:
a. Each stack has the same number of coins.
b. There is least number of stacks.
c. Each stack either has one rupee or five-rupee coins.
d. No coins are left over after creating stacks.
His first step to find the number of coins that should be in each stack is 195=1(180) +15. Given that he
has more of five-rupee coins than one-rupee coins, how many one-rupee coins stack can he make?
Option 1: 12
Option 2: 13
Option 3: 15
Option 4: 25
Correct Answer: Option 1
LOB: Apply Euclid Division Algorithm in order to prove results of positive integers in the form of ax+b where a
and b are constants
1. Given that p is a non-negative integer, which of these gives positive integers that are multiple of 5?
Option 1: 10p and 10p+2.
Option 2: 10p and 10p+3.
Option 3: 10p and 10p+4.
Option 4: 10p and 10p+5.
Correct Answer: Option 4
2. In the equation below, a, b, q, r are integers, 0≤r<b, a is a multiple of 3 and b=9.
a=bq+r
Which of the following forms represent a?
Option 1: Only 9q and 9q+3, as only these forms when divided by 3 gives r=0.
Option 2: Only 9q+1and 9q+4, as only these forms when divided by 3 gives r=1.
Option 3: Only 9q, 9q+3, and 9q+6, as only these forms when divided by 3 gives r=0.
Option 4: Only 9q+1, 9q+4, and 9q+7, as only these forms when divided by 3 gives r=1.
Correct Answer: Option 3
LOB: Use the Fundamental Theorem of Arithmetic in order to calculate HCF and LCM of the given numbers in
the context of the given problem
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