Chapter 1 of RIMC Math Chapter 1 Number Systems
Real Numbers :-
- Definition: Real numbers are numbers that can be represented on the number line.
- Types of Real Numbers:
- Natural Numbers (N): 1, 2, 3, ...
- Whole Numbers (W): 0, 1, 2, 3, ...
- Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational Numbers (Q): Numbers that can be expressed as p/q, where p and q are integers and q ≠ 0.
- Irrational Numbers: Numbers that cannot be expressed as p/q, where p and q are integers and q ≠ 0.
Properties of Real Numbers :-
- Commutativity: a + b = b + a, ab = ba
- Associativity: (a + b) + c = a + (b + c), (ab)c = a(bc)
- Distributivity: a(b + c) = ab + ac
- Identity: a + 0 = a, a × 1 = a
- Inverse: a + (-a) = 0, a × (1/a) = 1
Operations on Real Numbers :-
- Addition: a + b
- Subtraction: a - b
- Multiplication: a × b
- Division: a ÷ b
Laws of Exponents :-
- Product Rule: a^m × a^n = a^(m+n)
- Quotient Rule: a^m ÷ a^n = a^(m-n)
- Power Rule: (a^m)^n = a^(mn)
Roots :-
- Square Root: √a
- Cube Root: ∛a
- nth Root: ∜a
Rational Numbers :-
- Definition: Rational numbers are numbers that can be expressed as p/q, where p and q are integers and q ≠ 0.
- Types of Rational Numbers:
- Proper Fractions: p/q, where p < q
- Improper Fractions: p/q, where p ≥ q
- Mixed Fractions: a p/q
Decimal Representation :-
- Definition: Decimal representation of a number is its representation in the form of a + 0.b1b2b3...
- Types of Decimals:
- Terminating Decimals: Decimals that terminate after a finite number of digits.
- Non-Terminating Decimals: Decimals that do not terminate.
- Recurring Decimals: Decimals that repeat after a certain number of digits.
Important Formulae :-
- (a + b)^2 = a^2 + 2ab + b^2
- (a - b)^2 = a^2 - 2ab + b^2
- (a + b)(a - b) = a^2 - b^2
Key Points:
- Real numbers include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
- Properties of real numbers include commutativity, associativity, distributivity, identity, and inverse.
- Operations on real numbers include addition, subtraction, multiplication, and division.
- Laws of exponents include product rule, quotient rule, and power rule.
- Roots include square root, cube root, and nth root.
- Rational numbers can be expressed as p/q, where p and q are integers and q ≠ 0.
- Decimal representation of a number is its representation in the form of a + 0.b1b2b3...
Practice Questions:
1. Simplify: (2 + 3)^2
2. Find the value of x: 2x + 5 = 11
3. Simplify: (3^2 + 4^2) / (3 + 4)
4. Find the square root of: 256
5. Simplify: (2/3) × (3/4)
I hope these notes help you with your RIMC Math preparation! Let me know if you have any questions or need further clarification on any of the topics.
Here are the solutions to the practice questions:
Question 1: Simplify: (2 + 3)^2
Solution:
(2 + 3)^2 = 5^2
= 25
Question 2: Find the value of x: 2x + 5 = 11
Solution:
2x + 5 = 11
2x = 11 - 5
2x = 6
x = 6/2
x = 3
Question 3: Simplify: (3^2 + 4^2) / (3 + 4)
Solution:
(3^2 + 4^2) / (3 + 4)
= (9 + 16) / 7
= 25/7
Question 4: Find the square root of: 256
Solution:
√256 = √(16 × 16)
= 16
Question 5: Simplify: (2/3) × (3/4)
Solution:
(2/3) × (3/4)
= (2 × 3) / (3 × 4)
= 6/12
= 1/2
Here are some previous year questions (PYQs) for RIMC Math Chapter 1:
Question 1:
What is the value of x in the equation 2x + 5 = 11?
A) 2
B) 3
C) 4
D) 5
Answer: B) 3
Question 2:
Simplify: (3 + 4)^2
A) 49
B) 50
C) 51
D) 52
Answer: A) 49
Question 3:
Find the square root of 256.
A) 14
B) 15
C) 16
D) 17
Answer: C) 16
Question 4:
Simplify: (2/3) × (3/4)
A) 1/2
B) 1/3
C) 1/4
D) 2/3
Answer: A) 1/2
Question 5:
What is the value of (2^3 + 3^3) / (2 + 3)?
A) 5
B) 6
C) 7
D) 8
Answer: C) 7
Question 6:
Find the value of x in the equation x/2 + 3 = 5.
A) 4
B) 5
C) 6
D) 7
Answer: A) 4
Question 7:
Simplify: (5^2 - 3^2) / (5 + 3)
A) 4
B) 5
C) 6
D) 7
Answer: A) 4
Question 8:
What is the value of (2 + 3)^2 - (2 - 3)^2?
A) 16
B) 20
C) 24
D) 28
Answer: C) 24
Question 9:
Find the value of x in the equation 3x - 2 = 14.
A) 4
B) 5
C) 6
D) 7
Answer: B) 5
Question 10:
Simplify: (3/4) × (4/5)
A) 3/5
B) 3/4
C) 4/5
D) 1/2
Answer: A) 3/5
I hope these PYQs help you with your RIMC Math preparation! Let me know if you have any questions or need further clarification on any of the solutions.
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