📘 Review Exercise 1
Learn and practice Class 9 Mathematics Review Exercise 1 on Real Numbers with step-by-step solutions. This page includes free downloadable notes and comprehensive review questions covering all concepts from Chapter 1 as per the PECTAA 2025 syllabus.
Quick Links:
Chapter 1
Real Numbers
Chapter 2
Logarithms
Chapter 3
Sets and Functions
Chapter 4
Factorization and Algebraic Manipulation
Chapter 5
Linear Equations and Inequalities
Chapter 6
Trigonometry
Chapter 7
Coordinate Geometry
Chapter 8
Logic
Chapter 9
Similar Figures
Chapter 10
Graphs of Functions
Chapter 11
Loci and Construction
Chapter 12
Information Handling
Chapter 13
Probability
Review Exercise 1 - Real Numbers
This review exercise provides comprehensive practice covering all concepts from Chapter 1: Real Numbers.
Review Exercise 1 consolidates all the important concepts covered in Chapter 1, providing students with a comprehensive assessment of their understanding of real numbers. This exercise helps reinforce learning and identify areas that need more practice.
The review covers distributive property verification, associative property verification, rational numbers, trichotomy property, finding rational numbers between given numbers, simplification of radicals, word problems, and financial mathematics.
Key Topics Covered in Review
- Verification of distributive property with fractions
- Verification of associative property with fractions
- Properties of rational numbers
- Trichotomy property of real numbers
- Finding rational numbers between given numbers
- Simplification of radical expressions
- Consecutive integer problems
- Word problems with algebraic equations
- Simple interest calculations
Important Note:
This review exercise serves as excellent preparation for chapter tests and examinations. It covers all fundamental concepts of real numbers that form the foundation for advanced mathematical topics.
Sample Problems from Review Exercise
Problem 2: Verification of Distributive Property
If $a=\frac{3}{2}$, $b=\frac{5}{3}$ and $c=\frac{7}{5}$, then verify that:
(i) $a(b+c) = ab + ac$
(ii) $(a+b)c = ac + bc$
1
Substitute the values
Replace $a$, $b$, and $c$ with their given fractional values in both sides of the equations.
2
Simplify both sides
Perform the operations on both sides of the equation separately.
3
Compare results
Verify that the results on both sides of the equation are equal.
The distributive property is verified when both sides yield the same result.
Problem 3: Verification of Associative Property
If $a=\frac{4}{3}$, $b=\frac{5}{2}$ and $c=\frac{7}{4}$, then verify the associative property of real numbers with respect to addition and multiplication.
1
Associative property of addition
Verify that $a + (b + c) = (a + b) + c$
2
Associative property of multiplication
Verify that $a(bc) = (ab)c$
3
Simplify both sides
Perform the operations on both sides of each equation separately.
The associative property is verified when both grouping methods yield the same result.
Problem 8: Consecutive Odd Integers
The sum of three consecutive odd integers is 51. Find the three integers.
1
Define the variables
Let the first odd integer be $x$. Since they are consecutive odd integers, the next two will be $x+2$ and $x+4$.
2
Set up the equation
The sum of the three integers equals 51: $x + (x+2) + (x+4) = 51$
3
Solve the equation
Simplify and solve for $x$, then find all three integers.
The three consecutive odd integers can be found by solving the linear equation.
Problem 10: Simple Interest Calculation
Salma invested Rs. 3,50,000 in a bank, which paid simple profit at the rate of $7\frac{1}{4}\%$ per annum. After 2 years, the rate was increased to $8\%$ per annum. Find the amount she had at the end of 7 years.
1
Calculate profit for first 2 years
Use the simple interest formula: $P_1 = \frac{Principal \times Rate \times Time}{100}$
2
Calculate profit for next 5 years
Use the same formula with the new interest rate for the remaining time period.
3
Find total amount
Add the principal amount and both profit amounts to find the total amount after 7 years.
The total amount is the sum of principal and all interest earned over 7 years.
Created by Hira Science Academy | Aligned with PECTAA 2025 Syllabus