Beginner Algebra Course Syllabus

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Module 1: Fundamentals of Algebra

Topics Covered:

1. What is Algebra?
   • Definition and Applications
2. Understanding Variables and Constants
3. Algebraic Expressions
   • Terms, Coefficients, and Like Terms
4. Introduction to Basic Operations
   • Addition, Subtraction, Multiplication, and Division of Algebraic Expressions

Practice Questions:

1. Identify the terms, coefficients, and constants in 5x+35x + 35x+3.
2. Simplify 3a+7a3a + 7a3a+7a.
3. If x=3x = 3x=3, evaluate 4x+24x + 24x+2.

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Module 2: Real Numbers and Basic Properties

Topics Covered:

1. Types of Numbers
   • Natural Numbers, Whole Numbers, Integers, Rational and Irrational Numbers
2. Properties of Operations
   • Commutative, Associative, and Distributive Properties
3. Order of Operations (BODMAS)

Practice Questions:

1. Simplify 2+3×42 + 3 \times 42+3×4.
2. Verify the distributive property for 3(a+b)3(a + b)3(a+b).
3. Identify whether 2\sqrt{2}2​ is a rational or irrational number.

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Module 3: Solving Simple Equations

Topics Covered:

1. Understanding Equality
2. Solving Linear Equations with One Variable
3. Applications of Linear Equations

Practice Questions:

1. Solve: x+5=12x + 5 = 12x+5=12.
2. Solve: 2x−3=72x – 3 = 72x−3=7.
3. If 3x+4=193x + 4 = 193x+4=19, find xxx.

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Module 4: Introduction to Graphs

Topics Covered:

1. Cartesian Plane
   • X-axis, Y-axis, and the Origin
2. Plotting Points
3. Graphs of Simple Linear Equations

Practice Questions:

1. Plot the points (2,3),(4,−1),(−2,5)(2, 3), (4, -1), (-2, 5)(2,3),(4,−1),(−2,5) on the graph.
2. Draw the graph of y=2x+1y = 2x + 1y=2x+1.
3. Determine the coordinates of the point where the graph of y=x+3y = x + 3y=x+3 meets the X-axis.

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Module 5: Introduction to Polynomials

Topics Covered:

1. Definition and Degree of Polynomials
2. Types of Polynomials
   • Monomials, Binomials, Trinomials
3. Addition and Subtraction of Polynomials

Practice Questions:

1. Identify the degree of the polynomial 5×3+2×2−45x^3 + 2x^2 – 45×3+2×2−4.
2. Simplify (3×2+4x)+(5×2−2x+1)(3x^2 + 4x) + (5x^2 – 2x + 1)(3×2+4x)+(5×2−2x+1).
3. Classify 7x+57x + 57x+5 as monomial, binomial, or trinomial.

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Module 6: Factorization

Topics Covered:

1. Common Factors and Grouping
2. Factorization of Simple Quadratic Expressions
3. Applications in Simplifying Expressions

Practice Questions:

1. Factorize: x2+5x+6x^2 + 5x + 6×2+5x+6.
2. Factorize: 3xy+6x3xy + 6x3xy+6x.
3. Simplify: x2+3xx\frac{x^2 + 3x}{x}xx2+3x​.

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Module 7: Word Problems in Algebra

Topics Covered:

1. Translating Word Problems into Equations
2. Solving Word Problems
3. Common Scenarios: Age, Distance, and Money Problems

Practice Questions:

1. The sum of two numbers is 15, and one number is 9. Find the other number.
2. A train travels 60 km in 2 hours. What is its speed?
3. If 5 pencils cost Rs. 20, what is the cost of 8 pencils?

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Module 8: Basics of Inequalities

Topics Covered:

1. Understanding Inequalities
2. Solving Linear Inequalities
3. Representing Inequalities on the Number Line

Practice Questions:

1. Solve: 2x−5>72x – 5 > 72x−5>7.
2. Represent x<3x < 3x<3 on the number line.
3. Solve and graph: −3≤x<2-3 \leq x < 2−3≤x<2.

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Module 9: Introduction to Quadratic Equations

Topics Covered:

1. Basics of Quadratic Equations
2. Solving Simple Quadratic Equations by Factorization

Practice Questions:

1. Solve: x2−9=0x^2 – 9 = 0x2−9=0.
2. Solve: x2+5x+6=0x^2 + 5x + 6 = 0x2+5x+6=0.
3. If x=2x = 2x=2, verify the equation x2+3x=10x^2 + 3x = 10×2+3x=10.

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Module 10: Final Review and Mock Test

Topics Covered:

1. Comprehensive Revision
2. Mixed Practice Questions
3. Mock Test with Real-Life Problem Solving

Mock Test Sample Questions:

1. Solve for xxx: 3x+7=223x + 7 = 223x+7=22.
2. Simplify: 4a2−2a+5−3a2+7a4a^2 – 2a + 5 – 3a^2 + 7a4a2−2a+5−3a2+7a.
3. Factorize: x2+4x−12x^2 + 4x – 12×2+4x−12.
4. Plot the graph of y=−x+4y = -x + 4y=−x+4.
5. Solve the word problem: A box contains 50 apples. If each person gets 5 apples, how many people can the box serve?

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Additional Materials

• Worksheets for practice
• Quizzes at the end of each module
• Algebra Tips and Tricks PDF

This syllabus ensures a gradual progression from the basics of algebra to slightly more advanced topics, with plenty of practice for mastery.