CHAPTER – 1
CHAPTER – 1
By the end of this chapter, learners should be able to:
Perform Basic Algebraic Operations
Add, subtract, multiply, and divide algebraic expressions.
Apply rules for signs when performing multiplication and division.
Simplify Algebraic Fractions
Simplify and manipulate algebraic fractions using fundamental principles.
Understand and Apply Algebraic Identities
Use key algebraic identities
Factorize polynomials using different methods.
Work with Exponents and Indices
Apply the laws of exponents, including:
Transform and Rearrange Formulas
Make a given variable the subject of a formula.
Apply algebraic manipulation to real-world formulas.
Solve Simple and Quadratic Equations
Solve linear equations using algebraic techniques.
Solve quadratic equations using: Factoring, Completing the square and The quadratic formula
By learning these objectives, learners will develop a strong foundation in algebra, enabling them to solve mathematical problems with confidence and apply algebraic concepts in advanced studies or real-life applications.
(i) Subsitution
(ii) Elimination
(1) FACTORS
(2) COMPLETING THE SQUARE
(3) FORMULA
In this chapter, we explored fundamental algebraic concepts and techniques essential for solving mathematical problems.
Basic Algebraic Operations
Addition, subtraction, multiplication, and division of algebraic expressions were introduced with examples.
The rules of signs in multiplication and division were emphasized.
Fractions and Factoring
Simplification of algebraic fractions was covered, including methods for handling complex rational expressions.
Factoring techniques, such as common factor extraction, difference of squares, and trinomial factorization, were demonstrated.
Indices and Exponents
The laws of exponents were explored, covering multiplication, division, and power rules.
Special cases such as zero and negative exponents were explained.
Transformation of Formulas
Methods for rearranging equations to isolate a specific variable were discussed.
Practical applications in real-world formulas were demonstrated.
Solving Equations
Linear equations were solved using algebraic manipulation.
Quadratic equations were addressed using factoring, completing the square, and the quadratic formula.
Simultaneous Equations
The substitution and elimination methods were used to solve equations with two variables.
Word problems involving simultaneous equations were introduced.
Application in Word Problems
Algebraic equations were applied to real-life problems such as age, speed, distance, and time calculations.