CIE IGCSE Mathematics (0580) Introduction to algebra Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Introduction to algebra Study Notes
LEARNING OBJECTIVE
- Introduction to Algebra
Key Concepts:
- Introduction to Algebra
- Substituting Numbers into Expressions and Formulas
Introduction to Algebra
Introduction to Algebra
1. Using Letters to Represent Generalised Numbers
In algebra, letters (also called variables) are used to represent numbers. They allow us to write general rules or relationships that work for many values.
For example, the expression \( 2x \) means “2 times some number \( x \)”. If \( x = 3 \), then \( 2x = 6 \).
Common Algebraic Notations:
- \( a + b \): Add two numbers
- \( ab \) or \( a \times b \): Multiply \( a \) and \( b \)
- \( a^2 \): Square of a number
- \( \frac{a}{b} \): Division of \( a \) by \( b \)
Example :
Evaluate \( 3x + 4 \) when \( x = 5 \)
▶️ Answer/Explanation
Substitute \( x = 5 \):
\( 3(5) + 4 = 15 + 4 = 19 \)
Answer: 19
Example:
Write an expression for the perimeter of a square with side length \( s \).
▶️ Answer/Explanation
A square has 4 equal sides.
Perimeter = \( s + s + s + s = 4s \)
Answer: \( 4s \)
Substituting Numbers into Expressions and Formulas
Substituting Numbers into Expressions and Formulas
Substitution is the process of replacing a variable (letter) in an algebraic expression or formula with a specific numerical value.
Why Is It Useful?
Substitution helps evaluate expressions or apply formulas in practical problems. For example, in a formula like \( A = lw \) (area = length × width), you can substitute values for \( l \) and \( w \) to find the area.
Steps for Substitution:
- Identify the value(s) given for each variable.
- Replace the variable(s) with the value(s) inside brackets or directly.
- Use correct order of operations (BODMAS/BIDMAS).
Key Tips:
- Put substituted values in brackets, especially for negative numbers.
- Always follow the order: brackets, powers, multiplication/division, then addition/subtraction.
- Watch out for signs: e.g., \( -3^2 \) is not the same as \( (-3)^2 \).
Example :
Evaluate \( 5x – 2 \) when \( x = 4 \)
▶️ Answer/Explanation
\( 5(4) – 2 = 20 – 2 = 18 \)
Answer: 18
Example :
Evaluate \( A = \frac{1}{2}bh \) when \( b = 10 \) and \( h = 7 \)
▶️ Answer/Explanation
\( A = \frac{1}{2} \times 10 \times 7 = 5 \times 7 = 35 \)
Answer: 35