Chapter 1: Algebra
- Algebraic Expressions, Mathematical Models, and Real Numbers
- Indices and Surds
- Factorization and Simplification
- Rationalization
ENGFF047 – Mathematics for Engineers
, Algebraic Expressions
• Algebra uses letters (e.g. 𝑥, 𝑦), called variables, to represent numbe
or quantities.
• Examples of algebraic expressions:
𝑥
𝑥 + 6, 𝑥 – 6, 6 𝑥, , 3𝑥 + 5, 𝑥 2 – 3, 𝑥+7
6
• Many algebraic expressions involve exponents.
Exponent or Index or Power
3
6 = 6 x 6 x 6
Base
Shorthand way of Normal representation
representation (Base multiplied exponent number of times)
ENGFF047 – Mathematics for Engineers
, Evaluating Algebraic Expressions
• Finding the value of the expression for a given value of the variable.
• Often involves more than one operation.
The Order of Operations Agreement
1. Perform operations within innermost parentheses, work outward.
If fractions are involved, treat the numerator and denominator as if they were each enclose
parentheses.
2. Evaluate all exponential expressions.
3. Perform multiplications and divisions as they occur, working from le
right.
4. Perform additions and subtractions as they occur, working from left
right.
ENGFF047 – Mathematics for Engineers
, Exercise
Evaluate each algebraic expression for the given value of the variable
1. 4 + 5( x – 7)5, for x = 10
2. x2 – 3( x – y), for x = 8 and y = 2
2x + 3y
3. x + 1 , for x = – 2 and y = 4
ENGFF047 – Mathematics for Engineers
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