Essential Number Properties and Percentage Calculations
1. Prime Factorisation, HCF, and LCM
- Prime Factorisation:
- Breaking a number down into a product of its prime factors (usually using factor trees).
- Example: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
- Highest Common Factor (HCF):
- The largest factor that divides two or more numbers.
- Method (Venn Diagram): Multiply the numbers found in the intersection (overlap) of the prime factor sets.
- Lowest Common Multiple (LCM):
- The smallest multiple shared by two or more numbers.
- Method (Venn Diagram): Multiply all numbers
Simulation Modeling and Statistical Analysis Techniques
Fundamentals of Models and Simulation
A model is a simplified representation of a real-world system developed to understand, analyze, or predict its behavior. A model contains only the important characteristics of the actual system and ignores unnecessary details.
Models can be classified into several types. A physical model represents a system physically, such as a prototype of a machine. A mathematical model represents the system using equations, variables, and relationships. A deterministic model
Read MoreOperations Research and Queuing Theory Fundamentals
Operations Research for Decision-Making
Operations Research (OR) is a scientific approach to decision-making that involves the application of mathematical models, statistics, and algorithms to help organizations solve complex problems and improve performance.
Steps to Solve a Model
- Formulate the Problem: Define the problem clearly. Identify the objective (maximize profit, minimize cost), the decision variables (what to decide), and the constraints (limitations).
- Construct a Mathematical Model: Represent
College Algebra Math 1314 Essential Formulas
Radical Equations (\(x – \sqrt{\text{expr}} = c\)):
Isolate root \(\rightarrow \) square both sides \(\rightarrow \) solve quadratic \(\rightarrow \)Always check for extraneous solutions
Fractional Exponents (\((ax+b)^{1/3} + c = d\)):
Isolate exponent term \(\rightarrow \) cube both sides to eliminate the \(1/3\) power \(\rightarrow \) solve for \(x\).Rational Functions (\(\frac{\text{top}}{\text{bottom}}\)):
Set \(\text{bottom} \neq 0\). Solve to find excluded
Probability Formulas and Combinatorics Reference
Probability Formulas and Counting Techniques
1. Basic Probability Rules (7.2)
Probability of an Event: P(A) = (Number of favorable outcomes) / (Total number of outcomes) = n(A) / n(E)
Probability Range: 0 ≤ P(A) ≤ 1
P(A) = 0 means the event is impossible.
P(A) = 1 means the event is certain to occur.
Complementary Events (Not A): P(A’) = 1 – P(A) OR P(A) + P(A’) = 1
General Addition Formula (For any two events A and B): P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Mutually Exclusive Events: If A and B cannot
Market Research Methods and Business Strategies
1. Role of Market Research and Methods Used
Market research is the process of collecting, recording, and analyzing data about customers, competitors, and the market for a product. It helps businesses find out what consumers like or dislike, identify market size, predict future demand changes, and find their unique selling point (USP).
There are two main types of data collected:
- Quantitative research: Numerical data that can be put into tables, charts, or graphs.
- Qualitative research: Information about