PURE MATHEMATICS (FPMPOOO3) PDF
Introduction: This document provides an extensive overview of the Mathematics Pure course offered in the General Foundation Program at the University of Technology and Applied Sciences in the Sultanate of Oman. The course is structured into several chapters, each covering fundamental mathematical concepts.
Chapter 1: Graphs and Functions
- 1.1: Introduction to Graphs
- 1.2: Functions
- 1.4: Functions of Composition
- 1.5: Inverse Functions
Chapter 2: Quadratic Equations
- 2.1: Graphing Quadratic Functions
- 2.2: Logarithmic and Exponential Functions
- 2.3: Applications of Logarithmic and Exponential Functions
Chapter 3: Trigonometric Functions
- 3.1: Measures and Angles
- 3.2: Circular Functions
- 3.3: Trigonometric Identities
- 3.4: Difference and Sum Identities
Chapter 4: Oblique Triangles and Trigonometry
- 4.1: Inverse Trigonometric Functions
- 4.2: Solving Trigonometric Equations
- 4.3: Law of Sines for Non-right Triangles
- 4.4: Law of Cosines for Non-right Triangles
Chapter 5: Statistics
- 5.1: Central Tendency Measures
- 5.5: Summarizing Data into Graphs and Tables
Chapter 6: Probability
- 6.1: Basic Concepts of Probability
- 6.6: Using Probability with Combinations and Permutations
- 6.3: Introduction to GeoGebra
- 6.4: GeoGebra Applications
complete satisfactorily who student A should be able to:
(a) Demonstrate understanding of the definition of a graph and its function:
- Interpret and draw graphs to represent mathematical functions.
- Understand the relationship between input and output in a function.
(b) Solve quadratic equations using the quadratic formula:
- Apply the quadratic formula to find solutions for quadratic equations.
- Demonstrate proficiency in manipulating and solving quadratic equations.
(c) Define and manipulate logarithmic and exponential functions:
- Define logarithmic and exponential functions and their properties.
- Solve real-life problems involving logarithmic and exponential functions.
(d) Understand the relationship between logarithmic and exponential functions and their inverses:
- Demonstrate the inverse relationship between logarithmic and exponential functions.
- Solve problems related to the inverse relationship between logarithmic and exponential functions.
(e) Measure angles in radians and degrees and understand different types of angles:
- Define and measure angles in radians and degrees.
- Understand different types of angles and their properties.
(f) Analytically describe circular and trigonometric functions:
- Define circular and trigonometric functions analytically.
- Demonstrate understanding of their properties and applications.
(g) Demonstrate understanding of trigonometric identities:
- Understand and apply trigonometric identities in problem-solving.
- Demonstrate proficiency in manipulating trigonometric expressions.
(h) Use the law of sines and cosines to solve real-life problems involving triangles:
- Solve real-life problems involving triangles using the law of sines and cosines.
- Apply trigonometric concepts to analyze and solve problems.
(i) Use appropriate software to interpret graphs and equations:
- Utilize software tools to interpret and analyze mathematical graphs and equations.
(j) Understand basic concepts of descriptive statistics:
- Summarize data using mean, median, mode, and other descriptive statistics.
- Interpret and analyze simple graphs and charts.
(k) Compute basic probability using tree diagrams and concepts:
- Understand and apply basic concepts of probability.
- Compute probabilities of simple events using tree diagrams, combinations, and permutations.
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