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MTH103Sciences3 Unitsintermediate

Elementary Mathematics III

This course, Elementary Mathematics III, is a 3-credit unit compulsory course designed for the first semester. It spans 15 weeks, requiring 65 hours of study over 13 weeks. The course aims to develop mathematical skills in vectors, straight lines, circles, and conic sections. Students will learn to apply vectors, form equations of straight lines, derive equations of circles, and identify conic sections through eccentricity.

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65h
Study Time
13
Weeks
5h
Per Week
intermediate
Math Level
Course Keywords
VectorsStraight LineCircleConic SectionsElementary Mathematics

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Vectors and Scalars

2

Vector Addition

3

Straight Lines

4

Circle Geometry

5

Conic Sections

6

Parabola

7

Ellipse

8

Hyperbola

Total Topics8 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (2 methods)

Tutor Marked Assignment (TMAs)

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Computer Based Test

Career Opportunities

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Engineering Technician

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Mathematics Teacher

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Data Analyst

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Financial Analyst

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Research Assistant

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Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringFinanceEducationResearchTechnology

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Course Guide

5h

Orientation and course guide

5 study hours
  • •Read the course guide and understand the course requirements.
  • •Familiarize yourself with the Learning Management System (LMS).
Week
2

Module 1: Vectors

10h

Unit 1: Vectors and Scalars

5 study hours
  • •Define scalar and vector quantities with examples.
  • •Represent vectors geometrically and understand different types of vectors.

Unit 2: Addition of Vectors

5 study hours
  • •Understand the triangle law of vector addition.
  • •Learn the parallelogram law of vector addition.
Week
3

Module 1: Vectors

10h

Unit 3: Component of a vector in two dimensions

5 study hours
  • •Identify coordinate unit vectors in two dimensions.
  • •Calculate the modulus of a position vector.

Unit 4: Component of a vector in three dimensions

5 study hours
  • •Identify coordinate unit vectors in three dimensions.
  • •Calculate the angle between a position vector.
Week
4

Module 1: Vectors

5h

Unit 4: Products of Two Vectors

5 study hours
  • •Calculate scalar products of vectors.
  • •Apply dot product to find angles between vectors.
Week
5

Module 2: The straight line

10h

Unit 1: Distance between two points

5 study hours
  • •Define coordinates of points.
  • •Determine the distance between two points using Cartesian coordinates.

Unit 2: Gradients of lines

5 study hours
  • •Calculate the gradient of a line through two points.
  • •Calculate the angle of slope of a line.
Week
6

Module 2: The straight line

5h

Unit 3: Equation of a line

5 study hours
  • •Find the equation of a straight line given its gradient and intercept.
  • •Find the equation of a straight line given two points.
Week
7

Module 3: The geometry of a circle

5h

Unit 1: Circle centred at the origin.

5 study hours
  • •Define a circle and identify its center and radius.
  • •Find the equation of a circle centered at the origin.
Week
8

Module 3: The geometry of a circle

5h

Unit 2: General equation of a circle

5 study hours
  • •Find the equation of a circle with center (h, k) and given radius.
  • •Find the general equation of a circle.
Week
9

Module 3: The geometry of a circle

5h

Unit 3: The equation of a tangent to a circle at given point

5 study hours
  • •Define a tangent to a circle and a point of tangency.
  • •State the properties of the tangent to a circle.
Week
10

Module 3: The geometry of a circle

5h

Unit 4: The equation of a normal to a circle at given point

5 study hours
  • •Find the parametric equations of a circle.
  • •Find the equations of tangent to the circle at (rcosθ, rsinθ).
Week
11

Module 4: Conic sections

5h

Unit 1: Parabola

5 study hours
  • •State the four types of conic sections.
  • •State the values of eccentricity for the conic sections.
Week
12

Module 4: Conic sections

5h

Unit 2: Ellipse

5 study hours
  • •Define and describe an ellipse.
  • •Identify the foci, vertices, axes, and center of an ellipse.
Week
13

Module 4: Conic sections

5h

Unit 3: Hyperbola

5 study hours
  • •Locate a hyperbola's vertices and foci.
  • •Write equations of hyperbolas in standard form.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review vector operations and practice problems from Units 1-4 extensively.

2

Create flashcards for different forms of straight-line equations (Unit 6) and their properties.

3

Practice deriving equations of circles (Units 7-9) from given parameters like center and radius.

4

Focus on understanding the concept of eccentricity and its role in defining conic sections (Units 11-13).

5

Solve numerous problems on identifying and graphing parabolas, ellipses, and hyperbolas.

6

Dedicate time to understanding the relationships between vertices, foci, and asymptotes of conic sections.

7

Create concept maps linking geometric properties to algebraic equations for all shapes.

8

Practice past examination questions to familiarize yourself with the exam format and question types.

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