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MTH103

Elementary Mathematics III

  • Sciences
  • 100 level
  • 3 credit units
  • 140 pages
  • 14 units

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.

About this course

Difficulty
Intermediate
Study hours
65 hours
Maths
Intermediate
Content
Theoretical, problem solving
Practical work
No
How it is assessed
  • Tutor Marked Assignment (TMAs)
  • Final Examination

One paragraph, so you can see how it reads

MTH103 · Unit 1: Vectors and Scalars

Module Introduction This module introduces you to two physical quantities which are scalars and vectors. It then presents addition of vectors, multiplication of a vector by a scalar and position vectors, thereby showing how the position vectors are used in component of a vector in two and three dimensions.

What you should be able to do

  1. Apply vectors in coordinate systems.
  2. Form equations of straight lines using points, gradient, and intercepts.
  3. Derive equations of circles from radius and center information.
  4. Identify conic sections using eccentricity values.
  5. Solve problems related to vectors, straight lines, circles, and conic sections.
  6. Apply geometric principles to solve mathematical problems.

What it prepares you for

Careers
  • Engineering Technician
  • Mathematics Teacher
  • Data Analyst
  • Financial Analyst
  • Research Assistant
Where it is applied
  • Engineering
  • Finance
  • Education
  • Research
  • Technology

Where it gets hard

The units students slow down on, and what makes each one heavy.

  • Module 3: The geometry of a circle

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

    Requires strong visualization skills and understanding of geometric relationships.

  • Module 4: Conic sections

    Unit 3: Hyperbola

    Requires understanding of algebraic manipulation and geometric interpretation.

A suggested way through it

Suggested

13 weeks, about 80 hours in total. Yours will differ.

  1. Week 1Course Guide
    • Orientation and course guide · 5 hours

      Read the course guide and understand the course requirements.. Familiarize yourself with the Learning Management System (LMS)..

  2. Week 2Module 1: Vectors
    • Unit 1: Vectors and Scalars · 5 hours

      Define scalar and vector quantities with examples.. Represent vectors geometrically and understand different types of vectors..

    • Unit 2: Addition of Vectors · 5 hours

      Understand the triangle law of vector addition.. Learn the parallelogram law of vector addition..

  3. Week 3Module 1: Vectors
    • Unit 3: Component of a vector in two dimensions · 5 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 hours

      Identify coordinate unit vectors in three dimensions.. Calculate the angle between a position vector..

  4. Week 4Module 1: Vectors
    • Unit 4: Products of Two Vectors · 5 hours

      Calculate scalar products of vectors.. Apply dot product to find angles between vectors..

  5. Week 5Module 2: The straight line
    • Unit 1: Distance between two points · 5 hours

      Define coordinates of points.. Determine the distance between two points using Cartesian coordinates..

    • Unit 2: Gradients of lines · 5 hours

      Calculate the gradient of a line through two points.. Calculate the angle of slope of a line..

  6. Week 6Module 2: The straight line
    • Unit 3: Equation of a line · 5 hours

      Find the equation of a straight line given its gradient and intercept.. Find the equation of a straight line given two points..

  7. Week 7Module 3: The geometry of a circle
    • Unit 1: Circle centred at the origin. · 5 hours

      Define a circle and identify its center and radius.. Find the equation of a circle centered at the origin..

  8. Week 8Module 3: The geometry of a circle
    • Unit 2: General equation of a circle · 5 hours

      Find the equation of a circle with center (h, k) and given radius.. Find the general equation of a circle..

  9. Week 9Module 3: The geometry of a circle
    • Unit 3: The equation of a tangent to a circle at given point · 5 hours

      Define a tangent to a circle and a point of tangency.. State the properties of the tangent to a circle..

  10. Week 10Module 3: The geometry of a circle
    • Unit 4: The equation of a normal to a circle at given point · 5 hours

      Find the parametric equations of a circle.. Find the equations of tangent to the circle at (rcosθ, rsinθ)..

  11. Week 11Module 4: Conic sections
    • Unit 1: Parabola · 5 hours

      State the four types of conic sections.. State the values of eccentricity for the conic sections..

  12. Week 12Module 4: Conic sections
    • Unit 2: Ellipse · 5 hours

      Define and describe an ellipse.. Identify the foci, vertices, axes, and center of an ellipse..

  13. Week 13Module 4: Conic sections
    • Unit 3: Hyperbola · 5 hours

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

Preparing for the exam

What to do
  • Review vector operations and practice problems from Units 1-4 extensively.
  • Create flashcards for different forms of straight-line equations (Unit 6) and their properties.
  • Practice deriving equations of circles (Units 7-9) from given parameters like center and radius.
  • Focus on understanding the concept of eccentricity and its role in defining conic sections (Units 11-13).
  • Solve numerous problems on identifying and graphing parabolas, ellipses, and hyperbolas.
  • Dedicate time to understanding the relationships between vertices, foci, and asymptotes of conic sections.
  • Create concept maps linking geometric properties to algebraic equations for all shapes.
  • Practice past examination questions to familiarize yourself with the exam format and question types.

Questions students ask about this course

What is MTH103 about?

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.

How many units does MTH103 have?

MTH103, Elementary Mathematics III, has 14 units across 4 modules, over 140 pages of course material. You can read it one unit at a time.

How many credit units is MTH103?

MTH103 carries 3 credit units, at 100 level in Sciences.

Is MTH103 hard?

MTH103 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical and problem solving work.

How long does MTH103 take to study?

About 65 hours of study, spread across its 14 units.

How is MTH103 assessed?

MTH103 is assessed by Tutor Marked Assignment (TMAs) and Final Examination.

What can I do with MTH103?

Engineering Technician, Mathematics Teacher, Data Analyst, Financial Analyst and Research Assistant.

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