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Course / Course Details

UPPER SIXTH PURE MATHEMATICS WITH MECHANICS

  • High School Mathematics image

    By - High School Mathematics

  • 20 students
  • 50 Min
  • (0)

Course Requirements

Upper-Sixth Mathematics with Mechanics is a rigorous and comprehensive course designed to provide students with a deep understanding of advanced mathematical concepts and their applications in mechanics. This course is intended for students who have successfully completed Lower-Sixth Mathematics and are seeking to further develop their mathematical skills and knowledge. Throughout the course, students will explore various topics such as advanced calculus, differential equations, vectors, kinematics, dynamics, and statics. Emphasis will be placed on developing problem-solving skills and applying mathematical principles to real-world scenarios. To successfully complete Upper-Sixth Mathematics with Mechanics, students are required to attend all lectures, actively participate in class discussions, complete assigned readings, and engage in regular problem-solving exercises. 

Course Description

 UPPER-SIXTH MATHEMATICS WITH MECHANICS course is designed to provide students with an advanced understanding of mathematics and mechanics at the upper-sixth level. Through a comprehensive curriculum, students will delve into the intricate world of mathematical principles and their application in the field of mechanics. This course aims to equip students with the necessary skills and knowledge to excel in higher-level mathematics and mechanics, preparing them for further studies in engineering, physics, or related disciplines. 

Course Outcomes

Course Outline: UPPER-SIXTH MATHEMATICS WITH MECHANICS I. Introduction - Overview of the course - Importance of studying Upper-Sixth Mathematics with Mechanics - Goals and objectives II. Mechanics Fundamentals - Introduction to mechanics - Newton's laws of motion - Forces and motion - Equilibrium of particles - Work, energy, and power - Linear momentum and collisions III. Kinematics - One-dimensional motion - Projectile motion - Circular motion - Relative motion IV. Dynamics - Newton's second law - Frictional forces - Uniform circular motion - Centripetal force - Gravitational forces V. Statics - Equilibrium of rigid bodies - Moments and couples - Center of mass and centroid - Stability of equilibrium VI. Linear Motion - Linear motion with constant acceleration - Free fall and terminal velocity - Motion in a vertical circle VII. Circular Motion - Angular velocity and acceleration - Torque and rotational equilibrium - Rotational dynamics - Moment of inertia VIII. Oscillations and Waves - Simple harmonic motion - Damped and forced oscillations - Wave motion - Standing waves IX. Mathematical Methods - Vectors and vector algebra - Differentiation and integration techniques - Differential equations in mechanics X. Practical Applications - Application of mechanics principles in real-life scenarios - Engineering applications - Case studies and problem-solving exercises XI. Assessment and Evaluation - Grading criteria - Types of assessments (exams, quizzes, projects) - Weightage of each assessment - Evaluation methods XII. Resources and References - Recommended textbooks and study materials - Online resources and references - Additional reading materials and references Please note that this is a general course outline and may be subject to modifications based on specific curriculum requirements and teaching methodology.

Course Curriculum

  • 5 chapters
  • 195 lectures
  • 54 quizzes
  • 50 Min total length
Toggle all chapters
1 Equations of the circle: -Given centre and radius
5 Min


N/A


3 Equations of the circle - Given centre and radius [Quiz]
N/A


4 Given coordinates of the ends of a diameter
5 Min


N/A


6 Given coordinates of the ends of a diameter [Quiz]
N/A


7 Passing through three given points.
5 Min


N/A


9 Passing through three given points. [Quiz]
N/A


10 Intersection of a straight line with a circle
5 Min


N/A


12 Intersection of a straight line with a circle [Quiz]
N/A


13 Equation of a tangent to a circle
5 Min


N/A


15 Equation of a tangent to a circle [Quiz]
N/A


16 Length of a tangent from external point to a circle
5 Min


N/A


18 Length of a tangent from external point to a circle [Quiz]
N/A


19 Intersecting circles
5 Min


N/A


21 Intersecting circles [Quiz]
N/A


22 Condition for two circles to touch
5 Min


N/A


24 Condition for two circles to touch [Quiz]
N/A


25 Orthogonal circles
5 Min


N/A


27 Radical axis of two circles.
5 Min


28 The equation of a circle through the points of intersection of two given circles and a given point.
5 Min


N/A


N/A


1 Introduction to the Complex Number System
5 Min


N/A


3 Introducction to the Complex numbers system [Quiz]
N/A


4 The imaginary number i and its algebra -Complex Numbers
5 Min


N/A


6 The imaginary number i and its Algebra-Complex number [Quiz]
N/A


7 The conjugate of complex number
5 Min


N/A


9 The conjugate of complex number [Quiz]
N/A


10 Properties of the conjugate
5 Min


N/A


12 Properties of the conjugate [Quiz]
N/A


13 Addition and subtraction of complex numbers
5 Min


N/A


15 Addition and subtraction of complex numbers [Quiz]
N/A


16 Multiplication of complex number with a scalar
5 Min


N/A


18 Multiplication of complex number with a scalar [Quiz]
N/A


19 Multiplication of two complex numbers
5 Min


N/A


21 Multiplication of two complex numbers [Quiz]
N/A


22 Modulus and Argument of a Complex Number.
5 Min


N/A


24 Modulus and argument of a complex number [Quiz]
N/A


25 The triangle inequality
5 Min


N/A


27 The triangle inequality [Quiz]
N/A


28 The Argand Diagram
5 Min


29 The argand diagram [Quiz]
N/A


30 Modulus-Argument (Polar) form of a complex Number
5 Min


31 Complex Numbers
5 Min


32 Equality of Complex Numbers
5 Min


33 Complex conjugate
5 Min


34 Geometrical representation of a complex numbers
5 Min


35 Product and Quotient of Complex Numbers
5 Min


36 Square root of complex Numbers:
5 Min


37 Complex roots of a polynomial equation
5 Min


38 Simple equations and expansions
5 Min


39 Multiplication and Division in Polar form
5 Min


N/A


N/A


N/A


N/A


N/A


N/A


1 Vector representation
5 Min


2 Vector representation [Quiz]
N/A


3 Resolving a vector
5 Min


4 Resolving a vector [Quiz]
N/A


5 Cartesian vector notation
5 Min


6 Cartesian vector notation [Quiz]
N/A


7 Unit vector and direction vectors
5 Min


8 Unit vector and direction vectors [Quiz]
N/A


9 Vector equation of a line
5 Min


10 Vector equation of a line [Quiz]
N/A


11 A line through two points
5 Min


12 A line through two points [Quiz]
N/A


13 Recognising direction and finding points from the vector equation of a line
5 Min


14 Recognising direction and finding points from the vector equation of a line [Quiz]
N/A


15 The line of action of a force
5 Min


16 The line of action of a force [Quiz]
N/A


17 The equation of the path of a particle moving with constant velocity
5 Min


18 The equation of the path of a particle moving with constant velocity [Quiz]
N/A


19 Determination and resultant vectors
5 Min


20 Determination and resultant vectors [Quiz]
N/A


1 The argument of complex numbers
5 Min

The argument of complex numbers


2 the exponential form of complex numbers
4 Min

the exponential form of complex numbers


3 The second quadrant
4 Min

The second quadrant


4 The Radian Measure
7 Min

The Radian Measure


5 the polar or trigonometric form of complex numbers
5 Min

the polar or trigonometric form of complex numbers


6 The nth root of complex numbers
4 Min

The nth root of complex numbers


7 Special types of calculations of arguements in the first quadrant
3 Min

Special types of calculations of arguements in the first quadrant


8 Special Cases on the Properties of -i-
4 Min

Special Cases on the Properties of -i-


9 special case on the normal form of complexe numbers
4 Min

special case on the normal form of complexe numbers


10 Special Case On the Newton Raphsons Method
4 Min

Special Case On the Newton Raphsons Method


11 Special case on the multiplication of Complex Numbers
4 Min

Special case on the multiplication of Complex Numbers


12 Special Case On the Modullus Of Complex Numbers
3 Min

Special Case On the Modullus Of Complex Numbers


13 Special Case on the Location of roots
4 Min

Special Case on the Location of roots


14 Special Case on the division of Complex Numbers
3 Min

Special Case on the division of Complex Numbers


15 special case on second property of argument
5 Min

special case on second property of argument


16 special case on roots of complexe numbers
4 Min

special case on roots of complexe numbers


17 special case on problems with regards to exponential form of writting complexe numbers
4 Min

special case on problems with regards to exponential form of writting complexe numbers


18 special case on problems with regards to exponential form of writting complexe numbers
6 Min

special case on problems with regards to exponential form of writting complexe numbers


19 special case on interval bisection
3 Min

special case on interval bisection


20 Special Case on Equality of complex numbers
4 Min

Special Case on Equality of complex numbers


21 Special Case on Complex Conjugates
4 Min

Special Case on Complex Conjugates


22 special case on argan diagram
4 Min

special case on argan diagram


23 Special case of the third property of argument
3 Min

Special case of the third property of argument


24 Special case of acquiment in the second quadrant
4 Min

Special case of acquiment in the second quadrant


25 Roots of complex numbers
4 Min

Roots of complex numbers


26 Properties of i
6 Min

Properties of i


27 Properties of Conjugates
5 Min

Properties of Conjugates


28 Problems on the Properties of -i-
5 Min

Problems on the Properties of -i-


29 Problems involving the first quadrant
3 Min

Problems involving the first quadrant


30 Problems involving the first quadrant
5 Min

Problems involving the first quadrant


31 Polynomial Equations
5 Min

Polynomial Equations


32 Other Types of Problems Ivnolving Modulule of Complex Numbers
3 Min

Other Types of Problems Ivnolving Modulule of Complex Numbers


33 Other types of Problems inVolving properties of -i-
4 Min

Other types of Problems inVolving properties of -i-


34 other types of problems involving luci on an argan diagram
5 Min

other types of problems involving luci on an argan diagram


35 Other types Of Problems Involving Location of roots
3 Min

Other types Of Problems Involving Location of roots


36 Other types of Problems involving Equality of Complex Numbers
4 Min

Other types of Problems involving Equality of Complex Numbers


37 Other Types of Calculations Involving Division of complex numbers
3 Min

Other Types of Calculations Involving Division of complex numbers


38 Other types of calculations involving Addition And Subtraction of Complex Numbers
3 Min

Other types of calculations involving Addition And Subtraction of Complex Numbers


39 Other types of Calculations involvin the interval Bisection Method
3 Min

Other types of Calculations involvin the interval Bisection Method


40 other types of calculations on the exponential fom of complexe numbers
3 Min

other types of calculations on the exponential fom of complexe numbers


41 other type of calculations which on De moivres theorem
6 Min

other type of calculations which on De moivres theorem


42 Other type of calculations involving the Multiplication of Complex Numbers
3 Min

Other type of calculations involving the Multiplication of Complex Numbers


43 Other types of Problems inVolving properties of -i-
4 Min

Other types of Problems inVolving properties of -i-


44 other types of problems involving luci on an argan diagram
5 Min

other types of problems involving luci on an argan diagram


45 Other problems involving graphical method of coming out with approximate solutions
7 Min

Other problems involving graphical method of coming out with approximate solutions


46 Other Calculations Involving Neuteralson's Method
3 Min

Other Calculations Involving Neuteralson's Method


47 Other Calculations Involving Neuteralson's Method
3 Min

Other Calculations Involving Neuteralson's Method


48 other types of calculations involving roots of complex numbers
4 Min

other types of calculations involving roots of complex numbers


49 Numerical Methods (Ways And Methods
3 Min

Numerical Methods (Ways And Methods


50 normal form of complex numbers
3 Min

normal form of complex numbers


51 Newton Ralphson method
4 Min

Newton Ralphson method


52 Multiplication of Complex Numbers
6 Min

Multiplication of Complex Numbers


53 more calculations on the Nth root of complex numbers
7 Min

more calculations on the Nth root of complex numbers


54 more calculations on the Nth root of complex numbers
7 Min

more calculations on the Nth root of complex numbers


55 more calculations on De moivre's theorem
4 Min

more calculations on De moivre's theorem


56 More Calculations on the modullus of complex Numbers
3 Min

More Calculations on the modullus of complex Numbers


57 More Calculations on Equality of complex Numbers
4 Min

More Calculations on Equality of complex Numbers


58 More Calculations of Complex Conjugates
4 Min

More Calculations of Complex Conjugates


59 More Calculations involving the graprical method of coming up with approximate solutions
7 Min

More Calculations involving the graprical method of coming up with approximate solutions


60 More Calculations (Quadratic)
3 Min

More Calculations (Quadratic)


61 more calculation on the exponential form of complexe numbers
4 Min

more calculation on the exponential form of complexe numbers


62 More Calculation on Multiplication of Complex Numbers
4 Min

More Calculation on Multiplication of Complex Numbers


63 More Calculation on division of Complex Numbers
4 Min

More Calculation on division of Complex Numbers


64 More Calculation on Addition And Subtraction Of Complex Numbers
3 Min

More Calculation on Addition And Subtraction Of Complex Numbers


65 More Calculation Involving Location of roots
5 Min

More Calculation Involving Location of roots


66 Modullus of Complex Numbers
4 Min

Modullus of Complex Numbers


67 luci on an argan diagram
4 Min

luci on an argan diagram


68 Location of roots
6 Min

Location of roots


69 Introduction to the Interval Bisection Method of Finding Roots
3 Min

Introduction to the Interval Bisection Method of Finding Roots


70 Introduction to Complex Numbers
6 Min

Introduction to Complex Numbers


71 Graphical Method Of Locating roots
3 Min

Graphical Method Of Locating roots


72 Existence of roots
6 Min

Existence of roots


73 Equality of Complex Numbers
3 Min

Equality of Complex Numbers


74 Division Of Complex Numbers
6 Min

Division Of Complex Numbers


75 Division Of Complex Numbers
6 Min

Division Of Complex Numbers


76 De moivre's theorem
3 Min

De moivre's theorem


77 Continuation of problems on the graphical method of Finding Approximate solutions
7 Min

Continuation of problems on the graphical method of Finding Approximate solutions


78 Complex Conjugates
4 Min

Complex Conjugates


79 Calculations on the Moivre's Theorem
8 Min

Calculations on the Moivre's Theorem


80 calcutions on argan diagrams
4 Min

calcutions on argan diagrams


81 calculations which has to do with the polar form
4 Min

calculations which has to do with the polar form


82 calculations on roots of a complexe number
5 Min

calculations on roots of a complexe number


83 Calculations on Modullus of Complex Numbers
3 Min

Calculations on Modullus of Complex Numbers


84 Calculations on equality of complex Numbers
3 Min

Calculations on equality of complex Numbers


85 Calculations involving the Graphical Method of Aprroximate Solutions
5 Min

Calculations involving the Graphical Method of Aprroximate Solutions


86 Calculations involving the Graphical Method of Aprroximate Solutions
5 Min

Calculations involving the Graphical Method of Aprroximate Solutions


87 calculations involving the exponential form of writting complexe numbers
5 Min

calculations involving the exponential form of writting complexe numbers


88 Calculations Involving Location of Roots
3 Min

Calculations Involving Location of Roots


89 calculations involving a Loci on an argan diagram
6 Min

calculations involving a Loci on an argan diagram


90 calculation on 3rd property of arqument
4 Min

calculation on 3rd property of arqument


91 trigonometric form of complex numbers
5 Min

trigonometric form of complex numbers


92 Calculation Involving The Interval Bisection Method
4 Min

Calculation Involving The Interval Bisection Method


93 Calculation involving Complex Conjugates
4 Min

Calculation involving Complex Conjugates


94 argand diagram
3 Min

argand diagram


95 Approximate Solutions
4 Min

Approximate Solutions


96 Addition and Subtraction of Complex Numbers
4 Min

Addition and Subtraction of Complex Numbers


97 A loci of a circle
7 Min

A loci of a circle


98 3rd quadrant
3 Min

3rd quadrant


99 3rd quadrant
3 Min

3rd quadrant


100 Special case on Addition and Subtraction of Complex Numbers
3 Min

Special case on Addition and Subtraction of Complex Numbers


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High School Mathematics

Our High school mathematics Tutors plays a crucial role in equipping students with essential mathematical knowledge, problem-solving skills, and critical thinking abilities. 

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