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upper sixth pure Mathematics with statistics

  • High School Mathematics image

    By - High School Mathematics

  • 6 students
  • 166 Hours 40 Min
  • (0)

Course Requirements

Upper-Sixth Mathematics with Statistics 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 STATISTICS 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 Statistics 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

  • 11 chapters
  • 328 lectures
  • 114 quizzes
  • 166 Hours 40 Min total length
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1 calculations which has to do with the polar form
4 Min


2 Calculations involving Newton Raphson's Method
6 Min


3 The second Quadrant
4 Min


4 The Radian Measure
7 Min


5 The polar or trigonometric form of complex numbers
5 Min


6 The nth root of complex numbers
4 Min


7 The first quadrant
4 Min


8 The exponential form of complex numbers
4 Min


9 The argument of complex numbers
5 Min


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


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


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


13 Special Case On the Newton Raphsons Method
5 Min


14 Special case on the multiplication of Complex Numbers
4 Min


15 special case on the moivres theorem
4 Min


16 Special Case On the Modullus Of Complex Numbers
3 Min


17 Special Case on the Location of roots
4 Min


18 Special Case on the division of Complex Numbers
3 Min


19 special case on second property ofargument
5 Min


20 special case on roots of complexe numbers
4 Min


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


22 special case on luci on an argan diagram
6 Min


23 special case on interval bisection
3 Min


24 Special Case on Equality of complex numbers
4 Min


25 more calculations on the luci of an argand diagram
5 Min

more calculations on the luci of an argand diagram


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

special case on the normal form of complexe numbers


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

Special Cases on the Properties of -i-


3 Special case on the properties of -i- [Quiz]
N/A


4 The second quadrant
4 Min

The second quadrant


5 The second quadrant [Quiz]
N/A


6 the polar or trigonometric form of complex numbers
5 Min

the polar or trigonometric form of complex numbers


7 The polar or trigonometric form of complex numbers [Quiz]
N/A


8 The nth root of complex numbers
4 Min

The nth root of complex numbers


9 The nth root of complex numbers [Quiz]
N/A


10 The first quadrant
4 Min

The first quadrant


11 The first quadrant [Quiz]
N/A


12 The exponential form of complex numbers
4 Min

the exponential form of complex numbers


13 The exponential form of complex numbers [Quiz]
N/A


14 The argument of complex numbers
5 Min

The argument of complex numbers


15 The argument of complex numbers [Quiz]
N/A


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

Special types of calculations of arguements in the first quadrant


17 Special types of calculations of arguments in the first quadrant [Quiz]
N/A


18 special case on problems with regards to exponential form of writing complexe numbers
4 Min

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


19 Special case on problems with regards to exponential form of writing complexe numbers [Quiz]
N/A


20 The Radian Measure
7 Min


21 The unit vector in the direction of a given vector
4 Min


22 The Area of segment
7 Min


23 The Area of sector
5 Min


24 Multiplication of a vector by a matrixmp4
5 Min


25 Introduction to circle theorems
5 Min


26 Completing the Square Method
10 Min


27 Introduction to Circles and Parts of Circles
3 Min


28 Division of surds
5 Min


29 Complementary angles
6 Min


30 Special Case On the Newton Raphsons Method
4 Min

Special Case On the Newton Raphsons Method


31 Special case on the multiplication of Complex Numbers
4 Min

Special case on the multiplication of Complex Numbers


32 Special Case on the division of Complex Numbers
3 Min

Special Case on the division of Complex Numbers


33 Special Case on Equality of complex numbers
4 Min

Special Case on Equality of complex numbers


34 special case on the moivres theorem
4 Min

special case on the moivres theorem


35 Special Case on the Location of roots
4 Min

Special Case on the Location of roots


36 special case on roots of complexe numbers
4 Min

special case on roots of complexe numbers


37 special case on second property of argument
5 Min

special case on second property of argument


38 Special Case On the Modullus Of Complex Numbers
3 Min

Special Case On the Modullus Of Complex Numbers


39 special case on luci on an argan diagram
6 Min

special case on luci on an argan diagram


40 special case on interval bisection
3 Min

special case on interval bisection


41 Special Case on Complex Conjugates
4 Min

Special Case on Complex Conjugates


42 special case on argan diagram
4 Min

special case on argan diagram


43 Special case of the third property of argument
3 Min

Special case of the third property of argument


44 special case on luci on an argan diagram
6 Min

special case on luci on an argan diagram


45 Other types Of Problems Involving Location of roots
3 Min

Other types Of Problems Involving Location of roots


46 Special case of acquiment in the second quadrant
4 Min

Special case of acquiment in the second quadrant


47 Roots of complex numbers
4 Min

Roots of complex numbers


48 Properties of Conjugates
5 Min

Properties of Conjugates


49 Properties of i
6 Min

Properties of i


50 Problems on the Properties of -i-
5 Min

Problems on the Properties of -i-


51 Problems involving the first quadrant
3 Min

Problems involving the first quadrant


52 Polynomial Equations
5 Min

Polynomial Equations


53 Other Types of Problems Involving Modulule of Complex Numbers
3 Min

Other Types of Problems Involving Modulule of Complex Numbers


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

other types of problems involving luci on an argan diagram


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

Other types of Problems involving Equality of Complex Numbers


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

other types of calculations on the exponential fom of complexe numbers


57 other types of calculations on the exponential form of complexe numbers
3 Min

other types of calculations on the exponential form of complexe numbers


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

Other Types of Calculations Involving Division of complex numbers


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

Other types of calculations involving Addition And Subtraction of Complex Numbers


60 Other types of Calculations involving the interval Bisection Method
3 Min

Other types of Calculations involving the interval Bisection Method


61 other type of calculations associated with on De moivres theorem
6 Min

other type of calculations associated with on De moivres theorem


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

Other type of calculations involving the Multiplication of Complex Numbers


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

Other problems involving graphical method of coming out with approximate solutions


64 Other Calculations Involving Neuteralson's Method
3 Min

Other Calculations Involving Neuteralson's Method


65 more calculations on the luci of an argand diagram
5 Min

more calculations on the luci of an argand diagram


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

other types of calculations involving roots of complex numbers


67 Numerical Methods (Ways And Methods
3 Min

Numerical Methods (Ways And Methods


68 normal form of complex numbers
3 Min

normal form of complex numbers


69 Newton Ralphson method
4 Min

Newton Ralphson method


70 Multiplication of Complex Numbers
6 Min

Multiplication of Complex Numbers


71 More Calculation on division of Complex Numbers
4 Min

More Calculation on division of Complex Numbers


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

more calculations on the Nth root of complex numbers


73 More Calculations (Quadratic)
3 Min

More Calculations (Quadratic)


74 More Calculations on the modullus of complex Numbers
3 Min

More Calculations on the modullus of complex Numbers


75 more calculations on the argand diagram
6 Min

more calculations on the argand diagram


76 More Calculations on Equality of complex Numbers
4 Min

More Calculations on Equality of complex Numbers


77 more calculations on De moivre's theorem
4 Min

more calculations on De moivre's theorem


78 More Calculations of Complex Conjugates
4 Min

More Calculations of Complex Conjugates


79 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


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

more calculation on the exponential form of complexe numbers


81 More Calculation on Multiplication of Complex Numbers
4 Min

More Calculation on Multiplication of Complex Numbers


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

More Calculation on Addition And Subtraction Of Complex Numbers


83 More Calculation Involving Location of roots
5 Min

More Calculation Involving Location of roots


84 Modullus of Complex Numbers
4 Min

Modullus of Complex Numbers


85 Location of roots
6 Min

Location of roots


86 luci on an argan diagram
4 Min

luci on an argan diagram


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

Introduction to the Interval Bisection Method of Finding Roots


88 Introduction to Complex Numbers
6 Min

Introduction to Complex Numbers


89 Existence of roots
6 Min

Existence of roots


90 Graphical Method Of Locating roots
3 Min

Graphical Method Of Locating roots


91 Equality of Complex Numbers
3 Min

Equality of Complex Numbers


92 Division Of Complex Numbers
6 Min

Division Of Complex Numbers


93 De moivre's theorem
3 Min

De moivre's theorem


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

Continuation of problems on the graphical method of Finding Approximate solutions


95 Complex Conjugates
4 Min

Complex Conjugates


96 calculations on argan diagrams
4 Min

calculations on argan diagrams


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

calculations which has to do with the polar form


98 Calculations on the Moivre's Theorem
8 Min

Calculations on the Moivre's Theorem


99 calculations on roots of a complexe number
5 Min

calculations on roots of a complexe number


100 Calculations on Multiplication Of Complex Numbers
3 Min

Calculations on Multiplication Of Complex Numbers


101 Calculations on Modullus of Complex Numbers
3 Min

Calculations on Modullus of Complex Numbers


102 Calculations on equality of complex Numbers
3 Min

Calculations on equality of complex Numbers


103 Calculations on equality of complex Numbers
3 Min

Calculations on equality of complex Numbers


104 calculations involving a Loci on an argan diagram
6 Min

calculations involving a Loci on an argan diagram


105 Calculations on Division Of Complex Numbers
4 Min

Calculations on Division Of Complex Numbers


106 Calculations on Division Of Complex Numbers
4 Min

Calculations on Division Of Complex Numbers


107 Calculation involving Complex Conjugates
4 Min

Calculation involving Complex Conjugates


108 Calculations involving the Graphical Method of Aprroximate Solutions
5 Min

Calculations involving the Graphical Method of Aprroximate Solutions


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

calculations involving the exponential form of writting complexe numbers


110 Calculations Involving Location of Roots
3 Min

Calculations Involving Location of Roots


111 calculation on 3rd property of arqument
4 Min

calculation on 3rd property of arqument


112 Calculation Involving The Interval Bisection Method
4 Min

Calculation Involving The Interval Bisection Method


113 argand diagram
3 Min

argand diagram


114 Approximate Solutions
4 Min

Approximate Solutions


115 Addition and Subtraction of Complex Numbers
4 Min

Addition and Subtraction of Complex Numbers


116 A loci of a circle
7 Min

A loci of a circle


117 3rd quadrant
3 Min

3rd quadrant


118 3rd property of argument
3 Min

3rd property of argument


119 trigonometric form of complexe numbers
5 Min

trigonometric form of complexe numbers


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

Special case on Addition and Subtraction of Complex Numbers


121 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


122 The Circumference of a Circle
6 Min


1 Introduction to circle theorems.m4v
5 Min


N/A


3 Introduction to Circles and Parts of Circles.m4v
5 Min


4 The Circumference of a Circle
5 Min


5 Equations of the circle - Given centre and radius
5 Min


N/A


7 Given coordinates of the ends of a diameter
5 Min


N/A


9 Radical axis of two circles.
5 Min


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


N/A


N/A


N/A


N/A


N/A


N/A


N/A


N/A


1 Scatter diagram
5 Min


2 Scatter diagram [Quiz]
N/A


3 Regression function *Linear correlation and regression lines
5 Min


4 Regression functions *linear correlation and regression line [Quiz]
N/A


5 Least square regression lines
5 Min


6 Least square regression line [Quiz]
N/A


7 covariance
5 Min


8 Covariance [Quiz]
N/A


9 Regression coefficient
5 Min


10 Regression coefficient [Quiz]
N/A


11 calculating the equation of the least square regression lines
5 Min


12 Calculating the equation of the least square regression line [Quiz]
N/A


13 The product –moment correlation coefficient, r
5 Min


14 The product - moment correlation coefficient r [Quiz]
N/A


15 Spearman’s coefficient of Rank correlation and its significance and limitations
5 Min


16 Spear man's rank correlation coefficient and its significance and limitations [Quiz]
N/A


17 Kendall’s Rank correlation coefficient, its use and limitations
5 Min


N/A


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1 Definition of hypothesis and why test hypothesis
5 Min


2 Definition of hypothesis and why test hypothesis [Quiz]
N/A


3 The role of the null and alternative hypotheses in significance testing
5 Min


4 The role of Null and alternatives hypothesis in significant testing [Quiz]
N/A


5 Type I and Type II errors
5 Min


6 Type I and Type II errors [Quiz]
N/A


7 Significance level (critical values and critical regions)
5 Min


8 Significance level (critical values and critical regions) [Quiz]
N/A


9 Hypothesis of test procedure
5 Min


10 Hypothesis of test procedure [Quiz]
N/A


11 Significance testing of a hypothetical value for probability and for the mean of Poisson distribution
5 Min


12 Significance testing of a hypothetical value for probability and for the mean of poisson distribution [Quiz]
N/A


13 Significance testing for a population mean and the difference between two means using large scale(using central limit theorem)
5 Min


N/A


N/A


N/A


17 Significance testing for population mean and the difference between two mean using large scale(using central limit theorem) [Quiz]
N/A


1 Sampling with or without replacement from a finite population
5 Min


N/A


3 Random sampling and random number tables
5 Min


4 Sampling of attributes
5 Min


N/A


6 Sampling from an infinite population
5 Min


7 The sample mean
5 Min


N/A


9 Sampling methods
5 Min


10 Estimation of population parameters
5 Min


N/A


12 Point estimation-unbiased estimator
5 Min


13 Interval estimation (confidence intervals)
5 Min


N/A


15 Confidence interval for the population mean, population variance known
5 Min


16 Confidence interval for the population mean, population variance unknown
5 Min


N/A


18 Confidence interval for the difference between two populations.
5 Min


N/A


N/A


N/A


N/A


N/A


24 The central limit theorem
5 Min


N/A


26 The distribution of the sample mean
5 Min


N/A


N/A


N/A


N/A


N/A


1 The Probability density function of a continuous random variable
5 Min


N/A


3 Expectation, variance and mode of a continuous discrete random variable
5 Min


N/A


5 The cumulative distribution function
5 Min


N/A


7 The median and the other quartiles
5 Min


N/A


1 The exponential distribution including its mean an variance
5 Min


2 The uniform or rectangular distribution
5 Min


3 mean and variance.
5 Min


4 The use of the normal distribution as:  an approximation of the binomial with application of continuity correction  an approximation of the Poisson distribution with the application of cont
5 Min


N/A


N/A


N/A


N/A


N/A


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N/A


1 The binomial distribution -mean and variance
5 Min


2 cumulative binomial probability tables
5 Min


3 The uniform distribution and derivation of its expectation and variance
5 Min


4 The geometric distribution
5 Min


5 mean and variance
5 Min


6 Unit interval
5 Min


7 use of the poisson distribution as an approximation of the binomial distribution
5 Min


8 cumulative Poisson probability table
5 Min


9 Distribution of two independent Poisson variables
5 Min


N/A


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1 Elementary notions of discrete probability distributions.
5 Min


N/A


3 The probability mass function (p.m.f) or probability density function (p.d.f) and the probability distribution.
5 Min


N/A


5 The expectation of a random variable E(X)
5 Min


N/A


7 The expectation of any function of X, E[g(x)]
5 Min


N/A


9 The properties of the expectation.
5 Min


N/A


11 The variance Var(X) of X and its properties
5 Min


N/A


13 The cumulative distribution function of a discrete random variable
5 Min


N/A


15 The mode and median of a discrete random variable
5 Min


N/A


17 Moment generating functions
5 Min


N/A


1 Probability terminology
5 Min


2 Empirical or experimental method of obtaining probabilities (tossing coins and dice, drawing cards...).
5 Min


3 Possibility space and probability space for such experiments
5 Min


4 Classical definition of probability
5 Min


5 Probability of an event
5 Min


6 Probability laws - Limit law (probability scale)
5 Min


7 Complementary events
5 Min


8 The occurrence of only one of two events
5 Min


9 Mutually exclusive events
5 Min


10 Conditional probability
5 Min


11 Independent events and their applications
5 Min


12 Probability Trees
5 Min


13 Use of permutations and combinations to calculate probability Bayes’ theorem
5 Min


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High School Mathematics

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