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LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

  • High School Mathematics image

    By - High School Mathematics

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

Course Requirements

This course is designed to provide students with a comprehensive understanding of pure mathematics with a focus on statistical concepts. Through a rigorous curriculum, students will develop advanced mathematical skills and gain proficiency in statistical analysis. This course aims to equip students with the necessary knowledge and techniques required to solve complex mathematical problems and apply statistical methods in real-world scenarios. Prerequisites: 1. Completion of GCSE Mathematics or an equivalent qualification. 2. Proficiency in algebra, trigonometry, and calculus. 3. Basic knowledge of statistical concepts such as probability, data representation, and measures of central tendency. Course Objectives: 1. Develop a solid foundation in pure mathematics, including algebra, calculus, and trigonometry. 2. Understand and apply statistical concepts, including probability theory, data analysis, and hypothesis testing. 3. Enhance problem-solving skills through the application of mathematical techniques in statistical contexts. 4. Develop critical thinking and analytical skills necessary for mathematical and statistical reasoning. 5. Apply mathematical and statistical knowledge to real-world situations, such as analyzing data sets and making informed decisions

Course Description

This comprehensive course, Lower-Sixth Pure Mathematics with Statistics, offers students a rigorous and in-depth exploration of mathematical concepts and techniques, with a specific focus on statistics. Designed for aspiring mathematicians and those pursuing related fields, this course provides a solid foundation in pure mathematics while incorporating practical applications in statistical analysis. Through a series of engaging lectures, interactive exercises, and problem-solving tasks, students will develop their mathematical skills and gain a deep understanding of key statistical principles. Topics covered include advanced algebra, calculus, probability theory, hypothesis testing, and data analysis techniques. Emphasis is placed on the integration of statistical methods within the broader field of pure mathematics, enabling students to apply their knowledge to real-world scenarios and make informed decisions based on data. By the end of this course, students will have honed their analytical thinking, problem-solving, and critical reasoning abilities, equipping them with essential tools for success in higher education and professional endeavors. With a professional tone and expert instruction, Lower-Sixth Pure Mathematics with Statistics offers an enriching learning experience for those seeking to excel in the fascinating world of mathematics and statistics.

Course Outcomes

This course is designed to provide students with a comprehensive understanding of pure mathematics and its application in statistics. It aims to develop students' analytical and problem-solving skills, equipping them with the necessary tools to excel in both theoretical and practical aspects of mathematics and statistics. Through a combination of lectures, tutorials, and practical exercises, students will gain a solid foundation in key mathematical concepts and statistical techniques. Course Outline: 1. Introduction to Pure Mathematics - Number systems and their properties - Algebraic expressions and equations - Functions and their properties - Trigonometry and its applications 2. Calculus - Differentiation and integration - Applications of calculus in real-world problems - Techniques of differentiation and integration 3. Probability Theory - Basic concepts of probability - Probability distributions and their properties - Combinatorics and permutations - Conditional probability and independence 4. Statistical Analysis - Data collection and organization - Descriptive statistics: measures of central tendency and dispersion - Probability distributions: normal, binomial, and Poisson distributions - Hypothesis testing and confidence intervals

Course Curriculum

  • 20 chapters
  • 439 lectures
  • 204 quizzes
  • 166 Hours 40 Min total length
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1 special types of calculation of arguements in the first quadrant [Quiz]
N/A

N/A

3 The nth root of complex numbers
4 Min

The nth root of complex number

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

N/A

6 The Radian Measure
7 Min

The Radian Measure

7 THE RADIAN MEASURE [Quiz]
N/A

N/A

9 The second quadrant
4 Min

The second quadrant

10 THE SECOND QUADRANT [Quiz]
N/A

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 Discriminant of Quadratic Equations
9 Min

The Discriminant of Quadratic Equations

15 The Discriminant of Quadratic Equations [Quiz]
N/A

16 The second statement on angle properties
6 Min

17 The third statement on angle properties
6 Min

18 Set notation and ordinary english
6 Min

19 The first theorem under tangents
4 Min

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

21 Calculations involving volume of revolution about a line
8 Min

22 Calculations on area betweeen two curves
6 Min

23 Calculations on indefinite integrals
2 Min

24 The argument of complex numbers
5 Min

The argument of complex numbers

25 Applications of volume generated by area between two curves
4 Min

26 Third theorem of tangent
7 Min

27 The first statement on angle properties
6 Min

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

29 Basic Rules on solving Inequalities
5 Min

30 Basic rules of solving inequalities [Quiz]
N/A

31 Quadratic inequalities
5 Min

32 Quadratic inequalities [Quiz]
N/A

33 Linear Inequalities
5 Min

34 Linear inequalities [Quiz]
N/A

35 Inequalities involving the modulus or absolute value functions
5 Min

36 Inequalities involving the modulus or absolute value functions [Quiz]
N/A

37 Inequalities Involving rational functions
5 Min

38 Inequalities involving rational functions [Quiz]
N/A

39 System of inequalities
5 Min

40 System of inequalities [Quiz]
N/A

N/A

N/A

1 SOLVING LOGARITHNIC EQUATIONS
4 Min

SOLVING LOGARITHNIC EQUATIONS

N/A

3 SOLVING LOGARITHNIC EQUATIONS [Quiz]
N/A

4 CALCULATIONS INVOLVING SURDS
5 Min

CALCULATIONS INVOLVING SURDS

N/A

6 CALCULATIONS INVOLVING SURDS [Quiz]
N/A

7 Second Law of Logarithms
6 Min

Second Law of Logarithms

8 Second Law of Logarithms [Quiz]
N/A

9 Solving Problems involving First, Second and Third Law of Logarithms
5 Min

Solving Problems involving First, Second and Third Law of Logarithms

10 Solving Problems involving First, Second and Third Law of Logarithms [Quiz]
N/A

11 Index Notation
5 Min

12 Laws of Indices
5 Min

13 Applications of laws of Indices
5 Min

14 Exponential equations
5 Min

15 The graph
5 Min

16 Third Law of Logarithms
5 Min

Third Law of Logarithms

17 The Rules of Inequalities
6 Min

The Rules of Inequalities

18 SOLVING PROBLEMS WITH INDICES
6 Min

SOLVING PROBLEMS WITH INDICES

19 More Problems on Change of Base of Logarithms
5 Min

More Problems on Change of Base of Logarithms

20 Introduction to The Naperian Log
6 Min

Introduction to The Naperian Log

21 HOW TO SOLVE SIMULTANEOUS EQUATIONS
7 Min

HOW TO SOLVE SIMULTANEOUS EQUATIONS

22 Equations Involving Absolute Value
9 Min

Equations Involving Absolute Value

23 DIVISION OF SURDS
5 Min

DIVISION OF SURDS

N/A

N/A

26 Introduction to indices
4 Min

27 LAWS OF INDICES-LAW
5 Min

28 Laws of indices 2
6 Min

29 EXAMPLE OF LAWS OF INDICES
5 Min

1 Bijective Functions
12 Min

Bijective Functions

N/A

3 Bijective Function [Quiz]
N/A

4 Even Functions
6 Min

Even Functions

N/A

6 Even Functions [Quiz]
N/A

7 Domain, codomain and range (image set) of a function
5 Min

8 Parity of a function
N/A

N/A

10 Investigation of simple odd and even functions
5 Min

N/A

12 Composition of functions
5 Min

13 Identity mapping
5 Min

N/A

15 The inverse of a one-one function -Graphical and other representations of a function
5 Min

16 Graphical illustration of the relationship between a function and its inverse
5 Min

N/A

18 Periodicity of a function
5 Min

19 Surjective, Injective and Bijective mappings
5 Min

N/A

21 The Domain of a Function
4 Min

The Domain of a Function

22 Surjective Functions
6 Min

Surjective Functions

N/A

24 Odd Functions
7 Min

Odd Functions

N/A

N/A

27 Introduction to Partial Fractions
6 Min

Introduction to Partial Fractions

1 The quadratic function (sketching the graph)
5 Min

2 The quadratic function (sketching the graph) [Quiz]
N/A

3 Parabolas with horizontal and vertical shifts
5 Min

4 Parabolas with horizontal and vertical shifts [Quiz]
N/A

5 Quadratic expressions
5 Min

6 Quadratic expression [Quiz]
N/A

7 Quadratic equations
5 Min

8 Quadratic equations [Quiz]
N/A

9 The quadratic formula
5 Min

10 The quadratic formula [Quiz]
N/A

11 Applications of Nature of roots
5 Min

12 Application of the nature roots [Quiz]
N/A

13 Line of symmetry of the graph of y f(x)
5 Min

14 Line of the graph of symmetric of yof(x) [Quiz]
N/A

15 Relationship between roots and coefficients of a quadratic equation
5 Min

16 Relationship between roots and coefficients of quadratic equations [Quiz]
N/A

17 Symmetric properties of the roots of a quadratic equation
5 Min

18 Symmetric properties of the roots of quadratic equation [Quiz]
N/A

19 System of equations with 3 unknowns
5 Min

20 System of equations with 3 unknowns [Quiz]
N/A

21 Graphs and properties of quadratic Functions
5 Min

22 Graphs and properties of quadratic equations [Quiz]
N/A

23 Maxima and Minima
5 Min

24 Maxima and Minima [Quiz]
N/A

25 Simple transformations
5 Min

26 Simple transformation [Quiz]
N/A

27 Introduction to Algebraic Process
5 Min

Introduction to Algebraic Process

28 Use of the discriminant
5 Min

29 Use of the discriminant [Quiz]
N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

1 Equality of sets
5 Min

N/A

3 Equality of sets [Quiz]
N/A

4 Comparability of sets
5 Min

N/A

6 Cardinality of a set
5 Min

7 Power set
5 Min

8 Universal set
5 Min

9 Set operations
5 Min

10 De Morgan’s law
5 Min

11 Sets of numbers commonly used in Mathematics
5 Min

N/A

N/A

N/A

N/A

N/A

N/A

1 Graphs Of Absolute Value Functions and Inequalities
5 Min

2 Graphs Of Absolute Value Functions and Inequalities [Quiz]
N/A

1 Definition of polynomials
5 Min

N/A

3 Definition of polynomials [Quiz]
N/A

4 Addition and subtraction of polynomials
5 Min

N/A

6 Addition and subtraction of polynomials [Quiz]
N/A

7 Multiplication of polynomials
5 Min

N/A

9 Multiplication of polynomials [Quiz]
N/A

10 Division of polynomials
5 Min

N/A

12 Division of polynomials [Quiz]
N/A

13 Division of algorithm
5 Min

14 Division of algorithm [Quiz]
N/A

15 The Remainder and factor theorems (Remainder theorem)
5 Min

16 Remainder and factor theorem (Remainder theorem) [Quiz]
N/A

17 Remainder and factor theorem (factor theorem)
5 Min

18 Remainder and factor theorem (factor theorem) [Quiz]
N/A

19 Polynomial equations (n-root theorem)
5 Min

20 Polynomial equations (n-root theorem) [Quiz]
N/A

21 Algebra of polynomials
5 Min

22 Applications of the Remainder and Factor Theorem
5 Min

23 Factorisation of polynomials
5 Min

24 The Sum and the Product of Two Squares
9 Min

The Sum and the Product of Two Squares

25 Remainder and factor theorem (Remainder theorem)
5 Min

26 Applications of the Remainder and Factor Theorems
5 Min

27 Factorisation of polynomial
5 Min

1 Decomposition when degree of f(x)is less than degree of g(x)
5 Min

N/A

3 Decomposition when degree of f(x) is greater than or equal to g(x)
5 Min

N/A

1 LOGIC
5 Min

N/A

3 Basic concepts in logic
5 Min

N/A

5 A Statement and its negation
5 Min

N/A

7 Propositions, Composite statements
5 Min

N/A

9 Conjunction and disjunction -“If- then” statements: p⇒q Bi-conditional statements: p⇒q
5 Min

N/A

11 The converse of a conditional statement -The inverse of a conditional statement
5 Min

N/A

1 Binomial theorem for expansion of (𝑎 + 𝑏𝑥)𝑛, for positive integral indices n
5 Min

N/A

3 Pascal’s triangle for n ≤ 10
5 Min

N/A

5 -Binomial coefficients, general term for n > 0, r> 0 and r≤ 𝑛
5 Min

N/A

7 Binomial theorem for 𝑛𝜖Q
5 Min

N/A

9 The binomial expansion/The validity of the expansion
5 Min

N/A

11 Application to approximations
5 Min

N/A

1 Sequences
5 Min

N/A

3 Series
5 Min

N/A

5 Arithmetic Progression (AP)
5 Min

N/A

7 The nth term of an Arithmetic Progression
5 Min

N/A

9 Arithmetic Mean (AM)
5 Min

N/A

11 Sum of an A.P.
5 Min

N/A

13 Limit of a sequence
5 Min

N/A

15 Geometric Progression(G.P)
5 Min

N/A

17 The nth term of a G.Pc
5 Min

N/A

19 The geometric mean (G.M)
5 Min

N/A

21 Sum of a G.P
5 Min

N/A

23 Geometric Series
5 Min

N/A

25 Convergence of geometric sequence
5 Min

N/A

27 Limit of a sequence
5 Min

N/A

29 sequences diverging
5 Min

N/A

31 Convergence of geometric series Summation of simple finite series
5 Min

N/A

33 The sigma notation
5 Min

N/A

35 Summation of some Standard Series
50 Min

N/A

37 Use of partial fractions in summation of series
5 Min

N/A

1 LIMITS AND DIFFERENTIATION Limits of functions - Intuitive definition of limits
5 Min

N/A

3 General definition of a limit using Ɛ 𝑎𝑛𝑑 𝛿
5 Min

N/A

5 Uniqueness of limit
5 Min

N/A

7 Limit of sum, product and quotient
5 Min

N/A

9 Absolute Value Functions
9 Min

Absolute Value Functions

10 The Sum and the Product of Two Squares
9 Min

The Sum and the Product of Two Squares

11 The Sum and the Product of Two Squares [Quiz]
N/A

12 The Sum and the Difference of Two Cubes
11 Min

The Sum and the Difference of Two Cubes

13 The Sum and the Difference of Two Cubes [Quiz]
N/A

1 The notation of binary Relations
5 Min

N/A

3 Ordered Pairs
5 Min

N/A

5 Cartesian product of two sets
5 Min

N/A

7 Properties of relations
5 Min

N/A

9 Equivalence Relations
5 Min

N/A

11 Venn Diagram Illustration
5 Min

N/A

13 Partitions
5 Min

N/A

15 Fundamental theorem on equivalence Relation
5 Min

N/A

17 Ordered Relations
5 Min

N/A

19 Partial order
5 Min

N/A

21 Total Order
5 Min

N/A

23 Strict Order
5 Min

N/A

25 Inclusion Diagram
5 Min

N/A

1 Fundamental Counting Principle
5 Min

N/A

3 Factorial Notation
5 Min

N/A

5 Permutations -Successive operations in a row and in circular arrangements (independent situations)
5 Min

N/A

7 Mutually exclusive situations
5 Min

N/A

9 Ordered arrangements
5 Min

N/A

11 Permutations of objects selected from a group
5 Min

N/A

13 Arrangement of like and unlike objects
5 Min

N/A

15 Circular arrangements: (n 1)! 2 Consider arrangement in a circle and in a ring (like on beads)
5 Min

N/A

17 Simple problems involving arrangements
5 Min

N/A

19 Combinations -Selection of objects from a group:
5 Min

N/A

21 Simple problems involving selections Partition theory in permutations and combinations.
5 Min

N/A

1 The six Trigonometric. Ratios
5 Min

N/A

3 Trigonometric. Ratios for special angles
N/A

N/A

5 Trigonometric ratios of complementary angles
5 Min

N/A

7 The Radian and degree as units for measuring angles
5 Min

N/A

9 Mensuration of the Circle -Length of arcs  r
5 Min

N/A

11 Area of sector
5 Min

N/A

13 Area of segment
5 Min

N/A

15 Sine and cosine formulae
5 Min

N/A

17 The General Angle
5 Min

N/A

19 Trigonometric Functions - Angles and their measures
5 Min

N/A

21 Graphs of Trigonometric Functions
5 Min

N/A

23 Simple Transformations of graphs of Trigonometric function
5 Min

N/A

25 Amplitude
5 Min

26 The Area of a Circle
4 Min

The Area of a Circle

27 Graphical Illustration on the Inverse of a function
12 Min

Graphical Illustration on the Inverse of a function

28 Complementary angles
6 Min

Complementary angles

1 Point and line Geometry
5 Min

N/A

3 The Equations of a Straight Line:
5 Min

N/A

5 Pair of lines
5 Min

N/A

7 erpendicular distance of a point from a line
5 Min

N/A

9 Reduction to Linear form
5 Min

N/A

11 Loci using Cartesian or parametric forms.
5 Min

N/A

1 Definition of a matrix
5 Min

N/A

3 Algebra of matrices
5 Min

N/A

5 Transpose of a matrix
5 Min

N/A

7 Determinant of a square matrix
5 Min

N/A

9 Properties of determinant
5 Min

N/A

11 Singular matrices
5 Min

N/A

13 Multiplicative Inverse of a 33matrix
5 Min

N/A

15 Applications of matrix products to a system of equations
5 Min

N/A

17 Applications of matrix products to transformations in space/in a plane
5 Min

N/A

19 Applications of inverse matrix
5 Min

N/A

21 Applications of matrices in calculating areas and volumes
5 Min

N/A

23 Addition and subtraction of matrices
4 Min

Addition and subtraction of matrices

1 Geometric vectors and basic properties
5 Min

N/A

3 Algebraic operations of the addition of two vectors and the multiplication of a vector by a scalar, and their geometric significance
5 Min

N/A

5 The orthogonal unit vectors i, j, k and the Cartesian components of a vector.
5 Min

N/A

7 Orthogonal and parallel vectors
5 Min

N/A

9 Position vector and displacement vector
5 Min

N/A

11 Scalar product of two vectors, its geometrical significance and algebraic properties
5 Min

N/A

13 Application of scalar product
5 Min

N/A

15 -The equation of a line (i) through a point and parallel to a given vector (ii) through two given points
5 Min

N/A

17 Pair of lines
5 Min

N/A

19 Parallel and perpendicular lines
5 Min

N/A

21 Intersecting Lines
5 Min

N/A

23 Skew Lines
5 Min

N/A

25 Perpendicular distance from a point to a given Line
5 Min

N/A

27 Vector product of two vectors
5 Min

N/A

29 Triple product
5 Min

N/A

1 rates of change,
5 Min

N/A

3 Small Change
5 Min

N/A

5 percentage change
5 Min

N/A

7 tangents, normal
5 Min

N/A

9 local maxima and minima and points of inflexion. Monotonicity of a function (Decreasing and increasing functions)
5 Min

N/A

11 Rolle’s Theorem
5 Min

N/A

13 Mean value Theorem
5 Min

N/A

15 Curve sketching: stationary points, points of inflexion, intercepts with coordinate axes, asymptotes(vertical and horizontal only), chart of signs (Table of variation), investigation of the e
5 Min

N/A

17 The Sum and Products of Roots of a Quadratic Equation
6 Min

The Sum and Products of Roots of a Quadratic Equation

18 The Discriminant of Quadratic Equations
9 Min

The Discriminant of Quadratic Equations

19 Solving Quadratic Equations by Factorization Method
7 Min

Solving Quadratic Equations by Factorization Method

20 Solving Problems Involving The Sum and Products of Roots of a Quadratic Equation 2_1
11 Min

Solving Problems Involving The Sum and Products of Roots of a Quadratic Equation 2_1

21 Solving Problems Involving Quadratic Inequalities
8 Min

Solving Problems Involving Quadratic Inequalities

22 Solving Examples
10 Min

Solving Examples

23 Partial Fractions with Linear Factors
9 Min

Partial Fractions with Linear Factors

24 Introduction to The Theorem of Quadratics
4 Min

Introduction to The Theorem of Quadratics

25 Introduction to Quadratic Equations
3 Min

Introduction to Quadratic Equations

26 Introduction to Partial Fractions
6 Min

Introduction to Partial Fractions

27 Formula Method
9 Min

Formula Method

28 Completing the Square Method
10 Min

Completing the Square Method

1 Integration as the reverse of differentiation
5 Min

N/A

3 Indefinite and definite integrals
5 Min

N/A

5 Techniques of Integration (Decomposition into partial fractions, linear and nonlinear substitution)
5 Min

N/A

7 Integration by parts
5 Min

N/A

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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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  • Duration 166 Hours 40 Min

  • Lectures 439 lessons

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  • Category: Lowersixth science

  • 204 Quizzes

  • Language: English

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