YAKILI | LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

Course / Course Details

LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

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

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

6 The Radian Measure

7 Min

The Radian Measure

7 THE RADIAN MEASURE [Quiz]

N/A

9 The second quadrant

4 Min

The second quadrant

10 THE SECOND 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 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 Solving Problems Involving Quadratic inequalities

5 Min

30 Solving Problems Involving Quadratic inequalities [Quiz]

N/A

31 Inequalities involving the modulus or absolute value functions

5 Min

32 Inequalities involving the modulus or absolute value functions [Quiz]

N/A

33 Inequalities Involving rational functions

5 Min

34 Inequalities involving rational functions [Quiz]

N/A

35 Basic Rules on solving Inequalities

5 Min

36 Basic rules of solving inequalities [Quiz]

N/A

37 Linear Inequalities

5 Min

38 Linear inequalities [Quiz]

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 SOLVING PROBLEMS WITH INDICES

6 Min

SOLVING PROBLEMS WITH INDICES

12 More Problems on Change of Base of Logarithms

5 Min

More Problems on Change of Base of Logarithms

13 Introduction to The Naperian Log

6 Min

Introduction to The Naperian Log

14 HOW TO SOLVE SIMULTANEOUS EQUATIONS

7 Min

HOW TO SOLVE SIMULTANEOUS EQUATIONS

15 Equations Involving Absolute Value

9 Min

Equations Involving Absolute Value

16 LAWS OF INDICES-LAW

5 Min

17 Laws of indices 2

6 Min

18 WORKED EXAMPLE LAW OF INDICES

5 Min

19 The Sum and the Product of Two Squares

9 Min

The Sum and the Product of Two Squares

20 Graphical Illustration on the Inverse of a function

12 Min

Graphical Illustration on the Inverse of a function

21 Complementary angles

6 Min

Complementary angles

22 System of inequalities [Quiz]

N/A

23 The Sum and the Difference of Two Cubes

11 Min

The Sum and the Difference of Two Cubes

24 The Sum and the Difference of Two Cubes [Quiz]

N/A

25 The Sum and the Product of Two Squares

9 Min

The Sum and the Product of Two Squares

26 The Sum and the Product of Two Squares [Quiz]

N/A

27 The Area of a Circle

4 Min

The Area of a Circle

28 Addition and subtraction of matrices

4 Min

Addition and subtraction of matrices

29 Completing the Square Method

10 Min

Completing the Square Method

30 The Discriminant of Quadratic Equations

9 Min

The Discriminant of Quadratic Equations

31 The Sum and Products of Roots of a Quadratic Equation

6 Min

The Sum and Products of Roots of a Quadratic Equation

32 Solving Quadratic Equations by Factorization Method

7 Min

Solving Quadratic Equations by Factorization Method

33 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

34 Solving Problems Involving Quadratic Inequalities

8 Min

Solving Problems Involving Quadratic Inequalities

35 Solving Examples

10 Min

Solving Examples

36 Partial Fractions with Linear Factors

9 Min

Partial Fractions with Linear Factors

37 Introduction to The Theorem of Quadratics

4 Min

Introduction to The Theorem of Quadratics

38 Introduction to Partial Fractions

6 Min

Introduction to Partial Fractions

39 Formula Method

9 Min

Formula Method

40 Index Notation

5 Min

41 Laws of Indices

5 Min

42 Applications of laws of Indices

5 Min

43 Exponential equations

5 Min

44 The graph

5 Min

45 Third Law of Logarithms

5 Min

Third Law of Logarithms

46 The Rules of Inequalities

6 Min

The Rules of Inequalities

47 DIVISION OF SURDS

5 Min

DIVISION OF SURDS

48 Introduction to indices

4 Min

49 System of inequalities

5 Min

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 Remainder and factor theorem (Remainder theorem)

5 Min

25 Applications of the Remainder and Factor Theorems

5 Min

26 Factorisation of polynomial

5 Min

1 Bijective Functions

12 Min

Bijective Functions

N/A

3 Bijective Function [Quiz]

N/A

4 The Domain of a Function

4 Min

The Domain of a Function

N/A

6 Surjective Functions

6 Min

Surjective Functions

7 Odd Functions

7 Min

Odd Functions

N/A

9 Introduction to Partial Fractions

6 Min

Introduction to Partial Fractions

10 Introduction to Algebraic Process

5 Min

Introduction to Algebraic Process

N/A

12 Even Functions

6 Min

Even Functions

13 Even Functions [Quiz]

N/A

15 Periodicity of a function

5 Min

N/A

17 Surjective, Injective and Bijective mappings

5 Min

18 Domain, codomain and range (image set) of a function

5 Min

19 Parity of a function

N/A

21 Investigation of simple odd and even functions

5 Min

22 Composition of functions

5 Min

N/A

24 Identity mapping

5 Min

25 The inverse of a one-one function -Graphical and other representations of a function

5 Min

N/A

27 Graphical illustration of the relationship between a function and its inverse

5 Min

N/A

1 Use of partial fractions in summation of series

5 Min

2 Sequences

5 Min

N/A

4 Series

5 Min

N/A

6 Arithmetic Progression (AP)

5 Min

7 The nth term of an Arithmetic Progression

5 Min

8 Arithmetic Mean (AM)

5 Min

N/A

10 Sum of an A.P.

5 Min

N/A

12 Limit of a sequence

5 Min

13 Geometric Progression(G.P)

5 Min

N/A

15 The nth term of a G.Pc

5 Min

16 The geometric mean (G.M)

5 Min

N/A

18 Sum of a G.P

5 Min

19 Geometric Series

5 Min

N/A

21 Convergence of geometric sequence

5 Min

22 Limit of a sequence

5 Min

N/A

24 sequences diverging

5 Min

25 Convergence of geometric series Summation of simple finite series

5 Min

N/A

27 The sigma notation

5 Min

28 Summation of some Standard Series

5 Min

N/A

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

5 Min

2 General definition of a limit using Ɛ 𝑎𝑛𝑑 𝛿

5 Min

N/A

4 Uniqueness of limit

5 Min

N/A

6 Limit of sum, product and quotient

5 Min

7 Absolute Value Functions

9 Min

Absolute Value Functions

N/A

2 Partial order

5 Min

3 Total Order

5 Min

N/A

5 Strict Order

5 Min

6 Inclusion Diagram

5 Min

7 The notation of binary Relations

5 Min

N/A

9 Cartesian product of two sets

5 Min

10 Ordered Pairs

5 Min

N/A

12 Properties of relations

5 Min

13 Equivalence Relations

5 Min

N/A

15 Venn Diagram Illustration

5 Min

N/A

17 Partitions

5 Min

18 Ordered Relations

5 Min

N/A

20 Fundamental theorem on equivalence Relation

5 Min

N/A

1 Mensuration of the Circle -Length of arcs  r

5 Min

2 Area of sector

5 Min

3 Area of segment

5 Min

4 Sine and cosine formulae

5 Min

5 The General Angle

5 Min

6 Trigonometric Functions - Angles and their measures

5 Min

7 Graphs of Trigonometric Functions

5 Min

8 Simple Transformations of graphs of Trigonometric function

5 Min

9 Amplitude

5 Min

10 The six Trigonometric. Ratios

5 Min

11 Trigonometric ratios of complementary angles

5 Min

12 Trigonometric. Ratios for special angles

N/A

13 The Radian and degree as units for measuring angles

5 Min

N/A

1 Definition of a matrix

5 Min

2 Algebra of matrices

5 Min

3 Transpose of a matrix

5 Min

4 Determinant of a square matrix

5 Min

5 Properties of determinant

5 Min

6 Singular matrices

5 Min

7 Multiplicative Inverse of a 33matrix

5 Min

8 Applications of matrix products to a system of equations

5 Min

9 Applications of matrix products to transformations in space/in a plane

5 Min

10 Applications of inverse matrix

5 Min

11 Applications of matrices in calculating areas and volumes

5 Min

N/A

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 Introduction to Quadratic Equations

3 Min

Introduction to Quadratic Equations

2 rates of change,

5 Min

3 Small Change

5 Min

4 percentage change

5 Min

5 tangents, normal

5 Min

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

5 Min

7 Rolle’s Theorem

5 Min

8 Mean value Theorem

5 Min

9 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

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

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

1 Graphs Of Absolute Value Functions and Inequalities

5 Min

2 Graphs Of Absolute Value Functions and Inequalities [Quiz]

N/A

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 System of equations with 3 unknowns

5 Min

2 System of equations with 3 unknowns [Quiz]

N/A

3 Graphs and properties of quadratic Functions

5 Min

4 Graphs and properties of quadratic equations [Quiz]

N/A

5 Maxima and Minima

5 Min

6 Maxima and Minima [Quiz]

N/A

7 Use of the discriminant

5 Min

8 Use of the discriminant [Quiz]

N/A

9 The quadratic function (sketching the graph)

5 Min

10 The quadratic function (sketching the graph) [Quiz]

N/A

11 Parabolas with horizontal and vertical shifts

5 Min

12 Parabolas with horizontal and vertical shifts [Quiz]

N/A

13 Quadratic expressions

5 Min

14 Quadratic expression [Quiz]

N/A

15 Quadratic equations

5 Min

16 Quadratic equations [Quiz]

N/A

17 The quadratic formula

5 Min

18 The quadratic formula [Quiz]

N/A

19 Applications of Nature of roots

5 Min

20 Application of the nature roots [Quiz]

N/A

21 Line of symmetry of the graph of y f(x)

5 Min

22 Line of the graph of symmetric of yof(x) [Quiz]

N/A

23 Relationship between roots and coefficients of a quadratic equation

5 Min

24 Relationship between roots and coefficients of quadratic equations [Quiz]

N/A

25 Symmetric properties of the roots of a quadratic equation

5 Min

26 Symmetric properties of the roots of quadratic equation [Quiz]

N/A

27 Simple transformation [Quiz]

N/A

28 Simple transformations

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 Propositions, Composite statements

5 Min

N/A

3 Conjunction and disjunction -“If- then” statements: p⇒q Bi-conditional statements: p⇒q

5 Min

N/A

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

5 Min

6 LOGIC

5 Min

7 Basic concepts in logic

5 Min

N/A

9 A Statement and its negation

5 Min

N/A

1 Factorial Notation

5 Min

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

5 Min

3 Mutually exclusive situations

5 Min

4 Ordered arrangements

5 Min

5 Permutations of objects selected from a group

5 Min

6 Arrangement of like and unlike objects

5 Min

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

5 Min

8 Simple problems involving arrangements

5 Min

9 Combinations -Selection of objects from a group:

5 Min

10 Simple problems involving selections Partition theory in permutations and combinations.

5 Min

11 Fundamental Counting Principle

5 Min

N/A

1 Pair of lines

5 Min

2 erpendicular distance of a point from a line

5 Min

3 Reduction to Linear form

5 Min

4 Loci using Cartesian or parametric forms.

5 Min

5 Point and line Geometry

5 Min

6 The Equations of a Straight Line:

5 Min

N/A

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High School Mathematics

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