Yakili | LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

Course / Course Details

LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

By - High School Mathematics
15 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

19 chapters
427 lectures
157 quizzes
166 Hours 40 Min total length

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1 The quadratic function (sketching the graph)

2 Min

The quadratic function (sketching the graph)

N/A

3 Finding the maximum and minimum points

3 Min

Finding the maximum and minimum points

4 Parabolas with horizontal and vertical shifts

3 Min

Parabolas with horizontal and vertical shifts

N/A

6 Use of the Discriminant

3 Min

Use of the Discriminant

7 Applications of Maximum and Minimum Values

3 Min

Applications of Maximum and Minimum Values

N/A

9 Quadratic Functions

3 Min

Quadratic Functions

10 Sum and Product of the Roots of Quadratic Equations

3 Min

Sum and Product of the Roots of Quadratic Equations

N/A

12 Quadratic Inequalities

3 Min

Quadratic Inequalities

13 Problems Leading to Inequalities

3 Min

Problems Leading to Inequalities

14 Basic Rules on Solving Inequalities

3 Min

Basic Rules on Solving Inequalities

15 Linear Inequalities

2 Min

Linear Inequalities

16 Quadratic Inequalities

3 Min

Quadratic Inequalities

17 Inequalities Involving Rational Functions

3 Min

Inequalities Involving Rational Functions

18 Inequalities Involving Modulus or Absolute Value Functions

3 Min

Inequalities Involving Modulus or Absolute Value Functions

19 System of Inequalities in Two Unknowns

4 Min

System of Inequalities in Two Unknowns

20 Graphs of Absolute Value Functions and Inequalities

2 Min

Graphs of Absolute Value Functions and Inequalities

21 Definition of Polynomials

2 Min

Definition of Polynomials

22 Addition and Subtraction of Polynomials

3 Min

Addition and Subtraction of Polynomials

23 Multiplication of Polynomials

3 Min

Multiplication of Polynomials

24 Division of Polynomials

2 Min

Division of Polynomials

25 Division Algorithm for Polynomials

3 Min

Division Algorithm for Polynomials

26 Remainder and Factor Theorem

3 Min

Remainder and Factor Theorem

27 Remainder and factor theorem (factor theorem)

3 Min

Remainder and factor theorem (factor theorem)

28 Polynomial equations (n-root theorem)

3 Min

Polynomial equations (n-root theorem)

29 Applications of the Remainder and Factor Theorems

3 Min

Applications of the Remainder and Factor Theorems

30 Factorisation of polynomial

3 Min

Factorisation of polynomial

31 Decomposition when degree of f (x) is less than degree of g (x)

3 Min

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

32 Decomposition when degree of f (x) is greater than or equal to g (x)

4 Min

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

33 Logic

3 Min

Logic

34 Truth Tables

3 Min

Truth Tables

35 Connection with Set Theory

3 Min

Connection with Set Theory

36 Implication (Conditional Statements)

3 Min

Implication (Conditional Statements)

37 Converse of a Conditional Statement Subject

3 Min

Converse of a Conditional Statement Subject

38 Logical Equivalence

3 Min

Logical Equivalence

39 Tautologies

2 Min

Tautologies

40 Special Types of Calculations of Arguements in the First Quadrant

4 Min

41 special types of calculation of arguements in the first quadrant [Quiz]

N/A

42 The nth root of complex numbers

4 Min

The nth root of complex number

43 The nth root of complex numbers [Quiz]

N/A

44 The Radian Measure

7 Min

The Radian Measure

45 THE RADIAN MEASURE [Quiz]

N/A

46 The second quadrant

4 Min

The second quadrant

47 THE SECOND QUADRANT [Quiz]

N/A

48 The exponential form of complex numbers

4 Min

the exponential form of complex numbers

49 The exponential form of complex numbers [Quiz]

N/A

50 The Discriminant of Quadratic Equations

9 Min

The Discriminant of Quadratic Equations

51 The Discriminant of Quadratic Equations [Quiz]

N/A

52 The argument of complex numbers

4 Min

53 The argument of complex numbers [Quiz]

N/A

54 Solving Problems Involving Quadratic inequalities

5 Min

55 Solving Problems Involving Quadratic inequalities [Quiz]

N/A

56 The first statement on angle properties

6 Min

57 The second statement on angle properties

6 Min

58 The third statement on angle properties

6 Min

59 Set notation and ordinary english

6 Min

60 The first theorem under tangents

4 Min

61 The unit vector in the direction of a given vector

4 Min

62 Calculations involving volume of revolution about a line

8 Min

63 Calculations on area betweeen two curves

6 Min

64 Calculations on indefinite integrals

2 Min

65 The argument of complex numbers

5 Min

The argument of complex numbers

66 Applications of volume generated by area between two curves

4 Min

67 Third theorem of tangent

7 Min

N/A

1 SOLVING LOGARITHMIC EQUATIONS

4 Min

SOLVING LOGARITHMIC EQUATIONS

N/A

3 CALCULATIONS INVOLVING SURDS

5 Min

CALCULATIONS INVOLVING SURDS

4 Second Law of Logarithms

6 Min

Second Law of Logarithms

N/A

6 Solving Problems involving First, Second and Third Law of Logarithms

5 Min

Solving Problems involving First, Second and Third Law of Logarithms

7 SOLVING PROBLEMS WITH INDICES

6 Min

SOLVING PROBLEMS WITH INDICES

8 More Problems on Change of Base of Logarithms

5 Min

More Problems on Change of Base of Logarithms

9 Introduction to The Naperian Log

6 Min

Introduction to The Naperian Log

10 HOW TO SOLVE SIMULTANEOUS EQUATIONS

7 Min

HOW TO SOLVE SIMULTANEOUS EQUATIONS

11 Equations Involving Absolute Value

9 Min

Equations Involving Absolute Value

12 LAWS OF INDICES-LAW

5 Min

13 Laws of indices 2

6 Min

14 WORKED EXAMPLE LAW OF INDICES

5 Min

15 The Sum and the Product of Two Squares

9 Min

The Sum and the Product of Two Squares

16 Graphical Illustration on the Inverse of a function

12 Min

Graphical Illustration on the Inverse of a function

17 Complementary angles

6 Min

Complementary angles

18 The Sum and the Difference of Two Cubes

11 Min

The Sum and the Difference of Two Cubes

19 The Sum and the Product of Two Squares

9 Min

The Sum and the Product of Two Squares

20 The Area of a Circle

4 Min

The Area of a Circle

21 Addition and subtraction of matrices

4 Min

Addition and subtraction of matrices

22 Completing the Square Method

10 Min

Completing the Square Method

23 Introduction to The Theorem of Quadratics

4 Min

Introduction to The Theorem of Quadratics

24 The Discriminant of Quadratic Equations

9 Min

The Discriminant of Quadratic Equations

25 The Sum and Products of Roots of a Quadratic Equation

6 Min

The Sum and Products of Roots of a Quadratic Equation

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

11 Min

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

27 Solving Quadratic Equations by Factorization Method

7 Min

Solving Quadratic Equations by Factorization Method

28 Solving Problems Involving Quadratic Inequalities

8 Min

Solving Problems Involving Quadratic Inequalities

29 Solving Examples

10 Min

Solving Examples

30 Introduction to Partial Fractions

6 Min

Introduction to Partial Fractions

31 Partial Fractions with Linear Factors

9 Min

Partial Fractions with Linear Factors

32 Third Law of Logarithms

5 Min

Third Law of Logarithms

33 Introduction to indices

4 Min

34 The Rules of Inequalities

6 Min

The Rules of Inequalities

35 Formula Method

9 Min

Formula Method

36 Index Notation

5 Min

37 Laws of Indices

5 Min

38 Applications of laws of Indices

5 Min

39 Exponential equations

5 Min

40 The graph

5 Min

41 DIVISION OF SURDS

5 Min

DIVISION OF SURDS

42 System of inequalities

5 Min

N/A

1 Bijective Functions

12 Min

Bijective Functions

N/A

3 The Domain of a Function

4 Min

The Domain of a Function

4 Surjective Functions

6 Min

Surjective Functions

N/A

6 Odd Functions

7 Min

Odd Functions

7 Introduction to Partial Fractions

6 Min

Introduction to Partial Fractions

N/A

9 Introduction to Algebraic Process

5 Min

Introduction to Algebraic Process

10 Periodicity of a function

5 Min

N/A

12 Absolute Value Functions

9 Min

Absolute Value Functions

N/A

19 Equations of the circle

3 Min

20 Equation of a circle which has the line joining points (x1,y1) and (x2,y2) as its diameter

4 Min

21 Equation of a circle which Passes through three given points.

4 Min

22 Geometric properties of a circle

3 Min

23 Intersection of a straight line with a circle

4 Min

24 Equation of a tangent to a circle

3 Min

25 Length of a tangent from external point to a circle

3 Min

26 Intersecting circles

3 Min

27 Condition for two circles to touch

3 Min

28 Orthogonal circles

3 Min

29 Radical axis of two circles

4 Min

30 Parametric coordinates of a curve

4 Min

31 The conjugate of complex number

3 Min

32 Definition (properties of i)

3 Min

33 Properties of the conjugate

3 Min

34 Addition and subtraction of complex numbers

3 Min

35 Multiplication of complex number(with a real number and complex number)

4 Min

36 Division of complex numbers

4 Min

37 Properties of the modulus

3 Min

38 The modulus of a complex number

3 Min

39 The triangle inequality

4 Min

1 Definition of polynomials

5 Min

N/A

3 Composition of functions

5 Min

4 Surjective, Injective and Bijective mappings

5 Min

N/A

6 Identity mapping

5 Min

7 Investigation of simple odd and even functions

5 Min

N/A

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

5 Min

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

5 Min

N/A

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

5 Min

13 Addition and subtraction of polynomials

5 Min

14 Multiplication of polynomials

5 Min

15 Division of polynomials

5 Min

16 Division of algorithm

5 Min

17 The Remainder and factor theorems (Remainder theorem)

5 Min

18 Remainder and factor theorem (factor theorem)

5 Min

19 Polynomial equations (n-root theorem)

5 Min

20 Algebra of polynomials

5 Min

21 Applications of the Remainder and Factor Theorem

5 Min

22 Factorisation of polynomials

5 Min

23 Remainder and factor theorem (Remainder theorem)

5 Min

24 Applications of the Remainder and Factor Theorems

5 Min

25 Factorisation of polynomial

5 Min

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

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 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 rates of change,

5 Min

2 Small Change

5 Min

3 percentage change

5 Min

4 tangents, normal

5 Min

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

5 Min

6 Rolle’s Theorem

5 Min

7 Mean value Theorem

5 Min

8 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

9 Introduction to Quadratic Equations

3 Min

Introduction to Quadratic Equations

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 Comparability of sets

5 Min

N/A

5 Cardinality of a set

5 Min

6 Power set

5 Min

7 Universal set

5 Min

8 Set operations

5 Min

9 De Morgan’s law

5 Min

10 Sets of numbers commonly used in Mathematics

5 Min

N/A

1 Graphs Of Absolute Value Functions and Inequalities

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 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

7 The binomial expansion/The validity of the expansion

5 Min

N/A

9 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

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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