YAKILI | LOWER SIXTH PURE MATHEMATICS WITH STATISTICS

Course / Course Details

LOWER SIXTH PURE MATHEMATICS WITH STATISTICS

By - High School Mathematics
5 students
166 Hours 40 Min
(0)

Course Requirements

LOWER-SIXTH PURE MATHEMATICS WITH STATISTICS Course Description: 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

18 chapters
489 lectures
236 quizzes
166 Hours 40 Min total length

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1 Introduction to Quadratic Equations

5 Min

N/A

3 Introduction to Algebraic Process

5 Min

4 Solving Problems Involving The Sum and Products of Roots of a Quadratic Equation 2_1.m4v

5 Min

N/A

6 Solving Quadratic Equations by Factorization Method

5 Min

7 Solving Quadratic Equations by Factorization Method

5 Min

N/A

9 Solving Examples

5 Min

10 The quadratic function (sketching the graph)

5 Min

N/A

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

N/A

13 Introduction to The Theorem of Quadratics

5 Min

N/A

15 Introduction to the theorem of Quadratics [Quiz]

N/A

16 Maxima and Minima

5 Min

N/A

18 Maxima and Minima [Quiz]

N/A

19 The Discriminant of Quadratic Equations.m4v

5 Min

N/A

21 The discriminant of quadratic equations [Quiz]

N/A

22 Quadratic equations

5 Min

N/A

24 Quadratic equations [Quiz]

N/A

25 The quadratic formula

5 Min

N/A

27 The quadratic formula [Quiz]

N/A

28 Quadratic expressions

5 Min

N/A

30 Quadratic expressions [Quiz]

N/A

31 System of equations with 3 unknowns

5 Min

N/A

33 System of equation with 3 unknowns [Quiz]

N/A

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

5 Min

N/A

36 line of symmetry of the gragh of yof(x) [Quiz]

N/A

37 FACTORISATION METHOD

5 Min

N/A

39 Factorisation method [Quiz]

N/A

40 Graphs and properties of quadratic Functions

5 Min

N/A

42 Graghs and properties of quadratic functions [Quiz]

N/A

43 The Sum and Products of Roots of a Quadratic Equation.m4v

5 Min

44 Sum and product of the roots of quadratic equation [Quiz]

N/A

45 Applications of nature of roots

5 Min

46 The Sum and the Product of Two Squares.m4v

5 Min

47 Simple transformations

5 Min

48 Completing the Square Method.m4v

5 Min

49 Equations Involving Absolute Value

9 Min

Equations Involving Absolute Value

50 Relationship between roots and coefficients of a quadratic equation

5 Min

51 The Sum and the Difference of Two Cubes

5 Min

52 Solving quadratic equations using formula methods

9 Min

Solving quadratic equations using formula methods

53 Solving quadratic equations using formula methods

9 Min

Solving quadratic equations using formula methods

54 Solving Problems involving The Sum and Products of Roots of a Quadratic Equation

5 Min

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

5 Min

56 Formula Method

5 Min

1 The Sum and Products of Roots of a Quadratic Equation

5 Min

N/A

3 The Sum and Products of Roots of a Quadratic Equation [Quiz]

N/A

4 The Rules of Inequalities

5 Min

N/A

6 Solving Problems Involving Quadratic Inequalities

5 Min

7 Basic Rules on solving Inequalities

5 Min

N/A

9 Basic rules on solving inequalities [Quiz]

N/A

10 Linear Inequalities

5 Min

N/A

12 Linear inequalities [Quiz]

N/A

13 Quadratic inequalities

5 Min

N/A

15 Quadratic inequalities [Quiz]

N/A

16 Inequalities Involving rational functions

5 Min

17 Inequalities involving rational functions [Quiz]

N/A

18 Inequalities involving the modulus or absolute value

5 Min

19 Inequalities involving the modulus or absolute values [Quiz]

N/A

20 System of inequalities

5 Min

21 System of inequalities [Quiz]

N/A

22 Absolute Value Functions

5 Min

N/A

1 The Discriminant of Quadratic Equations

5 Min

N/A

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

5 Min

4 SOLVING LOGARITHNIC EQUATIONS

5 Min

N/A

6 Second Law of Logarithms

5 Min

7 HOW TO SOLVE SIMULTANEOUS EQUATIONS

5 Min

N/A

9 Introduction to The Naperian Logarithm

5 Min

10 More Problems on Change of Base of Logarithms

5 Min

11 Index Notation

5 Min

N/A

13 Laws of Indices

5 Min

14 Applications of laws of Indices

5 Min

N/A

16 Exponential equations

5 Min

17 The graph

5 Min

N/A

19 Surds -Rational and irrational numbers

5 Min

20 Surds - calculations involving surds .m4v

5 Min

N/A

22 DIVISION OF SURDS.m4v

5 Min

DIVISION OF SURDS

23 Rationalisation of denominators

5 Min

N/A

25 Introduction to The Naperian Log

5 Min

26 Logarithms - Common logarithms

5 Min

N/A

28 Laws of Logarithms

5 Min

N/A

30 Second Law of Logarithms.m4v

5 Min

31 Third Law of Logarithms.m4v

5 Min

32 Logarithmic equations

5 Min

N/A

34 More problems on change of Base of Logarithms.m4v

5 Min

35 Natural Logarithms Graphs - Logarithmic equations

5 Min

N/A

37 Applications of laws of logarithms

5 Min

N/A

39 CALCULATIONS INVOLVING SURDS

5 Min

CALCULATIONS INVOLVING SURDS

40 CALCULATIONS INVOLVING SURDS

5 Min

N/A

45 SOLVING PROBLEMS WITH INDICES

5 Min

1 The Sum and the Difference of Two Cubes

5 Min

N/A

3 The Sum and the Product of Two Squares

5 Min

4 LIMITS AND DIFFERENTIATION Limits of functions

5 Min

5 Intuitive definition of limits

5 Min

N/A

7 Uniqueness of limit

5 Min

N/A

9 Limit of sum, product and quotient

5 Min

10 Derivatives -The derivative defined as a limit

5 Min

N/A

12 Differentiation from first principles

5 Min

13 The gradient of a tangent as the limit of the gradient of a chord

5 Min

N/A

15 Differentiation of standard functions (Polynomial, Trigonometric logarithmic, exponential functions)

5 Min

16 Differentiation of composite functions

5 Min

N/A

18 Differentiation of sums, products and quotients

5 Min

19 Second derivative

5 Min

N/A

21 Differentiation of inverse functions (restricted to inverse trigonometric functions)

5 Min

22 Differentiation of functions expressed parametrically (two dimensions only)

5 Min

N/A

24 Differentiation of functions expressed implicitly (two dimensions only)

5 Min

25 Applications of differentiation - rates of change,

5 Min

N/A

27 Small Change

5 Min

28 Percentage change

5 Min

N/A

30 Tangents, normal,

5 Min

31 Local maxima and minima and points of inflexion.

5 Min

N/A

33 Monotonicity of a function (Decreasing and increasing functions)

5 Min

34 Rolle’s Theorem

5 Min

N/A

36 Mean value Theorem

5 Min

37 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

38 INTEGRATION Integration as the reverse of differentiation

5 Min

39 Indefinite and definite integrals

5 Min

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

5 Min

41 Integration by parts

5 Min

42 Absolute Value Functions

9 Min

Absolute Value Functions

N/A

1 Odd Functions

5 Min

2 Definition of Polynomials

5 Min

3 Definition of polynomials [Quiz]

N/A

4 Addition and subtraction of polynomials

5 Min

5 Addition and Subtraction of polynomials [Quiz]

N/A

6 Multiplication of polynomials

5 Min

7 Multiplication of polynomials [Quiz]

N/A

8 Division of polynomials

5 Min

9 Divisions of Polynomials [Quiz]

N/A

10 Polynomial equations (n-root theorem)

5 Min

11 Polynomial equation (n-root theorem) [Quiz]

N/A

12 The Remainder and factor theorems

5 Min

13 The remainder and factor theorem [Quiz]

N/A

14 Applications of the Remainder and Factor

5 Min

15 Application of the remainder and factor [Quiz]

N/A

16 Algebra of polynomials

5 Min

17 Algebra of polynomials [Quiz]

N/A

18 Factorisation of polynomials

5 Min

19 Factorisation of polynomials [Quiz]

N/A

1 Graphical Illustration on the Inverse of a function

5 Min

N/A

3 Bijective functions

12 Min

Bijective Functions

4 Surjective Functions

5 Min

N/A

6 Injective Functions. (incomplete video)mp4

5 Min

7 Domain of a function

5 Min

8 EVEN FUNCTIONS

6 Min

Even Functions

N/A

10 Graphical and other representations of a function

5 Min

11 Odd Functions

5 Min

N/A

13 Composition of functions

5 Min

14 Identity mapping

5 Min

N/A

16 The inverse of a one-one function

5 Min

N/A

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

5 Min

19 Continuous Functions - Discontinuity

5 Min

N/A

21 Periodicity of a function

5 Min

22 Continuous Functions - Discontinuity

5 Min

23 Absolute Value Functions

5 Min

N/A

25 Equations Involving Absolute Value

5 Min

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 Definition of a matrix

5 Min

N/A

3 Algebra of matrices

5 Min

N/A

5 Transpose of a matrix

5 Min

6 Determinant of a square matrix

5 Min

7 Properties of determinant

5 Min

N/A

9 Singular matrices

5 Min

N/A

11 Multiplicative Inverse of a 33matrix

5 Min

12 HOW TO SOLVE SIMULTANEOUS EQUATIONS

5 Min

N/A

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

5 Min

15 Applications of inverse matrix

5 Min

N/A

17 Applications of matrices in calculating areas and volumes

5 Min

N/A

24 Addition and subtraction of matrices

5 Min

1 The Area of a Circle

5 Min

2 Point and line Geometry Internal and external division of a line segment

5 Min

N/A

4 The Equations of a Straight Line:

5 Min

N/A

6 Pair of lines

5 Min

7 Perpendicular distance of a point from a line

5 Min

N/A

9 Reduction to Linear form

5 Min

10 Loci using Cartesian or parametric forms.

5 Min

N/A

1 Fundamental Counting Principles

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

N/A

13 Arrangement of like and unlike objects

5 Min

N/A

15 Consider arrangement in a circle and in a ring (like on beads) -Simple problems involving arrangements

5 Min

N/A

17 Combinations -Selection of objects from a group:

5 Min

N/A

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

5 Min

N/A

21 Introduction to Partial Fractions

5 Min

1 Completing the Square Method

10 Min

Completing the Square Method

2 Partial Fractions with Linear Factors

5 Min

1 Logic -Basic concepts in logic

5 Min

N/A

3 A Statement and its negation

5 Min

N/A

5 Propositions, Composite statements

5 Min

N/A

7 Conjunction and disjunction

5 Min

N/A

9 If- then” statements: p⇒q Biconditional statements: p⇒q

5 Min

N/A

11 The converse of a conditional statement

5 Min

N/A

13 The inverse of a conditional statement

5 Min

N/A

15 Mathematical Proofs - Direct proofs

5 Min

N/A

17 Proof by Counter example

5 Min

N/A

19 Proof by Contradiction

5 Min

N/A

21 Proof by Mathematical Induction

5 Min

N/A

1 pascal’s triangle for n ≤ 10;

5 Min

N/A

3 Binomial coefficients, general term for n > 0, r> 0 and r≤ 𝑛;

5 Min

N/A

5 Binomial theorem for 𝑛𝜖Q

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 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.P

5 Min

N/A

19 The geometric mean (G.M)

5 Min

N/A

21 Sum of a G.P. - Geometric Series.

5 Min

N/A

23 Convergence of geometric sequence

5 Min

N/A

25 Limit of a sequence -Sequences diverging

5 Min

N/A

27 Convergence of geometric series Summation of simple finite series The sigma notation

5 Min

N/A

29 Summation of some Standard Series

5 Min

N/A

31 Use of partial fractions in summation of series

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

N/A

7 Power set

5 Min

N/A

9 Universal set

5 Min

N/A

11 Set operations

5 Min

N/A

13 De Morgan’s law

5 Min

N/A

15 Sets of numbers commonly used in Mathematics

5 Min

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 Equivalence classes

5 Min

N/A

13 Venn Diagram Illustration

5 Min

N/A

15 Partitions

5 Min

N/A

17 Fundamental theorem on equivalence Relation

5 Min

N/A

19 Ordered Relations

5 Min

N/A

21 Partial order

5 Min

N/A

23 Total Order

5 Min

N/A

25 Strict Order

5 Min

N/A

27 Inclusion Diagram

5 Min

N/A

1 The six Trigonometric. Ratios

5 Min

2 Trigonometric. Ratios for special angles

5 Min

3 Trigonometric ratios of complementary angles

5 Min

4 -The Radian and degree as units for measuring angles

5 Min

5 Mensuration of the Circle -Length of arcs 

5 Min

6 Area of sector

5 Min

7 Area of segment

5 Min

8 Sine and cosine formulae

5 Min

9 The General Angle

5 Min

10 Complementary angles.m4v

6 Min

Complementary angles

11 Trigonometric Functions - Angles and their measures

5 Min

12 Graphs of Trigonometric Functions

5 Min

13 Simple Transformations of graphs of Trigonometric function

5 Min

14 Amplitude

5 Min

15 Period

5 Min

16 Phase shift

5 Min

17 Pythagorean Identities

5 Min

18 Compound angles formulae

5 Min

19 Double angle and half angle Identities

5 Min

20 Multiple Angles

5 Min

21 Factor formulae (addition formulae)

5 Min

22 The expression

5 Min

23 Solving trigonometric Equations -Solution of trigonometric equations

5 Min

24 Small Angles

5 Min

25 Graphs of inverse trigonometric functions

5 Min

26 Application to real life situations

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. Orthogonal and parallel vectors

50 Min

N/A

7 Position vector and displacement vector

5 Min

N/A

9 Scalar product of two vectors, its geometrical significance and algebraic properties

5 Min

N/A

11 Application of scalar product

5 Min

N/A

13 The equation of a line (i) through a point and parallel to a given vector (ii) through two given points

5 Min

N/A

16 Pair of lines

5 Min

N/A

18 Parallel and perpendicular lines

5 Min

N/A

20 Intersecting Lines

5 Min

N/A

22 Skew Lines

5 Min

N/A

24 Perpendicular distance from a point to a given Line

5 Min

N/A

26 Vector product of two vectors

5 Min

N/A

28 Triple product

5 Min

N/A

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High School Mathematics

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