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

19 chapters
575 lectures
236 quizzes
166 Hours 40 Min total length

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1 Completing the Square Method

10 Min

Completing the Square Method

2 Partial Fractions with Linear Factors

5 Min

1 The quadratic function (sketching the graph)

2 Min

2 Finding the maximum and minimum points

3 Min

3 Parabolas with horizontal and vertical shifts

3 Min

4 Use of the Discriminant

3 Min

5 Applications of Maximum and Minimum Values

3 Min

6 Quadratic Functions

3 Min

7 Sum and Product of the Roots of Quadratic Equations

3 Min

8 Quadratic Inequalities

3 Min

9 Problems Leading to Inequalities

3 Min

10 Basic Rules on Solving Inequalities

3 Min

11 Linear Inequalities

2 Min

12 Quadratic Inequalities

3 Min

13 Inequalities Involving Rational Functions

3 Min

14 System of Inequalities in Two Unknowns

4 Min

15 Inequalities Involving Modulus or Absolute Value Functions

3 Min

16 Graphs of Absolute Value Functions and Inequalities

2 Min

17 Definition of Polynomials

2 Min

18 Addition and Subtraction of Polynomials

3 Min

19 Multiplication of Polynomials

3 Min

20 Division of Polynomials

2 Min

21 Division Algorithm for Polynomials

3 Min

22 Remainder and factor theorem (factor theorem)

3 Min

23 Remainder and Factor Theorem

3 Min

24 Polynomial equations (n-root theorem)

3 Min

25 Applications of the Remainder and Factor Theorems

3 Min

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

3 Min

27 Factorisation of polynomial

3 Min

28 Logic

3 Min

29 30. Truth Tables

3 Min

30 Converse of a Conditional Statement Subject

3 Min

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

4 Min

32 Logical Equivalence

3 Min

33 Implication (Conditional Statements)

3 Min

34 Connection with Set Theory

3 Min

35 Tautologies

2 Min

36 Equations of the circle

3 Min

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

4 Min

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

3 Min

39 Geometric properties of a circle

3 Min

40 Intersection of a straight line with a circle

4 Min

41 Equation of a tangent to a circle

3 Min

42 Length of a tangent from external point to a circle

3 Min

43 Intersecting circles

3 Min

44 Condition for two circles to touch

3 Min

45 Radical axis of two circles

4 Min

46 Orthogonal circles

3 Min

47 Parametric coordinates of a curve

4 Min

48 The conjugate of complex number

3 Min

49 Definition (properties of i)

3 Min

50 Properties of the conjugate

3 Min

51 Addition and subtraction of complex numbers

3 Min

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

4 Min

53 Division of complex numbers

4 Min

54 Addition and subtraction of complex numbers

3 Min

55 Properties of the modulus

3 Min

56 The modulus of a complex number

3 Min

57 The triangle inequality

3 Min

58 The argument of a complex number

3 Min

59 Special cases

4 Min

60 Properties of arguments

3 Min

61 Polar or trigonometric form

4 Min

62 The different forms of a complex number (the normal form)

4 Min

63 Multiplying two complex numbers in a polar form

3 Min

64 Proof of De Moivre’s Theorem

3 Min

65 Application of De Moivre’s theorem to establish trigonometric identities

3 Min

66 Some important results

3 Min

67 The argand diagram

3 Min

68 Transformation of the complex plane

4 Min

69 Roots of a complex number

6 Min

70 Cube roots of a complex number

4 Min

71 The n th roots of unity

4 Min

72 Properties of the roots

6 Min

73 Geometrical representation of sums, products and quotients of complex numbers

6 Min

74 Vector representation

5 Min

75 Resolving a vector

5 Min

76 Cartesian vector notation

4 Min

77 Unit vector and direction vectors

4 Min

78 Vector equation of a line

4 Min

79 A line through two points

4 Min

80 Recognising direction and finding points from the vector equation of a line

4 Min

81 The line of action of a force

4 Min

82 46. The equation of the path of a particle moving with constant velocity

4 Min

83 Determination of resultant vectors

4 Min

84 The resultant of more than two coplanar vectors

4 Min

85 The position of a resultant force

4 Min

86 The turning effect of forces

4 Min

1 Introduction to Quadratic Equations

5 Min

N/A

3 Introduction to Algebraic Process

5 Min

4 Solving Quadratic Equations by Factorization Method

5 Min

N/A

6 Solving Quadratic Equations by Factorization Method

5 Min

7 Solving Examples

5 Min

N/A

9 The quadratic function (sketching the graph)

5 Min

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

N/A

12 Introduction to The Theorem of Quadratics

5 Min

13 Introduction to the theorem of Quadratics [Quiz]

N/A

15 Maxima and Minima [Quiz]

N/A

16 The discriminant of quadratic equations [Quiz]

N/A

17 Quadratic equations

5 Min

N/A

19 Quadratic equations [Quiz]

N/A

20 The quadratic formula

5 Min

N/A

22 The quadratic formula [Quiz]

N/A

23 Quadratic expressions

5 Min

N/A

25 Quadratic expressions [Quiz]

N/A

27 System of equations with 3 unknowns

5 Min

28 System of equation with 3 unknowns [Quiz]

N/A

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

5 Min

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

N/A

33 FACTORISATION METHOD

5 Min

34 Factorisation method [Quiz]

N/A

36 Equations Involving Absolute Value

9 Min

Equations Involving Absolute Value

37 Solving quadratic equations using formula methods

9 Min

Solving quadratic equations using formula methods

N/A

39 Solving quadratic equations using formula methods

9 Min

Solving quadratic equations using formula methods

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

5 Min

N/A

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

5 Min

43 Formula Method

5 Min

44 Graphs and properties of quadratic Functions

5 Min

45 Graghs and properties of quadratic functions [Quiz]

N/A

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

5 Min

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

N/A

48 Applications of nature of roots

5 Min

49 The Sum and the Product of Two Squares.m4v

5 Min

50 Simple transformations

5 Min

51 Completing the Square Method.m4v

5 Min

52 Relationship between roots and coefficients of a quadratic equation

5 Min

53 The Sum and the Difference of Two Cubes

5 Min

54 Maxima and Minima

5 Min

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

5 Min

56 The Discriminant of Quadratic Equations.m4v

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 Absolute Value Functions

5 Min

7 Solving Problems Involving Quadratic Inequalities

5 Min

8 Basic Rules on solving Inequalities

5 Min

N/A

10 Basic rules on solving inequalities [Quiz]

N/A

11 Linear Inequalities

5 Min

N/A

13 Linear inequalities [Quiz]

N/A

14 Quadratic inequalities

5 Min

N/A

16 Quadratic inequalities [Quiz]

N/A

17 Inequalities Involving rational functions

5 Min

18 Inequalities involving rational functions [Quiz]

N/A

19 Inequalities involving the modulus or absolute value

5 Min

20 Inequalities involving the modulus or absolute values [Quiz]

N/A

21 System of inequalities

5 Min

22 System of inequalities [Quiz]

N/A

1 Introduction to The Naperian Log

5 Min

N/A

3 The Discriminant of Quadratic Equations

5 Min

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

5 Min

N/A

6 SOLVING LOGARITHNIC EQUATIONS

5 Min

7 Second Law of Logarithms

5 Min

N/A

9 HOW TO SOLVE SIMULTANEOUS EQUATIONS

5 Min

10 More Problems on Change of Base of Logarithms

5 Min

N/A

12 DIVISION OF SURDS.m4v

5 Min

DIVISION OF SURDS

13 Index Notation

5 Min

N/A

15 CALCULATIONS INVOLVING SURDS

5 Min

CALCULATIONS INVOLVING SURDS

16 CALCULATIONS INVOLVING SURDS

5 Min

N/A

18 SOLVING PROBLEMS WITH INDICES

5 Min

19 Laws of Indices

5 Min

20 Applications of laws of Indices

5 Min

N/A

22 Exponential equations

5 Min

23 The graph

5 Min

N/A

25 Surds -Rational and irrational numbers

5 Min

26 Surds - calculations involving surds .m4v

5 Min

N/A

28 Rationalisation of denominators

5 Min

29 Logarithms - Common logarithms

5 Min

N/A

31 Laws of Logarithms

5 Min

32 Second Law of Logarithms.m4v

5 Min

N/A

34 Third Law of Logarithms.m4v

5 Min

35 Logarithmic equations

5 Min

N/A

37 More problems on change of Base of Logarithms.m4v

5 Min

38 Natural Logarithms Graphs - Logarithmic equations

5 Min

N/A

40 Applications of laws of logarithms

5 Min

41 Introduction to The Naperian Logarithm

5 Min

N/A

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 Absolute Value Functions

9 Min

Absolute Value Functions

5 LIMITS AND DIFFERENTIATION Limits of functions

5 Min

N/A

7 Intuitive definition of limits

5 Min

8 Uniqueness of limit

5 Min

N/A

10 Limit of sum, product and quotient

5 Min

N/A

12 Derivatives -The derivative defined as a limit

5 Min

13 Differentiation from first principles

5 Min

N/A

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

5 Min

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

5 Min

N/A

18 Differentiation of composite functions

5 Min

19 Differentiation of sums, products and quotients

5 Min

N/A

21 Second derivative

5 Min

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

5 Min

N/A

24 Differentiation of functions expressed parametrically (two dimensions only)

5 Min

25 Differentiation of functions expressed implicitly (two dimensions only)

5 Min

N/A

27 Applications of differentiation - rates of change,

5 Min

28 Small Change

5 Min

N/A

30 Percentage change

5 Min

31 Tangents, normal,

5 Min

N/A

33 Local maxima and minima and points of inflexion.

5 Min

34 Monotonicity of a function (Decreasing and increasing functions)

5 Min

N/A

36 Rolle’s Theorem

5 Min

37 Mean value Theorem

5 Min

38 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

39 INTEGRATION Integration as the reverse of differentiation

5 Min

40 Indefinite and definite integrals

5 Min

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

5 Min

42 Integration by parts

5 Min

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 Injective Functions. (incomplete video)mp4

5 Min

N/A

6 EVEN FUNCTIONS

6 Min

Even Functions

7 Graphical and other representations of a function

5 Min

8 Odd Functions

5 Min

N/A

10 Composition of functions

5 Min

N/A

12 Identity mapping

5 Min

13 The inverse of a one-one function

5 Min

N/A

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

5 Min

16 Continuous Functions - Discontinuity

5 Min

N/A

18 Periodicity of a function

5 Min

19 Continuous Functions - Discontinuity

5 Min

20 Absolute Value Functions

5 Min

N/A

22 Equations Involving Absolute Value

5 Min

N/A

24 Surjective Functions

5 Min

25 Domain of a function

5 Min

N/A

1 Addition and subtraction of matrices

5 Min

2 Definition of a matrix

5 Min

N/A

4 Algebra of matrices

5 Min

N/A

6 Transpose of a matrix

5 Min

7 Determinant of a square matrix

5 Min

8 Properties of determinant

5 Min

N/A

10 Singular matrices

5 Min

N/A

12 Multiplicative Inverse of a 33matrix

5 Min

13 HOW TO SOLVE SIMULTANEOUS EQUATIONS

5 Min

N/A

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

5 Min

16 Applications of inverse matrix

5 Min

N/A

18 Applications of matrices in calculating areas and volumes

5 Min

N/A

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 Introduction to Partial Fractions

5 Min

2 Fundamental Counting Principles

5 Min

3 Factorial Notation

5 Min

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

5 Min

5 Mutually exclusive situations

5 Min

6 Ordered arrangements

5 Min

7 Permutations of objects selected from a group

N/A

8 Arrangement of like and unlike objects

5 Min

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

5 Min

10 Combinations -Selection of objects from a group:

5 Min

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

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 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

6 The binomial expansion /The validity of the expansion

5 Min

N/A

8 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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