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Course / Course Details

LOWER SIXTH PURE MATHEMATICS WITH STATISTICS

  • High School Mathematics image

    By - High School Mathematics

  • 2 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

  • 17 chapters
  • 437 lectures
  • 215 quizzes
  • 166 Hours 40 Min total length
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1 The quadratic function (sketching the graph)
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3 The quadratic function (sketching the graph) [Quiz]
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4 Finding the maximum and minimum points
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6 Finding the maximum and minimum points [Quiz]
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7 Parabolas with horizontal and vertical shifts
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9 Parabolas with horizontal and vertical shifts [Quiz]
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10 Use of the discriminant
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12 Use of the discriminant [Quiz]
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13 Applications of maximum and minimum values
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15 Applications of maximum and minimum values [Quiz]
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16 Quadratic functions
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18 Quadratic functions [Quiz]
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19 Sum and Products of Roots of a Quadratic Equation
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21 Sum and Products of Roots of a Quadratic Equation [Quiz]
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22 Quadratic inequalities
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24 Quadratic inequalities [Quiz]
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25 Introduction to The Theorem of Quadratics.m4v
5 Min


26 Quadratic expressions
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28 Quadratic equations
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30 The Discriminant of Quadratic Equations.m4v
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31 The quadratic formula
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33 FACTORISATION METHOD
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34 Line of symmetry of the graph of y f(x)
5 Min


35 Maxima and Minima
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37 Graphs and properties of quadratic Functions
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38 Relationship between roots and coefficients of a quadratic equation
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40 The Sum and Products of Roots of a Quadratic Equation.m4v
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42 The Sum and the Product of Two Squares.m4v
5 Min


43 The Sum and the Difference of Two Cubes
5 Min


44 Simple transformations
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45 Applications of nature of roots
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46 System of equations with 3 unknowns
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47 Completing the Square Method.m4v
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48 Solving Examples
5 Min


49 Problems leading to inequalities [Quiz]
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1 Basic Rules on solving Inequalities
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3 Linear Inequalities
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5 Quadratic inequalities
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7 Inequalities Involving rational functions
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9 Inequalities involving the modulus or absolute value
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11 System of inequalities
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1 Algebra of polynomials
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3 The Remainder and factor theorems
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5 Applications of the Remainder and Factor
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7 Factorisation of polynomials
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1 Decomposition when degree of f(x) is less than degree of g(x)
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3 Decomposition when degree of f(x)is greater than or equal to g(x)
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1 Logic -Basic concepts in logic
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3 A Statement and its negation
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5 Propositions, Composite statements
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7 Conjunction and disjunction
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9 If- then” statements: p⇒q Biconditional statements: p⇒q
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11 The converse of a conditional statement
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13 The inverse of a conditional statement
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15 Mathematical Proofs - Direct proofs
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17 Proof by Counter example
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19 Proof by Contradiction
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21 Proof by Mathematical Induction
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1 pascal’s triangle for n ≤ 10;
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3 Binomial coefficients, general term for n > 0, r> 0 and r≤ 𝑛;
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5 Binomial theorem for 𝑛𝜖Q
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7 The binomial expansion /The validity of the expansion
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9 Application to approximations
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1 Domain of a function
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3 Odd Functions
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5 EVEN FUNCTIONS
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7 Composition of functions
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9 Identity mapping
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11 The inverse of a one-one function
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13 Graphical and other representations of a function
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15 Graphical illustration of the relationship between a function and its inverse
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17 Continuous Functions - Discontinuity
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19 Periodicity of a function
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21 Continuous Functions - Discontinuity
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23 Surjective Functions
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25 Bijective functions
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26 Absolute Value Functions
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28 Equations Involving Absolute Value
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1 Index Notation
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3 Laws of Indices
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4 Applications of laws of Indices
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6 Exponential equations
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7 The graph
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9 Surds -Rational and irrational numbers
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10 Surds - calculations involving surds .m4v
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12 DIVISION OF SURDS.m4v
5 Min


13 Rationalisation of denominators
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15 Logarithms - Common logarithms
5 Min


16 Laws of Logarithms
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18 Second Law of Logarithms.m4v
5 Min


19 Third Law of Logarithms.m4v
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21 Solving Problems involving First, Second and Third Law of Logarithms.m4v
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22 Logarithmic equations
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24 More problems on change of Base of Logarithms.m4v
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25 Introduction to The Naperian Logarithm
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27 Natural Logarithms Graphs - Logarithmic equations
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28 Applications of laws of logarithms
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30 SOLVING PROBLEMS WITH INDICES.m4v
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1 Sequences
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3 Series
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5 Arithmetic Progression (AP)
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7 The nth term of an Arithmetic Progression
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9 Arithmetic Mean (AM)
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11 Sum of an A.P.
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13 Limit of a sequence
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15 Geometric Progression(G.P)
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17 The nth term of a G.P
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19 The geometric mean (G.M)
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21 Sum of a G.P. - Geometric Series.
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23 Convergence of geometric sequence
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25 Limit of a sequence -Sequences diverging
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27 Convergence of geometric series Summation of simple finite series The sigma notation
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29 Summation of some Standard Series
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31 Use of partial fractions in summation of series
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1 Equality of sets
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3 Comparability of sets
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5 Cardinality of a set
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7 Power set
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9 Universal set
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11 Set operations
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13 De Morgan’s law
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15 Sets of numbers commonly used in Mathematics
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1 The notation of binary Relations
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3 Ordered Pairs
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5 Cartesian product of two sets
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7 Properties of relations
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9 Equivalence Relations
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11 Equivalence classes
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13 Venn Diagram Illustration
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15 Partitions
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17 Fundamental theorem on equivalence Relation
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19 Ordered Relations
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21 Partial order
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23 Total Order
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25 Strict Order
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27 Inclusion Diagram
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1 Fundamental Counting Principles
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3 Factorial Notation
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5 Permutations -Successive operations in a row and in circular arrangements (independent situations)
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7 Mutually exclusive situations
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9 Ordered arrangements
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11 Permutations of objects selected from a group
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13 Arrangement of like and unlike objects
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15 Consider arrangement in a circle and in a ring (like on beads) -Simple problems involving arrangements
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17 Combinations -Selection of objects from a group:
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19 Simple problems involving selections Partition theory in permutations and combinations.
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1 The six Trigonometric. Ratios
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2 Trigonometric. Ratios for special angles
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3 Trigonometric ratios of complementary angles
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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
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7 Area of segment
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8 Sine and cosine formulae
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9 The General Angle
5 Min


10 Complementary angles.m4v
5 Min


11 Trigonometric Functions - Angles and their measures
5 Min


12 Graphs of Trigonometric Functions
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13 Simple Transformations of graphs of Trigonometric function
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14 Amplitude
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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
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23 Solving trigonometric Equations -Solution of trigonometric equations
5 Min


24 Small Angles
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25 Graphs of inverse trigonometric functions
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26 Application to real life situations
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1 Point and line Geometry Internal and external division of a line segment
5 Min


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3 The Equations of a Straight Line:
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5 Pair of lines
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7 Perpendicular distance of a point from a line
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9 Reduction to Linear form
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11 Loci using Cartesian or parametric forms.
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1 Definition of a matrix
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3 Algebra of matrices
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5 Addition and subtraction of matrices.m4v
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7 Transpose of a matrix
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9 Determinant of a square matrix
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11 Properties of determinant
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13 Singular matrices
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15 Multiplicative Inverse of a 33matrix
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17 HOW TO SOLVE SIMULTANEOUS EQUATIONS
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19 Applications of matrix products to transformations in space/in a plane
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21 Applications of inverse matrix
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23 Applications of matrices in calculating areas and volumes
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1 Geometric vectors and basic properties
5 Min


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3 Algebraic operations of the addition of two vectors and the multiplication of a vector by a scalar, and their geometric significance
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5 The orthogonal unit vectors i, j, k and the Cartesian components of a vector. Orthogonal and parallel vectors
50 Min


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7 Position vector and displacement vector
5 Min


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


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11 Application of scalar product
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13 The equation of a line (i) through a point and parallel to a given vector (ii) through two given points
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16 Pair of lines
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18 Parallel and perpendicular lines
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20 Intersecting Lines
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22 Skew Lines
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24 Perpendicular distance from a point to a given Line
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26 Vector product of two vectors
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28 Triple product
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1 LIMITS AND DIFFERENTIATION Limits of functions
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3 Intuitive definition of limits
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5 Uniqueness of limit
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7 Limit of sum, product and quotient
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9 Derivatives -The derivative defined as a limit
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11 Differentiation from first principles
5 Min


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13 The gradient of a tangent as the limit of the gradient of a chord
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15 Differentiation of standard functions (Polynomial, Trigonometric logarithmic, exponential functions)
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17 Differentiation of composite functions
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19 Differentiation of sums, products and quotients
5 Min


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21 Second derivative
5 Min


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23 Differentiation of inverse functions (restricted to inverse trigonometric functions)
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25 Differentiation of functions expressed parametrically (two dimensions only)
5 Min


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27 Differentiation of functions expressed implicitly (two dimensions only)
5 Min


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29 Applications of differentiation - rates of change,
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31 Small Change
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33 Percentage change
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35 Tangents, normal,
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37 Local maxima and minima and points of inflexion.
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39 Monotonicity of a function (Decreasing and increasing functions)
5 Min


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41 Rolle’s Theorem
5 Min


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43 Mean value Theorem
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45 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


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47 INTEGRATION Integration as the reverse of differentiation
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49 Indefinite and definite integrals
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51 Techniques of Integration (Decomposition into partial fractions, linear and nonlinear substitution)
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53 Integration by parts
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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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