YAKILI | LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

Course / Course Details

LOWER SIXTH PURE MATHEMATICS WITH MECHANICS

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

Course Curriculum

20 chapters
320 lectures
159 quizzes
166 Hours 40 Min total length

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1 Quadratic expressions

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3 Quadratic equations

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5 The quadratic formula

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7 Relationship between roots and coefficients of a quadratic equation

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9 Symmetric properties of the roots of a quadratic equation

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11 Graphs and properties of quadratic Functions

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13 Maxima and Minima

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

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17 Simple transformations

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19 Applications of Nature of roots

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20 System of equations with 3 unknowns

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1 Basic Rules on solving Inequalities

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3 Quadratic inequalities

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5 Linear Inequalities

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7 Inequalities involving the modulus or absolute value functions

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9 Inequalities Involving rational functions

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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 Theorem

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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

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3 Basic concepts in logic

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5 A Statement and its negation

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7 Propositions, Composite statements

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

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

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1 Binomial theorem for expansion of (𝑎 + 𝑏𝑥)𝑛, for positive integral indices n

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3 Pascal’s triangle for n ≤ 10

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5 -Binomial coefficients, general term for n > 0, r> 0 and r≤ 𝑛

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7 Binomial theorem for 𝑛𝜖Q

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9 The binomial expansion/The validity of the expansion

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11 Application to approximations

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

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3 Parity of a function

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5 Investigation of simple odd and 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 -Graphical and other representations of a function

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

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15 Periodicity of a function

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17 Surjective, Injective and Bijective mappings

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1 Index Notation

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3 Laws of Indices

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5 Applications of laws of Indices

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7 Exponential equations

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8 The graph

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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.Pc

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19 The geometric mean (G.M)

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21 Sum of a G.P

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23 Geometric Series

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25 Convergence of geometric sequence

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27 Limit of a sequence

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29 sequences diverging

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31 Convergence of geometric series Summation of simple finite series

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33 The sigma notation

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35 Summation of some Standard Series

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37 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 Venn Diagram Illustration

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13 Partitions

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15 Fundamental theorem on equivalence Relation

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17 Ordered Relations

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19 Partial order

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21 Total Order

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23 Strict Order

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25 Inclusion Diagram

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1 Fundamental Counting Principle

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

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17 Simple problems involving arrangements

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19 Combinations -Selection of objects from a group:

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

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1 The six Trigonometric. Ratios

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3 Trigonometric. Ratios for special angles

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5 Trigonometric ratios of complementary angles

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7 The Radian and degree as units for measuring angles

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

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11 Area of sector

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13 Area of segment

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15 Sine and cosine formulae

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17 The General Angle

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19 Trigonometric Functions - Angles and their measures

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21 Graphs of Trigonometric Functions

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23 Simple Transformations of graphs of Trigonometric function

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25 Amplitude

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1 Point and line Geometry

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3 The Equations of a Straight Line:

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5 Pair of lines

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7 erpendicular 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 Transpose of a matrix

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7 Determinant of a square matrix

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9 Properties of determinant

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11 Singular matrices

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13 Multiplicative Inverse of a 33matrix

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15 Applications of matrix products to a system of equations

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

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19 Applications of inverse matrix

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21 Applications of matrices in calculating areas and volumes

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1 Geometric vectors and basic properties

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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.

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7 Orthogonal and parallel vectors

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9 Position vector and displacement vector

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

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13 Application of scalar product

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

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17 Pair of lines

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19 Parallel and perpendicular lines

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21 Intersecting Lines

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23 Skew Lines

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25 Perpendicular distance from a point to a given Line

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27 Vector product of two vectors

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29 Triple product

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

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3 General definition of a limit using Ɛ 𝑎𝑛𝑑 𝛿

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5 Uniqueness of limit

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7 Limit of sum, product and quotient

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1 rates of change,

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3 Small Change

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5 percentage change

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7 tangents, normal

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

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11 Rolle’s Theorem

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13 Mean value Theorem

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15 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

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1 Integration as the reverse of differentiation

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3 Indefinite and definite integrals

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

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7 Integration by parts

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Instructor

High School Mathematics

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