MATHEMATICS (ELECTIVE)

SCOPE OF CONTENTS ALGEBRA COORDINATE GEOMETRY VECTORS AND MECHANICS LOGIC TRIGONOMETRY CALCULUS MATRICES AND TRANSFORMATION STATISTICS AND PROBABILITY

SHS 1 GES KHAN ACADEMY Sets Surds Binary operation Relations and Functions Polynomial Function Rational Functions Binomial Theorem Inequalities and linear programming Coordinate geometry I Probability I Vectors I - Irrational and radicals Relation and functions Polynomial functions Rational relationship Binomial theorem Inequalities and linear programming Coordinate geometry Probability Vectors

SHS 1 SURDS TOPIC GES KHAN ACADEMY OPERATIONS ON SURDS OPERATIONS OF IRRATIONAL NUMBERS RATIONALIZATION OF SURDS WITH BINOMIAL DENOMINATORS EQUATION OF RADICALS

RELATIONS AND FUNCTIONS TOPIC GES KHAN ACADEMY BINARY OPERATION PROPERTIES OF BINARY OPERATION PROPERTIES:- CLOSURE IDENTITY AND INVERSE ELEMENTS RELATIONS AND FUNCTIONS GRAPHICAL REPRESENTATION OF A FUNCTION FUNCTIONS DOMAIN AND RANGE OF A FUNCTION

POLYNOMIAL FUNCTIONS TOPIC GES KHAN ACADEMY INVERSE OF A FUNCTION COMPOSITE FUNCTIONS POLYNOMIAL FUNCTIONS LINEAR AND QUADRATIC FUNCTIONS SKETCHING CURVES OF QUADRATIC FUNCTIONS SOLVING QUADRATIC EQUATIONS COMPLETING THE SQUARE QUADRATIC FORMULA

TOPIC GES KHAN ACADEMY ROOTS OF QUADRATIC EQUATIONS DEFINITION OF POLYNOMIAL FUNCTIONS INTRO. TO POLYNOMIALS ALGEBRA OF POLYNOMIALS:- ADDITION , SUBTRACTION AND MULTIPLICATION DIVISION SYNTHETIC DIVISION ADDITION , SUBTRACTION MULTIPLYING BINOMIALS LONG DIVISION REMAINDER AND FACTOR THEOREM BINOMIAL THEOREM BINOMIAL THEOREM AND PRACTICALS

COORDINATE GEOMETRY PROBABILITY TOPIC GES KHAN ACADEMY COORDINATE GEOMETRY WITH PRACTICALS PROBABILITY INTRODUCTION TO PROBABILITY CONDITIONAL PROBABILITY PERMUTATION COMBINATION BASIC THEORETICALS EXPERIMENTAL PROBABILITY RANDOM VARIABLES POISON DISTRIBUTIONS NORMAL DISTRIBUTIONS

TOPIC GES KHAN ACADEMY VECTORS REPRESENTATION OF VECTORS RESULTANT OF VECTORS LAWS OF ADDITION OF VECTORS SCALE DRAWING AND RESOLUTION OF VECTORS POSITION VECTORS --------------- UNIT VECTORS

SHS 2 GES KHAN ACADEMY COORDINATE GEOMETRY I SEQUENCE AND SERIES INDICES AND LOGARITHMS TRIGONOMETRIC RATIOS AND RULES COMPOUND AND MULTIPLE ANGLES TRIGONOMETRY FUNCTIONS AND EQUATIONS DIFFERENTIATION APPLICATION OF DIFFERENTIATION INTEGRATION APPLICATION OF INTEGRATION PERMUTATION AND COMBINATION PROBABILITY II STATISTICS I APPLICATION OF VECTORS IN GEOMETRY STATICS

COORDINATE GEOMETRY II TOPIC GES KHAN ACADEMY COORDINATE GEOMETRY II EQUATION OF A CIRCLE FINDING THE CENTRE AND RADIUS GIVEN THE EQUATION OF THE CIRCLE EQUATION OF TANGENT AND NORMAL TO A CIRCLE LOCI COORDINATE GEOMETRY WITH PRACTICALS EQUATION OF PARABOLA SKETCHING OF PARABOLA TANGENT AND NORMAL

TOPIC GES KHAN ACADEMY SEQUENCE AND SERIES APPLICATION OF LINEAR SEQUENCE EXPONENTIAL SEQUENCE RECURRENCE SEQUENCE ARITHMETIC SEQUENCE GEOMETRIC SEQUENCE ----- INDICES AND LOGARITHMS LAWS OF INDICES AND LOGARITHMS EQUATIONS INVOLVING INDICES EQUATIONS INVOLVING LOGARITHM AND CHANGE OF BASE GRAPH OF EXPONENTIAL RELATIONS AND THEIR APPLICATIONS INTRODUCTION TO LOGARITHMS SOLVING PROBLEMS USING INDICES SOLVING PROBLEMS USING LOGARITHMS GRAPH OF LOGARITHMIC FUNCTIONS

TOPIC GES KHAN ACADEMY INDICES AND LOGARITHMS ---------- ---------------- LOGARITHM SCALE NATURAL LOGARITHMS TRIGONOMETRY BASIC TRIGONOMETRIC RATIOS AND THEIR RECIPROCALS ANGLES IN RADIANS SINE AND COSINE RULES APPLICATIONS OF SINE AND COSINE RULES TO BEARINGS COMPOUND ANGLES INTRODUCTION TO TRIGONOMETRIC RATIOS AND THEIR RECIPROCALS ...........

TOPIC GES KHAN ACADEMY MULTIPLE ANGLES (UP TO 3A) GRAPH OF TRIGONOMETRIC FUNCTIONS SOLVING TRIGONOMETRIC EQUATIONS (UP TO QUADRATICS) MAXIMUM AND MINIMUM POINTS OF TRIGONOMETRIC FUNCTIONS ............... ......... GRAPH OF TRIGONOMETRIC FUNCTIONS. SOLVING TRIGONOMETRIC EQUATIONS ........... MODELING WITH RIGHT-ANGLED TRIANGLE

TOPIC GES KHAN ACADEMY CALCULUS DIFFERENTIATION LIMIT OF FUNCTIONS INTRO. LIMITS ------------------ -------------------- ---------------------- SQUEEZE THEOREM CONTINUITY AT A POINT TYPES OF DISCONTINUITY INTERMEDIATE VALUE THEOREM LIMIT OF SIMPLE TRIG. FUNCTIONS DIFFERENTIATION FROM FIRST PRINCIPLES RULES OF DIFFERENTIATION POWER RULES CHAIN RULES IMPLICIT DIFFERENTIATION -------------- DEFINITION AND BASIC RULES CHAIN RULE IMPLICIT DIFFERENTIATION

TOPIC GES KHAN ACADEMY CALCULUS DIFFERENTIATION DIFFERENTIATION OF INVERSE FUNCTIONS DIFFERENTIATION OF INVERSE TRIG. FUNCTIONS DISGUISED DERIVATIVE LOGARITHMETIC DIFFERENTIATION APPLICATION OF DIFFERENTIATION APPLICATIONS OF DIFFERENTIATION APPROXIMATION WITH LOCAL LINEARITY L’HOPITAL RULE COMPOSITE EXPONENTIAL FUNCTIONS

TOPIC GES KHAN ACADEMY CALCULUS DIFFERENTIATION CURVE SKETCHING LINEAR KINEMATICS PLANAR MOTIONS MEAN VALUE THEOREM EXTREME VALUE THEOREM PARAMETRIC EQUATION VECTOR – VALUED FUNCTIONS POLAR FUNCTIONS

INTEGRATION TOPIC GES KHAN ACADEMY CALCULUS INTEGRATION BY SUBSTITUTIONS INTEGRATION OF SIMPLE TRIGONOMETRY FUNDAMENTAL THEOREM OF CALCULUS ------------- APPLICATION OF INTEGRATIONS --------------- TRAPEZIUM RULE ------------------ RIEMANN SUMS ----------------- POWER SERIES

TOPIC GES KHAN ACADEMY STATISTICS HISTOGRAM, OGIVE HISTOGRAM , OGIVE MEASURES OF CENTRAL TENDENCY MEASURES OF DISPERSION MEASURES OF DISPERSTION ---------------- ------------------- BOX PLOT NORMAL DISTRIBUTION MARGINAL AND CONDITIONAL DISTRIBUTION STATICS ---------------(in PHYSICS)

SHS 3 GES KHAN ACADEMY MATRICES LINEAR TRANSFORMATION LOGIC CORRELATION AND REGRESSION SPEARMAN’S RANK CORRELATION DYNAMICS ------- ----------------- --------------( in PHYSICS)

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