Class XI : Mathematics Lecture Plan
|Lecture Plan : Mathematics|
|S.N.||Name of Chapter||No. of Lectures|
(Lec. Duration : 1hr 45min)
|1.||MAT (Mathematical Aptitude Tools)||07|
|4.||Properties of Triangles||02|
|8.||Sets, Relation & Function||05|
|11.||Permutation & Combinaton||05|
|15.||Points & Slopes||01|
|16.||Straight Line & Pair of Straight Lines||05|
|Total : ||80|
1. MAT (Mathematical Aptitude Tools) :
- L1 = Define wavy-curve method, Synthetic division, partial fraction, Concept of brackets & various graphs.
- L2 = Concept of function e.g. logarithmic function, Modulus function …, inequalities, Domain & Range.
- L3 = Problem Discussion.
- L4 = Concept of limits, and differentiation.
- L5 = Curve tracing.
- L6 & L7 = Problem discussion.
2. Trigonometric Ratio :
- L8 = Positive & Negative angle and its conversion. (Radians Degrees) . Relation between length of arc and radius of a circle. Sign of trigonometric function.
- L9 = Domain & Range of trigonometric functions and their graph and its shifting [y = f(x ± a), y = f(x) ± a, y = a f(x)]. Formula listing.
- L10 = Sum and difference formula. Identities related to sin 2x,cos 2x, tan2x, sin3x, cos3x, tan3x and N.C.E.R.T Exercise 3.3
- L11 = Greatest and Least value of asinθ ± bcosθ sum of sine and cosine series with angles are in A.P. and cosine formula for product when angles are in G.P. value of sin18o, sin36o, sin22½o etc.
- L12 = Problem Discussion.
3. Trigonometric Equation :
- L13 = Principal & general solution of sinθ=0, cosθ=0, tanθ=0 and sinθ=sinα, cosθ=cosα, tanθ=tanα; sin2θ=sin2α, cos2θ=cos2α, tan2θ=tan2α, acosθ + bsinθ = c.
- L14 = Problem Discussion.
4. Properties of Triangles :
- L15 = Simple application of Sine and Cosine formulae, Projection rule, Half angle formula & area of Triangle & Polygon.
- L16 = Area of Triangle, circum-radius and in-radius.
5. Mathematical Induction :
- L17 = Process of the proof by induction, The principle of Mathematical induction.
- L18 = Problem discussion.
6. Complex Number :
- L19 = Need for complex numbers, Imaginary number √ -1 , integral powers of iota, Algebra of complex numbers. The modulus & Argument of a complex number(NCERT Exercise 5.1).
- L20 = Representation of a complex number in various form, Demoivre's Theorem. Power's & root of a complex number(Square, cube etc.) concept of cube root(1,w,w2) & nth root of unity.
- L21 = Properties of roots of unity, modulas And conjugate. Logarithm of a complex number.
- L22 = Rotation theorem and its application with example. Basic of co-ordinate to be used in Argard plane to define locus, Solution of Quadratic Equation in complex number system.
- L23 = Geometry of complex number & locus with proof.
- L24 = Problem discussion.
7. Inequalities :
- L25 = Linear inequalities & their algebra solution on number line, Graphical solution of linear inequalities in two variable & words problem.
- L26 = Quadratic inequalities with properties & graph.
8. Sets, Relation & Function :
- L27 = Sets & their representation, Various type of set, Venn diagram.
- L28 = Operation of a set, Practical problem on union & intersection of two sets.
- L29 = Cartesian product of section, concept of relation.
- L30 = Function, Domain.
- L31 = Range & Composite function (fof, gof, gog (f ± g) (f × g)).
9. Progressions :
- L32 = Sequence & Series, Arithmetic progression(A.P.), Arithmetic Mean(A.M.).
- L33 = Geometric Progression,(G.P.), General term of G.P., Sum of n terms of a G.P., Artihmetic Geometric Series, Infinite G.P. & Its sum, Geometric mean(G.M.).
- L34 = Harmonic Progression, Sum to n-terms of the special Series Σk, Σk2 & Σk3, A.M., G.M. & H.M.
- L35 = Method of difference. Solved All Exercise.
- L36 = Problem discussion.
10. Binomial Theorem :
- L37 = Binomial theorem for positive integral indices. Pascal’s triangle.(NCERT 8.1) & the no of term in the expansion of (x ± y)n.
- L38 = General & middle term, Term independent of variable, Integral term, Coefficient of variable.
- L39 = Properties of Binomial coefficient & simple application greatest term.
- L40 = Binomial theorem for any index, multinomial theorem.
- L41 = Problem discussion.
11. Permutation & Combination :
- L42 = Fundamental principal of counting. Factorial n (n!), (NCERT Ex. 7.1 & 7.2)
- L43 = Permutation (nPr) (linear & circular arrangement), Rank of a word, permutation when all object are not distinct objects. (Ex. 7.3).
- L44 = Combinations (nCr) and its properties, Division into groups, Dearrangement, number of divisors.
- L45 = Multinomial theorem & its application in no of integral solution of linear equation & Exponent of prime P in n!.
- L46 = Problem discussion.
12. Probability :
- L47 = Random experiments, outcomes, sample space/set representation Events, occurence of events, "and" & "or" events, exhustive events & mutually exclusive events.(Ex. 16.1, 16.2).
- L48 = Axiomatic approach to probability, Probability of an event, Probability of events "A" & "B" probability of event not A.(Ex. 16.3).
- L49 = Use of permutation & combination in probability & Probability in Algebra.
- L50 = Problem discussion.
13. Statistics :
- L51 = Measures of dispersion, Mean deviation, Variance & standard deviation of ungrouped/grouped data.
- L52 = Analysis of frequency, distributions with equal means but different variances.
14. Mathematical Reasoning :
- L53 = Concept of true and false statement & logical operations And, or, implies, implied by, if & only, only if. Understanding of tautology, fallacy.
15. Points & Slopes :
- L54 = Rectangular co-ordinates in a plane(in-cartesian & polar form), Distance formula, Section formula, Area of triangle, Concept of centroid, circum-centre, ortho-centre, in-centre of a Triangle, Locus, Translation of axes. Slope of a line.
16. Straight Line & Pair of Straight Lines :
- L55 = Various forms of equation of line. Angle beteen two lines, Condition for parallel & perpendicular lines. Lines parallel and perpendicular to given lines.
- L56 = Distance of a point from a line, Distance between two parallel line, Transformation of general equation in different standard forms. Co-linearity of three points.Condition for concurrency of three lines.
- L57 = Foot of perpendicular, Image of point with respect to a line,Position of points with respect to a line. Equations of the bisectors of the angles between two straight lines.
- L58 = Equation of family of lines through the intersection of two given lines. General equation of 2nd degree, pair of straight lines & homogeneous equation of second degree. Angle between pair of lines. Bisectors of the angle between the lines given by a homogeneous equation. Separate equation of lines from 2nd degree equation.
- L59 = Problem discussion.
17. Circle :
- L60 = Definition of circle, Equation of circle in various form, Parametric equation of circle. Position of point with respect to circle.Intersection of a line & circle.
- L61 = Equation of tangent & Normal, Equation of common chord, Pair of tangents, Chord of contact, Chord with a given middle point, Length of common chord.
- L62 = Lengths of tangent, Common tangent to two circles, Director circle, Radical axis & Radical centre.
- L63 = Family of circle, Angle between two intersecting circles ,condition for orthogonality.
- L64 = Problem discussion.
18. Parabola :
- L65 = Definition of parabola, equation of parabola in Various form. Mathematical terms of a parabola, parametric form, Position of a point with respect to a parabola.
- L66 = Condition of tangency and normality. Equation of tangent & normal (point, slope & parametric form). Equation of pair of tangent. Concept of focal chord and its properties. Point of intersection of tangents.
- L67 = No of Normals & co-normal points, Combined equation of pair of tangent, director circle, Chord of contact, Chord with a given middle point.
- L68 = Problem discussion.
19. Ellipse :
- L69 = Definition of ellipse, equation in standard form, Mathematical terms of an ellipse (horizontal & vertical) and various formulas, Parametric form. Position of a point with respect to ellipse. Intersection of a line & Ellipse.
- L70 = Equation of tangent & Normal in point, slope & Parametric form, eccentric angle. Combined equation of pair of tangent, Director Circle, Auxiliary Circle.
- L71 = Equation of chord of contact, Equation of chord when middle is given.
- L72 = Problem discussion.
20. Hyperbola :
- L73 = Definition of Hyperbola, Equation in standard form hyperbola & conjugate hyperbola, Mathematical terms of hyperbola (simple & conjugate) and various formulas. Parametric form, Position of a point with respect to Hyperbola, Intersection of a line & Hyperbola.
- L74 = Equation of tangent & Normal in point, Slope, Parametric form, combined equation of pair of tangents, Director circle Auxiliary circle equation of diameter.
- L75 = Equation of chord of contact, equation of chord when middle is given, Concept of Asymptotes & Rectangular Hyperbola & Unsolved Exercise.
21. Limit :
- L76 = Concept of indeterminate form(meaning of ). Difference between limiting value and function value. Concept of ∞. Existence of limit (L.H.L. & R.H.L.) Algebra of limit. L'hospital rule.
- L77 = Limits of trigonometric function, Exponential & logarithmic function, limit of rational function & factor form.
- L78 = Problem discussion.
22. Differentiation :
- L79 = Definition of derivative, Relate it to slope of tangent to the curve, (Using first principle).
- L80 = Derivative of sum, Difference, Product & quotient of polynomial, Trigonometric function & Chain rule.