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### India Class XI Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Class XI
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Number theory – sets Number sets and their members
Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.
3 Number theory – operations Properties of real numbers using addition and multiplication
Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication.
4 Number theory – equations Transformations that produce equivalent equations
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.
5 Absolute value or modulus Solving and graphing inequalities
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.
6 Statistic-probability Probability of Simple Events
Objective: On completion of the lesson the student will be able to understand the probability of simple events.
7 Statistic-probability Rolling a pair of dice
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.
8 Statistic-probability Experimental probability
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.
9 Statistic-probability Tree diagrams – not depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes.
10 Statistic-probability Tree diagrams – depending on previous outcomes
Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes.
11 Statistic-probability The complementary result ..
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved.
12 Statistic-probability P[A or B] When A and B are both mutually and NOT mutually exclusive
Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both.
13 Functions Definition, domain and range
Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range.
14 Functions Notation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
15 Functions More on domain and range
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation.
16 Functions Domain and range from graphical representations
Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations.
17 Graphing-polynomials Graphing complex polynomials: quadratics with no real roots
Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it.
18 Graphing-polynomials General equation of a circle: determine and graph the equation
Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning.
19 Graphing-cubic curves Graphing cubic curves
Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information.
20 Absolute value equations Absolute value equations
Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio
21 Rect.hyperbola The rectangular hyperbola.
Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features.
22 Exponential function The exponential function.
Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1.
23 Log functions Logarithmic functions.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
24 Conic sections Introduction to conic sections and their general equation
Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.
25 Conic sections The parabola x. = 4ay
Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.
26 Conic sections Circles
Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.
27 Conic sections Ellipses
Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.
28 Conic sections Hyperbola
Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.
29 Functions Evaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
30 Functions Functions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
31 Functions Composition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
32 Functions Inverse functions
Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used.
33 Functions Rational functions Part 1
Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes.
34 Functions Rational functions Part 2
Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes.
35 Functions Polynomial addition etc in combining and simplifying functions (Stage 2)
Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra.
36 Trigonometry-exact ratios Trigonometric ratios of 30., 45. and 60. – exact ratios.
Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60.
37 Trig-reciprocal ratios Reciprocal ratios.
Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios.
38 Trig complementary angles Complementary angle results.
Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations.
39 Trig identities Trigonometric identities
Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities.
40 Trig larger angles Angles of any magnitude
Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle.
41 Trig larger angles Trigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees.
42 Graph sine Graphing the trigonometric ratios – I Sine curve.
Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period.
43 Graph cosine Graphing the trigonometric ratios – II Cosine curve.
Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period.
44 Graphs tan curve Graphing the trigonometric ratios – III Tangent curve.
Objective: On completion of the lesson the student will know how to recognise and draw the tan curve.
45 Graph reciprocals Graphing the trigonometric ratios – IV Reciprocal ratios.
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.
46 Trig larger angles Using one ratio to find another.
Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude.
47 Trig equations Solving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
48 Trig equations Solving trigonometric equations – Type II.
Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains.
49 Trig equations Solving trigonometric equations – Type III.
Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains.
50 Polar coordinates Plotting polar coordinates and converting polar to rectangular
Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.
51 Polar coordinates Converting rectangular coordinates to polar form
Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.
52 Polar coordinates Write and graph points in polar form with negative vectors (Stage 2)
Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.
53 Trigonometry Sin(A+B) etc sum and difference identities (Stage 2)
Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios.
54 Trigonometry Double angle formulas (Stage 2)
Objective: On completion of the lesson the student will derive and use the double angle trig identities.
55 Trigonometry Half angle identities (Stage 2)
Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities.
56 Trigonometry t Formulas (Stage 2)
Objective: On completion of the lesson the student will solve trig equations using the t substitution.
57 Logic Mathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
58 Logarithms-Complex numbers Imaginary numbers and standard form
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction.
59 Logarithms-Complex numbers Complex numbers – multiplication and division
Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division.
60 Logarithms-Complex numbers Plotting complex number and graphical representation
Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers.
61 Logarithms-Complex numbers Absolute value
Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers
62 Logarithms-Complex numbers Trigonometric form of a complex number
Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form.
63 Logarithms-Complex numbers Multiplication and division of complex numbers in trig form (Stage 2)
Objective: On completion of the lesson the student will use the trig form of complex numbers for multiplication and division.
64 Logarithms-Complex numbers DeMoivre’s theorem (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form.
65 Logarithms-Complex numbers The nth root of real and complex numbers (Stage 2)
Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form.
66 Logarithms-Complex numbers Fundamental theorem of algebra (Stage 2)
Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field.
67 Algebra-inequalities Solving Inequalities.
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.
68 Geometry – triangles Triangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
69 Vectors Vectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
70 Simultaneous equations Number of solutions (Stage 2)
Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same.
71 Vectors 2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
72 Linear systems Optimal solutions (Stage 2) – Vectors
Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions.
73 Statistic-probability Binomial Theorem – Pascal’s Triangle
Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers.
74 Statistic-probability Binomial probabilities using the Binomial Theorem
Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem
75 Statistic-probability Counting techniques and ordered selections – permutations
Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability.
76 Statistic-probability Unordered selections – combinations
Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen.
77 Sequences and Series General sequences.
Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula.
78 Sequences and Series Finding Tn given Sn.
Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term.
79 Arithmetic Progression The arithmetic progression
Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
80 Arithmetic Progression Finding the position of a term in an A.P.
Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression.
81 Arithmetic Progression Given two terms of A.P., find the sequence.
Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms
82 Arithmetic Progression Arithmetic means
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
83 Arithmetic Progression The sum to n terms of an A.P.
Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems.
84 Geometric Progression The geometric progression.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
85 Geometric Progression Finding the position of a term in a G.P.
Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems.
86 Geometric Progression Given two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
87 Sequences and Series-Geometric means Geometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
88 Sequences and Series-Sum of gp The sum to n terms of a G.P.
Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P).
89 Sequences and Series-Sigma notation Sigma notation
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.
90 Sequences and Series-Sum-infinity Limiting sum or sum to infinity.
Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems.
91 Sequences and Series-Recurring decimal infinity Recurring decimals and the infinite G.P.
Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number.
92 Sequences and Series-Compound interest Compound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
93 Sequences and Series-Superannuation Superannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.
94 Sequences and Series-Time payments Time payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.
95 Sequences and Series Applications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
96 Coordinate Geometry-the plane Distance formula.
Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.
97 Coordinate Geometry-midpoint, slope Mid-point formula
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run.
Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines.
100 Coordinate Geometry-straight line The straight line.
Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists.
101 Coordinate Geometry-slope, etc. Lines through the origin.
Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems.
102 Coordinate Geometry-equation of line General form of a line and the x and y Intercepts.
Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa.
103 Coordinate Geometry-intercept Slope intercept form of a line.
Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation.
104 Coordinate Geometry-point slope Point slope form of a line
Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line.
105 Coordinate geometry Solve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
106 Co-ordinate Geometry-Two point formula Two point formula: equation of a line which joins a pair of points.
Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line.
107 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
108 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
109 Co-ordinate Geometry-Perpendicular lines Perpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.
110 Co-ordinate Geometry-Inequalities Inequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.
111 Co-ordinate Geometry-Theorems Perpendicular distance
Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines.
112 Co-ordinate Geometry-Theorems Line through intersection of two given lines
Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition.
113 Co-ordinate Geometry-Theorems Angles between two lines
Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line.
114 Co-ordinate Geometry-Theorems Internal and external division of an interval
Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions.
115 Geometry-circles The equation of a circle: to find radii of circles
Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.
116 Geometry-circles The semicircle: to select the equation given the semi circle and vice versa
Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.
117 Geometry-parabola The parabola: to describe properties of a parabola from its equation
Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.
118 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
119 Functions and graphs Graphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
120 Graphing roots Graphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.
121 Geometry-constructions Orthocentre and centroids (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
123 Calculus Limits
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.
124 Calculus=1st prin Differentiation from first principles.
Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve.
125 Calculus=1st prin Differentiation of y = x to the power of n.
Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n.
126 Calculus-differential, integ Meaning of dy over dx – equations of tangents and normals.
Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve.
127 Calculus-differential, integ Function of a function rule, product rule, quotient rule.
Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule.
128 Logic Inductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
129 Logic Definition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
130 Logic Indirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
131 Logic Conditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
132 Statistic-probability The median
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores
133 Statistics – grouped data Calculating mean, mode and median from grouped data
Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values.
134 Statistics using a calculator Statistics and the student calculator
Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems.
135 Statistics – Range and dispersion Range as a measure of dispersion
Objective: On completion of the lesson the student will be able to determine the range and using it in decision making.
Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator.
137 Statistics – Standard deviation Standard deviation applications
Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean.
138 Statistics – Standard deviation Normal distribution
Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges.
139 Statistics – Interquartile range Measures of spread: the interquartile range
Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range
140 Statistics Stem and Leaf Plots along with Box and Whisker Plots
Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot.
141 Statistics Scatter Diagrams
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.
142 Statistics Frequency distribution table
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.
143 Statistics Frequency histograms and polygons
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.
144 Statistics Relative frequency
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.
145 Statistics The range.
Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table.
146 Statistic-probability The mode
Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon.
147 Statistic-probability The mean
Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column.
148 Statistic-probability Cumulative frequency
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.
149 Statistic-probability Calculating the median from a frequency distribution
Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon.
150 Exam Exam – Class XI
Objective: Exam