# Class XII Mathematics – India

### India Class XII Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Study Plan | Study plan – Class XII | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | 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. | |||

3 | Functions | Notation and evaluations | |

Objective: On completion of the lesson the student will be understand different notations for functions. | |||

4 | 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. | |||

5 | 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. | |||

6 | 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. | |||

7 | 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. | |||

8 | 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. | |||

9 | 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. | |||

10 | 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. | |||

11 | 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. | |||

12 | 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. | |||

13 | 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. | |||

14 | 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. | |||

15 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

16 | 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. | |||

17 | 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. | |||

18 | 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. | |||

19 | Trigonometry | Double angle formulas (Stage 2) | |

Objective: On completion of the lesson the student will derive and use the double angle trig identities. | |||

20 | 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. | |||

21 | Trigonometry | t Formulas (Stage 2) | |

Objective: On completion of the lesson the student will solve trig equations using the t substitution. | |||

22 | Matrices | Basic concepts – Matrices | |

Objective: On completion of the lesson the student will have had an introduction to matrices | |||

23 | Matrices | Addition and subtraction of matrices | |

Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations. | |||

24 | Matrices | Scalar matrix multiplication | |

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. | |||

25 | Matrices | Multiplication of one matrix by another matrix | |

Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. | |||

26 | Matrices | Translation in the number plane | |

Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix. | |||

27 | Matrices | Translation by matrix multiplication | |

Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane. | |||

28 | Transformations | Special transformations – reflections, rotations and enlargements. | |

Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||

29 | 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. | |||

30 | 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. | |||

31 | 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. | |||

32 | 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. | |||

33 | Linear systems | Linear systems with matrices (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||

34 | Linear systems | Row-echelon form (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form. | |||

35 | Linear systems | Gauss Jordan elimination method (Stage 2) | |

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method. | |||

36 | Calculus | Limits | |

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||

37 | 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. | |||

38 | 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. | |||

39 | 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. | |||

40 | 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. | |||

41 | Calculus-differential, integ | Increasing, decreasing and stationary functions. | |

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions. | |||

42 | Calculus | First Derivative – turning points and curve sketching | |

Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. | |||

43 | Calculus-2nd derivative | The second derivative – concavity. | |

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion. | |||

44 | Calculus – Curve sketching | Curve sketching | |

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. | |||

45 | Calculus – Maxima minima | Practical applications of maxima and minima | |

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. | |||

46 | Calculus – Integration | Integration – anti-differentiation, primitive function | |

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. | |||

47 | Calculus – Computation area | Computation of an area | |

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area. | |||

48 | Calculus – Computation volumes | Computation of volumes of revolution | |

Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy. | |||

49 | Calculus – Trapezoidal and Simpson’s rules | The Trapezium rule and Simpson’s rule | |

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve. | |||

50 | 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. | |||

51 | 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. | |||

52 | 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. | |||

53 | 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 | |||

54 | 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. | |||

55 | 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. | |||

56 | 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 | |||

57 | 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. | |||

58 | 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. | |||

59 | Conic sections | Circles | |

Objective: On completion of the lesson the student will identify the radius of a circle given in standard form. | |||

60 | Conic sections | Ellipses | |

Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse. | |||

61 | Conic sections | Hyperbola | |

Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola. | |||

62 | Functions | Evaluating and graphing piecewise functions | |

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||

63 | Functions | Functions combinations | |

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||

64 | Functions | Composition of functions | |

Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | Functions | Parametric equations (Stage 2) | |

Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range. | |||

69 | 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. | |||

70 | Functions | Parametric functions (Stage 2) | |

Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion. | |||

71 | Algebra-polynomials | Introduction to polynomials | |

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. | |||

72 | Algebra-polynomials | The sum, difference and product of two polynomials. | |

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. | |||

73 | Algebra-polynomials | Polynomials and long division. | |

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

74 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

75 | Remainder theorem | More on remainder theorem | |

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials. | |||

76 | Factor theorem | The factor theorem | |

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial. | |||

77 | Factor theorem | More on the factor theorem | |

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials. | |||

78 | Factor theorem | Complete factorisations using the factor theorem | |

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros. | |||

79 | Polynomial equations | Polynomial equations | |

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||

80 | Graphs, polynomials | Graphs of polynomials | |

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves. | |||

81 | Roots quad equations | Sum and product of roots of quadratic equations | |

Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots. | |||

82 | Roots quad equations | Sum and product of roots of cubic and quartic equations | |

Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations. | |||

83 | Approx roots | Methods of approximating roots | |

Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question. | |||

84 | Newton’s approx | Newton’s method of approximation | |

Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method. | |||

85 | Logic | Inductive and deductive reasoning | |

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||

86 | Logic | Definition and use of counter examples | |

Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||

87 | 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. | |||

88 | Logic | Mathematical induction | |

Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||

89 | 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. | |||

90 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||

91 | Quadratic equations | Problem solving with quadratic equations | |

Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||

92 | Quadratic equations | Solving simultaneous quadratic equations graphically | |

Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||

93 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | |

Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. | |||

94 | Geometry-locus | Constructions and loci – single condition | |

Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. | |||

95 | Geometry-locus | Constructions and loci – multiple conditions | |

Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. | |||

96 | 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. | |||

97 | 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. | |||

98 | 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. | |||

99 | Geometry | To identify collinear points, coplanar lines and points in 2 and 3 dimensions | |

Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. | |||

100 | Geometry – angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | |

Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. | |||

101 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

102 | 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. | |||

103 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

104 | 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. | |||

105 | 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. | |||

106 | 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. | |||

107 | 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. | |||

108 | 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. | |||

109 | 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 | |||

110 | 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. | |||

111 | Exam | Exam – Class XII | |

Objective: Exam |