 Text Book: Advanced Mathematics, A Precalculus Approach, by Ryan, Doubet, Fabricant and Rockhill; Prentice Hall Calculus, by Larson, Hostetler and Edwards( Sixth Edition) Course Goal: To enable the candidate to develop a sound basis of mathematical skills and knowledge that will aid in the further study of subjects with math applications. Course Description:IB math methods is a two-year course that requires a solid background of Algebra II and Trigonometry skills. Included in the course are : Numerical computations, Algebra and Coordinate Geometry, Geometry,Trigonometry , Functions and Calculus, Vectors, Probability and Statistics.
Part I: 1)Number and Algebra : 1.1 Number Systems 1.2 Sequences and series 1.3 Exponents and Logarithms 1.4 Binomial Theorem 2)Functions and Equations: 2.1 Domain, Range, composition, Inverse and Domain Restrictions of functions 2.2 Graphing Skills (Use of graphic calculators): horizontal/vertical asymptotes,max/min 2.3 Transformation of Graphs (Translations, stretches and reflection(in x/y axis) 2.4 Linear Equations, its graph ; slope and Y- intercept 2.5 The reciprocal function 1/x 2.6 Quadratic Function, its graph, vertex (h,k), y and x-intercept 2.7 The quadratic formula, intersection of linear and quadratic function 2.8 The exponential and the logarithmic functions, their graphs ; solution of ax = b 2.9 The functions ex and ln x and their applications in growth and decay 3)Circular Functions and Trigonometry: 3.1 The circle: Radian measure; arc length and area of sector 3.2 Definition of sin x, cos x and tan x and their graphs,The Pythagorean Identity,The Double Angle formula 3.3 Circular Functions, and their inverse functions Composite functions in the form F(x) = a Sin b (x + c) + d, Solution of linear and quadratic trigonometric functions 3.4 Solution of triangles using the Sine/Cosine rules Finding the area of a triangle 4)Vector Geometry 4.1 Column Vectors;Addition and multiplication by a scalar;Position Vectors;Magnitude or length of a vector;Sum of two vectors;Zero Vector 4.2 Writing vectors in component notation and ai + bj; Calculation of the resultant;Scalar product of two vectors;Perpendicular and Parallel vectors 4.3 Parametric equation of a line; The Cartesian equation of a line;Common point of two lines; parallel lines, coincident lines 4.4 Angle between two vectors;Distance of a point from a line 5)Statistics and Probability: 5.1 Population and Sample; Discrete and continuous data; Frequency tables 5.2 Histograms and mid-interval values 5.3 Measures of Central Tendency (Mean and Median) 5.4 Cumulative frequency graphs, quartiles, percentiles 5.5 Measures of Dispersion (range, interquartile range, standard deviation) 5.6 Probability sample space; Complementary events 5.7 Union and intersection of two events; Mutually exclusive events 5.8 Independent events; Conditional probability 5.9 Venn Diagrams; tree diagrams 6)Calculus: 6.1 Limit and Convergence; Derivative of Xn, sin x, cos x, ex and ln x; The Chain rule 6.2 Applications of First derivative in Max/Min, velocity, acceleration, tangents 6.3 Indefinite integration of Xn, Cos x, Sin x, e^x Application to acceleration and velocity 6.4 Antiderivatives with a boundary condition to determine the constant term; Definite integrals; Areas under the curve Part II:Further Calculus: 7.1 Derivatives using the product and quotient rules; The second derivative; Derivatives of a^x, log x, tan x 7.2 Graph behavior of functions for large | x |; Vertical and Horizontal asymptotes; The significance of the second derivative; Points of inflection 7.3 Integration by substitution 7.4 Iteration of a function; Graphical representation of convergence; Applications of Fixed-point iteration to the solution of F(x)=0 7.5 The Newton Raphson Method 7.6 The Trapezium Rule Calculus: a) Differentiation: - Differentiation of sums, products and quotients of: - polynomials - exponential functions - rational functions b) Applications of Differentiation: - Graphs and properties of functions involving e^x and ln x for x > 0 - Equations of the tangent and normal at a point on the graph of any of the above functions. - Stationary values. Tests for maxima, minima and points of inflection - Simple problems involving maxima and minima - Curve sketching for the functions listed in section 5-a - Use of the formula f(x + h) = f(x) + hf ' (x) for small h c) Integration: - Integration of polynomials - Integration of exponential functions - Integration of rational functions Calculus: Differentiation , Integration and Applications : - Finding areas using integrals - Finding the area between two curves using integrals - Properties and graphs of Exponential functions - Differentiation and integration of exponential functions - Properties and graphs of Natural logarithmic functions - Differentiation of natural logarithmic functions and Log Rule - Integration by Substitution - Numerical integration using the trapezium rule - Differentiation of Trigonometric functions such as (sine, cosine and tangent) - Integration of Sine, cosine and tangent functions - Newton-Raphson method for approximating zeros of a function - Cumulative reviews of IB core topics During these two bimesters, students will be involved in a cummulative review of the entire Math Methods program in preparation of the IB exams. This will involve a review of the core contents of parts I through VI and the optional topic (Further Calculus) Students will complete worksheets and projects on the six parts. Teacher Expectations Assessment  
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