# Prepare for IB Math (SL & HL) with Prep Zone Academy

##### VETERAN TRAINERS WITH A PHD IN MATH

Work with Prep Zone Academy’s certified trainers to improve your IB Math scores! Our math trainers are PhD degree holders with years of teaching experience.

We offer both individual and group course for IB Math (SL & HL). The group batches are run on an ad hoc basis, around school exams. The individual lessons are completely customisable and can be booked based on your schedule!

## Course Curriculum

This curriculum will be customised depends on the student’s needs.

### Standard Level Curriculum

 Session Topics Subtopics 1 Functions Function notation, composite/inverse functions, function transformations Quadratic functions Solving quadratic functions, quadratic roots, quadratic graphs Exponential and logarithmic functions Solving exponential equations, exponential functions, laws of logarithms and their functions/equations Rational functions Reciprocals and their functions, rational functions Patterns and Sequences Sigma notation and series, arithmetic/geometric series, convergent series and sums to infinity 2 Probability Venn diagrams, sample space diagrams and product rule, conditional probability, probability tree diagrams Descriptive statistics Univariate analysis, histograms, measures of central tendency/dispersion, cumulative frequency, variance, standard deviation Bivariate analysis Scatter diagrams, line of best fit, least squares regression, measuring correlation Probability distributions Random variables, binomial and normal distributions 3 Trigonometry Right-angled triangle trigonometry, sine and cosine rule, area of a triangle, radians, arcs, sectors Vectors Vector addition/subtraction, scalar product, vector equation of a line Circular functions The unit circle, trigonometric identities, graphing circular functions, translation and scaling of trigonometric functions, combined transformations with sine and cosine functions 4 Limits and derivatives Limits and convergence, tangent line, derivatives of polynomials and more, chain rule and higher order derivatives, rates of change and motion in a line, derivative and graphing, extrema and optimisation Integration Antiderivatives, indefinite and definite integrals, fundamental theorem of Calculus, volume of revolution Trigonometric calculus Derivatives of trigonometric functions, integrals of sine and cosine

### Higher Level Curriculum

HL Math students are required to study everything in the core curriculum and one topic under the option curriculum.

 Session Topics Subtopics 1a Patterns and Sequences Sigma notation and series, arithmetic/geometric series, mathematical induction Exponents and logarithms Law of exponents/logarithms, change of base Counting principles Permutations and combinations, binomial theorem 1b Complex numbers Operations with complex numbers, cartesian/polar form, complex plane, powers of complex numbers, complex roots, solving systems of equations Functions Function notation, odd/even functions, inverse/composite functions, one-to-one/many-to-one functions, graphs of functions, transformations of graphs, rational/exponential/logarithmic functions, polynomial functions and their graphs, factor and remainder theorems, fundamental theorem of algebra, solving quadratic equations, solving inequalities of functions 2 Statistics Population, sample, random sample, frequency distribution of discrete/continuous data, grouped data, mean, variance, standard deviation Probability Venn diagrams, combined/mutually-exclusive events, conditional probability, independent events, Bayes’ theorem, probability distributions, probability density functions, mean/mode/median/variance/standard deviation, binomial/poisson/normal distributions 3 Trigonometry Radian, arc length, sector area, the unit circle and trigonometric identities, special angles, Pythagorean identities, compound angle identities, double angle identities, cosine rule Trigonometric functions Trigonometric composite/inverse functions, solving trigonometric equations Vectors Vector addition/subtraction, scalar/vector product, vector equation of a line/plane, intersections of lines and planes 4 Limits and derivatives Limits, continuity and convergence, derivative of a function, tangents and normals, higher order derivatives, derivatives of different functions, product/quotient rules, chain rules for composite functions, related rates of change, implicit differentiation, maxima and minima, optimisation, relationship between derivatives Integration Antiderivatives, indefinite and definite integrals, area of regions enclosed by curves, volume of revolution, kinematics, integration by substitution/parts