IB Math (Standard Level)
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Topic 1:  Functions

• Introducing functions
• The domain and range of a relation on a Cartesian Plan
• Function notation
• Composite functions
• Inverse functions
• Transforming functions

 


 
Topic 2:  Equations, formulae and identities

• Solving quadratic equations
• The quadratic formula
• Roots of quadratic equations
• Graphs  of quadratic equations
• Applications of quadratics

 
Topic 3: Probability

• Definitions
• Venn diagrams
• Sample space diagrams and the product rule
• Conditional probability
• Probability tree diagrams

 

 
 
Topic 4: Exponential and logarithmic functions

• Exponents
• Solving exponential equations
• Exponential functions
• Properties of logarithms
• Logarithmic functions
• Laws of logarithms
• Exponential and logarithmic equations
• Applications of exponential and logarithmic functions

 




Topic 5: Rational functions

• Reciprocals
• The reciprocal function
• Rational functions

 
 


Topic 6: Patterns, sequences and series

• Patterns and sequences
• Arithmetic sequences
• Geometric sequences
• Sigma( ∑ )notation and series
• Arithmetic series
• Geometric Series
• Convergent series and sums to infinity
• Applications of geometric and arithmetic patterns
• Pascal’s triangle and the binomial expansion

 
 
 
 
 
Topic 7: Limit and derivatives

• Limits and convergence
• The tangent line and derivative of
• More rules for derivatives
• The chain rule and higher order derivatives
• Rates of change and motion in a line
• The derivative and graphing
• More on extrema and optimization problems

 




Topic 8:  Descriptive Statistics

• Univariate analysis
• Presenting data
• Measures of central tendency
• Measures of dispersion
• Cumulative frequency
• Variance and standard deviation

 




Topic 9:  Integration

• Antiderivatives and the indefinite integral
• More on indefinite integrals
• Area and definite integrals
• Fundamental Theorem of Calculus
• Area between two curves
• Volume of revolution
• Definite integrals with linear motion and other problems

 


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Topic 10:  Bivariate analysis

• Scatter diagram
• The line of best fit
• Least square regression
• Measuring correlation

 
Topic 11:  Trigonometry

• Right-angled triangle trigonometry
• Applications of right-angled triangle trigonometry
• Using the coordinate axes in trigonometry
• The sine rule
• The cosine rule
• Area of a triangle
• Radians, arcs and sectors

 




Topic 12:  Vectors

• Vectors: basic concepts
• Addition and subtraction of vectors
• Scalar product
• Vector equation of a line
• Application of vectors

 




Topic 13:  Circular functions

• Using the unit circle
• Solving equations using unit circle
• Trigonometric identities
• Graphing circular functions
• Translations and stretches of trigonometric functions
• Combined transformations with the sine and cosine functions
• Modeling with sine and cosine functions

 




Topic 14:  Calculus with trigonometric functions

• Derivatives of trigonometric functions
• More practice with derivatives
• Integral of sine and cosine
• Revisiting linear motion

 



 
Topic 15:  Probability distribution

• Random variables
• The binomial distribution
• The normal distribution

 
Topic 16:  The Exploration

• Random variables
• The binomial distribution
• The normal distribution

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Topic 17:  Using a graphic display calculator

• Functions
• Differential calculus
• Integral calculus
• Vectors
• Statistics and probability