Mathematics part of the six subject groups in the IB Diploma Programme. All IB students are expected to have at least the basic knowledge of Math and how that knowledge can be applied in other subject areas and in daily life. There are 4 different course options for the Mathematics subject group,

- Mathematical Studies Standard Level
- Mathematics Standard Level
- Mathematics Higher Level
- Further Mathematics Higher Level

Candidates are required to take at lease one Mathematics course. Not to worry, our experienced tutors will walk you through the key concepts, applications through examples and address any questions you may have to aid your understanding. Our course structure can be found below!

### Mathematical Studies Standard Level

*Math Studies Standard Level Course Structure*

Session | Topics | Subtopics |

1 | Numbers and Algebra 1 | Number sets, Approximation and error, Standard, SI units of measurement |

Mathematical Models | Functions, Linear models, Quadratic models, Exponential models, Graphs, Using GDC to solve equation graphs | |

Numbers and Algebra 2 | Arithmetic sequences, Geometric sequences,Currency conversions, Compound interest | |

2 | Descriptive Statistics | Data classification, Grouping continuous or discrete data, Cumulative frequency curves, Box and whisker graphs, Measures of dispersion |

Statistical Applications | Normal distribution, Correlation, Regression line, Chi-Squared Test | |

Sets and Probability | Basic set theory, Venn diagrams, Basic probability theory, Conditional probability, Sample space diagrams, Tree diagrams | |

Logic | Introduction to logic, Compound statements and symbols, Truth tables, Logical equivalence, Tautologies and contradictions, Arguments | |

3 | Geometry and trigonometry 1 | Gradient of line, Equations of lines, Sine and cosine rules,Sine, Cosine and tangent ratios |

Geometry and Trigonometry 2 | Geometry of three-dimensional solids, Distance between points, Angles between two lines or a line and a plane, Surface areas and Volume of three-dimensional solids | |

4 | Introducing Differential Calculus | Introduction to differentiation, Gradient function, Calculating gradient, Tangent and the normal to a curve, Rates of change, Local maximum and minimum points,Using differentiation in modeling: Optimization |

### Standard Level

*Math SL Course Structure*

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

*Math HL Course Structure*

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

**Sessions for core 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 |

## Request for a Math trial class

#### We will get back to you within 24 hours

By submitting this form, I agree to Prep Zone Academy’s Privacy Policy and Terms of Use.

## IB Subjects

Prep Zone Academy offers a range of IB subject preparation courses. You are invited to a free trial class with one of our IB certified trainers for any subjects of your choice!