## What will I learn?

The aims of all DP mathematics courses are to enable students to:

- Develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power;
- Develop an understanding of the concepts, principles and nature of mathematics;
- Communicate mathematics clearly, concisely and confidently in a variety of contexts;

- Develop logical and creative thinking, and patience and persistence in problem solving to instil confidence in using mathematics;
- Employ and refine their powers of abstraction and generalisation;
- Take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments in their local and global communities.

This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasises the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics.

The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.

Students who choose this subject at Standard Level should enjoy seeing mathematics used in real-world contexts and to solve real-world problems.

## What is the structure of the course?

The course is structured around these major areas of mathematics:

- Number and Algebra
- Functions
- Geometry and Trigonometry

- Statistics and Probability
- Calculus

## How will I be assessed?

**Assessment**

**Format**

**Mathematical Exploration (Coursework)**

Internal assessment in mathematics is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. Usually 12-20 pages long. 20% weighting.

**Paper One**

No technology allowed. **Section A:** compulsory short-response questions based on the syllabus. **Section B:** compulsory extended-response questions based on the syllabus. 40% weighting.

**Paper Two**

Technology allowed. **Section A:** compulsory short-response questions based on the syllabus. **Section B:** compulsory extended-response questions based on the syllabus. 40% weighting.

## Frequently Asked Questions

*Which CAS opportunities are available?*

There are many CAS projects that require mathematical skills, but in addition to such opportunities that you might explore you may seek to:

- Join the maths club and take part in the UKMT Maths Challenges and support young year groups in their preparation
- Support students with preparation for the GCSE Maths Exam
- Attend university style public lectures on interesting areas of maths and science

*Which opportunities for further study are available? *

The Mathematics IB prepares you for any university course that requires the continued study of mathematics, such as Economics, Pharmacy, Psychology and Dentistry as well as any other course that requires a higher qualification in mathematics.

*Is there anything else I need to know?*The study of mathematics can be one of the most challenging academic experiences a student can take on, but it is also one of the most rewarding and useful subjects to study due to its applicability in such a wide array of academic disciplines at University. Be prepared to study hard in your own time in order to understand some of the most challenging mathematics you have ever encountered.

You will require a graphical calculator for this course.

## Curriculum map

**Topics / Units**

Number; Sequences & Series; Functions

**Core Declarative Knowledge****What should students know?**

- Approximations, bounds and percentage error to report numerical information to different levels of accuracy and evaluate the validity of calculations
- Laws of exponents
- Scientific notation
- Logarithms as the inverse of exponents
- How to evaluate simple logarithmic expressions
- Arithmetic sequences and series
- Geometric sequences and series
- Sigma notation
- Applications such as compound interest, depreciation, annuities and population growth
- Different forms of equations of lines, gradients, intercepts and parallel and perpendicular lines
- Definitions of equations, formulae, identities, parameters, solutions and roots

**Core Procedural Knowledge****What should students be able to do?**

- Calculate approximations, bounds and percentage errors
- Analyse numerical information to different levels of accuracy
- Evaluate the validity of calculations
- Simplify exponential expressions using the laws of exponents
- Write numbers in scientific notation and compute calculations relevant to the real world
- Use logarithms to find the inverse of exponents
- Evaluate simple logarithmic expressions
- Calculate the sum of finite arithmetic sequences
- Calculate the sum of finite geometric sequences
- Use sigma notation as applied to series
- Calculate compound interest/depreciation/growth and solve related problems
- Solve linear equations
- Rearrange formulae
- Find the equation of a straight line and related parallel/perpendicular lines.

**Links to TOK**

- Do the names that we give things impact how we understand them? For instance, what is the impact of the fact that some large numbers are named, such as the googol and the googolplex, while others are represented in scientific form?
- Is all knowledge concerned with identification and use of patterns? Consider Fibonacci numbers and connections with the golden ratio.
- How do mathematicians reconcile the fact that some conclusions seem to conflict with our intuitions? Consider for instance that a finite area can be bounded by an infinite perimeter.
- Is mathematics invented or discovered? For instance, consider the number e or logarithms–did they already exist before man defined them?

**Topics / Units**

Functions

**Core Declarative Knowledge****What should students know?**

- Different forms of equations of lines, gradients, intercepts and parallel and perpendicular lines
- Definitions of equations, formulae, indenties, parameters, solutions and roots
- The concept of a function, domain, range and related graph
- Function notation
- Inverse function notation
- Graphs of functions and they key features including asymptotes
- How to use technology to graph and to solve functions
- The importance of modelling funtions and interpreting their features

**Core Procedural Knowledge****What should students be able to do?**

- Solve linear equations
- Rearrange formulae
- Find the equation of a straight line and related parallel/perpendicular lines.
- To state the domain and range of a function
- To sketch a function
- To find the inverse of a function and to do so with technology
- To solve using technology systems of equations
- Model linear, linear piecewise, quadratic, cubic, exponential, direct/inverse variate and trigonometric phenomena

**Links to TOK**

- Descartes showed that geometric problems could be solved algebraically and vice versa. What does this tell us about mathematical representation and mathematical knowledge?
- Does studying the graph of a function contain the same level of mathematical rigour as studying the function algebraically? What are the advantages and disadvantages of having different forms and symbolic language in mathematics?
- What role do models play in mathematics? Do they play a different role in mathematics compared to their role in other areas of knowledge?

**Topics / Units**

Geometry & Trigonometry

**Core Declarative Knowledge****What should students know?**

- The coordinate plane
- The Pythagorean Theorem
- The relationships between sine, cosine and tangent
- Know the sine and consine rules
- Know the formulae for volumes of complex 3D shapes
- Know the difference between volume and surface area
- When to apply pythagoras or trigonometry in real life situations

**Core Procedural Knowledge****What should students be able to do?**

- find the midpoint of two coordinates
- Calculate the distance between two points
- Use Pythagoras Theorem in a variety of contexts
- Find missing side lengths and angles using sin, cos and tan
- Find the area of a triangle using trigonometry
- Use the sine and cosine rules in non-right angled triangles
- Use formula to find the volume and surface area of complex 3D shapes

**Links to TOK**

- Is it ethical that Pythagoras gave his name to a theorem that may not have been his own creation?
- What criteria might we use to make such a judgment?
- If the angles of a triangle can add up to less than 180°, 180° or more than 180°, what does this tell us about the nature of mathematical knowledge?

**Topics / Units**

Probability & Statistics

**Core Declarative Knowledge****What should students know?**

- Probability of events
- Complementary events
- Probability of A and B
- Probability of A or B
- Venn Diagrams
- Tree Diagrams
- Two-way tables
- Population
- Sampling
- Reliability of data sources
- Presenting Data
- Averages and the Range
- Box and whisker plots
- Outliers

**Core Procedural Knowledge****What should students be able to do?**

- Concepts of population, sampling, random sampling, outliers (introduction), discrete and continuous data
- Reliability of data sources
- Sampling techniques and their effectiveness and bias in sampling
- Presenting data: frequency tables for discrete and continuous data, histograms, and cumulative frequency tables and graphs
- How to find median, quartiles, percentiles, range and interquartile range (IQR) and identify outliers
- Interpreting box-and-whisker plots, and comparing distributions using box-and-whisker plots
- Central tendency and spread of data; calculation of mean and standard deviation; effects of constant changes on the original data.

**Topics / Units**

Further Probability, Statistics & Normal Distribution

**Core Declarative Knowledge****What should students know?**

- Discrete Random Variables
- Expected Value
- Normal distribution
- Standardising normal variables
- Inverse normal calculations
- Binomial Distribution
- Applications

**Core Procedural Knowledge****What should students be able to do?**

- Discrete random variables and their probability distributions
- Expected value and the effect of linear transformations of X on its value
- The normal distribution: properties, normal probability calculations, and inverse normal calculations
- Standardising normal variables (z-values)
- Inverse normal calculations where mean and standard deviation are unknown
- The binomial distribution, including its mean and variance
- Applications of all the above concepts.