# Mathematics

### Course leaflets –

Applications of Mathematics NAT 4

Applications of Mathematics NAT 5

Mathematics is important in our everyday life, allowing us to make sense of the world around us and to manage our lives. Using mathematics enables us to model real life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.

Mathematics plays an important role in areas such as science or technologies, and is vital to research and development in fields such as engineering, computing science, medicine and finance. Learning mathematics gives children and young people access to the wider curriculum and the opportunity to pursue further studies and interests.

### Course Outline

Mathematics is taught to all pupils in S1 to S4. It is optional in S5/6 although the majority of pupils study the subject at some level. All classes are arranged into ability sets.

In S1 to S3 the mathematics experiences and outcomes are structured within three main organisers, each of which contains a number of subdivisions:

### Number, money and measure

- Estimation and rounding
- Number and number processes
- Multiples, factors and primes
- Powers and roots
- Fractions, decimal fractions and percentages
- Money
- Time
- Measurement
- Mathematics – its impact on the world, past, present and future
- Patterns and relationships
- Expressions and equations

### Shape, position and movement

- Properties of 2D shapes and 3D objects
- Angle, symmetry and transformation

### Information handling

### Data and analysis

Ideas of chance and uncertainty

In S4 to S6 the following courses are offered:

### National 4 Lifeskills Mathematics

The National 4 Lifeskills Mathematics course enables learners to apply mathematical ideas and strategies to managing finance, statistics, geometry and measurement in straightforward real-life contexts.

### National 4 Mathematics

The National 4 Mathematics course enables learners to select and apply straightforward mathematical skills in a variety of mathematical and real-life situations. Learners interpret, communicate and manage information in mathematical form.

### National 5 Lifeskills Mathematics

The National 5 Lifeskills Mathematics course enables learners to apply mathematical ideas and strategies to managing finance, statistics, geometry and measurement in real-life contexts.

### National 5 Mathematics

The National 5 Mathematics course enables learners to select and apply mathematical techniques in a variety of mathematical and real-life situations. Learners interpret, communicate and manage information in mathematical form.

### Higher (S5/6)

The Higher Course in Mathematics develops learners’ mathematical rigour and the ability to use precise and concise mathematical language assumes a particular importance at this stage.

Candidates who complete a Higher Mathematics course successfully are expected to have a competence and a confidence in applying mathematical techniques, manipulating symbolic expressions and communicating with mathematical correctness in the solution of problems.

The course has obvious relevance for candidates with interests in fields such as commerce, engineering and science where the mathematics learned will be put to direct use.

This course consists of three mandatory units as follows:

**Mathematics 1** comprises outcomes in the properties of the straight line, functions and graphs, basic differentiation and recurrence relations.

**Mathematics 2** comprises outcomes in the Factor/Remainder Theorem and quadratic theory, basic integration, trigonometric equations and formulae and the equation of the circle.

**Mathematics 3** comprises outcomes in vectors in three dimensions, further differentiation and integration, logarithmic and exponential functions and further trigonometric relationships.

### Advanced Higher (S6)

The Advanced Higher course extends learners’ mathematical knowledge in algebra, geometry and calculus. It includes matrix algebra, complex numbers and vectors and formalises the concept of mathematical proof.

Advanced Higher Mathematics emphasises the need for candidates to undertake extended thinking and decision making, to solve problems and integrate mathematical knowledge. The course offers candidates, in an interesting and enjoyable manner, an enhanced awareness of the range and power of mathematics.

This course consists of three mandatory units as follows:

**Mathematics 1**

This unit is the first of three units, which comprise the Advanced Higher Mathematics course. This unit extends the calculus and graphicacy work from Higher level and introduces matrices for solving systems of linear equations.

**Mathematics 2**

This unit extends the calculus in Mathematics 1 (AH), extends the work on recurrence relations at Higher level and introduces complex numbers and mathematical proof.

**Mathematics 3**

This unit introduces vector equations of lines and planes, matrices and their applications to geometrical transformations, and the Maclaurin series with simple applications, and extends number theory and proof. It also extends the work on differential equations from Mathematics 2.