National Curriculum
• Mathematical Methods Unit 1

### Description

This unit begins with a review of the basic algebraic concepts and techniques required for a successful introduction to the study of calculus. The basic trigonometric functions are then introduced. Simple relationships between variable quantities are reviewed, and these are used to introduce the key concepts of a function and its graph. The study of inferential statistics begins in this unit with a review of the fundamentals of probability and the introduction of the concepts of conditional probability and independence. Access to technology to support the computational aspects of these topics is assumed.

#### Learning Outcomes - By the end of this unit, students:

$\large\cdot$ understand the concepts and techniques in algebra, functions, graphs, trigonometric functions and probability
$\large\cdot$ solve problems using algebra, functions, graphs, trigonometric functions and probability
$\large\cdot$ apply reasoning skills in the context of algebra, functions, graphs, trigonometric functions and probability
$\large\cdot$ interpret and evaluate mathematical information and ascertain the reasonableness of solutions to problems
$\large\cdot$ communicate their arguments and strategies when solving problems.
• Mathematical Methods Unit 2

### Description

The algebra section of this unit focuses on exponentials and logarithms. Their graphs are examined and their applications in a wide range of settings are explored. Arithmetic and geometric sequences are introduced and their applications are studied. Rates and average rates of change are introduced, and this is followed by the key concept of the derivative as an ‘instantaneous rate of change’. These concepts are reinforced numerically, by calculating difference quotients both geometrically, as slopes of chords and tangents, and algebraically. Calculus is developed to study the derivatives of polynomial functions, with simple applications of the derivative to curve sketching, calculating slopes and equations of tangents, determining instantaneous velocities and solving optimisation problems.

Access to technology to support the computational aspects of these topics is assumed.

### Learning Outcomes

By the end of this unit, students:

$\large\cdot$ understand the concepts and techniques used in algebra, sequences and series, functions, graphs and calculus
$\large\cdot$ solve problems in algebra, sequences and series, functions, graphs and calculus
$\large\cdot$ apply reasoning skills in algebra, sequences and series, functions, graphs and calculus
$\large\cdot$ interpret and evaluate mathematical and statistical information and ascertain the reasonableness of solutions to problems
$\large\cdot$ communicate arguments and strategies when solving problems.
• Mathematical Methods Unit 3

### Description

In this unit the study of calculus continues with the derivatives of exponential and trigonometric functions and their applications, together with some differentiation techniques and applications to optimisation problems and graph sketching. It concludes with integration, both as a process that reverses differentiation and as a way of calculating areas. The fundamental theorem of calculus as a link between differentiation and integration is emphasised. In statistics, discrete random variables are introduced, together with their uses in modelling random processes involving chance and variation.

This supports the development of a framework for statistical inference.

Access to technology to support the computational aspects of these topics is assumed.

#### Learning Outcomes

By the end of this unit, students:

$\large\cdot$ understand the concepts and techniques in calculus, probability and statistics
$\large\cdot$ solve problems in calculus, probability and statistics
$\large\cdot$ apply reasoning skills in calculus, probability and statistics
$\large\cdot$ interpret and evaluate mathematical and statistical information and ascertain the reasonableness of solutions to problems.
$\large\cdot$ communicate their arguments and strategies when solving problems.
• Mathematical Methods Unit 4

### Description

The calculus in this unit deals with derivatives of logarithmic functions. In probability and statistics, continuous random variables and their applications are introduced and the normal distribution is used in a variety of contexts.

The study of statistical inference in this unit is the culmination of earlier work on probability and random variables. Statistical inference is one of the most important parts of statistics, in which the goal is to estimate an unknown parameter associated with a population using a sample of data drawn from that population. In Mathematical Methods statistical inference is restricted to estimating proportions in two-outcome populations.

Access to technology to support the computational aspects of these topics is assumed.

#### Learning Outcomes

By the end of this unit, students:

$\large\cdot$ understand the concepts and techniques in calculus, probabilty and statistics
$\large\cdot$ solve problems in calculus, probability and statistics
$\large\cdot$ apply reasoning skills in calculus, probability and statistics
$\large\cdot$ interpret and evaluate mathematical and statistical information and ascertain the reasonableness of solutions to problems.
$\large\cdot$ communicate their arguments and strategies when solving problems.
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