Mathematics 2 (Advanced Higher SQA UNIT D322 13)

Each mathematics unit at Advanced Higher level aims to build upon and extend candidates mathematical knowledge and skills in a manner which reinforces the essential nature of problem solving. New mathematical concepts and skills are within theoretical or practical applications, and the importance of algebraic manipulative skills is emphasised throughout. At the same time, the benefits of advanced technology in securing and consolidating understanding are acknowledged and there are frequent references to the use of such technology throughout the course content. Equally important is the need, where appropriate, for the limitations of the technology to be demonstrated and for checking of accuracy and sensibility of answers to be ever present.

In this unit, the second of three progressive Mathematics units, outcome 1 extends the differentiation covered in Mathematics 1 (AH) to inverse functions and introduces implicit and parametric differentiation.
Integration is correspondingly extended in outcome 2 to integration by parts and partial fractions and first order differential equations are introduced.

In Outcome 3, candidates are introduced to the complex number system and are required to demonstrate competence in operations on complex numbers.

Higher level work on recurrence relations is extended to the formal study of arithmetic and geometric sequences in outcome 4 and the groundwork is laid for the study of Maclaurin expansions in Mathematics 3 (AH).

As candidates progress in mathematics they should acquire a growing awareness of the importance of mathematical proof and the need for mathematical rigour. It is for this reason that outcome 5 contains an introduction to elementary number theory and methods of proof.

This is a self study course which means you can study at home, workplace or wherever you choose at times that are convenient for you. You do not have any classes to attend.

This course is delivered through an appointed Distance Learning Tutor. Your appointed tutor will make contact with you as soon as you have the materials for the course. They will make regular contact to offer support and guidance, usually by e-mail but sometimes by phone to ensure you are making good progress and to support your learning throughout. You must be able to study independently through the course materials.

HOW WILL I BE ASSESSED?

Acceptable performance in this unit will be the satisfactory achievement of the standards set out in this part of the unit specification. All sections of the statement of standards are mandatory and cannot be altered without reference to the Scottish Qualifications Authority.

OUTCOME 1

Use further differentiation techniques.
Performance criteria
(a) Differentiate an inverse trigonometric function (involving the chain rule).
(b) Find the derivative of a function defined implicitly.
(c) Find the first derivative of a function defined parametrically.

OUTCOME 2
Use further integration techniques.
Performance criteria
(a) Integrate a proper rational function where the denominator is a factorised quadratic.
(b) Integrate by parts with one application.
(c) Find a general solution of a first order differential equation (variables separable type).

OUTCOME 3
Understand and use complex numbers.
Performance criteria
(a) Perform a simple arithmetic operation on two complex numbers of the form a + bi.
(b) Evaluate the modulus and argument of a complex number.
(c) Convert from cartesian to polar form.
(d) Plot a complex number on an Argand diagram.

OUTCOME 4
Understand and use sequences and series.
Performance criteria
(a) Find the nth term and the sum of the first n terms of an arithmetic sequence.
(b) Find the nth term and the sum of the first n terms of a geometric sequence.
Mathematics: Unit Specification – Mathematics 2 (AH) 44
National Unit Specification: statement of standards (cont)
UNIT Mathematics 2 (Advanced Higher)

OUTCOME 5
Use standard methods to prove results in elementary number theory.
Performance criteria
(a) Disprove a conjecture by providing a counter-example.
(b) Use proof by contradiction in a simple example.

Evidence requirements
Evidence for this course is to be be presented in the form of a closed book test under controlled conditions. In assessment, candidates should be required to show their working in carrying out algorithms and processes.

ENTRY REQUIREMENTS

Candidates will normally be expected to have attained:

• Mathematics 1 (AH)