Mathematics 3 (Advanced Higher SQA UNIT D323 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 third of three progressive Mathematics units, the themes of earlier work at Higher and Advanced Higher are further developed. Outcome 1 builds on the vector content of Higher Mathematics and extends to the vector equations of lines and planes.

Matrices are studied in greater depth in Outcome 2 in applications to systems of equations.

The work on sequences and series in the previous unit is now, in Outcome 3, applied to Maclaurin expansions.

In Outcome 4, the study of first order differential equations in Mathematics 2 (AH) is continued.

The important topic of proof, also introduced in Mathematics 2 (AH), is further reinforced and developed in Outcome 5.

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 vectors in three dimensions.
Performance criteria
(a) Calculate a vector product.
(b) Find the equation of a line in parametric form.
(c) Find the equation of a plane in Cartesian form given a normal and a point in the plane.

OUTCOME 2
Use matrix algebra.
Performance criteria
(a) Perform matrix operations of addition, subtraction and multiplication.
(b) Calculate the determinant of a 3 × 3 matrix.
(c) Find the inverse of a 2 × 2 matrix.

OUTCOME 3
Understand and use further aspects of sequences and series.
Performance criteria
(a) Use the Maclaurin series expansion to find a stated number of terms of the power series for a simple function.
(b) Solve a simple non-linear equation using a simple iteration of the form xn + 1 = g(xn) where x0 is given.

OUTCOME 4
Solve further ordinary differential equations.
Performance criteria
(a) Solve a first order linear differential equation using the integrating factor.
Mathematics: Unit Specification – Numerical Analysis 1 (AH) 50
National Unit Specification: statement of standards (cont)
UNIT Mathematics 3 (Advanced Higher)

OUTCOME 5
Use further number theory and direct methods of proof.
Performance criteria
(a) Use proof by mathematical induction.
(b) Use Euclid’s algorithm to find the greatest common divisor of two positive integers.

Evidence requirements

Evidence would normally 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) and Mathematics 2 (AH)