Mathematics - Highers/Advanced Highers
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St. Andrew's & St. Bride's High School Platthorn Drive East Kilbride G74 1NL
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Higher Mathematics

Session 2017-2018 is the last academic year in which the Higher Mathematics course will consist of 3 units and an external exam.  (The mandatory assessment of units will be removed the following year.)
Officially, the course currently consists of three units (called Relationships & Calculus, Expressions & Functions, and Applications) but we have chosen to rearrange this content to create four units. This allows us to cover the course in our preferred order, to shorten the assessments and lessen the time between each assessment. Our unit assessments will each consist of three operational “Assessment Standards” (blocks of content), which are broken into a few sub-skills, and some problem-solving questions (also classed as Assessment Standards). For more details, see “Course Outline” below.


COURSE OUTLINE — New Higher Maths

Unit 1
Applications 1.1: Straight Line
Relationships & Calculus 1.1: Quadratics and Polynomials
Relationships & Calculus 1.2: Trigonometric Equations (Part 1)
(plus some problem solving)

Unit 2
Relationships & Calculus 1.3: Calculus: Differentiation
Relationships & Calculus 1.4: Calculus: Integration
Applications 1.4: Applying Calculus skills to Optimisation & Area
(plus some problem solving)

Unit 3
Applications 1.3: Recurrence Relations
Expressions & Functions 1.3: Applying algebraic and trigonometric skills to Functions
Expressions & Functions 1.1: Exponential & Logarithmic Functions
(plus some problem solving)

Unit 4
Expressions & Functions 1.4: Vectors
Applications 1.2: Circles
Relationships & Calculus 1.2: Trigonometric Equations (Part 2)
Expressions & Functions 1.2: Trigonometric Expansions/Identities and The Wave Function
(plus some problem solving)


Frequently Asked Questions

Q1. What is the recommended entry level?
Ans 1.
This course is intended for candidates who passed National 5 Maths in S4 or S5 (preferably with an ‘A’ or ‘B’ award if now in S6, but we will allow an S5 pupil with a 'C' pass to attempt the course, although it may effectively become a two-year course for many of them). The course is also available to candidates who failed Higher Maths last session, and to those who wish to try to upgrade their existing Higher Maths qualification.

Q2. What constitutes a pass for the new Units?
Ans 2  In order to pass a Unit, a candidate must pass all Assessment Standards being assessed in that unit. To pass an Assessment Standard labelled as 1.1, 1.2, 1.3 or 1.4, the candidate must successfully demonstrate more than half of the points of process and accuracy across that Assessment Standard. (See “Course Outline”). However, if at the end of the course, a candidate has scored at least 60% for one of the SQA's original units, there will be no need for a re-sit on the Assessment Standards from that unit. To pass a problem-solving Assessment Standard, the pass marks are either 2 out of 6 when starting problems and 2 out of 5 for the communication at the end of problems but these can also be overcome by scoring at least 60% for each of the SQA's original units.

Q3. What constitutes a pass for the course?
Ans 3. To pass the course, a candidate must pass all Units and must gain an A, B or C in the external SQA exam.

Q4. What happens if the student does not pass a unit at the first attempt?
Ans 4.
If the student does not meet the standards described in Q2 above, then a re-sit will be required, but only for Assessment Standards that were failed. The pupil would be required to achieve at least the threshold score for each Assessment Standard (but there is no "60% rule" this time). The re-sits take place towards the end of the course to allow for previous disappointments to be swept aside by the "60% rule" (which will not become clear until other unit assessments have been sat).

Q5. What happens if the candidate fails the re-assessment?
Ans 5
. Only one re-assessment is allowed for each Unit. If a re-sit for a unit is failed, the candidate cannot achieve a full course award, but if other units are achieved, these successes will appear on the candidate's final SQA certificate.

Q6. Can calculators be used in Unit assessments?
Ans 6.
Yes, provided that the calculator cannot perform “symbolic manipulation” (i.e. algebra).

Q7. Do successful unit assessment results mean likely success in the final external exams?
Ans 7.
Not necessarily. Even if no re-sits were required, the level of the Unit tests are below the standard of the external exam since questions in the final exam can combine sub-skills in ways not previously assessed. Furthermore, retention could be more of an issue at the end of the course; unit assessments took place after only three or four chapters. Candidates should avoid complacency!


Q8. How can learners, parents and staff tell if a (quality) pass is probable?
Ans 8
  In order to give everyone a better idea of whether or not a (quality) pass in the external exam is likely, it is necessary to sit tests which are more difficult than Unit assessments. Some questions will attempt to integrate knowledge from different Assessment Standards/units. Two of these assessments will be class tests and another will be a prelim..

Q9. What is the format of the final external exam?
Ans 9
. The New Higher exam consists of two papers.
Paper 1 will consist of non-calculator questions worth a total of 60 marks and lasts for 1 hour and 10 minutes.
Paper 2 will allow the use of calculators (but not calculators which can perform symbolic manipulation - i.e. algebra). It contains 70 marks and runs for 1 hour and 30 minutes.

Q10.  How can candidates maximise their potential?
Ans10
  In order to achieve a course award, candidates ought to set their sights beyond the requirements for passing a unit. They should try to master more difficult content and gain problem-solving experience by completing even the hardest questions in their textbooks, seeking their teachers’ help whenever necessary.
Candidates should give their best effort to all hand-in homework exercises. These are found on the departmental website (see back page). Pupils have a week to complete these tasks and should try the homework early in the week and seek the teacher’s help for questions that they find too difficult. Pupils should not miss out any questions or even parts of questions.
Completing all nightly homework tasks (from their textbook) and all hand-in exercises (homework sheets) on time is necessary, but not sufficient. Studying must be done over and above homework.
If pupils bring in a flash drive, they can be given a wealth of revision materials including past papers & solutions/marking schemes. If pupils work through these questions and ask for help, it will be of enormous benefit.
The department strongly advises pupils to use their own calculators daily so that they can learn how they work, as some work differently from others.

Q11. How can parents help with revision at home, particularly if the content is unfamiliar?
Ans 11
.  Ensure that your son/daughter is not simply sitting back reading their notes or re-writing their notes. The best way to prepare for Maths is to attempt as many questions as possible at home and seek help in school.
A useful starting point is to recognise that each teacher’s notes will contain questions and answers (& rules/formulae). Encourage your son/daughter to cover up each answer and then try each question. Can it be done without having a look at the solution along the way? Even if the answer is correct, has the working been set out in the same manner as the original note? Each time the answer is “No”, ask for the technique to be studied again at home, then cover it up and try again.
No matter what level of Maths parents are familiar with, they can assist and make comment on areas such as presentation of work, look for questions in homework exercises that have been missed out (indicating possible problems) and encourage students to approach a member of the department for help.


Advanced Higher Mathematics

Officially the course consists of three units called “Methods in Algebra & Calculus”, “Applications in Algebra & Calculus”, and “Geometry, Proof and Systems of Equations” but we have chosen to rearrange this content to create four units. This allows us to cover the course in our preferred order, to shorten the assessments and lessen the time between each assessment. For more details, see “Course Outline” below.

COURSE OUTLINE — New Advanced Higher Maths

First Unit
1.1  Partial Fractions (after some introductory algebra)
1.2/2.5  Differentiation (including in context)
2.1/3.3  Binomial Theorem and Complex Numbers

Second Unit
2.4  Properties of Functions
3.1  Systems of Equations and Matrices
1.3/2.5  Integration (including in context)

Third Unit
1.4  First and Second Order Differential Equations
2.2  Sequences and Series (Arithmetic, Geometric & Maclaurin’s)
3.5  Some Methods of Proof (but not Proof by Induction)

Fourth Unit
2.3  Summation and Proof by Induction
3.2  Vectors
3.4  Number Theory (Euclidean Algorithm & Number Bases)

Frequently Asked Questions

Q1. What is the recommended entry level?
Ans 1.
A candidate ought to have attained a Higher Mathematics award (preferably at grade ‘A’ or ’B’).

Questions and answers 2 to 8 - as above (please see Q2 to Q8 under "Higher Mathematics").

Q9.  What is the format of the final external exam?
Ans 9.
There is one three-hour exam.  (There is now a formulae sheet, but candidates must learn many other formulae & methods “off by heart”.)

Q10.  How can candidates maximise their potential?
Ans10
  In order to achieve a course award, candidates ought to set their sights well beyond the requirements for passing a unit. They should try to master more difficult content and gain problem-solving experience by completing even the hardest questions in their folders and books, seeking their teachers’ help whenever necessary.  Furthermore, on the department's website (http://www.mathshomework.wikispaces.com) there are past paper questions by topic, all of which should be tackled as each new topic is completed.  There are full solutions to these questions which candidates should study carefully after attempting each question by themselves.  Despite these solutions being carefully written, some candidates will still require their teachers' help and should not hesitate to ask either of them for further explanation should this prove necessary.  These questions will replace hand-in homework exercises.

Q11 & Ans 11 - as above (please see Q11 under "Higher Mathematics")