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From the Principal Welcome to our Christmas newsletter. As you read through these pages, you will see something of life here over the term. While teaching and learning in the classroom are the core work of any school, a co-curricular programme is essential to ensure the holistic development of our students. Many girls are involved in the wide range of activities on offer and I thank the many teachers and prefects who give of their time week after week to provide such opportunities.
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Publié par
Nombre de lectures 25
Langue English


Intermediate 1
Fourth edition – published March 2002NOTE OF CHANGES TO ARRANGEMENTS
COURSE TITLE: Mathematics (Intermediate 1)
FOR ENTRY TO COURSES: C100 10 Mathematics: Maths 1, 2 and 3
C101 10 Mathematics: Maths 1, 2 and Applications
National Course Specification
Course Details: Course structure section has been updated to show the
new codes and titles for entry to courses in
Mathematics with optional routes.
National Units Specification
All Units: No changes.National Course Specification
COURSE NUMBERS C100 10 Mathematics: Maths 1, 2 and 3
C101 10 Mathematics: Maths 1, 2 and Applications
In order to ensure the accurate and complete transfer of data to and from centres, new codes and titles
for entry to courses in Mathematics with optional routes have been introduced to reflect the options
chosen by candidates. The course code C056 10 for Mathematics (Intermediate 1) will no longer be
acceptable for entry for the summer or winter diets. The codes detailed below must be used.
Unit codes and titles remain unchanged. There will be no change to the titles of the Mathematics
courses as they appear on the certificate.
C100 10 Mathematics: Maths 1, 2 and 3
This course consists of three mandatory units as follows;
D321 10 Mathematics 1 (Int 1) 1 credit (40 hours)
D322 10atics 2 (Int 1)
D323 10 Mathematics 3 (Int 1)
C101 10 Mathematics: Maths 1, 2 and Applications
This course consists of three mandatory units as follows;
D321 10 Mathematics 1 (Int 1) 1 credit (40 hours)
D322 10atics 2 (Int 1)
D324 10 Applications of Mathematics (Int 1)
In common with all courses, this course includes 40 hours over and above the 120 hours for the
component units. This may be used for induction, extending the range of learning and teaching
approaches, support, consolidation, integration of learning and preparation for external assessment.
This time is an important element of the course and advice on its use is included in the course details.
Administrative Information
Publication date: March 2002
Source: Scottish Qualifications Authority
Version: 04
© Scottish Qualifications Authority 2002
This publication may be reproduced in whole or in part for educational purposes provided that no profit is derived from
reproduction and that, if reproduced in part, the source is acknowledged.
Additional copies of this course specification (including unit specifications) can be purchased from the Scottish Qualifications
Authority for £7.50. Note: Unit specifications can be purchased individually for £2.50 (minimum order £5).
2National Course Specification: general information (cont)
COURSE Mathematics (Intermediate 1)
While entry is at the discretion of the centre, candidates will normally be expected to have attained
one of the following:
• Standard Grade Mathematics Foundation award
• Using Mathematics 3 (Acc 3) unit
• equivalent
This course gives automatic certification of the following:
Complete core skills for the course Numeracy Int 1
Additional core skills components for the course Critical Thinking Int 1
For information about the automatic certification of core skills for any individual unit in this course,
please refer to the general information section at the beginning of the unit.
Additional information about core skills is published in Automatic Certification of Core Skills in
National Qualifications (SQA, 1999).
Mathematics: Intermediate 1 Course 3National Course Specification: course details
COURSE Mathematics (Intermediate 1)
As with all mathematics courses, Intermediate 1 Mathematics aims to build upon and extend
candidates’ mathematics in a way that recognises problem solving as an essential skill and enables
them to integrate their knowledge of different aspects of the subject.
Because of the importance of these features, the grade descriptions for mathematics emphasise the
need for candidates to undertake extended thinking and decision making, so as to solve problems and
integrate mathematical knowledge. The use of coursework tasks to help meet the grade descriptions
in problem solving is encouraged.
Where appropriate, mathematics should be developed in context, and the use of mathematical
techniques should be applied in social and vocational contexts related to likely future work and study.
The Intermediate 1 Mathematics course, which contains Mathematics 1 (Int 1), 2 (Int 1) and 3 (Int 1)
is designed to meet the needs of candidates who wish to progress to Intermediate 2 Mathematics. In
this course, the emphasis is placed on developing an appreciation of the power of mathematical
language and the efficiency of algorithms in preparation for the Intermediate 2 course.
Mathematics 1 (Int 1) and 2 (Int 1) taken together with Applications of Mathematics (Int 1) form the
basis of a course designed to meet the needs of candidates who require a mathematics qualification at
Intermediate 1 level, but who do not intend to proceed to a mathematics course at Intermediate 2
level. The course aims to enhance candidates’ skills in applying their mathematics in a range of
contexts with the emphasis on real-life applications.
The skills and knowledge of mathematics at Intermediate 1 level can be illustrated in technological,
vocational, scientific, social and environmental contexts. Candidates’ experiences of placing
mathematics in context and basing their learning on the solution of problems allows the course to
contribute to other areas of learning, to communication skills, to creative thinking and to personal and
social development.
The syllabus is designed to build upon and extend candidates’ previous mathematical learning, to
introduce them to the areas of algebra and elementary statistics and, depending on the optional unit
chosen, to introduce trigonometry and extend algebraic methods or to broaden the candidate’s
mathematical experience by considering applications of mathematics. The course makes demands
over and above the requirements of individual units. Candidates should be able to integrate their
knowledge across the component units of the course. Some of the 40 hours of flexibility time should
be used to ensure that candidates satisfy the grade descriptions for mathematics courses that involve
solving problems, and which require more extended thinking and decision making. Candidates should
be exposed to coursework tasks that require them to interpret problems, select appropriate strategies,
come to conclusions and communicate intelligibly.
Mathematics: Intermediate 1 Course 4National Course Specification: course details (cont)
COURSE Mathematics (Intermediate 1)
Where appropriate, mathematical topics should be taught and skills in applying mathematics
developed through real-life contexts. Candidates should be encouraged throughout the course to make
use of their skills in mental and paper and pencil calculation. They should also be able to make
efficient use of calculators and to apply the strategy of checking.
Numerical checking or checking a result against the context in which it is set is an integral part of
every mathematical process. In many instances, the checking can be done mentally, but on occasions,
to stress its importance, there should be evidence of a checking procedure within the calculation.
There are various checking procedures which could be used:
• relating to a context – ‘How sensible is my answer?’
• estimate followed by a repeated calculation
• calculation in a different order
The need for checking arises in all mathematical processes and candidates should, therefore, be
prepared to provide evidence of checking of more than just numerical calculations within the course
assessment, eg, checking the solution of an equation by substitution into the original equation.
It is expected that candidates will be able to demonstrate attainment in the algebraic, trigonometric
and statistical content of the course without the use of computer software or sophisticated calculators.
In assessments, candidates are required to show their working in carrying out algorithms and
Mathematics: Intermediate 1 Course 5National Course Specification: course details (cont)
The content listed below should be covered in teaching the course. All of this content will be subject to sampling in the external assessment. Part of this
assessment will be carried out in a question paper where a calculator will not be allowed. Any of the topics may be sampled in this part of the assessment.
The external assessment will also assess problem solving skills, see the grade descriptions on pages 17 and 18. Where comment is offered, this is intended to
help in the effective teaching of the course.
Mental, pencil and paper and calculator computation should be employed as appropriate to the context and the computational ability of the candidate.
Necessary checking procedures should be emphasised.
References shown in this style indicate the depth of treatment appropriate to Grades A and B.
Mathematics 1 (Int 1)
Basic calculations
find a percentage of a quantity eg calculations such as 17½% of £240 in the
contexts of discount, VAT, simple interest for
whole year and
for a fraction of a year [A/B]
express one quantity as a percentage of
another [A/B]
round calculations to a given degree of accuracy:
to nearest whole number;
to nearest 10, 100, 1000;
to a given number of decimal places
solve simple problems on direct proportion
Mathematics: Intermediate 1 Course 6National Course Specification: course details (cont)
Basic geometric properties
find the areas of simple composite shapes Composite shapes should include rectangles and
right-angled triangles
find the volumes of cubes and cuboids and semi-circles [A/B].
find the area and circumference of a circle An investigative approach to areas and
circumferences of circles should be taken.
Expressions and formulae
evaluate expressions eg If a = 20 and b = 4 evaluate 2b – a.
evaluate formulae expressed in words eg Profit is given by selling price less cost price.
evaluate simple formulae expressed in symbols eg Evaluate L = 3a + 2b, s = vt, A = ½ bh, Formulae from other areas of the curriculum,
R = V ÷ I; for whole number values of variables. such as Physics, could be used here.
Calculations in everyday contexts
carry out calculations involving money in eg Wage rise (added to initial wage); commission; Wherever possible, candidates should use real-
appropriate social contexts bonus; overtime; hire purchase; insurance life examples, such as information leaflets from
premium at £2.90 per £1000 on amount of banks, newspaper tables providing exchange
use exchange rates to convert from £64,500. rates and insurance tables issued by companies.
pounds sterling to foreign currency The importance of checking that an answer is
foreign currency to pounds sterling [A/B] sensible should be stressed here.
Mathematics: Intermediate 1 Course 7National Course Specification: course details (cont)
Mathematics 2 (Int 1)
plot and read coordinates in all four quadrants
add and subtract positive and negative integers Mainly in practical contexts, eg, temperature, Candidates who intend to complete the course
height above sea-level, etc. containing Mathematics 3 (Int 1) require to
eg 3 – (–2) [A/B]
subtract a negative integer from an integer develop a facility with integers for algebraic
[A/B] manipulation and the solution of equations.
multiply two integers where one is positive and
one is negative and divide a negative integer by a
positive integer
multiply and divide two integers where both
are negative and multiply three or more
integers [A/B]
Speed, distance and time
interpret distance–time graphs
recognise the significance of the point of Software packages which draw distance–time
intersection of two graphs, where the graphs are graphs could be used here.
in context
calculate time intervals, including those over Examples would involve straightforward
midnight or midday on the 12-hour clock quantities of time such as quarter of an hour.
distance, speed, time – calculate one, given the Where candidates have access to a scientific
other two calculator, the use of the fraction key could be
Mathematics: Intermediate 1 Course 8National Course Specification: course details (cont)
The Theorem of Pythagoras
solve problems in right-angled triangles using the An investigative approach should be used to
Theorem of Pythagoras introduce the theorem of Pythagoras.
Simple graphs, charts and tables
extract and interpret data from bar graphs, line Sources of graphs include the media, social
graphs, pie charts and stem-and-leaf diagrams subjects, vocational contexts and social
contexts, including anything of direct interest to
construct bar graphs, line graphs and stem-and- Data could be in the form of an ungrouped the candidate (eg sport).
leaf diagrams frequency table. Candidates could use advanced calculators with
statistical functions and computers (eg
interpret trends in graphs spreadsheets), to manipulate and graph data.
The technology could also be used to graph the
construct a frequency table from data without same set of data in different ways to compare
class intervals the suitability of each method.
The emphasis should be on comparison and
construct and interpret a scattergraph The scattergraph should show high positive or interpretation of graphs and diagrams, including
negative correlation, ie, indicate the connection discussion of a wide variety of graphs.
draw a best-fitting straight line by eye on a between the variables.
scattergraph and use it to estimate the value of It may be helpful to students to discuss the use
one variable given the other of the point ( ) as a ‘hangx, y er’ for a best-fitting
straight line but it is not a requirement at this
level. Similarly, the method of semi-averages
(split the data in half and plot the average of
each half) may be useful in introducing this
There should be informal discussion of
correlation, interpolation and extrapolation and
the high possibilities of errors in interpreting
Mathematics: Intermediate 1 Course 9

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