ifymb002 mathematics business 2019-20mathematics in subject-related contexts appropriate for entry...

International Foundation Year (IFY)

IFYMB002 Mathematics Business

2019-20

Related Item:

Formula Booklet

© 2019 Northern Consortium UK Ltd. of 30

Amendment History

Release

Date

Version

No.

Summary of Main Changes Author

Aug 2019 V3.3 Core texts updated to new editions Academic Team

June 2019 V3.2 Updated to 19/20 Formatting updated

Reference to using Cite Them Right in

Section 9 removed

Academic Team

May 2018 V3.2 Updated to 18/19 Academic Team

May 2017 V3.1 Updated to 17/18

Minor formatting amendments

Textbooks updated

Academic Team

June 2016 V3.0 Section B Coursework Guidance

amended.

Academic Team

May 2016 V2.1 Dates updated

Section 7 updated as NCUK will now

write the IFY assessments. Some

centres may set their own

assessments but must receive

permission from NCUK before doing

so.

Academic Team

June 2015 V2.0 The content of this module has been

reviewed in full (Section 4).

The following changes have been made

across all IFY modules:

Final Examination duration reduced

from 3 hours (plus 10 minutes reading

time) to 2 hours and 30 minutes (plus

10 minutes reading time).

Module assessments are now

consistent across all modules. This

has been done to remove assessment

elements that contribute little to a

student’s performance in the module

and to reduce administrative

requirements on delivery partners and

NCUK. The change is not intended to

reduce student workload.

An exemplar teaching has been

introduced. The purpose of this is

allow judgements to be made on the

ability of the syllabus to be delivered

in the time available and to provide

teachers with a suggested, but not

mandated, delivery plan.

The duration of the End of Semester

One Test (EOS1 Test) is 2 hours.

Peter Davies (Module

Leader), Programme

Validation Panel and

Academic Team.

Please note that the amendments previously introduced to this syllabus are detailed in the

version that was released for 2014-15 teaching.

This syllabus is valid for the 2019-20 academic year.

IFYMB002 Maths (Business) Syllabus 2019-20


Contents

1. Module Specification 4

2. Aims 5

3. General Learning Outcomes 6

4. Module Content 7

5. Specific Learning Outcomes 10

6. Teaching and Learning Methods 14

7. Assessment 16

8. Resources 17

9. Core Text and Reading List 18

Appendix A Exemplar Teaching Plan 19

Appendix B Coursework Guidance 29

Appendix C Formulae Booklet 30


1. Module Specification

Module Code IFYMB002

Module Name Mathematics Business

Programme Name International Foundation Year

Percentage breakdown of

Coursework

30%

Percentage breakdown of Exam 70%

Delivery period The syllabus will usually be delivered over two

15 week semesters

Recommended minimum teaching

hours

4 hours per week

Recommended minimum hours

(including independent study hours)

8 hours per week

Related documents NCUK IFY Programme Framework

NCUK Academic Handbook



2. Aims

To develop student’s key knowledge, understanding, skills and application of

mathematics in subject-related contexts appropriate for entry to a degree course at

any one of the NCUK Partner Universities.

2.1 General Aims

2.1.1 To develop abilities to think logically, to recognise incorrect reasoning and to

express ideas clearly.

2.1.2 To develop an enthusiasm for the subject and the skills required to apply the

knowledge to both the further study and application of mathematics.

2.1.3 To develop in students an understanding of how theory and application work

together.

2.1.4 To develop students’ skills in modelling and the interpretation of results.

2.1.5 To develop the necessary English mathematics vocabulary and terminology to

use their mathematics knowledge effectively in a UK/Western university

context.

2.1.6 To acquire the skills needed to use technology such as calculators and

computers effectively, recognise when such use may be inappropriate and be

aware of limitations.

2.1.7 To encourage students towards a level of independence in both the planning

and organisation of their studies.

2.1.8 To assist the development of competence and confidence of the students as

learners, taking responsibility for their own learning through directed reading

and study.

2.2 Specific Aims

2.2.1 To revise basic skills and develop further skills in algebra.

2.2.2 To demonstrate basic skills in trigonometry and coordinate geometry.

2.2.3 To differentiate and integrate, including the selection and use of appropriate

rules and techniques, and the application of the calculus.

2.2.4 To develop concepts in probability and statistics relevant to business planning.

2.2.5 To be confident and competent with the operations of a scientific calculator and

its use.

2.2.6 To apply mathematical techniques to simple “real life” problems.

2.2.7 To familiar with, and competent in, the use of computer software to solve pure

and applied mathematical problems.



3. General Learning Outcomes

On successful completion of this module, a student will be able to:

Knowledge and

understanding

Recognise, recall and apply specific mathematical facts,

principles and techniques.

Select, organise and present relevant information clearly

and logically.

Select and apply appropriate mathematical and

statistical techniques to solving problems.

Intellectual skills Apply mathematical techniques to problems from a

variety of relevant discipline areas.

Present and interpret data in tables, diagrams and

graphs, using generic and specific software packages.

Carry out appropriate calculations using a formula

booklet, a calculator and/or computer software where

appropriate.

Discuss and interpret results obtained, including an

estimate of accuracy.

Practical skills Specify what data are required for a given task.

Collect relevant data in an effective and efficient way.

Transferable skills Write mathematically-based reports that deliver both a

cogent argument and a neat and well-organised

presentation style.

Study independently and make personal notes for

problem-solving and revision purposes.

Source and retrieve information from a variety of original

and derived locations, such as textbooks, the internet,

etc.

Select and employ problem-solving skills (description,

formulation, solution/analysis, interpretation).

Manage and present data in a variety of formats.

Use and apply information technology.



4. Module Content

All topics must be covered. Appendix A provides an Exemplar Teaching Plan which

indicates the proportion of time to be spent on each topic and activities to support

student learning.

SEMESTER ONE

Topic Content

A Linear Equations The equation of a line, parallel and perpendicular

lines. Solving pairs of simultaneous equations using

elimination, substitution and graphical methods.

B Simple probability Define probability, use sample space diagrams to

help calculate probabilities. Combining probabilities

and using tree diagrams. (Knowledge of conditional

probability is not expected in this module).

C Quadratic Equations,

inequalities and Remainder

Theorem

Quadratic Functions: Factorising, completing the

square and using the quadratic formula.

Remainder Theorem: Simple algebraic division; use

of the factor theorem and the remainder theorem.

Graphs of quadratic and cubic functions.

Geometrical interpretation of algebraic solutions of

equations.

Inequalities: Manipulating inequalities, solving linear

and quadratic equations and inequalities.

D Binomial Expansions,

Sequences and Series

Binomial expansions: Pascal’s triangle, factorials,

binomial expansion (positive integer powers,

binomial coefficient notation, evaluation of specific

terms)

Sequences and series: Sequences, series, sigma

notation. Finite Arithmetic Progressions (AP) and

series including sum. Geometric Progressions (GP)

and series including sum. Convergence and

divergence of geometric series.

E Indices, Exponential and

Logarithmic Functions

Laws of Indices for all rational exponents.

Exponential function: Exponential function and its

graph, introduction to rates of growth, solution of

equations involving exponential functions.

Logarithmic function: Rules and manipulation of

logarithms, logarithmic function and its graph,

relationship between exponential/logarithm

functions, solution of equations involving either

exponential or logarithmic functions.



F Trigonometric Functions Angles (degree/radian measure). Trigonometric

ratios, trigonometric functions (sine, cosine, tangent)

and their graphs. The identity cos� � + sin� � ≡ 1.

Solutions of simple trigonometric equations.

G Calculus - differentiation Principles: Gradients of tangents and normals to

curves, limit form, polynomial rules (inc. First

Principles). Derivatives of simple functions

(exponential, log, trigonometric. The trigonometric

functions are sin x, cos x and tan x only.) Use of

Formula Booklet (see Appendix C).

Generic applications: Using derivatives to help sketch

curves. Equations of tangents and normals. Maxima,

minima and points of inflexion which are stationary

points. Use of the second derivative.

H Calculus - integration Principles: Inverse of differentiation, standard

integrals (monomial, trigonometric, exponential),

indefinite and definite integration. (The trigonometric

functions are sin x and cos x only).

Area under a curve.

SEMESTER TWO

Topic Content

I Introduction to Statistics Data collection: Introduction to sampling and

probability for marketing research and

experimentation. Collection and presentation of

statistical data. Histograms and the cumulative

frequency polygon and curve.

Data summaries: Mode, median and mean.

Standard deviation. Quartiles and interquartile

range.

J Further Probability and Set

Theory

Further Probability: Mutually exclusive events and

independent events. Laws of Probability. Conditional

Probability.

Set Theory: Sets, intersections, unions,

complements. Venn diagrams, including their use to

solve probability problems.

K Correlation, Linear

Regression and Time Series

Correlation: Scatter graphs. Calculation and

interpretation of the coefficient of correlation.

Linear Regression: Calculation of the equation of a

least-squares linear regression line.

Time Series: Trend-line, moving averages.

L Probability Distributions Discrete random variables: Probability distributions

given algebraically or in tables. Calculate the mean

E(�) and the variance Var(�).



Distributions: Binomial distribution. Normal

distribution and confidence intervals.

M Financial Mathematics Percentage and percentage change. Interest.

Appreciation and Depreciation.

N Further Differentiation Rules: Sum, product , quotient rules and the chain

rule (composite functions)

Implicit differentiation.

O Further Integration Integration by substitution. Change of variable. Use

of Formula Booklet (see Appendix C).

Partial fractions (linear factors, repeated linear

factors, improper fractions), integration by partial

fractions.

Integration by parts.



5. Specific Learning Outcomes On successful completion of the module, a student should be able to:

A Linear Equations

A1 Find the equation of a straight line using coordinate geometry.

A2 Find parallel and perpendicular lines and sketch appropriate graphs.

A3 Solve pairs of simultaneous equations using elimination, substitution and

graphical methods.

B Simple probability

B1 Find the probability of a single event.

B2 Recognise that �(�) and �(��) mean the probabilities of event � occurring and

event � not occurring respectively.

B3 Find, for two events � and �, the probabilities of both � and � occurring, and

the probabilities of either � or � occurring. (the use of the symbols ∩ and ∪

will not be expected in this module).

B4 Construct and use a simple tree diagram.

C Quadratic Equations, inequalities and Remainder Theorem

C1 Carry out the process of completing the square to locate vertices (turning

points) of graphs.

C2 Use the discriminant to determine the number of real roots.

C3 Use surds to give exact solutions.

C4 Use algebraic division by a monomial or quadratic function.

C5 Sketch the graphs of quadratic and cubic functions.

C6 Use the Remainder Theorem to determine the remainder when a polynomial

is divided by (�� + �).

C7 Solve by substitution a linear and quadratic pair of simultaneous

Equations: plot the functions using graph paper.

C8 Recognise and solve linear/quadratic equalities and inequalities.

C9 Use algebraic and graphical methods to solve inequalities.

C10 Recognise and distinguish between open and closed intervals.

D Binomial Expansions, Sequences and Series

D1 Expand (1 + �)� for small positive integer �.

D2 Use Pascal’s triangle to find binomial coefficients.

D3 Expand (� + �)� where � is a small positive integer.

D4 Understand idea of sequence of terms using general formulae and

Recurrence relations.

D5 Use sigma notation for series representations.

D6 Recognise and sum a finite arithmetic series (AP).

D7 Recognise and sum a geometric series (GP).

D8 Define, explain and test for convergence of a series.

D9 Use an AP or a GP to solve certain practical problems.

E Indices, Exponential and Logarithmic Functions

E1 Know the equivalences e.g. �� × �! ≡ ��"! and �� ÷ �! ≡ ��$!.

E2 Use a calculator to evaluate exponential and logarithmic expressions.



E3 Sketch the graphs of % = '( and % = '$( .

E4 Apply exponential functions to problems.

E5 Apply the rules of logarithms to problems.

E6 Change the base of a logarithm.

E7 Solve equations involving exponential and logarithmic functions.

F Trigonometric Functions

F1 Convert from radians to degrees and vice versa.

F2 Find sin, cos, and tan of any angle and plot their graphs.

F3 Know the area of a triangle formula )

�� sin *.

F4 Calculate inverse trigonometric functions.

F5 Find particular solutions of simple trigonometric equations. (these equations

will take the form: � sin � = +; cos �� = +; tan� � = + over any range).

F6 Apply the sine and cosine rules to an arbitrary triangle.

G Calculus - differentiation

G1 Evaluate the gradient of a curve at a point.

G2 Recognise and explain the notation ./

.( and 0�(�).

G3 Sketch the derivative graph ./

.( .

G4 Apply the limit formula to simple functions (first principles). (this will be

confined to single integral powers of �.)

G5 Use formula booklet to obtain derivatives of standard functions,

Including '1( where 2 is a constant.

G6 Explain second-derivative notation.

G7 Apply second derivatives to practical problems.

G8 Find stationary points for a given function.

G9 Distinguish between local maximum, local minimum and point of

Inflexion which are stationary points.

G10 Apply G8 to practical optimisation problems.

G11 Obtain the equation of tangent and normal of a curve at a specified point.

H Calculus - integration

H1 Identify integration as the inverse of differentiation.

H2 Use formula booklet to determine indefinite integrals including )

�("! where �

and � are constants.

H3 Form and explain the definite integral.

H4 Evaluate definite integrals.

H5 Calculate the area between a curve and the x -axis, including areas

Partly above and partly below the axis.

I Introduction to Statistics

I1 Distinguish between continuous and discrete data.

I2 Construct frequency distributions.

I3 Draw a line graph using discrete data, a histogram using continuous data.

I4 Evaluate mode, median and mean.

I5 Understand what “standard deviation” means.

I6 Evaluate the standard deviation (divisor �).

I7 Evaluate the mean and standard deviation of data in a frequency distribution.



I8 Know how to display and interpret a cumulative frequency distribution.

I9 Use a cumulative frequency graph to estimate the median, the quartiles and

the interquartile range of a set of data.

I10 Identify a distribution which appears to be skewed.

J Further Probability and Set Theory

J1 Explain set definitions.

J2 Compose two sets by union or intersection.

J3 Illustrate sets by using Venn diagrams.

J4 Use the laws of probability

J5 Distinguish between mutually exclusive and independent events.

J6 Compute conditional probabilities.

J7 Illustrate probabilities using Venn diagrams and more complicated tree

diagrams.

J8 Calculate the probabilities of combined events (the understanding of set

notation will be expected).

K Correlation, Linear Regression and Time Series

K1 Explain the term “correlation” in relation to data sets where both variables

must be random.

K2 Compute correlation coefficient and evaluate result in relation to appearance

of the scatter graph and with reference to values close to -1, 0 and 1.

K3 Explain the principle of least-squares approximation.

K4 Compute the equation of a least-squares linear regression line for random

variable 3 and non-random variable �.

K5 Be able to interpret in context the uncertainties of estimating a value

K6 Construct time series charts

K7 Calculate moving averages of a time series.

K8 Construct the trend-line of a time series.

K9 Extrapolate a trend line but be aware of the dangers. (calculating seasonal

variations and residuals will not be expected.)

L Probability Distributions

L1 Recognise and describe the nature of a “distribution”.

L2 Construct a probability distribution relating to a given situation involving a

discrete random variable �.

L3 Evaluate the expected value and variance of a linear function of a random

variable.

L4 Distinguish between discrete and continuous distributions

L5 Describe the binomial distribution

L6 Perform calculations with the binomial distribution

L7 Use the binomial distribution tables.

L8 Use of standardised Normal Distribution table

L9 Convert general data into the standardised form.

L10 Set up a confidence interval for a mean where the background distribution of

any samples will be Normal with a known standard deviation.



M Financial Mathematics

M1 Carry out any calculation involving direct percentage, reverse percentage,

percentage error and percentage change.

M2 Perform calculations involving simple and compound interest.

M3 Calculate appreciation and depreciation using knowledge of a geometric

progression gained in D7.

M4 Estimate when a certain value is reached in an appreciation or depreciation

situation using knowledge of logarithms gained in E5.

N Further Differentiation

N1 Apply the product rule, quotient rule and chain rule.

N2 Find ./

.( of an implicit function.

N3 Know the result .

.( �( = �( Ln �.

O Further Integration

O1 Integrate standard functions such as '�(,)

�( ,

56(()

5(() .

O2 Clarify what is meant by the term ‘partial fraction’.

O3 Find partial fractions for linear and repeated linear factors.

O4 Find partial fractions for improper fractions.

O5 Use substitution to evaluate indefinite and definite integrals.

O6 Apply integration by substitution to practical problems.

O7 Carry out integration by parts.



6. Teaching and Learning Methods

Teachers should use a range of different learning and delivery styles in order to give

students experience of the types of approach they will encounter in a Western university

e.g. lectures and tutorials. Appendix A (Exemplar Teaching Plan) suggests a delivery

format designed to facilitate the delivery of each topic. The centre is at liberty to diverge

from this Plan. Also, the centre may increase the minimum number of teaching hours

(4 hours per week) to meet the needs and abilities of students.

The range of teaching and learning activities should be employed in lectures, tutorials,

laboratories and directed self-study. The use of video clips and internet-based activity

is to be encouraged where it might lead to enhanced learning (much higher-quality CAL

software is now available).

A standard Formula Booklet (see Appendix C) should be used throughout the year, and

each student should be issued with a copy of this booklet at the start of the year.

Students will require access to computers with both MS Excel and some mode of

electronic/automated calculation platform installed.

A primary aim of the module is to develop in students an understanding of how theory

and application work together, and it is emphasised that teachers should develop and

illustrate applications of relevant mathematics in order to encourage this

development in business and management contexts.

Lectures will be used to transmit, explain and demonstrate much of the factual material,

and to develop and illustrate problem-solving methods. These sessions can be

augmented as appropriate with handout material, demonstration experiments and the

use of visual aids. These materials could be designed in collaboration with an EAP

teacher.

It is important for the development of students’ English language and study skills that

the delivery of the subject material is integrated with EAP, EAPPU or RCS. Regular

communication between the subject module teacher(s) and the EAP, EAPPU or RCS

teacher(s) will provide a basis on which to support and guide students. Students will

benefit from collaborative activities, where the subject module and EAP/EAPPU/RCS

teachers jointly deliver classes in relation to activities such as essay writing style and

using academic sources.

As part of study for the EAP, EAPPU or RCS module, students will learn the Harvard

referencing system. Subject teachers will ensure that students carry these learning into

the work produced for this module; see Section 9 of the syllabus for details of the

referencing guide recommended by NCUK. For further information about referencing

and citation, please consult the EAP or RCS syllabus (as relevant) for the texts and

online resources recommended by NCUK.

Students will have different backgrounds in the subject and it will be necessary to give

opportunities for directed self-study, and so allow each student to develop at their own



pace to reach the required level for the examinations. Activities (homework) for self-

study should be set weekly.

Tutorials should not be managed in the same way as lectures. Tutorials should involve

both group and individual activities, with a strong emphasis on applying knowledge from

lectures and reading to problem-solving. It is important for all students to have

opportunities to speak in English during each tutorial. Suggested activities include

students being encouraged to explain in English their answers jointly in pairs or small

groups, students providing answers to the whole class whilst standing at the front of

the group, and group activities that require discussion. These classes should be used

to verify that students are capable of using a scientific calculator correctly. Tutorials

may be used to discuss practical applications of mathematics, particularly with respect

to the content of the Business courses, including how to handle and analyse data.

Teaching staff are advised to prepare examples for this purpose. The sessions can also

be used for individual counselling of students and to assess student understanding of

the subject.

Students should use Microsoft Office software in the analysis of data and preparation

and presentation of reports.



7. Assessment

Formative

It is important that students are given the opportunity to engage in and submit

formative coursework assessments and receive feedback on this work. Formative

assessment should be designed to inform students of their progress and enable them

to develop and practice coursework and examination skills.

Summative

Summative assessments contribute to the student’s final grade for the module. The

summative assessment structure for the module is as follows:

COURSEWORK

30%

FINAL EXAM

70%

Semester 1

Coursework

1

10%

Semester 2

Coursework 2

10%

End of Semester 1

Test

10%

End of Module Exam

(Set by NCUK)

Level 1

(A – H)

Level 2

(I – O)

Length of Test: 2

hours plus 10 minutes

reading time

Length of Exam: 2

hours 30 mins plus 10

minutes reading time

Section A: Compulsory

40 marks

Section B: Choose 4

out of 6 questions

60 marks

Section A: Compulsory

45 marks

Section B: Choose 4

out of 6 questions

80 marks

100 marks 100 marks 100 marks 100 marks

Unless the centre has been given permission by NCUK to write its own summative

coursework assessments, NCUK will produce all summative coursework assessments for

the module in accordance with the task rubric information presented in Appendix

B. Where the centre has received permission from NCUK to write the summative

coursework, it will do this in accordance with the information and guidance given in

Appendix B and the regulations set out in the NCUK Academic Handbook, IFY

Coursework Writing and NCUK Approval.

The examination paper will be provided by NCUK and it will contribute a maximum of

70% to the final module grade. The paper will cover a broad range of the specific

learning outcomes.

It is essential that coursework and examinations are administered in accordance with

NCUK regulations. Please refer to the following sections of the NCUK Academic

Handbook for details:

Coursework Administration and Regulations

Centre Marking and Recording Results

Academic Misconduct Policy

Examination Administration



Requirement for the End of Semester 1 Test and Final Examination

It is the centre’s responsibility to provide the following materials for the end of semester

1 test and final examinations:

Calculator (refer to NCUK policy ‘Calculator Regulations’)

Graph Paper

Formulae Booklet ‘Data, Formulae and Relationships’ (refer to Appendix C of this

syllabus)

8. Resources

Microsoft Excel (or similar) processing package.



9. Core Text and Reading List

Please note that while resources are checked at the time of publication, materials may

be withdrawn from circulation and website locations may change at any time.

Core Text Gurney, L., Rayner, D. & Williams, P. (2017). Essential Maths A

Level Pure Mathematics Book 1. Elmwood Education Limited

ISBN: 9781906622657

Gurney, L., Rayner, D. & Williams, P. (2018). Essential Maths A

Level Pure Mathematics Book 2. Elmwood Education Limited

ISBN: 9781906622701

The above texts cover the common core aspects of pure

mathematics.

Pledger, K. et al (2009). AS and A Level Modular Mathematics-

Statistics 1. Pearson Education

ISBN: 9780435519308

Further Reading

Emanuel, R. & Wood, J. (2005). Advanced Mathematics AS Core

for Edexcel. Longman

ISBN 0582842379

This text book also includes a self-study CD

ISBN: 9780582842373

Useful Websites

http://www.revision-notes.co.uk/A_Level/Maths/

http://maxima.sourceforge.net for a copy of the mathematical

program Maxima

http://www.geogebra.org for a copy of the mathematical

program GeoGebra

Recommended

Referencing

Guide

Refer to the Harvard Referencing Guide in the Academic

Handbook for NCUK guidelines on this, though using online

Harvard Reference Guides to support assessment writing can

also be beneficial. When referencing, the main objectives are

clarity, consistency, accuracy of key information and ability to

locate the source.

Additional publications and online resources are listed in the

EAP and RCS syllabuses

http://www.revision-notes.co.uk/A_Level/Maths/

http://www.maxima.sourceforge.net/

http://www.geogebra.org/



Appendix A Exemplar Teaching Plan

Method of delivery notation:

L – by lectures; E – by doing exercises; T – use of tutorials; O – other (will be

specified)

Week Hour Topic + Lesson/activity/teacher guidance Further Notes

1 1

1

1

1

A. Linear Equations. Identify the gradient and

intercept in the equation of a straight line; calculate

gradients of the normal. (L/E)

Find equations of other lines which are parallel to or

perpendicular to the equation of a particular line.

Solve pairs of linear simultaneous equations using

elimination, substitution and graphical methods.

(L/E)

Continue with simultaneous equations. Carry out

practice examples on linear equations. (Mostly E)

B. Simple Probability. Evaluate the probability of

a single event. Familiarity with the notation 7(8)

and 7(8�) and realise that 7(8�) = 9 − 7(8). (L/E/T)

There may be

considerable

variation in the

algebraic ability of

students.

Any practice in this

area will probably

be good for

independent and

directed study.

2 1

1

1

1

Simple Probability. For two events 8 and ;, work

out the probability of both happening, and of either

happening. (Set notation is not required at this

level – neither will candidates be expected to be

aware of mutual exclusivity). Construct a tree

diagram and use it to work out combined

probabilities. (Mostly L)

C. Quadratic Functions and Equations. Carry

out a completing the square process and be able to

sketch the graph of a quadratic function. (L/E)

Solve quadratic equations by factorising,

completing the square and using the quadratic

formula [if time runs short, there is scope for

continuing the process of solving by factorisation in

the following week]. Candidates must be able to

present answers in surd form and understand the

significance of the discriminant (but will not be

expected to evaluate the size of coefficients in the

original equation which give, for example, two real

roots). (L/E)

Continuation of previous session. (T & mostly E)

Handling algebra is

often a weak spot,

so what was said

about independent

and directed study

in the previous

week probably

applies here.

e.g. questions

asking to find range

of values of < in

=> + ?<= + < − > = @

to give two real

roots will not be

set.



3 1

1

1

1

C. Further simultaneous equations. Solve by

substitution two equations – one of which is

quadratic and the other linear. (E & mostly L)

C. Inequalities. Solve linear and quadratic

inequalities, either by using algebra or graphical

methods. Recognise open and closed intervals and

what an integer is. (L/E)

C. Remainder Theorem. Use the Remainder

Theorem to show a given monomial is a factor of a

polynomial, or to find its remainder upon division if

it is not a factor. Candidates will be expected to

divide a polynomial by a monomial or quadratic

expression, and to be able to factorise an

expression completely. (L/E)

Continuation of previous session. (Mostly E)

Candidates should

be aware of the

term ‘factor

theorem’ and relate

its connection with

the remainder

theorem.

4 1

1

1

1

D. Binomial Expansions. Revise expansion of

quadratic functions. Use Pascal’s Triangle to find

binomial coefficients, and be able to expand

completely (9 + =)A and (B + C)A where A is a small

positive integer (normally not more than 5). (L/E)


Consolidation of previous two sessions. Candidates

will be expected to pick out single terms in the

expansion of (B + C)A where A is much larger but still

an integer. Candidates must also know what a

coefficient is. (L/E/T)

D. Progressions. Start on progressions and

introduce the difference between an Arithmetic

Progression (AP) and a Geometric Progression (GP).

Identify the first term and common difference in an

AP. (E & mostly L)

Candidates could

be asked to write

down the first few

terms in ascending

powers of = of an

expansion with A ≫

E. The meaning of

‘ascending’ or

‘descending’ will

always be given.

5 1

1

1

D. Progressions. Use the relevant formulae to

find the AFG term and the sum of the first A terms

of an AP and a GP. (L/E)

Candidates should be able to find the common

difference, common ratio and first term having been

given the AFG term or sum of the first A terms. (L &

mostly E)

Candidates could

be asked to find the

first term of a GP,

or how many terms

are needed for

geometric series, to

exceed a certain

value. This should

only be done once

logs have been

covered.



1

Use sigma notation and be able to generate a

progression from a sigma expression. (L/E)

Understand the idea of convergence and the

conditions needed. Find the sum to infinity of a

convergent series. (L/E)

6 1

1

1

1

E. Indices. Know that =B × =C ≡ =B"C and =B ÷

=C ≡ =B$C; and that (H=)I ≡ H=I. Use fractional

and negative indices. (L/E)

Find the exact solutions of equations which use

indices. (L & mostly E)

E. Exponential Functions. Understand what an

exponential is and be able to sketch the graphs of

I = J= and I = J$=. (Mostly L)

Relate exponential change to a real-situation e.g.

population growth and decomposition of a solid into

a liquid or a gas. (L/E/T)

Investigating

exponential growth

and decay could

provide good

material for

independent and

directed study.

7 1

1

1

1

E. Logarithmic Functions. Understand how a

logarithm behaves and compare it to real-life

situations such as the Richter and pH scales.

(Mostly L)

Establish the connection between logarithms and

exponentials. (L/E)

Use the logarithmic laws and apply them to solve

equations and simplify expressions. (L & mostly E)

Consolidation of previous work and practice in the

use of logarithms. (E/T)

Practice at using

and manipulating

logs would be

invaluable time

spent for

independent and

directed study.

8 1

1

F. Trigonometric Functions. Understand the

definition of a radian; convert angles from degrees

to radians and vice versa. Calculate the sin, cos and

tan of any angle and be familiar with their graphs.

(L/E)

Know how to find the inverse of a trigonometric

expression and solve simple trigonometric

equations (These equations will take the form:

B KLM = = N; OPK C= = N; QRM> = = < over any range

where N can be positive or negative.) Candidates

will also need to be able to quote and recognise the

exact values of the trigonometric functions of 0, 30,



1

1

45, 60 and 90 degrees and their radian equivalents.

(L/E)

Consolidation of previous two sessions and practice

at examples – particularly solving the equations and

identifying all the angles in a given interval. (E/T)

Apply the sine and cosine formulae to a non right-

angled triangle and use the formula for the area of

a triangle 9

>BC KLM S. Candidates should be familiar

with the identity OPK> = + KLM> = ≡ 9 . (L/T)

It is probably a case

of the more time

that students spend

at practising

examples in

independent and

directed study, the

better

9 1

1

1

1

G. Differentiation. Revision of finding the

gradient of a straight line; understand the definition

of the gradient of a curve at a point and, using first

principles, find an expression for this gradient

(using single integral powers of = only). (Mostly L)

Using first principles, find gradient functions of

other small powers of =. Introduce the idea of

differentiating any power of =. (Mostly L)

Use TI

T= and U�(=) and be able to differentiate any

polynomial and any power of =. (L/E)

Practice at differentiating polynomials and

substituting in values of =. (Mostly E)

A re-visit to the

binomial

expansions section

may be useful here

for

10 1

1

1

1

G. Differentiation. Extend differentiation to find

the equations of a tangent and a normal to a curve

at a specified point. (L/E)

Extend the process to differentiation of exponentials

(expressions of the form I = J<=) and logarithms.

(L/E)

Differentiation of trigonometric expressions (sin =,

cos = and tan = only). Use of the formula booklet to

obtain derivatives of standard functions. (L/E)

Consolidation of the previous two weeks’ work with

plenty of practice at differentiation. (E/T)

Plenty of scope

here for practice in

independent and

directed study.

11 1

1

G. Differentiation. Find the second derivative of

a function and be familiar with the notation T>I

T=> and

U��(=). (L/E)

Find the stationary points of a function. (L/E)

Points of inflexion

will be identified



1

1

Determine the nature of any stationary point. (L/E)

Sketch the graph of a function once the turning

points are known. Sketch the graph of a derivative.

(Mostly E)

only in instances of

zero gradient.

12 1

1

1

1

G. Differentiation. Extend the process of finding

stationary values to practical optimisation

problems. Typical cases could be to find the

maximum volume of a solid which has a fixed

surface area, and to find the minimum surface area

of a solid with a fixed volume. (Mostly L)

Extension of previous session. (L/E)

More practice at optimisation problems and start of

a general consolidation of differentiation. (Mostly E)

Completion of the consolidation started the

previous session. (E/T)

Other examples

could be

maximising an area

of a shape with

fixed perimeter.

In view of the size

of this topic, a long

consolidation will

probably be

necessary.

13 1

1

1

1

H. Integration. Identify integration as the inverse

of differentiation. Integrate any power of =. (Mostly

L)

Integrate J<= where < is a constant; integrate

sin = and cos =. (L/E)

Realise the integration of 9

= = ln = + N. Use the

formula booklet to determine indefinite integrals

including integrals of the form 9

B="C where B and C

are constants. (L/E)

Find the indefinite integral of any of the functions

above. (Mostly E)

Practice at

integration would

probably be time

usefully spent in

independent and

directed study.

14 1

1

1

1

H. Integration. Evaluate definite integrals. (L/E)

Apply definite integrals to finding the area between

the curve and the = − axis. (L/E)

Find more difficult areas, including those below the

= −axis. (L & mostly E)

Extend integration to finding an area which is bound

by two or more curves. (E/T)

Students should

realise that areas

below the = − axis

will give negative

values and

appreciate the

meaning of an

integral giving zero.

15 1

1

Revision

Revision



1

2

Revision

End of Semester Test

16 1

1

1

1

I. Introduction to Statistics. Distinguish

between, and give examples of, continuous and

discrete data. Evaluate mean, mode and median.

(L/E)

Calculate a standard deviation and understand what

it means. Construct a frequency table and use it to

find the mean and standard deviation. (L/E)

Use grouped frequencies to estimate the mean and

standard deviation. (L/E)

Draw a line graph to illustrate discrete data and a

histogram to illustrate continuous data. (L/E)

Students should

take care to label

axes and will be

expected to scale

them sensibly.

17 1

1

1

1

I. Introduction to Statistics. Evaluate cumulative

frequency and construct a cumulative frequency

graph. (L/E)

Use the graph to estimate the median, quartiles and

interquartile range. Identify possible skew in a

distribution, giving a reason. (L & mostly E)

J. Further Probability and Set Theory. Be

familiar with set notation (knowledge of the

following symbols will be expected: ∩, ∪, ∅, ∈ RMX ′).

(L/E)

Construct, and interpret, Venn diagrams. Use them

to find probabilities. (Mostly E)

If students are

questioned about

skew, they will not

be asked to identify

if it is positive or

negative.

18 1

1

1

1

J. Further Probability and Set Theory.

Construct, and interpret, more complicated tree

diagrams. (L/E)

Combine probabilities using tree diagrams and Venn

diagrams. (L/E)

Use the laws of probability (these are in the formula

booklet). (L/E)

Distinguish between independent and mutually

exclusive events. Calculate conditional

probabilities. (L/E/T)

Tree diagrams will

not have more than

three branches

from any given

point.

Candidates will

need to be aware of

7(8 ∩ ;) = @ for

mutually exclusive

events and 7(8 ∩

;) = 7(8) × 7(;) for

independent

events.



19 1

1

1

1

K. Correlation. Draw a scatter graph and the line

of best fit. (L/E)

Obtain some idea of sign and strength of

correlation. (L/E)

Calculate the correlation coefficient and relate its

value to the strength and type of correlation, with

particular reference to values close to -1, 0 and 1.

Appreciation that correlation does not imply

causation. (L & mostly E)

Continuation of previous session and further

practice at calculating and interpreting correlation.

(Mostly E)

Candidates will not

have to carry out

significance tests.

Unless there are

very few pairs of

readings, the data

will normally be

presented in

summary form in

an examination. In

a coursework task

students may have

more readings but

will be expected to

use Excel or other

similar package.

20 1

1

1

1

K. Linear Regression. Explain the principle of

least-squares approximation, and compute the

equation of a least-squares linear regression line for

random variable Z and non-random variable [.

(L/E)

Use the equation to estimate values but be aware

of the reliability of estimates. The equation will

normally be in the form I = B= + C and candidates

will be expected to know what B and C represent,

and to recognise if their values make sense. (L/E)

K. Time Series. Calculate the moving averages of

a time series. (L/E)

Construct a time series chart and draw a trend-line.

Candidates may be asked to extrapolate the trend

line for a short distance but may also be asked to

explain why extrapolation cannot be relied on.

(Calculating seasonal variations and residuals will

not be expected.) (L/E)

The above also

applies concerning

the numbers of

pairs of readings.

Students may have

to draw the

equation on a

scatter graph.

Questions asking

for an equation of [

on Z in the form = =

BI + C will not be

set.

Any number of

points could be

asked, but they will

normally be 3 or 4

point.

21 1

1

1

L. Probability Distributions. Understand what a

distribution is and be able to recognise and describe

one. Distinguish between discrete and continuous

distributions. (Mostly L)

Construct a probability distribution relating to a

given situation involving a discrete random variable

[. Evaluate the expected value of a random

variable. Appreciate the connection between

expected value and mean. (L/E)

Students can

usefully use

independent and



1

Evaluate the variance and standard deviation. Find

the expected value and variance for expressions like

?[ − >. (L/E)

Describe the binomial distribution and perform

simple calculations involving small values of A.

(L/E)

directed study time

practising typical

examination

questions on this

topic.

22 1

1

1

1

L. Probability Distributions. Perform

calculations using the binomial distribution and

larger values of A. Use the cumulative binomial

distribution tables. Appreciate important

assumptions when using the binomial distribution.

(L/E)

Describe the Normal distribution and use the

standardised Normal distribution table. Convert

data into standardised form. Be aware of the

limitations of the Normal distribution (e.g. the

assumption that there is no restriction on the values

taken by = but this is not usually the case in reality).

(Mostly L and some E)


Set up a confidence interval (any samples will be

taken from a background distribution which is

assumed to be Normal with a known standard

deviation.) Explain what is meant by a confidence

interval. (L/E/T)

Students can

usefully spend time

in independent and

directed study

practising examples

in the binomial and

Normal

distributions.

Students should be

aware of the

Central Limit

Theorem but will

not have to apply it

in an examination.

23 1

1

1

1

M. Financial Mathematics. Be thoroughly

familiar with all types of percentage. Calculate any

direct and reverse percentage, and evaluate any

percentage change and error. (L/E/T)

Identify what type of percentage is required in a

miscellany of examples. (L/E/T)

Appreciate what interest on an investment is.

Calculate simple interest and compound interest.

(L/T)

Compare two types of investment to see which

gives the better interest. (Mostly E)

Students can use

the compound

interest formula

and may need to

draw on their

knowledge of logs.

24 1

M. Financial Mathematics. Consolidate on

previous week and extend the ideas to finding, for



1

1

1

example, the total interest as a percentage of what

was originally invested. (E/T)

Calculate appreciation. (L/E)

Calculate depreciation. In both this session and the

previous one, students will be expected to work out

the value of an article after any number of years by

applying the idea of a geometric progression

(specific learning outcome D7). They will also be

expected to work out the expected time that a

certain value is reached by applying logarithms

(specific learning outcome E5). (L/E)

Consolidate on appreciation and depreciation. A

task could ask students to investigate if the benefits

of appreciation in one part of a project outweigh the

drawbacks of depreciation in another part of the

same project. (E/T)

Examples may be

the price of

property or a car.

There must be an

awareness of why

Mathematical

models may not be

reliable in the long

run (e.g. interest

rates may change).

25 1

1

1

1

N. Further Differentiation. Know that the

differentiation of B= LK B= \M B. Apply the product

rule. (L/E)

Apply the quotient rule (L/E)

Apply the chain rule. (L/E)

Practise examples using a mixture of the above

rules. (L/T)

Candidates may be

asked to derive

certain results (e.g.

showing that the

derivative of sec =

is sec = tan =.)

Practice at

differentiation in

independent and

directed study time

will be invaluable.

26 1

1

1

1

N. Further Differentiation. Understand what an

implicit function is and how to apply differentiation.

(Mostly L)

Find TI

T= of an implicit function which could involve

use of the product rule. (L/E)

Find the equations of a tangent and a normal at a

point. (L/E)

Find stationary values. (L/E)

In this module,

candidates will be

expected to draw

on concepts learnt

in module G.

Students will not

have to find the

nature of turning

points.

Again, time spent

practising in

independent and

directed study will

be invaluable.

27 1

1

O. Further Integration. Integrate standard

functions such as JB=,9

B= ,

U6(=)

U(=) . (L/E)

Resolve expressions into partial fractions. (L/E)

Expressions will

have linear and



1

1

Resolve improper fractions into partial fractions.

(L/E)

Integrate expressions which have been resolved

into partial fractions. (L/E)

repeated factors

only, with no

quadratic factors.

28 1

1

1

1

O. Further Integration. Use substitution to

evaluate indefinite and definite integrals. (L/E)

Use integration by parts. (L/E)

Consolidation of integration by substitution and by

parts. (Mostly E)

Practice at recognising and performing any integral.

(E/T)

The substitution will

normally be given.

Integration by parts

will need to be

applied not more

than twice.

With regard to

independent and

directed study, the

more practice the

better.

29 1

1

1

1

Revision

Revision

Revision

Revision

30 Final Exam Week



Appendix B Coursework Guidance

Continuous assessment makes up 30% of the final grade and tasks are set locally by

the teacher(s) delivering the module. Assessments should comprise substantive tasks

requiring students to demonstrate different skills and knowledge identified in the

module learning outcomes.

Students should complete three assignments, which must be undertaken in advance of

the end of module examination.

These assignments are:

A. Two pieces of coursework.

One of these is based on Maths Semester 1 (modules A – H) and the other on

Semester 2 (modules I - O).

The coursework is made of three tasks. Each should be based on an application

exercise to investigate a substantial multi-part problem. The project reports

should include narrative and models/calculations. An outline structure of the

coursework reports should include:

Introduction and background (approximately 100 words)

Description of how the task was carried out, outlining any methods used and

any assumptions made.

Results and findings, example relevant calculations/solutions, charts and tables

Case study and/or validation with narrative to describe the study.

Summary and conclusions. Approximately 100 words which should include any

limitations to any relevant results. Suggestions for further investigation or

improvements to the work.

Summary including key points and conclusion, any limitation and suggestion for

further investigation or improvements.

Each piece of coursework will contribute 10% towards the final module grade.

Students should be given 2 weeks to complete the coursework task.

Students will be expected to make use of ICT in at least one of the coursework

tasks.

The first piece of coursework will normally be carried out in the second half of

Semester 1 and the second piece during the second half of Semester 2.

B. End of Semester 1 Test

Held in class during the 15th week. The test will be two hours long (with ten minutes’

reading time) and will contribute a maximum of 10% towards the final module grade.

Section A is compulsory and carries a total of 40 marks.

Section B carries 60 marks and students are required to choose 4 out of 6

questions. The total for this paper is 100 marks.



Appendix C Formulae Booklet

Refer to separate formula booklet.

It is the centre’s responsibility to print “clean” (new) copies of the Formula Booklet for

the end-of-semester 1 test and final examination. (Refer to Section 7 Assessment)

ifymb002 mathematics business 2019-20mathematics in subject-related contexts appropriate for entry...

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