Download mathematics syllabus d (4024*)

CONTENTS
page
Notes
2
GCE Ordinary Level and School Certificate Syllabuses
Mathematics (Syllabus D) 4024
3
Additional Mathematics 4037
11
Statistics 4040*
16
GCE Advanced Level and Higher School Certificate (Principal) Syllabus
Further Mathematics 9231
18
Mathematical Notation
26
Booklists
30
*Available in the November examination only.
Important: Vertical black lines in the margins denote major changes to the syllabus.
The Advanced level syllabus for Mathematics has been completely revised for first examination
in 2002. Details of the revised syllabus (9709) are in the separate Advanced Level Mathematics
booklet, which also includes the new Advanced Subsidiary qualification available for the first time
in 2001.
The Advanced level syllabus for Further Mathematics has been completely revised for first
examination in 2002 and details of this new syllabus (9231), which will be available in June and
November, are contained in this booklet.
For examinations in and after 2002 the Additional/Subsidiary Mathematics syllabus (4031, 8172,
8175) will no longer be available. This syllabus is succeeded by the new Advanced Subsidiary
Mathematics syllabus (8709), which has been designed to be suitable for candidates who would
formerly have studied for Additional or Subsidiary Mathematics. The new Advanced Subsidiary
(AS) syllabus, which will be available in June and November, allows Centres the flexibility to
choose from three different routes to AS Mathematics - Pure Mathematics only or Pure
Mathematics and Mechanics or Pure Mathematics and Probability and Statistics.
The new Additional Mathematics Ordinary Level syllabus (4037) in this booklet has a Pure
Mathematics only syllabus content. This syllabus, which will be examined in June and November,
will be available for the first time in June 2002.
1
NOTES
Mathematical Tables
The Cambridge Elementary Mathematical Tables (Second Edition) will continue to be provided for
use where necessary in SC/O level Mathematics Syllabus D Paper 2 (Papers 4024/2, 4029/2) and
in SC/O level Statistics (Papers 4040/1 and 2). Further copies of these tables may be obtained
from the Cambridge University Press, The Edinburgh Building, Shaftesbury Road, Cambridge and
through booksellers. No mathematical tables other than these are permitted in the examination on
any of the syllabuses included in this booklet.
The use of tables is prohibited in SC/O level Mathematics Syllabus D Paper 1 (4024/1 and
4029/1).
Electronic Calculators
1. At all centres the use of electronic calculators is prohibited in Ordinary Level and S.C.
Mathematics Syllabus D Paper 1 (4024/1), (4029/1 for centres in Mauritius in November).
2. At all centres the use of silent electronic calculators is expected in S.C./O level Additional
Mathematics (4037) and Statistics (4040), and in Advanced Level and H.S.C. Further
Mathematics (9231).
3. For examinations in and after 2001, the non-calculator version (4004) of O level/S.C.
Mathematics Syllabus D will no longer be available. Centres wishing to enter candidates for O
level/S.C. Mathematics Syllabus D must use Mathematics Syllabus D (4024). The use of
silent electronic calculators is expected for Paper 2 (4024/2).
4. All centres in Mauritius must use Syllabus Code 4029 in November.
5. The General Regulations concerning the use of electronic calculators are contained in the
Handbook for Centres.
Mathematical Instruments
Apart from the usual mathematical instruments, candidates may use flexicurves in all the
examinations.
Mathematical Notation
Attention is drawn to the list of mathematical notation on pages 26-29.
Examiners' Reports (SR(I) booklets)
Reports on the June examinations are distributed to Caribbean Centres in November/December
and reports on the November examinations are distributed to other International Centres in
April/May. Further copies of each are available from the Syndicate.
2
MATHEMATICS SYLLABUS D (4024*)
GCE ORDINARY LEVEL AND SCHOOL CERTIFICATE
(Syllabus Code 4029 is to be used by Centres in Mauritius in November.)
*For examinations in and after 2001, the non-calculator version (4004) of O level/S.C.
Mathematics Syllabus D will no longer be available.
Introduction
The syllabus demands understanding of basic mathematical concepts and their applications,
together with an ability to show this by clear expression and careful reasoning.
In the examination, importance will be attached to skills in algebraic manipulation and to
numerical accuracy in calculations.
Learning Aims
The course should enable students to:
1. increase intellectual curiosity, develop mathematical language as a means
communication and investigation and explore mathematical ways of reasoning;
of
2. acquire and apply skills and knowledge relating to number, measure and space in
mathematical situations that they will meet in life;
3. acquire a foundation appropriate to a further study of Mathematics and skills and
knowledge pertinent to other disciplines;
4. appreciate the pattern, structure and power of Mathematics and derive satisfaction,
enjoyment and confidence from the understanding of concepts and the mastery of skills.
Assessment Objectives
The examination will test the ability of candidates to:
1.
recognise the appropriate mathematical procedures for a given situation;
2.
perform calculations by suitable methods, with and without a calculating aid;
3.
use the common systems of units;
4.
estimate, approximate and use appropriate degrees of accuracy;
5.
interpret, use and present information in written, graphical, diagrammatic and tabular
forms;
6.
use geometrical instruments;
7.
recognise and apply spatial relationships in two and three dimensions;
8.
recognise patterns and structures in a variety of situations and form and justify
generalisations;
9.
understand and use mathematical language and symbols and present mathematical
arguments in a logical and clear fashion;
10. apply and interpret Mathematics in a variety of situations, including daily life;
11. formulate problems into mathematical terms, select, apply and communicate appropriate
techniques of solution and interpret the solutions in terms of the problems.
3
Units
SI units will be used in questions involving mass and measures: the use of the centimetre will
continue.
Both the 12-hour clock and the 24-hour clock may be used for quoting times of the day. In the
24-hour clock, for example, 3.15 a.m. will be denoted by 03 15; 3.15 p.m. by 15 15, noon by
12 00 and midnight by 24 00.
Candidates will be expected to be familiar with the solidus notation for the expression of
3
compound units, e.g. 5 cm/s for 5 centimetres per second, 13.6 g/cm for 13.6 grams per
cubic centimetre.
Scheme of Papers
Component
Paper 1
Paper 2
Time Allocation
2 hours
2½ hours
Type
Short answer questions
Structured questions
Maximum Mark
80
100
Weighting
50%
50%
Paper 1 will consist of about 25 short answer questions. Neither mathematical tables nor slide
rules nor calculators will be allowed in this paper. All working must be shown in the spaces
provided on the question paper. Omission of essential working will result in loss of marks.
Paper 2 will consist of two sections: Section A (52 marks) will contain about six questions with no
choice. Section B (48 marks) will contain five questions of which candidates will be required to
answer four. Omission of essential working will result in loss of marks.
Candidates are expected to cover the whole syllabus. Each paper may contain questions on any
part of the syllabus and questions will not necessarily be restricted to a single topic.
Calculating Aids
PAPER 1
The use of all calculating aids is prohibited.
PAPER 2
(a) It is assumed that all candidates will have an electronic calculator. A scientific calculator with
trigonometric functions is strongly recommended. However, the Cambridge Elementary
Mathematical Tables may continue to be used to supplement the use of the calculator, for
example for trigonometric functions and square roots.
(b) The use of slide rules will no longer be permitted.
(c) Unless stated otherwise within an individual question, three figure accuracy will be required.
This means that four figure accuracy should be shown throughout the working, including
cases where answers are used in subsequent parts of the question.
Premature
approximation will be penalised, where appropriate.
(d) In Paper 4024/2, candidates with suitable calculators are encouraged to use the value of p
from their calculators. The value of p will be given as 3.142 to 3 decimal places for use by
other candidates. This value will be given on the front page of the question paper only.
4
Detailed Syllabus
THEME OR TOPIC
SUBJECT CONTENT
1. Number.
Candidates should be able to:
-use natural numbers, integers (positive, negative
and zero), prime numbers, common factors and
common multiples, rational and irrational numbers,
real numbers; continue given number sequences,
recognise patterns within and across different
sequences and generalise to simple algebraic
statements (including expressions for the nth term)
relating to such sequences.
2. Set language and notation.
-use set language and set notation, and Venn
diagrams, to describe sets and represent
relationships between sets as follows:
Definition of sets, e.g.
A = {x: x is a natural number}
B = {(x,y): y = mx + c}
C = {x: a ≤ x ≤ b}
D = {a,b,c.... }
Notation:
Union of A and B
Intersection of A and B
Number of elements in set A
". . . is an element of . . ."
A È B
A Ç B
n(A)
Î
Ï
". . . is not an element of . . ."
Complement of set A
The empty set
Universal set
A is a subset of B
A is a proper subset of B
AÍ B
AÌ B
A is not a subset of B
A is not a proper subset of B
A⊈B
AËB
A'
Ø
3. Function notation.
-use function notation,
e.g. f(x) = 3x – 5, f: x a 3x – 5
to describe simple functions, and the notation
x +5
x +5
–1
–1
f (x) =
and f : x a
3
3
to describe their inverses.
4. Squares, square roots, cubes and cube roots.
-calculate squares, square roots, cubes and cube
roots of numbers.
5. Directed numbers.
-use directed numbers in practical situations
(e.g. temperature change, tide levels).
5
6. Vulgar and decimal fractions and
percentages.
-use the language and notation of simple vulgar
and decimal fractions and percentages in
appropriate contexts; recognise equivalence and
convert between these forms.
7. Ordering.
-order quantities by magnitude and demonstrate
familiarity with the symbols =, ≠, >, <, ≥ , ≤.
8. Standard form.
-use the standard form A x 10 where n is a positive
or negative integer, and 1 ≤ A < 10.
9. The four operations.
-use the four operations for calculations with whole
numbers, decimal fractions and vulgar (and mixed)
fractions, including correct ordering of operations
and use of brackets.
10. Estimation.
-make estimates of numbers, quantities and
lengths, give approximations to specified numbers
of significant figures and decimal places and round
off answers to reasonable accuracy in the context
of a given problem.
11. Limits of accuracy.
-give appropriate upper and lower bounds for data
given to a specified accuracy (e.g. measured
lengths);
-obtain appropriate upper and lower bounds to
solutions of simple problems (e.g. the calculation of
the perimeter or the area of a rectangle) given data
to a specified accuracy.
12. Ratio, proportion, rate.
-demonstrate an understanding of the elementary
ideas and notation of ratio, direct and inverse
proportion and common measures of rate; divide a
quantity in a given ratio; use scales in practical
situations, calculate average speed;
-express direct and inverse variation in algebraic
terms and use this form of expression to find
unknown quantities.
13. Percentages.
-calculate a given percentage of a quantity; express
one quantity as a percentage of another, calculate
percentage increase or decrease; carry out
calculations involving reverse percentages, e.g.
finding the cost price given the selling price and the
percentage profit.
14. Use of an electronic calculator or logarithm
tables.
-use an electronic calculator or logarithm tables
efficiently; apply appropriate checks of accuracy.
15. Measures.
-use current units of mass, length, area, volume
and capacity in practical situations and express
quantities in terms of larger or smaller units.
16. Time.
-calculate times in terms of the 12-hour and 24-hour
clock; read clocks, dials and timetables.
17. Money.
-solve problems involving money and convert from
one currency to another.
n
6
18. Personal and household finance.
-use given data to solve problems on personal and
household finance involving earnings, simple
interest, discount, profit and loss; extract data from
tables and charts.
19. Graphs in practical situations.
-demonstrate familiarity with cartesian coordinates
in two dimensions; interpret and use graphs in
practical situations including travel graphs and
conversion graphs; draw graphs from given data;
-apply the idea of rate of change to easy kinematics
involving distance-time and speed-time graphs,
acceleration and retardation; calculate distance
travelled as area under a linear speed-time graph.
20. Graphs of functions.
-construct tables of values and draw graphs for
n
functions of the form y = ax where n = -2, -1, 0, 1,
2, 3, and simple sums of not more than three of
x
these and for functions of the form y = ka where a
is a positive integer; interpret graphs of linear,
quadratic, reciprocal and exponential functions; find
the gradient of a straight line graph; solve equations
approximately by graphical methods; estimate
gradients of curves by drawing tangents.
21. Straight line graphs.
-calculate the gradient of a straight line from the
coordinates of two points on it; interpret and obtain
the equation of a straight line graph in the form
y = mx + c; calculate the length and the coordinates
of the midpoint of a line segment from the
coordinates of its end points.
22. Algebraic representation and formulae.
-use letters to express generalised numbers and
express basic arithmetic processes algebraically,
substitute numbers for words and letters in
formulae; transform simple and more complicated
formulae; construct equations from given situations.
23. Algebraic manipulation.
-manipulate directed numbers; use brackets and
extract common factors; expand products of
algebraic expressions; factorise expressions of the
2 2
2 2
form ax + ay; ax + bx + kay + kby; a x - b y ;
2
2
2
a + 2ab + b ; ax + bx + c; manipulate simple
algebraic fractions.
24. Indices.
-use and interpret positive, negative, zero and
fractional indices.
25. Solutions of equations and inequalities.
-solve simple linear equations in one unknown;
solve fractional equations with numerical and linear
algebraic denominators; solve simultaneous linear
equations in two unknowns; solve quadratic
equations by factorisation and either by use of the
formula or by completing the square; solve simple
linear inequalities.
7
26. Graphical representation of inequalities.
-represent linear inequalities in one or two variables
graphically. (Linear Programming problems are not
included.)
27. Geometrical terms and relationships.
-use and interpret the geometrical terms: point, line,
plane, parallel, perpendicular, right angle, acute,
obtuse and reflex angles, interior and exterior angles,
regular and irregular polygons, pentagons, hexagons,
octagons, decagons;
-use and interpret vocabulary of triangles, circles,
special quadrilaterals;
-solve problems and give simple explanations
involving similarity and congruence;
-use and interpret vocabulary of simple solid figures:
cube, cuboid, prism, cylinder, pyramid, cone, sphere;
-use the relationships between areas of similar
triangles, with corresponding results for similar
figures, and extension to volumes of similar solids.
28. Geometrical constructions.
-measure lines and angles; construct simple
geometrical figures from given data, angle bisectors
and perpendicular bisectors using protractors or set
squares as necessary; read and make scale
drawings. (Where it is necessary to construct a
triangle given the three sides, ruler and compasses
only must be used.)
29. Bearings.
-interpret and use three-figure bearings measured
clockwise from the north (i.e. 000°-360°).
30. Symmetry.
-recognise line and rotational symmetry (including
order of rotational symmetry) in two dimensions, and
properties of triangles, quadrilaterals and circles
directly related to their symmetries;
-recognise symmetry properties of the prism
(including cylinder) and the pyramid (including cone);
-use the following symmetry properties of circles:
(a) equal chords are equidistant from the centre;
(b) the perpendicular bisector of a chord passes
through the centre;
(c) tangents from an external point are equal in
length.
31. Angle.
-calculate unknown angles and give simple
explanations using the following geometrical
properties:
(a) angles on a straight line;
(b) angles at a point;
(c) vertically opposite angles;
(d) angles formed by parallel lines;
(e) angle properties of triangles and quadrilaterals;
(f) angle properties of polygons including angle sum;
(g) angle in a semi-circle;
(h) angle between tangent and radius of a circle;
(i) angle at the centre of a circle is twice the angle at
the circumference;
(j) angles in the same segment are equal;
(k) angles in opposite segments are supplementary.
8
32. Locus.
-use the following loci and the method of intersecting
loci:
(a) sets of points in two or three dimensions
(i) which are at a given distance from a given
point,
(ii) which are at a given distance from a given
straight line,
(iii) which are equidistant from two given points;
(b) sets of points in two dimensions which are
equidistant from two given intersecting straight
lines.
33. Mensuration.
-solve problems involving
(i) the perimeter and area of a rectangle and a
triangle,
(ii) the circumference and area of a circle,
(iii) the area of a parallelogram and a trapezium,
(iv) the surface area and volume of a cuboid, cylinder,
prism, sphere, pyramid and cone (formulae will be
given for the sphere, pyramid and cone),
(v) arc length and sector area as fractions of the
circumference and area of a circle.
34. Trigonometry.
-apply Pythagoras Theorem and the sine, cosine and
tangent ratios for acute angles to the calculation of a
side or of an angle of a right-angled triangle (angles
will be quoted in, and answers required in, degrees
and decimals of a degree to one decimal place);
-solve trigonometrical problems in two dimensions
including those involving angles of elevation and
depression and bearings;
-extend sine and cosine functions to angles between
90° and 180°; solve problems using the sine and
cosine rules for any triangle and the formula 12 ab sin
C for the area of a triangle;
-solve simple trigonometrical problems in three
dimensions. (Calculations of the angle between two
planes or of the angle between a straight line and
plane will not be required.)
35. Statistics.
-collect, classify and tabulate statistical data; read,
interpret and draw simple inferences from tables and
statistical diagrams;
-construct and use bar charts, pie charts,
pictograms, simple frequency distributions and
frequency polygons;
-use frequency density to construct and read
histograms with equal and unequal intervals;
-calculate the mean, median and mode for
individual data and distinguish between the
purposes for which they are used;
-construct and use cumulative frequency
diagrams; estimate the median, percentiles,
quartiles and interquartile range;
-calculate the mean for grouped data; identify the
modal class from a grouped frequency distribution.
9
36. Probability.
-calculate the probability of a single event as
either a fraction or a decimal (not a ratio);
-calculate the probability of simple combined
events, using possibility diagrams and tree
diagrams where appropriate.
(In possibility
diagrams outcomes will be represented by points
on a grid and in tree diagrams outcomes will be
written at the end of branches and probabilities by
the side of the branches.)
37. Matrices.
-display information in the form of a matrix of any
order; solve problems involving the calculation of
the sum and product (where appropriate) of two
matrices, and interpret the results; calculate the
product of a scalar quantity and a matrix; use the
algebra of 2 x 2 matrices including the zero and
identity 2 x 2 matrices; calculate the determinant
and inverse of a non-singular matrix.
-1
( A denotes the inverse of A.)
38. Transformations.
-use the following transformations of the plane:
reflection (M), rotation (R), translation (T),
enlargement (E), shear (H), stretching (S) and
their combinations (If M(a) = b and R(b) = c the
notation RM(a) = c will be used; invariants under
these transformations may be assumed.);
-identify and give precise descriptions of
transformations
connecting
given
figures;
describe transformations using coordinates and
matrices. (Singular matrices are excluded.)
39. Vectors in two dimensions.
-describe
a
translation by using a vector
æxö
represented by çè y ÷ø , AB or a; add vectors and
multiply a vector by a scalar;
-calculate
æç x ö÷ as
èyø
the
magnitude
of
a
vector
x2 + y 2 .
(Vectors will be printed as AB or a and their
magnitudes denoted by modules signs, e.g.
I AB I or I a I. ln all their answers to questions
candidates are expected to indicate a in some
definite way, e.g. by an arrow or by underlining,
thus AB or a);
-represent vectors by directed line segments; use
the sum and difference of two vectors to express
given vectors in terms of two coplanar vectors;
use position vectors.
10
ADDITIONAL MATHEMATICS (4037)
GCE ORDINARY LEVEL AND SCHOOL CERTIFICATE
Syllabus Aims
The course should enable students to:
1. consolidate and extend their elementary mathematical skills, and use these in the context of
more advanced techniques;
2. further develop their knowledge of mathematical concepts and principles, and use this
knowledge for problem solving;
3. appreciate the interconnectedness of mathematical knowledge;
4. acquire a suitable foundation in mathematics for further study in the subject or in mathematics
related subjects;
5. devise mathematical arguments and use and present them precisely and logically;
6. integrate information technology to enhance the mathematical experience;
7. develop the confidence to apply their mathematical skills and knowledge in appropriate
situations;
8. develop creativity and perseverance in the approach to problem solving;
9. derive enjoyment and satisfaction from engaging in mathematical pursuits, and gain an
appreciation of the beauty, power and usefulness of mathematics.
Assessment Objectives
The examination will test the ability of candidates to:
1. recall and use manipulative technique;
2. interpret and use mathematical data, symbols and terminology;
3. comprehend numerical, algebraic and spatial concepts and relationships;
4. recognise the appropriate mathematical procedure for a given situation;
5. formulate problems into mathematical terms and select and apply appropriate techniques of
solution.
Examination Structure
There will be two papers, each of 2 hours and each carries 80 marks.
Content for PAPER 1 and PAPER 2 will not be dissected.
Each paper will consist of approximately 10-12 questions of various lengths. There will be no
choice of question except that the last question in each paper will consist of two alternatives, only
one of which must be answered. The mark allocations for the last question will be in the range of
10-12 marks.
Detailed Syllabus
Knowledge of the content of the Syndicate's Ordinary level Syllabus D (or an equivalent Syllabus)
is assumed. Ordinary level material which is not repeated in the syllabus below will not be tested
directly but it may be required in response to questions on other topics.
Proofs of results will not be required unless specifically mentioned in the syllabus.
Candidates will be expected to be familiar with the scientific notation for the expression of
-1
compound units e.g. 5 ms for 5 metres per second.
11
THEME OR TOPIC
CURRICULUM OBJECTIVES
Candidates should be able to:
1. Set language and notation.
-use set language and notation, and Venn diagrams to
describe sets and represent relationships between sets
as follows:
A = {x: x is a natural number}
B = {( x, y ): y = mx + c }
C = { x: a ≤ x ≤ b }
D = {a, b, c,. . . }
-understand and use the following notation:
2. Functions.
Union of A and B
Intersection of A and B
Number of elements in set A
". . . is an element of . . . "
". . . is not an element of . . ."
Complement of set A
The empty set
Universal set
A is a subset of B
A is a proper subset of B
A È B
A ÇB
n(A)
Î
Ï
A'
Ø
A is not a subset of B
A is not a proper subset of B
A⊈B
AËB
AÍB
AÌB
-understand the terms function, domain, range (image
set), one-one function, inverse function and composition
of functions;
-1
-use the notation f(x) = sin x, f: x a lg x, (x > 0),f (x)
2
and f (x) [=f(f(x))];
-understand the relationship between y = f(x) and
y = | f(x) |, where f(x) may be linear, quadratic or
trigonometric;
-explain in words why a given function is a function or
why it does not have an inverse;
-find the inverse of a one-one function and form
composite functions;
-use sketch graphs to show the relationship between a
function and its inverse.
12
Candidates should be able to:
3. Quadratic functions.
-find the maximum or minimum value of the quadratic
2
function f : x a ax + bx + c by any method;
-use the maximum or minimum value of f(x) to sketch the
graph or determine the range for a given domain;
-know the conditions for f(x) = 0 to have (i) two real roots,
(ii) two equal roots, (iii) no real roots; and the related
conditions for a given line to (i) intersect a given curve,
(ii) be a tangent to a given curve, (iii) not intersect a
given curve;
-solve quadratic equations for real roots and find the
solution set for quadratic inequalities.
4. Indices and surds.
-perform simple operations with indices and with surds,
including rationalising the denominator.
5. Factors of polynomials.
-know and use the remainder and factor theorems;
-find factors of polynomials;
-solve cubic equations.
6. Simultaneous equations.
-solve simultaneous equations in two unknowns with at
least one linear equation.
7. Logarithmic and exponential functions.
-know simple properties and graphs of the logarithmic
x
and exponential functions including lnx and e (series
expansions are not required);
-know and use the laws of logarithms (including change
of base of logarithms);
x
-solve equations of the form a = b.
8. Straight line graphs.
-interpret the equation of a straight line graph in the
form y = m x + c ;
n
-transform given relationships, including y = ax and
x
y = Ab , to straight line form and hence determine
unknown constants by calculating the gradient or
intercept of the transformed graph;
-solve questions involving mid-point and length of a
line;
-know and use the condition for two lines to be parallel
or perpendicular.
9. Circular measure.
-solve problems involving the arc length and sector
area of a circle, including knowledge and use of radian
measure.
13
Candidates should be able to:
10. Trigonometry.
-know the six trigonometric functions of angles of any
magnitude (sine, cosine, tangent, secant, cosecant,
cotangent);
-understand amplitude and periodicity and the
relationship between graphs of e.g. sin x and sin 2x;
-draw and use the graphs of y = a sin(bx) + c,
y = a cos(bx) + c, y = a tan(bx) + c, where a, b are
positive integers and c is an integer;
-use the relationships
cosA
2
sinA
cosA
= tan A,
2
= cot A, sin A + cos A = 1,
sinA
2
2
2
2
sec A = 1 + tan A, cosec A = 1 + cot A, and solve
simple trigonometric equations involving the six
trigonometric functions and the above relationships
(not including general solution of trigonometric
equations)
-prove simple trigonometric identities.
11. Permutations and combinations.
-recognise and distinguish between a permutation case
and a combination case;
-know and use the notation n!, (with 0! = 1), and the
expressions for permutations and combinations of n
items taken r at a time;
-answer simple problems on arrangement and selection
(cases with repetition of objects, or with objects arranged
in a circle or involving both permutations and
combinations, are excluded).
12. Binomial expansions.
n
-use the Binomial Theorem for expansion of (a + b) for
positive integral n;
ænö n - r r
-use the general term çç ÷÷ a
b ,0<r≤n
èr ø
(knowledge of the greatest term and properties of the
coefficients is not required).
13. Vectors in 2 dimensions.
æaö
-use vectors in any form, e.g. çç ÷÷ , AB , p, ai - bj;
èbø
-know and use position vectors and unit vectors;
-find the magnitude of a vector, add and subtract vectors
and multiply vectors by scalars;
-compose and resolve velocities;
-use relative velocity including solving problems on
interception (but not closest approach).
14
Candidates should be able to:
14. Matrices.
-display information in the form of a matrix of any order
and interpret the data in a given matrix;
-solve problems involving the calculation of the sum and
product (where appropriate) of two matrices and interpret
the results;
-calculate the product of a scalar quantity and a matrix;
-use the algebra of 2 x 2 matrices (including the zero and
identity matrix);
-calculate the determinant and inverse of a non-singular
2 x 2 matrix and solve simultaneous line equations.
15. Differentiation and integration.
-understand the idea of a derived function;
dy d 2 y é d æ dy ö ù
,
ê= ç ÷ú;
dx dx 2 ë dx è dx ø û
n
-use the derivatives of the standard functions x (for any
x
rational n), sin x, cos x, tan x, e , lnx, together with
constant multiples, sums and composite functions of
these;
-use the notations f'(x), f"(x),
-differentiate products and quotients of functions;
-apply differentiation to gradients, tangents and normals,
stationary points, connected rates of change, small
increments and approximations and practical maxima
and minima problems;
-discriminate between maxima and minima by any
method;
-understand integration as the reverse process of
differentiation;
-integrate sums of terms in powers of x excluding
1
x
;
n
-integrate functions of the form ( ax + b )
ax+b
(excluding n = -1), e , sin ( ax + b ), cos ( ax + b );
-evaluate definite integrals and apply integration to the
evaluation of plane areas;
-apply differentiation and integration to kinematics
problems that involve displacement, velocity and
acceleration of a particle moving in a straight line with
variable or constant acceleration, and the use of x-t and
v-t graphs.
15
STATISTICS (4040)
ORDINARY LEVEL AND SCHOOL CERTIFICATE
(AVAILABLE ONLY IN THE NOVEMBER EXAMINATION)
Scheme of Papers
There will be two written papers, each of 2¼ hours. Each will consist of six compulsory
short questions in Section A (36 marks) and a choice of four out of five longer questions in
Section B (64 marks).
A high standard of accuracy will be expected in calculations and in the drawing of diagrams
and graphs. All working must be clearly shown. The use of an electronic calculator is
expected in both papers.
Past papers are available from UCLES.
SYLLABUS
NOTES
1. General ideas of sampling and surveys. Bias:
how it arises and is avoided.
Including knowledge of the terms: random
sample, stratified random sample, quota
sample, systematic sample.
2. The nature of a variable.
Including knowledge of the terms: discrete,
continuous, quantitative and qualitative.
3. Classification, tabulation and interpretation of
data. Pictorial representation of data; the
purpose and use of various forms, their
advantages and disadvantages.
Including pictograms, pie charts, bar charts,
sectional and percentage bar charts, dual bar
charts, change charts.
4. Frequency distributions; frequency polygons
and histograms.
Including class boundaries and mid-points,
class intervals.
5. Cumulative frequency distributions, curves
(ogives) and polygons.
6. Measures of central tendency and their
appropriate use; mode and modal class,
median and mean. Measures of dispersion
and
their
appropriate
use;
range,
interquartile range, variance and standard
deviation.
7. Index numbers, composite index numbers, price
relatives, crude and standardised rates.
16
Calculation of the mean, the variance and the
standard deviation from a set of numbers, a
frequency distribution and a grouped frequency
distribution, including the use of an assumed
mean.
Estimation of the median, quartiles and
percentiles from a set of numbers, a
cumulative frequency curve or polygon and by
linear
interpolation
from
a
cumulative
frequency table.
The effect on mean and standard deviation of
adding a constant to each observation and of
multiplying each observation by a constant.
Linear transformation of data to a given mean
and standard deviation.
8. Moving averages.
Including knowledge of the terms: time series,
trend, seasonal variation, cyclic variation.
Centering will be expected, where appropriate.
9. Scatter diagrams; lines of best fit.
Including the method of semi-averages for
fitting a straight line; the derivation of the
equation of the fitted straight line in the form
y = mx + c .
10.Elementary ideas of probability.
Including the treatment of mutually exclusive and
independent events.
11.Simple probability and frequency distributions
for a discrete variable. Expectation.
Including expected profit and loss in simple
games; idea of a fair game.
17
FURTHER MATHEMATICS (9231)
GCE ADVANCED LEVEL AND HIGHER SCHOOL CERTIFICATE (PRINCIPAL SUBJECT)
Syllabus Aims and Objectives
The aims and objectives for Advanced level Mathematics 9709 apply, with appropriate emphasis.
Scheme of Papers
The examination in Further Mathematics will consist of two three-hour papers, each carrying
50% of the marks, and each marked out of 100.
Paper 1 A paper consisting of about 11 questions of different marks and lengths on Pure
Mathematics. Candidates will be expected to answer all questions, except for the
last question (worth 12 to 14 marks), which will offer two alternatives, only one of
which must be answered.
Paper 2 A paper consisting of 4 or 5 questions of different marks and lengths on Mechanics
(worth a total of 43 or 44 marks), followed by 4 or 5 questions of different marks
and lengths on Statistics (worth a total of 43 or 44 marks), and one final question
worth 12 or 14 marks. The final question consists of two alternatives, one on
Mechanics and one on Statistics. Candidates will be expected to answer all
questions, except for the last question, where only one of the alternatives must be
answered.
It is expected that candidates will have a calculator with standard 'scientific' functions for
use in the examination. Graphic calculators will be permitted but candidates obtaining
results solely from graphic calculators without supporting working or reasoning will not
receive credit. Computers, and calculators capable of algebraic manipulation, are not
permitted. All the regulations in the Handbook for Centres apply with the exception that, for
examinations on this syllabus only, graphic calculators are permitted.
PAPER 1
Knowledge of the syllabus for Pure Mathematics (units P1and P3) in Mathematics 9709 is
assumed, and candidates may need to apply such knowledge in answering questions.
THEME OR TOPIC
CURRICULUM OBJECTIVES
Candidates should be able to:
1. Polynomials and rational functions.
-recall and use the relations between the
roots and coefficients of polynomial
equations, for equations of degree 2, 3, 4
only;
-use a given simple substitution to obtain an
equation whose roots are related in a simple
way to those of the original equation;
-sketch graphs of simple rational functions,
including the determination of oblique
asymptotes, in cases where the degree of
the numerator and the denominator are at
most 2 (detailed plotting of curves will not be
required, but sketches will generally be
expected to show significant features, such
as
turning
points,
asymptotes
and
intersections with the axes).
18
2. Polar coordinates.
-understand the relations between cartesian
and polar coordinates (using the convention
r ≥ 0) , and convert equations of curves from
cartesian to polar form and vice versa ;
-sketch simple polar curves, for 0 ≤ θ < 2 p or
- p < θ ≤ p or a subset of either of these
intervals (detailed plotting of curves will not be
required, but sketches will generally be
expected to show significant features, such as
symmetry, the form of the curve at the pole and
least/greatest values of r);
-recall the formula
1 β 2
r dθ for the area of a
2 òα
sector, and use this formula in simple cases.
3. Summation of series.
−use the standard results for
to find related sums;
år , år2 , år3
-use the method of differences to obtain the
sum of a finite series, e.g. by expressing the
general term in partial fractions;
-recognise, by direct consideration of a sum to
n terms, when a series is convergent, and find
the sum to infinity in such cases.
4. Mathematical induction.
-use the method of mathematical induction to
establish a given result (questions set may
involve divisibility tests and inequalities, for
example);
-recognise situations where conjecture based
on a limited trial followed by inductive proof is a
useful strategy, and carry this out in simple
x
cases e.g. find the n th derivative of x e .
5. Differentiation and integration.
-obtain an expression for
d2 y
in cases where the
dx 2
relation between y and x is defined implicitly or
parametrically;
-derive and use reduction formulae for the
evaluation of definite integrals in simple cases;
-use integration to find
mean values and centroids of two- and threedimensional figures (where equations are
expressed in cartesian coordinates, including
the use of a parameter), using strips, discs or
shells as appropriate,
arc lengths (for curves with equations in
cartesian coordinates, including the use of a
parameter, or in polar coordinates),
surface areas of revolution about one of the
axes (for curves with equations in cartesian
coordinates, including the use of a parameter,
but not for curves with equations in polar
coordinates).
19
6. Differential equations.
-recall
the
meaning
of
the
terms
‘complementary
function'
and
‘particular
integral' in the context of linear differential
equations, and recall that the general solution
is the sum of the complementary function and a
particular integral;
-find the complementary function for a second
order linear differential equation with constant
coefficients;
-recall the form of, and find, a particular
integral for a second order linear differential
equation in the cases where a polynomial or
bx
a e or a cos px + b sin px is a suitable form,
and in other simple cases find the appropriate
coefficient(s) given a suitable form of particular
integral;
-use a substitution to reduce a given differential
equation to a second order linear equation with
constant coefficients;
-use initial conditions to find a particular solution to
a differential equation, and interpret a solution in
terms of a problem modelled by a differential
equation.
7. Complex numbers.
-understand de Moivre's theorem, for a positive
integral exponent, in terms of the geometrical
effect of multiplication of complex numbers;
-prove de Moivre's theorem for a positive integral
exponent;
-use de Moivre's theorem for positive integral
exponent to express trigonometrical ratios of
multiple angles in terms of powers of
trigonometrical ratios of the fundamental angle;
-use de Moivre's theorem, for a positive or
negative rational exponent
in expressing powers of sin θ and cos θ in terms
of multiple angles,
in the summation of series,
in finding and using the nth roots of unity.
8. Vectors.
-use the equation of a plane in any of the forms
ax + by + cz = d or r.n. = p or r = a + l b +mc,
and convert equations of planes from one form to
another as necessary in solving problems;
-recall that the vector product a x b of two vectors
can be expressed either as I a II b I sin θ n̂ , where
n̂ is a unit vector, or in component form as
( a 2 b 3 – a3 b2 ) i + ( a 3 b1 – a 1 b 3 ) j + ( a 1 b 2 – a 2 b 1 )
k;
-use equations of lines and planes, together with
scalar and vector products where appropriate, to
solve problems concerning distances, angles and
intersections, including
determining whether a line lies in a plane, is
parallel to a plane or intersects a plane, and
finding the point of intersection of a line and a
plane when it exists,
finding the perpendicular distance from a point
20
to a plane,
finding the angle between a line and a plane,
and the angle between two planes,
finding an equation for the line of intersection
of two planes,
calculating the shortest distance between two
skew lines,
finding an equation for the common
perpendicular to two skew lines.
9. Matrices and linear spaces.
-recall and use the axioms of a linear (vector)
space (restricted to spaces of finite dimension
over the field of real numbers only);
-understand the idea of linear independence, and
determine whether a given set of vectors is
dependent or independent;
-understand the idea of the subspace spanned by
a given set of vectors;
-recall that a basis for a space is a linearly
independent set of vectors that spans the space,
and determine a basis in simple cases;
-recall that the dimension of a space is the
number of vectors in a basis;
-understand the use of matrices to represent
linear transformations from ℝ ® ℝ ;
-understand the terms ‘column space', ‘row
space', ‘range space' and ‘null space', and
determine the dimensions of, and bases for,
these spaces in simple cases;
-determine the rank of a square matrix, and use
(without proof) the relation between the rank, the
dimension of the null space and the order of the
matrix;
-use methods associated with matrices and linear
spaces in the context of the solution of a set of
linear equations;
-evaluate the determinant of a square matrix and
find the inverse of a non-singular matrix (2 x 2
and 3 x 3 matrices only), and recall that the
columns (or rows) of a square matrix are
independent if and only if the determinant is nonzero;
-understand the terms
‘eigenvalue'
and
‘eigenvector', as applied to square matrices;
-find eigenvalues and eigenvectors of 2 x 2 and
3 x 3 matrices (restricted to cases where the
eigenvalues are real and distinct);
-1
-express a matrix in the form QDQ , where D is a
diagonal matrix of eigenvalues and Q is a matrix
whose columns are eigenvectors, and use this
expression, e.g. in calculating powers of
matrices.
n
21
m
PAPER 2
Knowledge of the syllabuses for Mechanics (units M1 and M2) and Probability and Statistics (units
S1 and S2) in Mathematics 9709 is assumed. Candidates may need to apply such knowledge in
answering questions; harder questions on those units may also be set.
THEME OR TOPIC
CURRICULUM OBJECTIVES
Candidates should be able to:
MECHANICS (Sections 1 to 5)
1. Momentum and impulse.
-recall and use the definition of linear
momentum, and show understanding of its
vector nature (in one dimension only);
-recall Newton's experimental law and the
definition of the coefficient of restitution, the
property 0 ≤ e ≤ 1, and the meaning of the
terms ‘perfectly elastic' ( e =1) and ‘inelastic'
( e = 0);
-use conservation of linear momentum
and/or Newton's experimental law to solve
problems that may be modelled as the direct
impact of two smooth spheres or the direct
or oblique impact of a smooth sphere with a
fixed surface;
-recall and use the definition of the impulse
of a constant force, and relate the impulse
acting on a particle to the change of
momentum of the particle (in one dimension
only).
2. Circular motion.
-recall and use the radial and transverse
components of acceleration for a particle
moving in a circle with variable speed;
-solve problems which can be modelled by
the motion of a particle in a vertical circle
without loss of energy (including finding the
tension in a string or a normal contact force,
locating points at which these are zero, and
conditions for complete circular motion).
3. Equilibrium of a rigid body under coplanar
forces.
-understand and use the result that the effect
of gravity on a rigid body is equivalent to a
single force acting at the centre of mass of
the body, and identify the centre of mass by
considerations of symmetry in suitable
cases;
-calculate the moment of a force about a
point in 2 dimensional situations only
(understanding of the vector nature of
moments is not required);
-recall that if a rigid body is in equilibrium
under the action of coplanar forces then the
vector sum of the forces is zero and the sum
of the moments of the forces about any point
is zero, and the converse of this;
-use Newton's third law in situations
involving the contact of rigid bodies in
equilibrium;
22
-solve problems involving the equilibrium of
rigid bodies under the action of coplanar
forces (problems set will not involve
complicated trigonometry).
4. Rotation of a rigid body.
-understand and use the definition of the
moment of inertia of a system of particles about
a fixed axis as
å mr
2
, and the additive
property of moment of inertia for a rigid body
composed of several parts (the use of
integration to find moments of inertia will not be
required);
-use the parallel and perpendicular axes
theorems (proofs of these theorems will not be
required);
-recall and use the equation of angular motion
C = I q&& for the motion of a rigid body about a
fixed axis (simple cases only, where the
moment C arises from constant forces such as
weights or the tension in a string wrapped
around the circumference of a flywheel;
knowledge of couples is not included and
problems will not involve consideration or
calculation of forces acting at the axis of
rotation);
-recall and use the formula
1
2
Ιw 2 for the kinetic
energy of a rigid body rotating about a fixed
axis;
-use conservation of energy in solving problems
concerning mechanical systems where rotation
of a rigid body about a fixed axis is involved.
5. Simple harmonic motion.
-recall a definition of SHM and understand the
concepts of period and amplitude;
-use standard SHM formulae in the course of
solving problems;
-set up the differential equation of motion in
problems leading to SHM, recall and use
appropriate forms of solution, and identify the
period and amplitude of the motion;
-recognise situations where an exact equation
of motion may be approximated by an SHM
equation, carry out necessary approximations
(e.g. small angle approximations or binomial
approximations) and appreciate the conditions
necessary for such approximations to be useful.
23
STATISTICS (Sections 6 to 9)
6. Further work on distributions.
-use the definition of the distribution function as
a probability to deduce the form of a distribution
function in simple cases, e.g. to find the
3
distribution function for Y, where Y = X and X
has a given distribution;
-understand conditions under which a
geometric distribution or negative exponential
distribution may be a suitable probability model;
-recall and use the formula for the calculation of
geometric or negative exponential probabilities;
-recall and use the means and variances of a
geometric distribution and negative exponential
distribution.
7. Inference using normal and t-distributions.
-formulate hypotheses and apply a hypothesis
test concerning the population mean using a
small sample drawn from a normal population
of unknown variance, using a t-test;
-calculate a pooled estimate of a population
variance from two samples (calculations based
on either raw or summarised data may be
required);
-formulate hypothesis concerning the difference
of population means, and apply, as appropriate,
a 2-sample t-test,
a paired sample t-test,
a test using a normal distribution
(the ability to select the test appropriate to the
circumstances of a problem is expected);
-determine a confidence interval for a
population mean, based on a small sample
from a normal population with unknown
variance, using a t-distribution;
-determine a confidence interval for a difference
of population means, using a t-distribution, or a
normal distribution, as appropriate.
8. c –tests.
-fit a theoretical distribution, as prescribed by a
given hypothesis, to given data (questions will
not involve lengthy calculations);
2
-use a c -test, with the appropriate number of
degrees of freedom, to carry out the
corresponding goodness of fit analysis (classes
should be combined so that each expected
frequency is at least 5);
2
-use a c -test, with the appropriate number of
degrees of freedom, for independence in a
contingency table (Yates’ correction is not
required, but classes should be combined so
that the expected frequency in each cell is at
least 5).
2
24
9. Bivariate data.
-understand the concept of least squares,
regression lines and correlation in the context of
a scatter diagram;
-calculate, both from simple raw data and from
summarised data, the equations of regression
lines and the product moment correlation
coefficient, and appreciate the distinction
between the regression line of y on x and that
of x on y;
-recall and use the facts that both regression
lines pass through the mean centre (x, y) and
that the product moment correlation coefficient r
and the regression coefficients b 1, b 2 are
2
related by r = b 1 , b 2 ;
-select and use, in the context of a problem, the
appropriate regression line to estimate a value,
and understand the uncertainties associated
with such estimations;
-relate, in simple terms, the value of the product
moment
correlation
coefficient
to
the
appearance of the scatter diagram, with
particular reference to the interpretation of
cases where the value of the product moment
correlation coefficient is close to +1, -1 or 0;
-carry out a hypothesis test based on the
product moment correlation coefficient.
25
MATHEMATICAL NOTATION
The list which follows summarises the notation used in the Syndicate’s Mathematics examinations.
Although primarily directed towards Advanced/HSC (Principal) level, the list also applies, where
relevant, to examinations at all other levels, i.e. O/SC, AO/HSC (Subsidiary).
Mathematical Notation
1. Set Notation
Î
Ï
is an element of
{x1, x2,…}
the set with elements x1, x2,…
{x:…}
the set of all x such that…
n (A)
the number of elements in set A
Æ
the empty set
is not an element of
universal set
A'
the complement of the set A
ℕ
the set of positive integers, {1, 2, 3, …}
ℤ
the set of integers {0, ± 1, ± 2, ± 3, …}
ℤ+
the set of positive integers {1, 2, 3, …}
ℤn
the set of integers modulo n, {0, 1, 2, …, n –1}
ℚ
the set of rational numbers
ℚ+
the set of positive rational numbers, {x Î ℚ: x > 0}
+
ℚ
0
ℝ
the set of real numbers
ℝ+
ℝ
the set of positive rational numbers and zero, {x Î ℚ: x ≥ 0}
+
0
the set of positive real numbers {x Î ℝ: x > 0}
the set of positive real numbers and zero {x Î ℝ: x ≥ 0}
ℝn
the real n tuples
ℂ
the set of complex numbers
⊆
is a subset of
⊂
is a proper subset of
⊈
is not a subset of
⊄
is not a proper subset of
È
Ç
union
[a, b]
the closed interval {x Î ℝ: a ≤ x ≤ b}
[a, b)
the interval {x Î ℝ: a ≤ x < b}
(a, b]
the interval {x Î ℝ: a < x ≤ b}
(a, b)
the open interval {x Î ℝ: a < x < b}
yRx
y is related to x by the relation R
y~x
y is equivalent to x, in the context of some equivalence relation
intersection
26
2. Miscellaneous Symbols
=
is equal to
¹
º
»
@
µ
is not equal to
<; ≪
is less than; is much less than
≤ ,
is less than or equal to or is not greater than
>; ≫
is greater than; is much greater than
≥,
is greater than or equal to or is not less than
¥
infinity
is identical to or is congruent to
is approximately equal to
is isomorphic to
is proportional to
3 Operations
a+b
a–b
a x b, ab, a.b
a ¸ b,
a
, a/b
b
a:b
a plus b
a minus b
a multiplied by b
a divided by b
the ratio of a to b
n
åa
i =l
i
a1 + a2 + . . . + an
√a
the positive square root of the real number a
│a│
the modulus of the real number a
n!
n factorial for n Î ℕ (0! = 1)
n!
ænö
ç ÷
èrø
the binomial coefficient
, for n, r Î ℕ, 0 ≤ r ≤ n
r!(n - r )!
n(n - 1)...(n - r + 1)
, for n Î ℚ, r Î ℕ
r!
4. Functions
f
function f
f ( x)
the value of the function f at x
f : A →B
f is a function under which each element of set A has an image in set B
f:xay
the function f maps the element x to the element y
f –1
the inverse of the function f
o
g f, gf
the composite function of f and g which is defined by
(g o f)(x) or gf (x) = g(f(x))
lim f (x)
the limit of f(x) as x tends to a
Dx; d x
an increment of x
x ®a
dy
dx
dn y
dx n
the derivative of y with respect to x
the nth derivative of y with respect to x
27
f'(x), f"(x), …, f(n)(x)
the first, second, …, nth derivatives of f(x) with respect to x
∫ydx
indefinite integral of y with respect to x
∫ydx
the definite integral of y with respect to x for values of x between a
and b
b
a
¶y
¶x
x&, &x&,...
the partial derivative of y with respect to x
the first, second, . . . derivatives of x with respect to time
5. Exponential and Logarithmic Functions
e
base of natural logarithms
x
e , exp x
exponential function of x
loga x
logarithm to the base a of x
ln x
natural logarithm of x
lg x
logarithm of x to base 10
6. Circular and Hyperbolic Functions and Relations
sin, cos, tan,
cosec, sec, cot
–1
–1
the circular functions
–1
sin , cos , tan ,
–1
–1
–1
cosec , sec , cot
the inverse circular relations
sinh, cosh, tanh,
cosech, sech, coth
the hyperbolic functions
–1
–1
–1
sinh , cosh , tanh ,
–1
–1
–1
cosech , sech , coth
the inverse hyperbolic relations
7. Complex Numbers
i
z
square root of –1
a complex number, z = x + iy
+
= r (cos θ + i sin θ ), r Î ℝ 0
= re iθ , r Î ℝ
+
0
Re z
the real part of z,
Re (x + iy) = x
Im z
the imaginary part of z, Im (x + iy) = y
|z|
the modulus of z, | x+ iy | = Ö(x + y ), | r (cos θ + i sin θ )| = r
arg z
the argument of z, arg (r(cos θ + i sin θ )) = θ , – p < θ ≤
z*
the complex conjugate of z, (x + iy)* = x – iy
2
28
2
p
8. Matrices
a matrix M
M
M
-1
the inverse of the square matrix M
M
T
the transpose of the matrix M
det M
the determinant of the square matrix M
9. Vectors
a
AB
the vector a
the vector represented in magnitude and direction by the directed line
segment AB
â
a unit vector in the direction of the vector a
i, j, k
unit vectors in the directions of the cartesian coordinate axes
|a|
the magnitude of a
|AB|
the magnitude of AB
a.b
the scalar product of a and b
a×b
the vector product of a and b
10. Probability and Statistics
A, B, C etc.
events
AÈB
union of events A and B
AÇB
intersection of the events A and B
P ( A)
probability of the event A
A'
complement of the event A, the event ‘not A’
P(A|B)
probability of the event A given the event B
X, Y, R, etc.
random variables
x, y, r, etc.
values of the random variables X, Y, R, etc.
x1, x2, …
observations
f1, f2, …
frequencies with which the observations x1, x 2, … occur
p(x)
the value of the probability function P(X = x) of the discrete random
variable X
p1, p2, …
probabilities of the values x1, x2, … of the discrete random variable X
f(x), g(x), …
the value of the probability density function of the continuous random
variable X
F(x), G(x), …
the value of the (cumulative) distribution function P(X ≤ x) of the
random variable X
E(X)
expectation of the random variable X
E[g(X)]
expectation of g(X)
Var(X)
variance of the random variable X
G(t)
the value of the probability generating function for a random variable
which takes integer values
B(n, p)
binomial distribution, parameters n and p
N( µ, σ )
normal distribution, mean m and variance s
µ
population mean
2
29
2
s2
s
population variance
x
sample mean
s
2
population standard deviation
unbiased estimate of population variance from a sample,
s2 =
1
n -1
å (x - x )
2
f
probability density function of the standardised normal variable with
distribution N (0, 1)
F
corresponding cumulative distribution function
ρ
linear product-moment correlation coefficient for a population
r
linear product-moment correlation coefficient for a sample
Cov(X, Y)
covariance of X and Y
30
BOOKLISTS
These titles represent some of the texts available in the UK at the time of printing this booklet.
Teachers are encouraged to choose texts for class use which they feel will be of interest to
their students and will support their own teaching style. ISBN numbers are provided wherever
possible.
O LEVEL MATHEMATICS SYLLABUS D 4024
Bostock, L, S Chandler, A Shepherd, E Smith ST(P) Mathematics Books 1A to 5A
(Stanley Thornes)
Book 1A
0
7487 0540 6
Book 1B
0
7487 0143 5
Book 2A
0
7487 0542 2
Book 2B
0
7487 0144 3
Book 3A
0
7487 1260 7
Book 3B
0
7487 0544 9
Book 4A
0
7487 1501 0
Book 4B
0
7487 1583 5
Book 5A
0
7487 1601 7
Buckwell, Geoff Mastering Mathematics (Macmillan Education Ltd) 0 333 62049 6
Collins, J, Warren, T and C J Cox Steps in Understanding Mathematics (John Murray)
Book 1
0
7195 4450 5
Book 2
0
7195 4451 3
Book 3
0
7195 4452 1
Book 4
0
7195 4453 X
Book 5
0
7195 4454 8
Cox, C J and D Bell Understanding Mathematics Books 1 – 5 (John Murray)
Book 1
0
7195 4752 0
Book 2
0
7195 4754 7
Book 3
0
7195 4756 3
Book 4
0
7195 5030 0
Book 5
0
7195 5032 7
Farnham, Ann Mathematics in Focus (Cassell Publishers Ltd) 0 304 31741 1
Heylings, M R Graded Examples in Mathematics (8 topic books and 1 revision book) (Schofield
& Sims)
Mathematics in Action Group Mathematics in Action Books 1, 2, 3B, 4B, 5B (Nelson Blackie)
Book 1
0
17 431416 7
Book 2
0
17 431420 5
Book 3B
0
17 431434 5
Book 4B
0
17 431438 8
MSM Mathematics Group MSM Mathematics Books 1, 2, 3Y, 4Y, 5Y (Nelson)
Murray, Les Progress in Mathematics Books 1E to 5E (Stanley Thornes)
Book 1E
0
85950
744 0
Book 2E
0
85950
745 9
Book 3E
0
85950
746 7
Book 4E
0
85950
747 5
Book 5E
0
85950
733 5
31
National Mathematics Project (NMP) Mathematics for Secondary Schools Red Track Books 1
to 5 (Longman Singapore Publishers Pte Ltd)
Book 1
0 582 206960
Book 2
0 582 206987/206995
Book 3
0 582 20727 4
Book 4
0 582 20725 8
Book 5
0 582 20726 6
Smith, Ewart Examples in Mathematics for GCSE Higher Tier (Second edition) (Stanley
Thornes) 7487 27647
Smith, Mike and Ian Jones Challenging Maths for GCSE and Standard Grade (Heinemann)
SSMG/Heinemann Team Heinemann Mathematics 14-16 Upper Course (Heinemann)
O LEVEL ADDITIONAL MATHEMATICS 4037
Backhouse, J K and Houldsworth, S P T Pure Mathematics: A First Course (Longmans)
0 582 35386
Bostock & Chandler Mathematics: The Core Course for A Level (Stanley Thornes)
085950 306 2
Forman, R P C Additional Mathematics Pure and Applied (Stanley Thornes) 085950 1507
Harwood Clarke, L Additional Pure Mathematics (Heinemann) 0435 51187 4
Heard, T J Extending Mathematics (OUP)
Peart-Jackson, W J P Additional Mathematics O Level (Elektra Educational Publishing)
Perkins & Perkins Advanced Mathematics 1 (Bell & Hyman)
O LEVEL STATISTICS 4040
Greer, A A First Course in Statistics (Stanley Thornes) 0 8590 043 8
Baker, David Facts and Figures, A Practical Approach to Statistics (Stanley Thornes)
07487 0040 4 Pupil's book
07487 0041 2 Teacher's notes
Clegg, Frances Simple Statistics (Cambridge University Press) 0 521 28802 9
Loveday, R Practical Statistics and Probability (Cambridge University Press) 0 521 20291 4
Whitehead, Paul and Whitehead, Geoffrey Statistics for Business (Pitman) 0 273 01975 9
Hartley, Alick Basic Statistics (Impart Books) 0 9513233 4 2
32
A LEVEL MATHEMATICS (9709) AND A LEVEL FURTHER MATHEMATICS (9231)
Pure Mathematics
Backhouse, Houldsworth, Horill & Wood Essential Pure Mathematics (Longman)
0582 066581
Bostock & Chandler Core Maths for A Level ( Second edition ) (Stanley Thornes)
07487 1779
Bostock, Chandler & Rourke Further Pure Mathematics (Stanley Thornes) 085950
1035
Butcher & Megeny Access to Advanced Level Maths (Stanley Thornes) 07487 29992 (short
introductory course)
Hashmi Advanced Level Pure Mathematics (Vijay Pandit) 09460-87865
Martin Pure Mathematics: Complete Advanced Level Mathematics (Stanley Thornes)
07487 45238
Martin, Brown, Rigby, et al Complete Advanced Level Mathematics: Pure Mathematics:
Core Text (Stanley Thornes) 07487 35585
Mehta Advanced Level Pure Mathematics (Vijay Pandit) 09460 87512
MEW Group Exploring Pure Maths (Hodder & Stoughton) 0340 53159 2
Morely Pure Mathematics (Hodder & Stoughton Educational) 0340 701676
Perkins & Perkins Advanced Mathematics - A Pure Course (Collins) 000 322239 X
Sadler & Thorning Understanding Pure Mathematics (OUP) 019 914243 2
Sherran & Crawshaw A Level Questions and Answers: Pure Mathematics (Letts Educational
Ltd) 1857 584656
Solomon Advanced Level Mathematics (3 volumes) (John Murray) 0 7195 5344 X
Young Pure Mathematics (Hodder & Stoughton) 07131 76431
Further Pure Mathematics
Bostock, Chandler & Rourke Further Pure Mathematics (Stanley Thornes) 085950 1035
Integrated Courses
Berry & Fentern Discovering Advanced Mathematics-AS Mathematics (Collins Educational)
000 322502X (published April 2000)
Celia, Nice & Elliot Advanced Mathematics (3 volumes) (Macmillan) 0333 399838,
0333 231937, 0333 348273
Gough The Complete A Level Mathematics (Heinemann) 0435 513451
Morris A Level Maths Revision Notes (Letts Educational Ltd) 18408 50922
Moss & Kenwood Longman Exam Practice Kit: A-level and AS-level Mathematics (Addison
Wesley Longman Higher Education) 0582 303893
Perkins & Perkins Advanced Mathematics Book 1 (Collins Educational) 000 3222691
Perkins & Perkins Advanced Mathematics Book 2 (Collins Educational) 000 3222993
Solomon Advanced Level Mathematics (DP Publications) 18580 51347
33
Mechanics
Adams, Haighton, Trim Complete Advanced Level Mathematics: Mechanics: Core Text
(Stanley Thornes) 07487 35593
Bostock & Chandler Mechanics and Probability (Stanley Thornes) 08595 01418
Bostock & Chandler Mechanics for A Level (Stanley Thornes) 0748 775962
Bostock & Chandler Further Mechanics and Probability (Stanley Thornes) 08595 01426
Bostock & Chandler Module E-Mechanics 1and Module F-Mechanics 2 (Stanley Thornes)
07487 15029, 07487 17749
Horril Applied Mathematics (Longman) 0582 35575 3
MEW Group Exploring Mechanics (Hodder & Stoughton) Student book: 0340 49933 8
Teacher book: 0340 49934 6
Nunn & Simmons Mechanics (Hodder & Stoughton Educational) 0340 701668
Perkins & Perkins Advanced Mathematics - An Applied Course (Collins Educational)
000 3222705
Sadler & Thorning Understanding Mechanics (OUP) 019 9140979
Solomon Advanced Level Mathematics: Mechanics (John Murray) 0719 570824
Young Mechanics (Hodder & Stoughton) 07131 78221
Statistics
Bryers Advanced Level Statistics (Collins Educational) 000 3222837
Clarke & Cooke A Basic Course in Statistics (Arnold) 03407 19958
Crawshaw & Chambers A Concise Course in A Level Statistics (Stanley Thornes)
07487 17579
Crawshaw & Chambers A-Level Statistics Study Guide (Stanley Thornes) 07487 29976
Francis Advanced Level Statistics (Stanley Thornes) 0859 508137
Hugill Advanced Statistics (Collins) 0 00 3222152
McGill, McLennan, Migliorini Complete Advanced Level Mathematics: Statistics: Core Text
(Stanley Thornes) 0748 735607
MEW Group Exploring Statistics (Hodder & Stoughton) 0340 53158 4
Miller Statistics for Advanced Level (Cambridge University Press) 0521 367727
Morris A Level Questions and Answers: Statistics (Letts Educational Ltd) 18575 84864
Plews Introductory Statistics (Heinemann) 0435 537504
Rees Foundations of Statistics (Chapman & Hall) 0 412 28560 6
Smith Statistics (Hodder & Stoughton Educational) 0 340 70165 X (a collection of statistics
questions)
Upton & Cook Introducing Statistics (OUP) 0 19 914562 8
Upton & Cook Understanding Statistics (OUP) 0 19 914351
Wagner Introduction to Statistics (Collins Educational) 006 4671348
1/01/SA/S07087/2
34