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CONTENTSpage

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 examinationin 2002. Details of the revised syllabus (9709) are in the separate Advanced Level Mathematicsbooklet, which also includes the new Advanced Subsidiary qualification available for the first timein 2001.

The Advanced level syllabus for Further Mathematics has been completely revised for firstexamination in 2002 and details of this new syllabus (9231), which will be available in June andNovember, 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 SubsidiaryMathematics syllabus (8709), which has been designed to be suitable for candidates who wouldformerly 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 tochoose from three different routes to AS Mathematics - Pure Mathematics only or PureMathematics and Mechanics or Pure Mathematics and Probability and Statistics.

The new Additional Mathematics Ordinary Level syllabus (4037) in this booklet has a PureMathematics only syllabus content. This syllabus, which will be examined in June and November,will be available for the first time in June 2002.

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NOTESMathematical Tables

The Cambridge Elementary Mathematical Tables (Second Edition) will continue to be provided foruse where necessary in SC/O level Mathematics Syllabus D Paper 2 (Papers 4024/2, 4029/2) andin SC/O level Statistics (Papers 4040/1 and 2). Further copies of these tables may be obtainedfrom the Cambridge University Press, The Edinburgh Building, Shaftesbury Road, Cambridge andthrough booksellers. No mathematical tables other than these are permitted in the examination onany of the syllabuses included in this booklet.

The use of tables is prohibited in SC/O level Mathematics Syllabus D Paper 1 (4024/1 and4029/1).

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 AdditionalMathematics (4037) and Statistics (4040), and in Advanced Level and H.S.C. FurtherMathematics (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 Olevel/S.C. Mathematics Syllabus D must use Mathematics Syllabus D (4024). The use ofsilent 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 theHandbook for Centres.

Mathematical Instruments

Apart from the usual mathematical instruments, candidates may use flexicurves in all theexaminations.

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/Decemberand reports on the November examinations are distributed to other International Centres inApril/May. Further copies of each are available from the Syndicate.

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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 tonumerical accuracy in calculations.

Learning Aims

The course should enable students to:

1. increase intellectual curiosity, develop mathematical language as a means ofcommunication and investigation and explore mathematical ways of reasoning;

2. acquire and apply skills and knowledge relating to number, measure and space inmathematical situations that they will meet in life;

3. acquire a foundation appropriate to a further study of Mathematics and skills andknowledge 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 tabularforms;

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 justifygeneralisations;

9. understand and use mathematical language and symbols and present mathematicalarguments 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 appropriatetechniques of solution and interpret the solutions in terms of the problems.

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UnitsSI units will be used in questions involving mass and measures: the use of the centimetre willcontinue.

Both the 12-hour clock and the 24-hour clock may be used for quoting times of the day. In the24-hour clock, for example, 3.15 a.m. will be denoted by 03 15; 3.15 p.m. by 15 15, noon by12 00 and midnight by 24 00.

Candidates will be expected to be familiar with the solidus notation for the expression ofcompound units, e.g. 5 cm/s for 5 centimetres per second, 13.6 g/cm3 for 13.6 grams percubic centimetre.

Scheme of Papers

Component Time Allocation Type Maximum Mark WeightingPaper 1 2 hours Short answer questions 80 50%Paper 2 2½ hours Structured questions 100 50%

Paper 1 will consist of about 25 short answer questions. Neither mathematical tables nor sliderules nor calculators will be allowed in this paper. All working must be shown in the spacesprovided 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 nochoice. Section B (48 marks) will contain five questions of which candidates will be required toanswer 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 anypart 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 withtrigonometric functions is strongly recommended. However, the Cambridge ElementaryMathematical Tables may continue to be used to supplement the use of the calculator, forexample 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, includingcases where answers are used in subsequent parts of the question. Prematureapproximation will be penalised, where appropriate.

(d) In Paper 4024/2, candidates with suitable calculators are encouraged to use the value of �from their calculators. The value of � will be given as 3.142 to 3 decimal places for use byother candidates. This value will be given on the front page of the question paper only.

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Detailed Syllabus

THEME OR TOPIC SUBJECT CONTENT

1. Number. Candidates should be able to:

-use natural numbers, integers (positive, negativeand zero), prime numbers, common factors andcommon multiples, rational and irrational numbers,real numbers; continue given number sequences,recognise patterns within and across differentsequences and generalise to simple algebraicstatements (including expressions for the nth term)relating to such sequences.

2. Set language and notation. -use set language and set notation, and Venndiagrams, to describe sets and representrelationships 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 A � BIntersection of A and B A � BNumber of elements in set A n(A)". . . is an element of . . ." �

". . . is not an element of . . ." �

Complement of set A A'The empty set ØUniversal setA is a subset of B A � BA is a proper subset of B A � BA is not a subset of B A ⊈ BA is not a proper subset of B A � B

3. Function notation. -use function notation,e.g. f(x) = 3x – 5, f: x � 3x – 5to describe simple functions, and the notation

f –1(x) =

35�x

and f –1: x �3

5�x

to describe their inverses.

4. Squares, square roots, cubes and cube roots. -calculate squares, square roots, cubes and cuberoots of numbers.

5. Directed numbers. -use directed numbers in practical situations(e.g. temperature change, tide levels).

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6. Vulgar and decimal fractions andpercentages.

-use the language and notation of simple vulgarand decimal fractions and percentages inappropriate contexts; recognise equivalence andconvert between these forms.

7. Ordering. -order quantities by magnitude and demonstratefamiliarity with the symbols =, ≠, >, <, ≥ , ≤.

8. Standard form. -use the standard form A x 10n where n is a positiveor negative integer, and 1 ≤ A < 10.

9. The four operations. -use the four operations for calculations with wholenumbers, decimal fractions and vulgar (and mixed)fractions, including correct ordering of operationsand use of brackets.

10. Estimation. -make estimates of numbers, quantities andlengths, give approximations to specified numbersof significant figures and decimal places and roundoff answers to reasonable accuracy in the contextof a given problem.

11. Limits of accuracy. -give appropriate upper and lower bounds for datagiven to a specified accuracy (e.g. measuredlengths); -obtain appropriate upper and lower bounds tosolutions of simple problems (e.g. the calculation ofthe perimeter or the area of a rectangle) given datato a specified accuracy.

12. Ratio, proportion, rate. -demonstrate an understanding of the elementaryideas and notation of ratio, direct and inverseproportion and common measures of rate; divide aquantity in a given ratio; use scales in practicalsituations, calculate average speed;-express direct and inverse variation in algebraicterms and use this form of expression to findunknown quantities.

13. Percentages. -calculate a given percentage of a quantity; expressone quantity as a percentage of another, calculatepercentage increase or decrease; carry outcalculations involving reverse percentages, e.g.finding the cost price given the selling price and thepercentage profit.

14. Use of an electronic calculator or logarithm tables.

-use an electronic calculator or logarithm tablesefficiently; apply appropriate checks of accuracy.

15. Measures. -use current units of mass, length, area, volumeand capacity in practical situations and expressquantities in terms of larger or smaller units.

16. Time. -calculate times in terms of the 12-hour and 24-hourclock; read clocks, dials and timetables.

17. Money. -solve problems involving money and convert fromone currency to another.

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18. Personal and household finance. -use given data to solve problems on personal andhousehold finance involving earnings, simpleinterest, discount, profit and loss; extract data fromtables and charts.

19. Graphs in practical situations. -demonstrate familiarity with cartesian coordinatesin two dimensions; interpret and use graphs inpractical situations including travel graphs andconversion graphs; draw graphs from given data;-apply the idea of rate of change to easy kinematicsinvolving distance-time and speed-time graphs,acceleration and retardation; calculate distancetravelled as area under a linear speed-time graph.

20. Graphs of functions. -construct tables of values and draw graphs forfunctions of the form y = axn where n = -2, -1, 0, 1,2, 3, and simple sums of not more than three ofthese and for functions of the form y = kax where ais a positive integer; interpret graphs of linear,quadratic, reciprocal and exponential functions; findthe gradient of a straight line graph; solve equationsapproximately by graphical methods; estimategradients of curves by drawing tangents.

21. Straight line graphs. -calculate the gradient of a straight line from thecoordinates of two points on it; interpret and obtainthe equation of a straight line graph in the formy = mx + c; calculate the length and the coordinatesof the midpoint of a line segment from thecoordinates of its end points.

22. Algebraic representation and formulae. -use letters to express generalised numbers andexpress basic arithmetic processes algebraically,substitute numbers for words and letters informulae; transform simple and more complicatedformulae; construct equations from given situations.

23. Algebraic manipulation. -manipulate directed numbers; use brackets andextract common factors; expand products ofalgebraic expressions; factorise expressions of theform ax + ay; ax + bx + kay + kby; a 2x2 - b2 y2; a2 + 2ab + b2; ax2 + bx + c; manipulate simplealgebraic fractions.

24. Indices. -use and interpret positive, negative, zero andfractional indices.

25. Solutions of equations and inequalities. -solve simple linear equations in one unknown;solve fractional equations with numerical and linearalgebraic denominators; solve simultaneous linearequations in two unknowns; solve quadraticequations by factorisation and either by use of theformula or by completing the square; solve simplelinear inequalities.

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26. Graphical representation of inequalities. -represent linear inequalities in one or two variablesgraphically. (Linear Programming problems are notincluded.)

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 explanationsinvolving similarity and congruence;-use and interpret vocabulary of simple solid figures:cube, cuboid, prism, cylinder, pyramid, cone, sphere;-use the relationships between areas of similartriangles, with corresponding results for similarfigures, and extension to volumes of similar solids.

28. Geometrical constructions. -measure lines and angles; construct simplegeometrical figures from given data, angle bisectorsand perpendicular bisectors using protractors or setsquares as necessary; read and make scaledrawings. (Where it is necessary to construct atriangle given the three sides, ruler and compassesonly must be used.)

29. Bearings. -interpret and use three-figure bearings measuredclockwise from the north (i.e. 000°-360°).

30. Symmetry. -recognise line and rotational symmetry (includingorder of rotational symmetry) in two dimensions, andproperties of triangles, quadrilaterals and circlesdirectly 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 simpleexplanations using the following geometricalproperties:(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.

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32. Locus. -use the following loci and the method of intersectingloci:(a) sets of points in two or three dimensions

(i) which are at a given distance from a givenpoint,

(ii) which are at a given distance from a givenstraight 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 begiven for the sphere, pyramid and cone),

(v) arc length and sector area as fractions of thecircumference and area of a circle.

34. Trigonometry. -apply Pythagoras Theorem and the sine, cosine andtangent ratios for acute angles to the calculation of aside or of an angle of a right-angled triangle (angleswill be quoted in, and answers required in, degreesand decimals of a degree to one decimal place);-solve trigonometrical problems in two dimensionsincluding those involving angles of elevation anddepression and bearings;-extend sine and cosine functions to angles between90° and 180°; solve problems using the sine andcosine rules for any triangle and the formula ab sinC for the area of a triangle;-solve simple trigonometrical problems in threedimensions. (Calculations of the angle between twoplanes or of the angle between a straight line andplane will not be required.)

35. Statistics. -collect, classify and tabulate statistical data; read,interpret and draw simple inferences from tables andstatistical diagrams;-construct and use bar charts, pie charts,pictograms, simple frequency distributions andfrequency polygons; -use frequency density to construct and readhistograms with equal and unequal intervals;-calculate the mean, median and mode forindividual data and distinguish between thepurposes for which they are used;-construct and use cumulative frequencydiagrams; estimate the median, percentiles,quartiles and interquartile range;-calculate the mean for grouped data; identify themodal class from a grouped frequency distribution.

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36. Probability. -calculate the probability of a single event aseither a fraction or a decimal (not a ratio);-calculate the probability of simple combinedevents, using possibility diagrams and treediagrams where appropriate. (In possibilitydiagrams outcomes will be represented by pointson a grid and in tree diagrams outcomes will bewritten at the end of branches and probabilities bythe side of the branches.)

37. Matrices. -display information in the form of a matrix of anyorder; solve problems involving the calculation ofthe sum and product (where appropriate) of twomatrices, and interpret the results; calculate theproduct of a scalar quantity and a matrix; use thealgebra of 2 x 2 matrices including the zero andidentity 2 x 2 matrices; calculate the determinantand inverse of a non-singular matrix. (A-1 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) andtheir combinations (If M(a) = b and R(b) = c thenotation RM(a) = c will be used; invariants underthese transformations may be assumed.);-identify and give precise descriptions oftransformations connecting given figures;describe transformations using coordinates andmatrices. (Singular matrices are excluded.)

39. Vectors in two dimensions. -describe a translation by using a vector

represented by ����

��

yx

, AB or a; add vectors and

multiply a vector by a scalar;

-calculate the magnitude of a vector

����

��

yx as 22 yx � .

(Vectors will be printed as AB or a and theirmagnitudes denoted by modules signs, e.g.I AB I or I a I. ln all their answers to questionscandidates are expected to indicate a in somedefinite way, e.g. by an arrow or by underlining,thus AB or a);-represent vectors by directed line segments; usethe sum and difference of two vectors to expressgiven vectors in terms of two coplanar vectors;use position vectors.

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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 ofmore advanced techniques;

2. further develop their knowledge of mathematical concepts and principles, and use thisknowledge 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 mathematicsrelated 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 appropriatesituations;

8. develop creativity and perseverance in the approach to problem solving;

9. derive enjoyment and satisfaction from engaging in mathematical pursuits, and gain anappreciation 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 ofsolution.

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 nochoice of question except that the last question in each paper will consist of two alternatives, onlyone of which must be answered. The mark allocations for the last question will be in the range of10-12 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 testeddirectly 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 ofcompound units e.g. 5 ms-1 for 5 metres per second.

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THEME OR TOPIC CURRICULUM OBJECTIVES

1. Set language and notation.

Candidates should be able to:

-use set language and notation, and Venn diagrams todescribe sets and represent relationships between setsas 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:

Union of A and B A � BIntersection of A and B A � BNumber of elements in set A n(A)". . . is an element of . . . " �

". . . is not an element of . . ." �

Complement of set A A'The empty set �

Universal set A is a subset of B A � BA is a proper subset of B A � BA is not a subset of B A ⊈ BA is not a proper subset of B A � B

2. Functions. -understand the terms function, domain, range (imageset), one-one function, inverse function and compositionof functions;

-use the notation f(x) = sin x, f: x � lg x, (x > 0),f -1(x)and f2 (x) [=f(f(x))];

-understand the relationship between y = f(x) andy = � f(x) �, where f(x) may be linear, quadratic ortrigonometric;

-explain in words why a given function is a function orwhy it does not have an inverse;

-find the inverse of a one-one function and formcomposite functions;

-use sketch graphs to show the relationship between afunction and its inverse.

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Candidates should be able to:3. Quadratic functions. -find the maximum or minimum value of the quadratic

function f : x � ax2 + bx + c by any method;

-use the maximum or minimum value of f(x) to sketch thegraph 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 relatedconditions for a given line to (i) intersect a given curve,(ii) be a tangent to a given curve, (iii) not intersect agiven curve;

-solve quadratic equations for real roots and find thesolution 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 atleast one linear equation.

7. Logarithmic and exponential functions. -know simple properties and graphs of the logarithmicand exponential functions including lnx and ex (seriesexpansions are not required);

-know and use the laws of logarithms (including changeof base of logarithms);

-solve equations of the form ax= b.

8. Straight line graphs. -interpret the equation of a straight line graph in theform y = m x + c ;

-transform given relationships, including y = axn andy = Abx, to straight line form and hence determineunknown constants by calculating the gradient orintercept of the transformed graph;

-solve questions involving mid-point and length of aline;

-know and use the condition for two lines to be parallelor perpendicular.

9. Circular measure. -solve problems involving the arc length and sectorarea of a circle, including knowledge and use of radianmeasure.

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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 therelationship 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 arepositive integers and c is an integer;

-use the relationships A

A

cossin

= tan A,

A

A

sincos

= cot A, sin2 A + cos2 A = 1,

sec2 A = 1 + tan2 A, cosec2 A = 1 + cot2 A, and solvesimple trigonometric equations involving the sixtrigonometric functions and the above relationships(not including general solution of trigonometricequations)

-prove simple trigonometric identities.

11. Permutations and combinations. -recognise and distinguish between a permutation caseand a combination case;

-know and use the notation n!, (with 0! = 1), and theexpressions for permutations and combinations of nitems taken r at a time;

-answer simple problems on arrangement and selection(cases with repetition of objects, or with objects arrangedin a circle or involving both permutations andcombinations, are excluded).

12. Binomial expansions. -use the Binomial Theorem for expansion of (a + b)n forpositive integral n;

-use the general term ���

����

�

rn

a n - r b

r, 0 < r ≤ n

(knowledge of the greatest term and properties of thecoefficients is not required).

13. Vectors in 2 dimensions.-use vectors in any form, e.g. ��

�

����

�

ba

, AB , p, ai - bj;

-know and use position vectors and unit vectors;

-find the magnitude of a vector, add and subtract vectorsand multiply vectors by scalars;

-compose and resolve velocities;

-use relative velocity including solving problems oninterception (but not closest approach).

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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 andproduct (where appropriate) of two matrices and interpretthe results;

-calculate the product of a scalar quantity and a matrix;

-use the algebra of 2 x 2 matrices (including the zero andidentity matrix);

-calculate the determinant and inverse of a non-singular2 x 2 matrix and solve simultaneous line equations.

15. Differentiation and integration. -understand the idea of a derived function;

-use the notations f'(x), f"(x), ;dd

dd

dd

,dd

2

2

��

���

���

�

��

x

y

xx

y

x

y

-use the derivatives of the standard functions xn (for anyrational n), sin x, cos x, tan x, ex, lnx, together withconstant multiples, sums and composite functions ofthese;

-differentiate products and quotients of functions;

-apply differentiation to gradients, tangents and normals,stationary points, connected rates of change, smallincrements and approximations and practical maximaand minima problems;

-discriminate between maxima and minima by anymethod;

-understand integration as the reverse process ofdifferentiation;

-integrate sums of terms in powers of x excludingx

1;

-integrate functions of the form (ax + b)n

(excluding n = -1), eax+b, sin (ax + b), cos (ax + b);

-evaluate definite integrals and apply integration to theevaluation of plane areas;

-apply differentiation and integration to kinematicsproblems that involve displacement, velocity andacceleration of a particle moving in a straight line withvariable or constant acceleration, and the use of x-t andv-t graphs.

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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 compulsoryshort questions in Section A (36 marks) and a choice of four out of five longer questions inSection B (64 marks).

A high standard of accuracy will be expected in calculations and in the drawing of diagramsand graphs. All working must be clearly shown. The use of an electronic calculator isexpected 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: randomsample, stratified random sample, quotasample, systematic sample.

2. The nature of a variable. Including knowledge of the terms: discrete,continuous, quantitative and qualitative.

3. Classification, tabulation and interpretation ofdata. Pictorial representation of data; thepurpose and use of various forms, theiradvantages and disadvantages.

Including pictograms, pie charts, bar charts,sectional and percentage bar charts, dual barcharts, change charts.

4. Frequency distributions; frequency polygonsand histograms.

Including class boundaries and mid-points,class intervals.

5. Cumulative frequency distributions, curves(ogives) and polygons.

6. Measures of central tendency and theirappropriate use; mode and modal class,median and mean. Measures of dispersionand their appropriate use; range,interquartile range, variance and standarddeviation.

Calculation of the mean, the variance and thestandard deviation from a set of numbers, afrequency distribution and a grouped frequencydistribution, including the use of an assumedmean.Estimation of the median, quartiles andpercentiles from a set of numbers, acumulative frequency curve or polygon and bylinear interpolation from a cumulativefrequency table.The effect on mean and standard deviation ofadding a constant to each observation and ofmultiplying each observation by a constant.Linear transformation of data to a given meanand standard deviation.

7. Index numbers, composite index numbers, pricerelatives, crude and standardised rates.

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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 forfitting a straight line; the derivation of theequation of the fitted straight line in the formy = mx + c.

10.Elementary ideas of probability. Including the treatment of mutually exclusive andindependent events.

11.Simple probability and frequency distributionsfor a discrete variable. Expectation.

Including expected profit and loss in simplegames; idea of a fair game.

18

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 carrying50% of the marks, and each marked out of 100.

Paper 1 A paper consisting of about 11 questions of different marks and lengths on PureMathematics. Candidates will be expected to answer all questions, except for thelast question (worth 12 to 14 marks), which will offer two alternatives, only one ofwhich 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 marksand lengths on Statistics (worth a total of 43 or 44 marks), and one final questionworth 12 or 14 marks. The final question consists of two alternatives, one onMechanics and one on Statistics. Candidates will be expected to answer allquestions, except for the last question, where only one of the alternatives must beanswered.

It is expected that candidates will have a calculator with standard 'scientific' functions foruse in the examination. Graphic calculators will be permitted but candidates obtainingresults solely from graphic calculators without supporting working or reasoning will notreceive credit. Computers, and calculators capable of algebraic manipulation, are notpermitted. All the regulations in the Handbook for Centres apply with the exception that, forexaminations on this syllabus only, graphic calculators are permitted.

PAPER 1Knowledge of the syllabus for Pure Mathematics (units P1and P3) in Mathematics 9709 isassumed, and candidates may need to apply such knowledge in answering questions.

THEME OR TOPIC CURRICULUM OBJECTIVES

1. Polynomials and rational functions.

Candidates should be able to:

-recall and use the relations between theroots and coefficients of polynomialequations, for equations of degree 2, 3, 4only;

-use a given simple substitution to obtain anequation whose roots are related in a simpleway to those of the original equation;

-sketch graphs of simple rational functions,including the determination of obliqueasymptotes, in cases where the degree ofthe numerator and the denominator are atmost 2 (detailed plotting of curves will not berequired, but sketches will generally beexpected to show significant features, suchas turning points, asymptotes andintersections with the axes).

19

2. Polar coordinates. -understand the relations between cartesianand polar coordinates (using the conventionr ≥ 0), and convert equations of curves fromcartesian to polar form and vice versa;-sketch simple polar curves, for 0 ≤ θ < 2� or-� < θ ≤ � or a subset of either of theseintervals (detailed plotting of curves will not berequired, but sketches will generally beexpected to show significant features, such assymmetry, the form of the curve at the pole andleast/greatest values of r);

-recall the formula �β

α2r

21

dθ for the area of a

sector, and use this formula in simple cases.

3. Summation of series. −use the standard results for� r , �2r , �

3r

to find related sums;

-use the method of differences to obtain thesum of a finite series, e.g. by expressing thegeneral term in partial fractions;-recognise, by direct consideration of a sum ton terms, when a series is convergent, and findthe sum to infinity in such cases.

4. Mathematical induction. -use the method of mathematical induction toestablish a given result (questions set mayinvolve divisibility tests and inequalities, forexample);-recognise situations where conjecture basedon a limited trial followed by inductive proof is auseful strategy, and carry this out in simplecases e.g. find the nth derivative of xex.

5. Differentiation and integration.-obtain an expression for

2

2

ddx

y in cases where the

relation between y and x is defined implicitly orparametrically;

-derive and use reduction formulae for theevaluation of definite integrals in simple cases;

-use integration to findmean values and centroids of two- and three-dimensional figures (where equations areexpressed in cartesian coordinates, includingthe use of a parameter), using strips, discs orshells as appropriate,arc lengths (for curves with equations incartesian coordinates, including the use of aparameter, or in polar coordinates),surface areas of revolution about one of theaxes (for curves with equations in cartesiancoordinates, including the use of a parameter,but not for curves with equations in polarcoordinates).

20

6. Differential equations. -recall the meaning of the terms‘complementary function' and ‘particularintegral' in the context of linear differentialequations, and recall that the general solutionis the sum of the complementary function and aparticular integral;-find the complementary function for a secondorder linear differential equation with constantcoefficients;-recall the form of, and find, a particularintegral for a second order linear differentialequation in the cases where a polynomial oraebx or a cos px + b sin px is a suitable form,and in other simple cases find the appropriatecoefficient(s) given a suitable form of particularintegral;-use a substitution to reduce a given differentialequation to a second order linear equation withconstant coefficients;-use initial conditions to find a particular solution toa differential equation, and interpret a solution interms of a problem modelled by a differentialequation.

7. Complex numbers. -understand de Moivre's theorem, for a positiveintegral exponent, in terms of the geometricaleffect of multiplication of complex numbers;-prove de Moivre's theorem for a positive integralexponent;-use de Moivre's theorem for positive integralexponent to express trigonometrical ratios ofmultiple angles in terms of powers oftrigonometrical ratios of the fundamental angle;-use de Moivre's theorem, for a positive ornegative rational exponent

in expressing powers of sin θ and cos θ in termsof 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 formsax + by + cz = d or r.n. = p or r = a + � b +�c,and convert equations of planes from one form toanother as necessary in solving problems;-recall that the vector product a x b of two vectorscan be expressed either as I a II b I sin θ n̂ , wheren̂ is a unit vector, or in component form as(a2 b3 – a3 b2) i + (a3 b1 – a1 b3) j + (a1 b2 – a2 b1)k;-use equations of lines and planes, together withscalar and vector products where appropriate, tosolve problems concerning distances, angles andintersections, including

determining whether a line lies in a plane, isparallel to a plane or intersects a plane, andfinding the point of intersection of a line and aplane when it exists,finding the perpendicular distance from a point

21

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 intersectionof two planes,calculating the shortest distance between twoskew lines, finding an equation for the commonperpendicular to two skew lines.

9. Matrices and linear spaces. -recall and use the axioms of a linear (vector)space (restricted to spaces of finite dimensionover the field of real numbers only);-understand the idea of linear independence, anddetermine whether a given set of vectors isdependent or independent;-understand the idea of the subspace spanned bya given set of vectors;-recall that a basis for a space is a linearlyindependent set of vectors that spans the space,and determine a basis in simple cases;-recall that the dimension of a space is thenumber of vectors in a basis;-understand the use of matrices to representlinear transformations from ℝn � ℝm;-understand the terms ‘column space', ‘rowspace', ‘range space' and ‘null space', anddetermine 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, thedimension of the null space and the order of thematrix;-use methods associated with matrices and linearspaces in the context of the solution of a set oflinear equations;-evaluate the determinant of a square matrix andfind the inverse of a non-singular matrix (2 x 2and 3 x 3 matrices only), and recall that thecolumns (or rows) of a square matrix areindependent if and only if the determinant is non-zero;-understand the terms ‘eigenvalue' and‘eigenvector', as applied to square matrices;-find eigenvalues and eigenvectors of 2 x 2 and3 x 3 matrices (restricted to cases where theeigenvalues are real and distinct);-express a matrix in the form QDQ-1, where D is adiagonal matrix of eigenvalues and Q is a matrixwhose columns are eigenvectors, and use thisexpression, e.g. in calculating powers ofmatrices.

22

PAPER 2

Knowledge of the syllabuses for Mechanics (units M1 and M2) and Probability and Statistics (unitsS1 and S2) in Mathematics 9709 is assumed. Candidates may need to apply such knowledge inanswering 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 linearmomentum, and show understanding of itsvector nature (in one dimension only);-recall Newton's experimental law and thedefinition of the coefficient of restitution, theproperty 0 ≤ e ≤ 1, and the meaning of theterms ‘perfectly elastic' (e =1) and ‘inelastic'(e = 0);-use conservation of linear momentumand/or Newton's experimental law to solveproblems that may be modelled as the directimpact of two smooth spheres or the director oblique impact of a smooth sphere with afixed surface;-recall and use the definition of the impulseof a constant force, and relate the impulseacting on a particle to the change ofmomentum of the particle (in one dimensiononly).

2. Circular motion. -recall and use the radial and transversecomponents of acceleration for a particlemoving in a circle with variable speed;-solve problems which can be modelled bythe motion of a particle in a vertical circlewithout loss of energy (including finding thetension in a string or a normal contact force,locating points at which these are zero, andconditions for complete circular motion).

3. Equilibrium of a rigid body under coplanarforces.

-understand and use the result that the effectof gravity on a rigid body is equivalent to asingle force acting at the centre of mass ofthe body, and identify the centre of mass byconsiderations of symmetry in suitablecases;-calculate the moment of a force about apoint in 2 dimensional situations only(understanding of the vector nature ofmoments is not required);-recall that if a rigid body is in equilibriumunder the action of coplanar forces then thevector sum of the forces is zero and the sumof the moments of the forces about any pointis zero, and the converse of this;-use Newton's third law in situationsinvolving the contact of rigid bodies inequilibrium;

23

-solve problems involving the equilibrium ofrigid bodies under the action of coplanarforces (problems set will not involvecomplicated trigonometry).

4. Rotation of a rigid body. -understand and use the definition of themoment of inertia of a system of particles abouta fixed axis as � 2mr , and the additiveproperty of moment of inertia for a rigid bodycomposed of several parts (the use ofintegration to find moments of inertia will not berequired);-use the parallel and perpendicular axestheorems (proofs of these theorems will not berequired);-recall and use the equation of angular motionC = I��� for the motion of a rigid body about afixed axis (simple cases only, where themoment C arises from constant forces such asweights or the tension in a string wrappedaround the circumference of a flywheel;knowledge of couples is not included andproblems will not involve consideration orcalculation of forces acting at the axis ofrotation);

-recall and use the formula 2

2

1�Ι for the kinetic

energy of a rigid body rotating about a fixedaxis;-use conservation of energy in solving problemsconcerning mechanical systems where rotationof a rigid body about a fixed axis is involved.

5. Simple harmonic motion. -recall a definition of SHM and understand theconcepts of period and amplitude;-use standard SHM formulae in the course ofsolving problems;-set up the differential equation of motion inproblems leading to SHM, recall and useappropriate forms of solution, and identify theperiod and amplitude of the motion;-recognise situations where an exact equationof motion may be approximated by an SHMequation, carry out necessary approximations(e.g. small angle approximations or binomialapproximations) and appreciate the conditionsnecessary for such approximations to be useful.

24

STATISTICS (Sections 6 to 9)

6. Further work on distributions. -use the definition of the distribution function asa probability to deduce the form of a distributionfunction in simple cases, e.g. to find thedistribution function for Y, where Y = X3 and Xhas a given distribution;-understand conditions under which ageometric distribution or negative exponentialdistribution may be a suitable probability model;-recall and use the formula for the calculation ofgeometric or negative exponential probabilities;-recall and use the means and variances of ageometric distribution and negative exponentialdistribution.

7. Inference using normal and t-distributions. -formulate hypotheses and apply a hypothesistest concerning the population mean using asmall sample drawn from a normal populationof unknown variance, using a t-test;-calculate a pooled estimate of a populationvariance from two samples (calculations basedon either raw or summarised data may berequired);-formulate hypothesis concerning the differenceof 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 thecircumstances of a problem is expected);-determine a confidence interval for apopulation mean, based on a small samplefrom a normal population with unknownvariance, using a t-distribution;-determine a confidence interval for a differenceof population means, using a t-distribution, or anormal distribution, as appropriate.

8. � 2–tests. -fit a theoretical distribution, as prescribed by agiven hypothesis, to given data (questions willnot involve lengthy calculations);-use a �2-test, with the appropriate number ofdegrees of freedom, to carry out thecorresponding goodness of fit analysis (classesshould be combined so that each expectedfrequency is at least 5);-use a �2-test, with the appropriate number ofdegrees of freedom, for independence in acontingency table (Yates’ correction is notrequired, but classes should be combined sothat the expected frequency in each cell is atleast 5).

25

9. Bivariate data. -understand the concept of least squares,regression lines and correlation in the context ofa scatter diagram;-calculate, both from simple raw data and fromsummarised data, the equations of regressionlines and the product moment correlationcoefficient, and appreciate the distinctionbetween the regression line of y on x and thatof x on y;-recall and use the facts that both regressionlines pass through the mean centre (x, y) andthat the product moment correlation coefficient rand the regression coefficients b1, b2 arerelated by r2 = b1,b2;-select and use, in the context of a problem, theappropriate regression line to estimate a value,and understand the uncertainties associatedwith such estimations;-relate, in simple terms, the value of the productmoment correlation coefficient to theappearance of the scatter diagram, withparticular reference to the interpretation ofcases where the value of the product momentcorrelation coefficient is close to +1, -1 or 0;-carry out a hypothesis test based on theproduct moment correlation coefficient.

26

MATHEMATICAL NOTATIONThe 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, whererelevant, to examinations at all other levels, i.e. O/SC, AO/HSC (Subsidiary).

Mathematical Notation

1. Set Notation

� is an element of

� is not 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� the empty set

universal set

A' the complement of the set Aℕ 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 � ℚ: x > 0}

ℚ0� the set of positive rational numbers and zero, {x � ℚ: x ≥ 0}

ℝ the set of real numbersℝ+ the set of positive real numbers {x � ℝ: x > 0}

ℝ0� the set of positive real numbers and zero {x � ℝ: x ≥ 0}

ℝn the real n tuplesℂ 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

� union� intersection

[a, b] the closed interval {x � ℝ: a ≤ x ≤ b}

[a, b) the interval {x � ℝ: a ≤ x < b}(a, b] the interval {x � ℝ: a < x ≤ b}

(a, b) the open interval {x � ℝ: a < x < b}

yRx y is related to x by the relation Ry ~ x y is equivalent to x, in the context of some equivalence relation

27

2. Miscellaneous Symbols

= is equal to� is not equal to� is identical to or is congruent to� is approximately equal to � is isomorphic to� is proportional 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

3 Operationsa + b a plus ba – b a minus ba x b, ab, a.b a multiplied by b

a � b, ba , a/b a divided by b

a : b the ratio of a to b

��

n

iia

l

a1 + a2 + . . . + an

√a the positive square root of the real number a│a│ the modulus of the real number an! n factorial for n � ℕ (0! = 1)

��

���

�

r

nthe binomial coefficient

)!(!!

rnrn�

, for n, r � ℕ, 0 ≤ r ≤ n

!1)1)...((

rrnnn ���

, for n � ℚ, r � ℕ

4. Functions

f function f

f (x) the value of the function f at xf : A →B f is a function under which each element of set A has an image in set B

f : x � y the function f maps the element x to the element y

f –1 the inverse of the function fg o f, gf the composite function of f and g which is defined by

(g o f)(x) or gf (x) = g(f(x))

lima�x

f (x) the limit of f(x) as x tends to a

�x;� x an increment of x

xy

dd

the derivative of y with respect to x

n

n

xy

dd

the nth derivative of y with respect to x

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

b

∫

28

and b

xy�

�the partial derivative of y with respect to x

,...x,x ��� the first, second, . . . derivatives of x with respect to time

5. Exponential and Logarithmic Functions

e base of natural logarithms

ex, exp x exponential function of xloga x logarithm to the base a of xln 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 the circular functions

sin–1, cos–1, tan–1, cosec–1, sec–1, cot–1 the inverse circular relations

sinh, cosh, tanh,cosech, sech, coth the hyperbolic functions

sinh–1, cosh–1, tanh–1,cosech–1, sech–1, coth–1 the inverse hyperbolic relations

7. Complex Numbers

i square root of –1z a complex number, z = x + iy

= r (cos θ + i sin θ ), r � ℝ = re θi , r � ℝ

Re z the real part of z, Re (x + iy) = xIm z the imaginary part of z, Im (x + iy) = y| z | the modulus of z, | x+ iy | = �(x2 + y2), | r (cos θ + i sin θ )| = rarg z the argument of z, arg (r(cos θ + i sin θ )) = θ , –� < θ ≤ �z* the complex conjugate of z, (x + iy)* = x – iy

a

+0

+0

29

8. Matrices

M a matrix MM-1 the inverse of the square matrix M

MT the transpose of the matrix M

det M the determinant of the square matrix M

9. Vectors

a the vector aAB the vector represented in magnitude and direction by the directed line

segment AB� a unit vector in the direction of the vector ai, 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 ba � b the vector product of a and b

10. Probability and Statistics

A, B, C etc. events

A� B union of events A and BA� B 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, … occurp(x) the value of the probability function P(X = x) of the discrete random

variable Xp1, p2, … probabilities of the values x1, x2, … of the discrete random variable Xf(x), g(x), … the value of the probability density function of the continuous random

variable XF(x), G(x), … the value of the (cumulative) distribution function P(X ≤ x) of the

random variable XE(X) expectation of the random variable X

E[g(X)] expectation of g(X)Var(X) variance of the random variable XG(t) the value of the probability generating function for a random variable

which takes integer valuesB(n, p) binomial distribution, parameters n and pN( 2σµ, ) normal distribution, mean � and variance 2

�

µ population mean

30

2� population variance

� population standard deviationx sample means2 unbiased estimate of population variance from a sample,

� �22

11

� ��

� xxn

s

� probability density function of the standardised normal variable withdistribution N (0, 1)

� corresponding cumulative distribution function

ρ linear product-moment correlation coefficient for a population

r linear product-moment correlation coefficient for a sampleCov(X, Y) covariance of X and Y

31

BOOKLISTSThese 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 totheir students and will support their own teaching style. ISBN numbers are provided whereverpossible.

O LEVEL MATHEMATICS SYLLABUS D 4024Bostock, L, S Chandler, A Shepherd, E Smith ST(P) Mathematics Books 1A to 5A (Stanley Thornes)Book 1A 0 7487 0540 6Book 1B 0 7487 0143 5Book 2A 0 7487 0542 2Book 2B 0 7487 0144 3Book 3A 0 7487 1260 7 Book 3B 0 7487 0544 9Book 4A 0 7487 1501 0Book 4B 0 7487 1583 5Book 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 5Book 2 0 7195 4451 3Book 3 0 7195 4452 1Book 4 0 7195 4453 XBook 5 0 7195 4454 8

Cox, C J and D Bell Understanding Mathematics Books 1 – 5 (John Murray)Book 1 0 7195 4752 0Book 2 0 7195 4754 7Book 3 0 7195 4756 3Book 4 0 7195 5030 0Book 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 7Book 2 0 17 431420 5Book 3B 0 17 431434 5Book 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 0Book 2E 0 85950 745 9Book 3E 0 85950 746 7Book 4E 0 85950 747 5Book 5E 0 85950 733 5

32

National Mathematics Project (NMP) Mathematics for Secondary Schools Red Track Books 1to 5 (Longman Singapore Publishers Pte Ltd)Book 1 0 582 206960Book 2 0 582 206987/206995Book 3 0 582 20727 4Book 4 0 582 20725 8Book 5 0 582 20726 6

Smith, Ewart Examples in Mathematics for GCSE Higher Tier (Second edition) (StanleyThornes) 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 book07487 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

33

A LEVEL MATHEMATICS (9709) AND A LEVEL FURTHER MATHEMATICS (9231)

Pure MathematicsBackhouse, 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) 0859501035

Butcher & Megeny Access to Advanced Level Maths (Stanley Thornes) 07487 29992 (shortintroductory 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 EducationalLtd) 1857 584656

Solomon Advanced Level Mathematics (3 volumes) (John Murray) 0 7195 5344 X

Young Pure Mathematics (Hodder & Stoughton) 07131 76431

Further Pure MathematicsBostock, Chandler & Rourke Further Pure Mathematics (Stanley Thornes) 085950 1035

Integrated CoursesBerry & 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 (AddisonWesley 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

34

MechanicsAdams, 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 17749Horril 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

StatisticsBryers 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 statisticsquestions)

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