v

Exam Strategies1. Remembertowritedownyourschoolcode,classandclassnumberatthebottomofthefirstpageofthe

exampaper.2. Thereareabout50questionsinanexampaperandthetimeallowedis65minutes.Youshouldtherefore

spendabout1minuteforeachquestionandallow15minutesforfinalchecking.3. Doyourroughworkontheroughworksheet.4. Showyourworkclearlyandneatly.5. Donotbestuckinanyoneofthequestions.Skipitandgoontoanotherone.6. Whensolvingapplicationproblems,readthequestionscarefully.7. Whenyou are asked to ‘Showyourworking’, you should show formulas and steps rather than just

writingdowntheanswers.Incaseyoudonotgetthecorrectanswer,youcangetthemarksforthecorrectmethodsused.Besides,makesureyouhavegivenaunit,ifany,toeachanswer.

Example:Itisgiventhatthebaseradiusandtheheightofacylinderare4cmand6cmrespectively.Findthevolumeofthecylinderintermsofp.

(Showyourworking) Goodpresentation:

Volume=p(4)2(6)cm2

=96pcm2

or p(4)2(6)cm2

=96pcm2

Thevolumeis96pcm2.

Poorpresentationresultinginmarkdeduction:

Thevolumeis96pcm2. or p(4)2(6)cm2

=96pcm2

8. Although the latest exemplars ofKeyStage3donot involve filling inmathematical terms, studentsshouldstillkeeptheminmindinordertoavoidmarkdeduction.

9. There are lots of formulas throughout the curriculum fromS.1 toS.3.Students should remember andunderstandallofthem,withoutambiguity.

10. Explanationsandreasonsarenecessarywhendealingwithaproof.

vii

Basic Competency for KeyStage 3 (Trial Version)Number and Algebra Dimension

Code Learning Unit

Number and Number Systems

NA1 Directed Numbers and the Number Line

NA2 Numerical Estimation

NA3 Approximation and Errors

NA4 Rational and Irrational Numbers

Comparing Quantities

NA5 Using Percentages

NA6 More about Percentages

NA7 Rate and Ratio

Observing Patterns and Expressing Generality

NA8 Formulating Problems with Algebraic Language

NA9 Manipulations of Simple Polynomials

NA10 Laws of Integral Indices

NA11 Factorization of Simple Polynomials

Algebraic Relations and Functions

NA12 Linear Equations in One Unknown

NA13 Linear Equations in Two Unknowns

NA14 Identities

NA15 Formulas

NA16 Linear Inequalities in One Unknown

: Included in this book

Measures, Shape and Space Dimension

Code Learning Unit

Measures in 2-D and 3-D Figures

MS1 Estimation in Measurement

MS2 Simple Idea of Areas and Volumes

MS3 More about Areas and Volumes

Learning Geometry through an Intuitive Approach

MS4 Introduction to Geometry

MS5 Transformation and Symmetry

MS6 Congruence and Similarity

MS7 Angles related with Lines and Rectilinear Figures

MS8 More about 3-D Figures

Learning Geometry through a Deductive Approach

MS9 Simple Introduction to Deductive Geometry

MS10 Pythagoras’ Theorem

MS11 Quadrilaterals

Learning Geometry through an Analytic Approach

MS12 Introduction to Coordinates

MS13 Coordinate Geometry of Straight Lines

Trigonometry

MS14 Trigonometric Ratios and Using Trigonometry

Data Handling Dimension

Code Learning Unit

Organization and Representation of data

DH1 Introduction to Various Stages of Statistics

DH2 Construction and Interpretation of Simple Diagrams and Graphs

Analysis and Interpretation of data

DH3 Measures of Central Tendency

Probability

DH4 Simple Idea of Probability

: Included in this book

viii

Chapter 1 Rate and Ratio

1

Number and Algebra Dimension

Learning Unit Code Descriptors

Rate and RatioNA7

KS3-NA7-1 demonstrate recognition of the difference between rate and ratio

KS3-NA7-2 represent a ratio in the form a : b (or ab

), a : b : c

KS3-NA7-3 find the other quantity from a given ratio a : b and the value of either a or b (including similar calculations for the case of a : b : c)

KS3-NA7-4 use rate and ratio to solve simple real-life problems including mensuration problems

Be aware of the use of a given ratio.Example 1:

It is given that a : b : c = 4 : 6 : 9. If a = 2, find the values of b and c.

✓ Correct ✗ Wrong

a : b = 4 : 6 and a : c = 4 : 9

ab

b

=

=

46

2 46

ac

c

=

=

49

2 49

b = 3 and c = 4.5

a : b : c = 4 : 6 : 9 = (4 - 2) : (6 - 2) : (9 - 2) = 2 : 4 : 7\ b = 4 and c = 7

and

and

Chapter 1 Rate and Ratio

Separate the continued

ratio into 2 two-term ratios

involving variable a, and

substitute the value of a to

find other variables.

Analysis

Chapter 2 Laws of Integral Indices

7

Number and Algebra Dimension

Learning Unit Code Descriptors

Laws of Integral IndicesNA10

KS3-NA10-2use the laws of integral indices to simplify simple algebraic expressions (up to 2 variables and at most 2 applications of integral index laws)

Be aware of the use of the law of integral indices to simplify expressions.Example 1:

Simplify xx y

5

6 2- and express the answer with positive indices.

✓ Correct ✗ Wrong

xx y

x y

x y

yx

5

6 25 6 2

1 2

2

−−

−

=

=

=

xx y

x y

x y

5

6 25 6 2

11 2

−− − − −=

=

( ) ( )

Example 2:

Simplify (a3)2 × (b4)2.

✓ Correct ✗ Wrong

(a3)2 × (b4)2 = a3 × 2 × b4 × 2

= a6b8(a3)2 × (b4)2 = a b3 42 2

× = a9b16

Chapter 2 Laws of Integral Indices

By the l aw o f i n teg ra l

Indices am

an = am - n, we have

x5

x6 = x5 - 6.

Analysis

By the l aw o f i n teg ra l

Indices (am)n = amn, we have

(a3)2 × (b4)2 = a3 × 2 × b4 × 2.

Analysis

52

TSA Assorted Exercises and Summative Test Mathematics S2

Section A: Choose the best answer for each question.

KS3-MS7-3

1. Inthefigure,findx.

A. 14° B. 18°

C. 24° D. 28°

2. Inthefigure,ABCisastraightline.Findm.

A. 33° B. 35°

C. 37° D. 39°

3. Inthefigure,ACDisastraightline.Findx.

A. 8° B. 9°

C. 10° D. 11°

KS3-MS7-4

4. Inthefigure,AB//CDandAC=BC.Findz.

A. 50° B. 65°

C. 115° D. 130°

5. Inthefigure,DABCisanequilateraltriangle.Findx.

A. 140° B. 150°

C. 160° D. 170°

KS3-MS7-3 KS3-MS7-4

6. Inthefigure,BCDisastraightline.Findy.

A. 126° B. 128°

C. 130° D. 132°

Territory-wide System AssessmentSecondary 2 Mathematics

Summative Test

Marker’s Use OnlyDimension Question MarksNumber and

Algebra 1 – 12, 21 – 31, 41 – 44 /38

Measures, Shape and Space 13 – 19, 32 – 39, 45 – 49 /32

Data Handling 20, 40, 50 /5

Instructions: 1. The time allowed is 65 minutes.

2. Write ALL your answers in the spaces provided.

3. The use of HKEAA approved calculators is permitted.

4. Rough work should be done on the rough work sheet provided.

5. Write your Name, Class and Class Number in the spaces below.

Name Class Class No.

© Hong Kong Educational Publishing Company

✄

Rate and Ratio Laws of Integral Indices(a) Rateisthecomparisonof2quantitiesofdifferentkinds.

(b) (i) Ratioisthecomparisonofquantitiesofthesamekind. (ii) Theratioofatobisusuallyexpressedas

a:borab

(wherea≠0andb≠0).

Foranypositiveintegersmandn,andanynon-zeronumbersaandb:

(a) am×an=am+n (b) am÷an=am-n

(c) (am)n=amn (d) (ab)n=anbn

(e)ab

ab

n n

n

= (f) a0=1

(g) aa

nn

− =1

Significant Figures Scientific Notation

(a) Forallnumbers, all‘0’sbetweentwonon-zerodigitsaresignificantfigures.

(b) Forallintegers, all ‘0’safter the lastnon-zerodigit arenotsignificant

figures.

(c) Fordecimalssmallerthan1, all ‘0’sbetweenthedecimalpointandthefirstnon-zero

digitarenotsignificantfigures.

Allnon-zeronumberscanbeexpressed intheforma×10n,where1≤a<10andnisaninteger.

Identities and Factorization Sequences(a) Someusefulidentities: (i) (a+b)(a-b)≡a2-b2

(ii) (a+b)2≡a2+2ab+b2

(iii) (a-b)2≡a2-2ab+b2

(b) (i) Theprocessofrewritingapolynomialasaproductofitsfactorsiscalledfactorization.

(ii) Factorizationisthereverseprocessofexpansion.

(a) A list of numbers arranged in an order is called asequence.

(b) Eachnumberinasequenceiscalledaterm.

(c) Forasequencewithacertainpattern,wecanrepresentthesequencebyageneralterm.

Simultaneous Linear Equations in Two Unknowns Angles of Triangles and Convex PolygonsIf two linear equations in two unknowns have commonunknowns,thentheyarecalledsimultaneouslinearequationsintwounknowns.Simultaneouslinearequationsintwounknownscanbesolvedbyusingthefollowingmethods:(i) Algebraicmethods, including themethodofelimination

andthemethodofsubstitution(ii) Graphicalmethod

(a) Triangle Foranytriangle: a+b+c=180° (∠ sumofD ) a+b=d (ext.∠ ofD )

(b) ConvexPolygon Sumofinterioranglesofann-sided

polygon=(n-2)×180° Sumofexteriorangles=360°

1 3

5

9 11

13 15

7

TSA Assorted Exercises and Summative Test Mathematics S2

2

Chapter 1 Rate and Ratio

Section A1. C

2. D 450g:3.5kg

=450g:3500g=9:70

3. A a:b=2:5 =8:20 b:c=4:7 =20:35 \ a:b:c=8:20:35

4. D a:b=5:6

ab

bb

=

=

=

56

125 56150

5. B x:z=5:4

xzx

x

=

=

=

54

6547 5.

y:z=2:4

yzy

y

=

=

=

24

6243

x-y=7.5-3 =4.5

6. C x:12=9:4

x

x12

9427

=

= 12:36=4:y

1236

4

12

=

=y

y

7. C Speedofthecar

= 453

km/h

=15km/h

8. D Ratiooftheirweights

=135g:105g:90g=9:7:6

9. C NumberofpiecesofcraftpaperreceivedbyAmy

=112× 44 3 1+ +

=56 NumberofpiecesofcraftpaperreceivedbyCathy

=112× 14 3 1+ +

=14 Difference

=56-14=42

10.A LetycmbethelengthofHenry’sshoe.

18 4

313 5

yy

=

= .\ ThelengthofHenry’sshoeis13.5cm.

Section B1. (i) Rate/Ratio (ii)Rate/Ratio

2. 2:3

3. 4:3:8 b=80-20 =60 c=2×80 =160 a:b:c=80:60:160 =4:3:8

4. 15:40:12 a:b=3:8 =15:40 a:c=5:4 =15:12 \ a:b:c=15:40:12