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1 Eam Strategies 1. Rememer to write down your school code, class and class numer at the ottom of the first page of the eam paper. 2. There are aout 0 questions in an eam paper and the time allowed is 6 minutes. You should therefore spend aout 1 minute for each question and allow 1 minutes for final checking. 3. Do your rough work on the rough work sheet. 4. Show your work clearly and neatly.. Do not e stuck in any one of the questions. Skip it and go on to another one. 6. When solving application prolems, read the questions carefully. 7. When you are asked to Show your working, you should show formulas and steps rather than just writing down the answers. In case you do not get the correct answer, you can get the marks for the correct methods used. Besides, make sure you have given a unit, if any, to each answer. Eample: It is given that the ase radius and the height of a cylinder are 4 cm and 6 cm respectively. Find the volume of the cylinder in terms of p. (Show your working) Good presentation: Volume p(4) 2 (6) cm 2 or 96p cm 2 p(4) 2 (6) cm 2 96p cm 2 The volume is 96p cm 2. Poor presentation resulting in mark deduction: The volume is 96p cm 2. or p(4) 2 (6) cm 2 96p cm 2 8. Although the latest eemplars of Key Stage 3 do not involve filling in mathematical terms, students should still keep them in mind in order to avoid mark deduction. 9. There are lots of formulas throughout the curriculum from S.1 to S.3. Students should rememer and understand all of them, without amiguity. 10. Eplanations and reasons are necessary when dealing with a proof. v

2 Basic Competency for Key Stage 3 (Trial Version) Numer and Algera Dimension Code NA1 NA2 NA3 NA4 NA NA6 NA7 NA8 NA9 NA10 NA11 NA12 NA13 NA14 NA1 NA16 Learning Unit Numer and Numer Systems Directed Numers and the Numer Line Numerical Estimation Approimation and Errors Rational and Irrational Numers Comparing Quantities Using Percentages More aout Percentages Rate and Ratio Oserving Patterns and Epressing Generality Formulating Prolems with Algeraic Language Manipulations of Simple Polynomials Laws of Integral Indices Factorization of Simple Polynomials Algeraic Relations and Functions Linear Equations in One Unknown Linear Equations in Two Unknowns Identities Formulas Linear Inequalities in One Unknown : Included in this ook vii

3 Measures, Shape and Space Dimension Code MS1 MS2 MS3 MS4 MS MS6 MS7 MS8 MS9 MS10 MS11 MS12 MS13 MS14 Learning Unit Measures in 2-D and 3-D Figures Estimation in Measurement Simple Idea of Areas and Volumes More aout Areas and Volumes Learning Geometry through an Intuitive Approach Introduction to Geometry Transformation and Symmetry Congruence and Similarity Angles related with Lines and Rectilinear Figures More aout 3-D Figures Learning Geometry through a Deductive Approach Simple Introduction to Deductive Geometry Pythagoras Theorem Quadrilaterals Learning Geometry through an Analytic Approach Introduction to Coordinates Coordinate Geometry of Straight Lines Trigonometry Trigonometric Ratios and Using Trigonometry Data Handling Dimension Code DH1 DH2 DH3 DH4 Learning Unit Organization and Representation of data Introduction to Various Stages of Statistics Construction and Interpretation of Simple Diagrams and Graphs Analysis and Interpretation of data Measures of Central Tendency Proaility Simple Idea of Proaility : Included in this ook viii

Chapter 1 Rate and Ratio Chapter 1 Rate and Ratio Numer and Algera Dimension Learning Unit Code Descriptors Rate and Ratio KS3-NA7-1 demonstrate recognition of the difference etween rate and ratio

4 Chapter 1 Rate and Ratio Chapter 1 Rate and Ratio Numer and Algera Dimension Learning Unit Code Descriptors Rate and Ratio KS3-NA7-1 demonstrate recognition of the difference etween rate and ratio NA7 KS3-NA7-2 represent a ratio in the form a : (or a ), a : : c KS3-NA7-3 KS3-NA7-4 find the other quantity from a given ratio a : and the value of either a or (including similar calculations for the case of a : : c) use rate and ratio to solve simple real-life prolems including mensuration prolems Be aware of the use of a given ratio. Eample 1: It is given that a : : c 4 : 6 : 9. If a 2, find the values of and c. Correct a : 4 : 6 and a : c 4 : 9 a 4 a 4 and 6 c and 6 c 9 3 and c 4. Wrong a : : c 4 : 6 : 9 (4-2) : (6-2) : (9-2) 2 : 4 : 7 \ 4 and c 7 Analysis Separate the continued ratio into 2 two-term ratios involving variale a, and sustitute the value of a to find other variales. 1

Chapter 2 Laws of Integral Indices Chapter 2 Laws of Integral Indices Numer and Algera Dimension Learning Unit Code Descriptors Laws of Integral Indices NA10 KS3-NA10-2 use the laws of integral

5 Chapter 2 Laws of Integral Indices Chapter 2 Laws of Integral Indices Numer and Algera Dimension Learning Unit Code Descriptors Laws of Integral Indices NA10 KS3-NA10-2 use the laws of integral indices to simplify simple algeraic epressions (up to 2 variales and at most 2 applications of integral inde laws) Be aware of the use of the law of integral indices to simplify epressions. Eample 1: Simplify 6-2 y 6 2 y and epress the answer with positive indices. Correct 6 2 y 1 2 y 2 y 6 2 y Wrong ( 6) ( 2) 11 2 y y Analysis B y t h e l a w o f i n t e g r a l Indices am a n am - n, we have 6-6. Eample 2: Simplify (a 3 ) 2 ( 4 ) 2. Correct Wrong (a 3 ) 2 ( 4 ) 2 a a 6 8 (a 3 ) 2 ( 4 ) 2 a a Analysis B y t h e l a w o f i n t e g r a l Indices (a m ) n a mn, we have (a 3 ) 2 ( 4 ) 2 a

6 TSA Assorted Eercises and Summative Test Mathematics S2 Section A: Choose the est answer for each question. KS3-MS In the figure, find. A. 14 B. 18 C. 24 D In the figure, ABC is a straight line. Find m. A. 33 B. 3 C. 37 D In the figure, ACD is a straight line. Find. A. 8 B. 9 C. 10 D. 11 KS3-MS In the figure, AB // CD and AC BC. Find z. A. 0 B. 6 C. 11 D In the figure, DABC is an equilateral triangle. Find. A. 140 B. 10 C. 160 D. 170 KS3-MS7-3 KS3-MS In the figure, BCD is a straight line. Find y. A. 126 B. 128 C. 130 D

7 Territory-wide System Assessment Secondary 2 Mathematics Summative Test Marker s Use Only Dimension Question Marks Numer and Algera Measures, Shape and Space 1 12, 21 31, / , 32 39, 4 49 /32 Data Handling 20, 40, 0 / Instructions: 1. The time allowed is 6 minutes. 2. Write ALL your answers in the spaces provided. 3. The use of HKEAA approved calculators is permitted. 4. Rough work should e done on the rough work sheet provided.. Write your Name, Class and Class Numer in the spaces elow. Name Class Class No. Hong Kong Educational Pulishing Company

8 Rate and Ratio Laws of Integral Indices (a) Rate is the comparison of 2 quantities of different kinds. () (i) Ratio is the comparison of quantities of the same kind. (ii) The ratio of a to is usually epressed as a a : or (where a 0 and 0). For any positive integers m and n, and any non-zero numers a and : (a) a m a n a m + n () a m a n a m - n (c) (a m ) n a mn (d) (a) n a n n (e) n n a a n (f) a 0 1 (g) a n 1 n a Significant Figures (a) For all numers, all 0 s etween two non-zero digits are significant figures. () For all integers, all 0 s after the last non-zero digit are not significant figures. (c) For decimals smaller than 1, all 0 s etween the decimal point and the first non-zero digit are not significant figures. 1 3 Scientific Notation All non-zero numers can e epressed in the form a 10 n, where 1 a < 10 and n is an integer. Identities and Factorization Sequences 7 (a) Some useful identities: (i) (a + )(a - ) a 2-2 (ii) (a + ) 2 a 2 + 2a + 2 (iii) (a - ) 2 a 2-2a + 2 () (i) The process of rewriting a polynomial as a product of its factors is called factorization. (ii) Factorization is the reverse process of epansion. (a) A list of numers arranged in an order is called a sequence. () Each numer in a sequence is called a term. (c) For a sequence with a certain pattern, we can represent the sequence y a general term. Simultaneous Linear Equations in Two Unknowns 9 11 Angles of Triangles and Conve Polygons If two linear equations in two unknowns have common unknowns, then they are called simultaneous linear equations in two unknowns. Simultaneous linear equations in two unknowns can e solved y using the following methods: (i) Algeraic methods, including the method of elimination and the method of sustitution (ii) Graphical method (a) Triangle For any triangle: a + + c 180 ( sum of D) a + d (et. of D) () Conve Polygon Sum of interior angles of an n-sided polygon (n - 2) 180 Sum of eterior angles

9 TSA Assorted Eercises and Summative Test Mathematics S2 Chapter 1 Rate and Ratio Section A 1. C 2. D 40 g : 3. kg 40 g : 300 g 9 : A a : 2 : 8 : 20 : c 4 : 7 20 : 3 \ a : : c 8 : 20 : 3 4. D a : : 6 a B : z : 4 z y : z 2 : 4 y 2 z 4 y y 3 - y C : 12 9 : : 36 4 : y y y C Speed of the car 4 3 km/h 1 km/h 8. D Ratio of their weights 13 g : 10 g : 90 g 9 : 7 : 6 9. C Numer of pieces of craft paper received y Amy Numer of pieces of craft paper received y Cathy Difference A Let y cm e the length of Henry s shoe y 3 y 13. \ The length of Henry s shoe is 13. cm. Section B 1. (i) Rate / Ratio (ii) Rate / Ratio 2. 2 : : 3 : c a : : c 80 : 60 : : 3 : : 40 : 12 a : 3 : 8 1 : 40 a : c : 4 1 : 12 \ a : : c 1 : 40 : 12 2

Mathematics Benchmark Achievements Senior Math

Mathematics Benchmark Achievements Senior Math Ages 12+ College Bound Objectives at this age: Continue with a systematic approach to developing math skills. Please note that levels listed below are not