Public Assessment of the HKDSE Mathematics Examination 1. Public Assessment The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in the Compulsory Part is shown below. Component Weighting Duration Public Examination Paper 1 Conventional questions Paper 2 Multiple-choice questions 65% 35% 2 1 4 hours 1 1 4 hours The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in Module 1 (Calculus and Statistics) is shown below. Component Weighting Duration Public Examination Conventional questions 100% 2 1 2 hours The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in Module 2 (Algebra and Calculus) is shown below. Component Weighting Duration Public Examination Conventional questions 100% 2 1 2 hours 2. Standards-referenced Reporting The HKDSE makes use of standards-referenced reporting, which means candidates’ levels of performance will be reported with reference to a set of standards as defined by cut scores on the variable or scale for a given subject. The following diagram represents the set of standards for a given subject: Cut scores U 1 2 3 4 5 Variable/ scale Within the context of the HKDSE there will be five cut scores, which will be used to distinguish five levels of performance (1–5), with 5 being the highest. The Level 5 candidates with the best performance will have their results annotated with the symbols ∗∗ and the next top group with the symbol ∗. A performance below the threshold cut score for Level 1 will be labelled as ‘Unclassified’ (U). IV
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Public Assessment of the HKDSE Mathematics Examination1.PublicAssessmentThe mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in the Compulsory Part is shown below.
Component Weighting Duration
Public Examination Paper 1 Conventional questionsPaper 2 Multiple-choice questions
65%35%
21 4 hours11 4 hours
The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in Module 1 (Calculus and Statistics) is shown below.
The mode of public assessment of the Hong Kong Diploma of Secondary Education (HKDSE) Mathematics Exam in Module 2 (Algebra and Calculus) is shown below.
2.Standards-referencedReportingThe HKDSE makes use of standards-referenced reporting, which means candidates’ levels of performance will be reported with reference to a set of standards as defined by cut scores on the variable or scale for a given subject. The following diagram represents the set of standards for a given subject:
Cut scores
U 1 2 3 4 5
Variable/scale
Within the context of the HKDSE there will be five cut scores, which will be used to distinguish five levels of performance (1–5), with 5 being the highest. The Level 5 candidates with the best performance will have their results annotated with the symbols ∗∗ and the next top group with the symbol ∗. A performance below the threshold cut score for Level 1 will be labelled as ‘Unclassified’ (U).
IV
Exam StrategiesA. GeneralStrategies
1. Beforethestartoftheexamination
• Make sure that the time on your watch matches with that of the examination centre.
• Listen carefully to the invigilator for any errors and changes in the examination papers.
• Read carefully the instructions on the cover of the question-answer book or question book.
• Check carefully whether there are any omitted or blank pages in the examination paper according to the invigilator’s instruction.
2. Duringtheexamination
• Use proper stationery.
– Paper 1: use a pen mainly, but an HB pencil for drawing.
– Paper 2: use an HB pencil.
• Show your work clearly and neatly.
• Do not get stuck on any one of the questions. Skip it and go on to another one.
3. Afteransweringallthequestions
• Do not be tempted to leave early.
• Check whether there are any questions that were missed.
• Go back to questions skipped earlier.
• Check whether there are any careless mistakes or not.
• Do not cross out anything unless you have enough time to replace it correctly.
• Make sure you write your candidate number on the answer book, supplementary answer sheets and multiple-choice answer sheet.
B. SpecificStrategies
1. Paper1(214
hours)
• Allocate a reasonable proportion of time to each section.
Sections Suggested Time Allocation Approximate Time per QuestionA (1) 40 minutes 3 − 5 minutesA (2) 40 minutes 5 – 10 minutes
B 50 minutes 5 – 15 minutes
– In general, spend 5 minutes for every 4 marks.
– Allow 5 minutes for final checking.V
Comparison between HKDSEand HKCEE Syllabuses
1. Topicsremovedfromandaddedtothesyllabus
Section Topicsremoved Topicsadded
NumberandAlgebraStrand
Quadratic equations in one unknown
• Sum of roots and product of roots• Operations of complex numbers
Functions and graphs • Concepts of domains and co-domains of functions
More about graphs of functions • Enlargement and reduction
Exponential and logarithmic functions • Change of base
More about polynomials • G.C.D. and L.C.M. of polynomials
• Operations of rational functions
More about equations • Using a given quadratic graph to solve another quadratic equation
Arithmetic and geometric sequences and their summations
• Properties of arithmetic and geometric sequences
Inequalities and linear programming
• Solving quadratic inequalities in one unknown by the algebraic method
• Solving compound linear inequalities involving ‘or’
Measures,ShapeandSpaceStrand
Locus • Describing the locus of points with algebraic equations
Equations of straight lines and circles
• Possible intersection of two straight lines
• Intersection of a straight line and a circle
DataHandlingStrand
Permutation and combination • Concepts and notations of permutation and combination
II
16Trigonometry
16
Trigonometric Ratios of Angles1.
Fig.16.1
3.SignsofTrigonometricFunctions:
Fig.16.3
cosθ = ac
, tanθ = ba
and
sinθ = bc
wherec a b= +2 2
Reducing Trigonometric Ratios
Table16.2
Reducing Trigonometric Ratios
Table
180°-θ 180°+θ 360°-θsin sin θ -sin θ -sin θcos -cos θ -cos θ cos θtan -tan θ tan θ -tan θ
Transformation on the Graphs of Trigonometric Functions Considerthegraphofy =sinx.1.Translation (a) Vertical:y =sinx+k (b) Horizontal:y =sin(x+k°)2.Reflection Aboutthex-axis:y =-sinx3.ReductionorEnlargement (a) Vertical:y =ksinx (b) Horizontal:y =sin (kx)
Rate
Rate is a comparison between two different kinds of quantities. For two
different quantities x and y, the rate is given by xy
or yx
and it has a unit.
For example, a worker cleans 20 cars in 5 hours.
The cleaning speed = 20 cars5 hours
= 4 cars/hour.
The cleaning time for each car = 5 hours20 cars
= 0.25 hour/car.
Ratio
Ratio is a comparison between two or more quantities of the same kind.
The ratio of a to b is a : b or ab
and it has no unit. The ratio for three or
more quantities such as a : b : c is called a continued ratio.
For example, the weights of A, B and C are 80 kg, 50 kg and 20 kg respectively. Weight of A : Weight of B = 80 : 50 = 8 : 5.Weight of A : Weight of B : Weight of C = 80 : 50 : 20 = 8 : 5 : 2.
A
B
A continued ratio cannot be
expressed as a fraction.
22Determine whether each of the following statements is true or false.
1. Rate is a comparison between two different kinds of quantities.
2. Ratio is a comparison between two or more quantities of the same kind.
3. If 5m = 8n, then m : n = 5 : 8.
4. If a : b = 1 : 2 and b : c = 1 : 3, then a : b : c = 1 : 2 : 3.
5. The speed of a car, say 80 km/h, is an example of rate.
6. The speeds of two cars, say 80 km/h and 90 km/h, can be expressed by the ratio 8 : 9.
(a) Thereare550computersproducedinafactory.Eachcomputerisassignedadistinctnumberfrom001to550.Tendistinctnumbersaregeneratedrandomlysoas toselect10computers to formasample.