Major Revision on Senior Secondary Mathematics Curriculum
Maths S4 – S6 Curriculum (2015)
[Current Curriculum]
Maths S4 – S6 New Curriculum (2017)
[Implemented in September 2023]
2 Functions and Graphs
The remark ‘Finding the domain of a function is required but need not be stressed’ of the original Learning Objective 2.1 was deleted.
A remark ‘The method of completing the square is required’ was added to the original Learning Objective 2.4.
3 Exponential and Logarithmic Functions
4 More about Polynomials
The curriculum content on the definition of and evaluating expressions such as in the remark of the original Learning Objective 3.1 was moved to Key Stage 3.
The description about f (x) = log
ax was added to the remark ‘the function f (x) = a
xincreases (decreases) as x increases for a > 1 (0 < a < 1)’ of the original Learning Objective 3.4.
A remark ‘Students are required to use factor theorem to factorize polynomials such as x
3± a
3’ was added to the original Learning Objective 4.3.
8 Inequalities and
Linear Programming A remark ‘Solving the problems on triangle inequalities is required’
was added to the original Learning Objective 8.1.
10 Basic Properties of Circles A remark ‘Knowledge on geometry learnt at Key Stage 3 can be involved in the geometric proofs’ was added to the original Learning Objective 10.6.
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na
−
3 8
The condition ‘maintaining a fixed distance from a line segment’
was deleted from the remark of the original Learning Objective 11.2.
11 Loci
12 Equations of Straight Lines and Circles
The Learning Unit ‘Equations of Straight Lines and Circles’ was separated into Learning Unit 10 ‘Equations of straight lines’ and Learning Unit 13 ‘Equations of circles’. The teaching of the
Learning Unit 10 ‘Equations of straight lines’ was suggested to be arranged in the first term of S4.
13 More about Trigonometry
16 Measures of Dispersion The operations ‘adding an item to the set of data’ and ‘removing an item from the set of data’ were deleted from the original Learning Objective 16.7.
• The curriculum content on the concept of projection, the angle between a line and a plane, and the angle between 2 planes was moved from Key Stage 3 to this Learning Unit.
• A new Learning Objective ‘understand theorem of three perpendiculars’ was added.
The curriculum content on recognizing the relation between slope and inclination was moved from Key Stage 3 to Learning Unit 10
‘Equations of straight lines’.
Problem on the distance between points was added to the remark of the original Learning Objective 13.6.
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Delete
Reorganize
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I. Number and Algebra Strand
1.
Quadratic equations in one unknown
1.1 solve quadratic equations by the factor method
9
1.2 form quadratic equations from given roots
9
1.3 solve the equation ax2 + bx + c = 0 by plotting the graph of the parabola y = ax2 + bx + c and
reading the x-intercepts
9
1.4 solve quadratic equations by the quadratic formula
9
1.5 understand the relations between the discriminant of a quadratic equation and the nature of its roots
9
1.6 solve problems involving quadratic equations
9
1.7 understand the relations between the roots and coefficients and form quadratic equations using these
relations
9
1.8 appreciate the development of the number systems including the system of complex numbers
9
1.9 perform addition, subtraction, multiplication and division of complex numbers
9
2. Functions and graphs
2.1 recognise the intuitive concepts of functions, domains and co-domains, independent and dependent variables
2.2 recognise the notation of functions and use tabular, algebraic and graphical methods to represent
functions
9
2.3 understand the features of the graphs of quadratic functions
9
2.4 find the maximum and minimum values of quadratic functions by the algebraic method
Learning Unit Learning Objective Learning Objective [New Curriculum]
‘Finding the domain of a function is required but need not be stressed’ in the remark was deleted. Delete
Syllabuses for Maths S4 – S6 (2015) vs New Maths Curriculum S4 – S6 (2017)
A remark ‘The method of completing the square is required’ was added. Adjust
3. Exponential and
logarithmic functions
3.1 understand the definitions of rational indices
3.2 understand the laws of rational indices
9
3.3 understand the definition and properties of logarithms (including the change of base)
9
3.4 understand the properties of exponential functions and logarithmic functions and recognise the features of their graphs
3.5 solve exponential equations and logarithmic equations
9
3.6 appreciate the applications of logarithms in real-life situations
9
3.7 appreciate the development of the concepts of logarithms
9
4. More about polynomials
4.1 perform division of polynomials
9
4.2 understand the remainder theorem
9
4.3 understand the factor theorem
4.4 understand the concepts of the greatest common divisor and the least common multiple of
polynomials
9
4.5 perform addition, subtraction, multiplication and division of rational functions 5. More about
equations
5.1 use the graphical method to solve simultaneous equations in two unknowns, one linear and one
quadratic in the form y = ax2 + bx + c
9
5.2 use the algebraic method to solve simultaneous equations in two unknowns, one linear and one
quadratic
9
Learning Unit Learning Objective Learning Objective [New Curriculum]
The definition of na and ‘Students are also expected to evaluate expressions such as 3− ’ in the remark 8 was moved to Key Stage 3. Move to KS3
The description about f (x) = loga x was added to the remark ‘the function f (x) = ax increases (decreases) as x increases for a > 1 (0 < a < 1)’. Adjust
A remark ‘Students are required to use factor theorem to factorize polynomials such as x3 ± a3 ’ was added.
Adjust
A remark ‘Rational functions refer to algebraic fractions
at Key Stage 3’ was added. Adjust
5.3 solve equations (including fractional equations, exponential equations, logarithmic equations and
trigonometric equations) which can be transformed into quadratic equations
9
5.4 solve problems involving equations which can be transformed into quadratic equations
9
6. Variations 6.1 understand direct variations (direct proportions) and inverse variations (inverse proportions), and their applications to solving real-life problems
6.2 understand the graphs of direct and inverse variations
9
6.3 understand joint and partial variations, and their applications to solving real-life problems
9
7. Arithmetic and geometric sequences and their
summations
7.1 understand the concept and the properties of arithmetic sequences
9
7.2 understand the general term of an arithmetic sequence
7.3 understand the concept and the properties of geometric sequences
9
7.4 understand the general term of a geometric sequence
9
7.5 understand the general formulae of the sum to a finite number of terms of an arithmetic sequence
and a geometric sequence and use the formulae to solve related problems
9
7.6 explore the general formulae of the sum to infinity for certain geometric sequences and use the
formulae to solve related problems
9
7.7 solve related real-life problems
9
8. Inequalities and linear programming
8.1 solve compound linear inequalities in one unknown
8.2 solve quadratic inequalities in one unknown by the graphical method
9
8.3 solve quadratic inequalities in one unknown by the algebraic method
9
8.4 represent the graphs of linear inequalities in two unknowns on a plane
9
8.5 solve systems of linear inequalities in two unknowns
9
8.6 solve linear programming problems
9
Learning Unit Learning Objective Learning Objective [New Curriculum]
Note that students learnt direct proportion and inverse proportion at KS3. Teaching Remark
A remark ‘Solving the problems on triangle inequalities is required’ was added. Adjust Note that ‘Finding the general term of a sequence’ was deleted at KS3. Teaching Remark
9.
More about graphs of functions
9.1 sketch and compare graphs of various types of functions including constant, linear, quadratic,
trigonometric, exponential and logarithmic functions
9
9.2 solve the equation f (x) = k using the graph of y = f (x)
9
9.3 solve the inequalities f (x) > k, f (x) < k, f (x) k and f (x) k using the graph of y = f (x)
9
9.4 understand the transformations of the function f (x) including f (x) + k, f (x + k), k f (x) and f (kx) from tabular, symbolic and graphical perspectives
II. Measures, Shape and Space Strand
10. Basic
properties of circles
10.1 understand the properties of chords and arcs of a circle
9
10.2 understand the angle properties of a circle
9
10.3 understand the properties of a cyclic quadrilateral
9
10.4 understand the tests for concyclic points and cyclic quadrilaterals
9
10.5 understand the properties of tangents to a circle and angles in the alternate segments
9
10.6 use the basic properties of circles to perform simple geometric proofs
11. Locus
11.1 understand the concept of loci9
11.2 describe and sketch the locus of points satisfying given conditions
11.3 describe the locus of points with algebraic equations
9
Learning Unit Learning Objective Learning Objective [New Curriculum]
Learning Unit Learning Objective Learning Objective [New Curriculum]
A remark ‘Knowledge on geometry learnt at Key Stage 3 can be involved in the geometric proofs’ was added.
Adjust Note that dilation / contraction is not required in the curriculum at KS3. Teaching Remark
The condition ‘maintaining a fixed distance from a line segment’ in the remark was deleted. Delete
12. Equations of straight lines and circles
12.1 understand the equation of a straight line
12.2 understand the possible intersection of two straight lines
9
12.3 understand the equation of a circle
9
12.4 find the coordinates of the intersections of a straight line and a circle and understand the possible
intersection of a straight line and a circle
9
13. More about trigonometry
13.1 understand the functions sine, cosine and tangent, and their graphs and properties, including
maximum and minimum values and periodicity
9
13.2 solve the trigonometric equations a sin ș = b , a cos ș = b, a tan ș = b (solutions in the interval from
0° to 360° ) and other trigonometric equations (solutions in the interval from 0° to 360°)
9
13.3 understand the formula ½ ab sin C for areas of triangles
9
13.4 understand the sine and cosine formulae
9
13.5 understand Heron’s formula
9
13.6 use the above formulae to solve 2-dimensional and 3-dimensional problems
Learning Unit Learning Objective Learning Objective [New Curriculum]
•This Learning Unit was separated into Learning Unit 10 ‘Equations of straight lines’ and Learning Unit 13 ‘Equations of circles’.
•The teaching of the Learning Unit 10 ‘Equations of straight lines’ was suggested to be arranged in the first term of S4.
Reorganize The curriculum content on recognizing the relation between slope and inclination was moved from Key Stage 3 to this Learning Objective. Add
• The Learning Objectives ‘understand the concept of projection’ and ‘understand the angle between a line and a plane, and the angle between 2 planes’
were moved from Key Stage 3 to this Learning Unit.
• The Learning Objective ‘understand the theorem of three perpendiculars’ was added.
Add Problem on the distance between points was
added to the remark. Adjust
III. Data Handling Strand
14. Permutation and
combination
14.1 understand the addition rule and multiplication rule in the counting principle
9
14.2 understand the concept and notation of permutation
9
14.3 solve problems on the permutation of distinct objects without repetition
9
14.4 understand the concept and notation of combination
9
14.5 solve problems on the combination of distinct objects without repetition
9
15. More about probability
15.1 recognise the notation of set language including union, intersection and complement
9
15.2 understand the addition law of probability and the concepts of mutually exclusive events and
complementary events
9
15.3 understand the multiplication law of probability and the concept of independent events
9
15.4 recognise the concept and notation of conditional probability
9
15.5 use permutation and combination to solve problems relating to probability
9
16. Measures of dispersion
16.1 understand the concept of dispersion
9
16.2 understand the concepts of range and inter-quartile range
9
16.3 construct and interpret the box-and-whisker diagram and use it to compare the distributions of
different sets of data
9
16.4 understand the concept of standard deviation for both grouped and ungrouped data sets
16.5 compare the dispersions of different sets of data using appropriate measures
9
16.6 understand the applications of standard deviation to real-life problems involving standard scores and
the normal distribution
9
Learning Unit Learning Objective Learning Objective [New Curriculum]
A remark ‘Students are required to recognize the term
‘‘variance’’ and that variance equals to the square of standard deviation’ was modified. Adjust
16.7 explore the effect of the following operations on the dispersion of the data:
(i) adding an item to the set of data (ii) removing an item from the set of data
(iii) adding a common constant to each item of the set of data (iv) multiplying each item of the set of data by a common constant
17. Uses and
abuses of statistics
17.1 recognise different techniques in survey sampling and the basic principles of questionnaire design
9
17.2 discuss and recognise the uses and abuses of statistical methods in various daily-life activities or
investigations
9
17.3 assess statistical investigations presented in different sources such as news media, research
reports, etc.
9
Learning Unit Learning Objective Learning Objective [New Curriculum]
Delete
IV. Further Learning Unit
18. Further applications
Solve more sophisticated real-life and mathematical problems that may require students to search the information for clues, to explore different strategies, or to integrate various parts of mathematics which they have learned in different areas
The main focuses are:
(a) to explore and solve more sophisticated real-life problems
(b) to appreciate the connections between different areas of mathematics
19. Inquiry and
investigation
Through various learning activities, discover and construct knowledge, further improve the ability toinquire, communicate, reason and conceptualise mathematical concepts
9
Notes:
1. Learning units are grouped under three strands (“Number and Algebra”, “Measures, Shape and Space” and “Data Handling”) and a Further Learning Unit.
2. Related learning objectives are grouped under the same learning unit.
3. The learning objectives underlined are the Non-foundation Topics.
Learning Unit Learning Objective Learning Objective [New Curriculum]
The example ‘investigate the causes and effects of the three crises in mathematics’ in the remark was
deleted. Delete
