Maths Syllabus (For Reference Only)
(1) Numbers/Algebra
(2) Geometry / Measurement
(3) Statistics/Probability
<< Sec 1 >> <<Sec 2>><<Sec 3/4>> | << Sec 1 >> <<Sec 2>><<Sec 3/4>> | |||||
| NT | NA | O | |||
N1 Number and Operation | 1.1 | Negative Numbers and Prime | 1.1 | Primes and prime factorisation | " | |
1.2 | Integers and four operations | 1.2 | Finding HCF/LCM/Square/cubes/sq roots/cube roots by prime factorisation | " | ||
1.3 | Four operations on fractions and decimals | 1.3 | -ve no, integers, rational, real nos and their 4 operations | " | ||
1.4 | Calculation with calculator,, square, cubes, square roots and cube roots | 1.4 | Calculation with calculator | " | ||
1.5 | Representation and ordering of numbers on the number line | 1.5 | Representation and ordering of numbers on the number line | " | ||
1.6 | Use of < > ,, | 1.6 | Use of < > ,, | " | ||
1.7 | Approximation/estimation (rounding off to req dec or sig fig, est result | 1.7 | Approximation/estimation (rounding off to req dec or sig fig, est result | " | ||
1.8 | Use of index notation for integer powers | Use of index notation for integer powers | ||||
1.9 | Use of std form A x 10n, n = integer, 1 <= A < 10 | 1.8 | Use of std form A x 10n, n = integer, 1 <= A < 10 | |||
1.9 | +ve, -ve, zero and fractional indices | |||||
1.10 | Laws of Indices | |||||
N2 Ratio and Proportion | 2.1 | Comparison between 2 or more qty by ratio | 2.1 | Ratios involving rational numbers | " | |
2.2 | Diving a qty in a given ratio | 2.2 | Writing ratio in its simplest form | " | ||
2.3 | Ratios involving fractions and dec | 2.3 | Problems involving ratio | " | ||
2.4 | Equivalent Ratio |
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2.5 | Writing ratio in its simplest form |
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2.6 | Direct and Inverse Proportion | 2.4 | Direct and Inverse Proportion | " | ||
2.7 | Map scale (Distance and area) |
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N3 %age | 3.1 | Expressing percentage as a fraction or dec | 3.1 | " | " | |
3.2 | Finding whole given a % part | 3.2 | Comparing 2 qties by percentage | " | ||
3.3 | Expressing 1 qty as a % of another | 3.3 | % greater than 100% | " | ||
3.4 | Comparing 2 qty given % and the other qty | 3.4 | Increase/Decr a qty by given % (incl concept of % point) | " | ||
3.5 | % greater than 100% | 3.5 | Reverse % | " | ||
3.6 | Find 1 qty given % and the other qty | 3.5 | Problems involving % | " | ||
3.7 | Increasing/dec a qty by a given % | 3.6 |
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3.8 | Finding % increase/decr | 3.7 |
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N4 Rate and Speed | 4.1 | Rates and average rates (incl speed and avg speed) | 4.1 | Concept of average rate, speed, constant and avg speed | " | |
4.2 | Conversion of units ( eg : km/h to m/s) | 4.2 | Conversion of units (km/h - m/s) | " | ||
4.3 | Problems involving rate and speed | " | ||||
N5 Algeb Expr and Formulae | 5.1 | Using letters to rep numbers | 5.1 | " | " | |
5.2 | Interpreting notations: Ab = a x b abas a ÷ b or a x 1/b a2 as a x a , a3 as a x a x a, a2b as a x a x b 3y as y + y+ y , 3 x y , 3y 3(x + y) as 3 (x + y) as 3x + 3y 3 + y/5 as (3 + y) ÷ 5 or 1/5 (3 + y) | 5.2 | " | " | ||
5.3 | Evaluation of algebraic expressions and formulae | 5.3 | " | " | ||
5.4 | Recognising no. seq (incl eval nth term like n + 3 and 2n + 1) | 5.4 | " | " | ||
5.5 | Real-world situation into algebraic expression (words prob) | 5.5 | " | " | ||
5.6 | Addition and Subtraction of linear Expression | 5.6 | " | " | ||
5.7 | Simplify Linear Expression, e.g. . -2(3x - 5) + 4x . 2x/3 - 3(x - 5)/2 | 5.7 | Simplify linear exp with integral coeff . 2(x - 3) . 4x - 2(3x - 5) . 3(x - y) - (2y + x) - y | " | ||
5.8 | Number sequences (incl finding alg exp for n + 3, 2n + 1) | 5.8 | Simplify with fractional coeff 2x/3 - 3(x - 5)/2 | " | ||
5.9 | Expansion of product of 2 linear exp | 5.9 | Expansion of product of 2 linear exp | |||
5.13 | Factorisation of l.exp ax + kay | 5.10 | Use brackets / extract common factors | " | ||
5.14 | Fac of quadratic Exp : x2+ px + q Excl : . use of (a ± b)2 = a2± 2ab + b2 . a2 - b2 = (a + b)(a - b) + - fractions 1/x + 1/(x-1) | 5.11 | Fac quad expression x2 + px + q Use of . use of (a ± b)2 = a2 ± 2ab + b2 . a2 - b2 = (a + b)(a - b) | " | ||
5.10 | Mult and Div of alg exp e.g. (3a/4b2)(5ab/3); 3a/4 ÷ 9a2/10 | 5.13 | Mult and Div of alg exp e.g. (3a/4b2)(5ab/3); 3a/4 ÷ 9a2/10 | " | ||
5.12 | Factorise ax2 + bx + c | " | ||||
5.12 | Find value of unknown qty in a given formula | 5.17 | Find value of unknown qty in a given formula | " | ||
5.11 | Changing subject of a simple formula | 5.16 | Changing subject of a formual | " | ||
5.14 | Factorise ax + bx + kay +kby | " | ||||
5.18 | Addition/Sub of alg fractions . 1/(x -2) + 2/(x - 3) . 1/(x2 - 9) + 2/(x - 3) . 1/(x + 3) + 2/(x -3)2 | " | ||||
N6 Functions and Graphs | 6.1 | Cartesian coordinates in 2 dimensions | 6.1 | " | " | |
6.2 | Graph of set of ordered pairs as rep of relationship betw 2 variables | 6.2 | " | " | ||
6.3 | Linear Functions y = ax + b | 6.3 | " | " | ||
6.4 | Graph of linear functions | 6.4 | " | " | ||
6.5 | Gradient of linear graph as ratio of vertical chg to hori chg (+ and - type) | 6.5 | " | " | ||
6.6 | Quadratic functions (y = ax2 + bx + c) <sec 4> | 6.6 | Quadratic functions (y = ax2 + bx + c) | " | ||
6.7 | Graphs of quad functions and their properties <Sec 4> . +ve / -ve coefficients of x2 . maximum and minimum points . symmetry | 6.7 | Graphs of quad functions and their properties . +ve / -ve coefficients of x2 . maximum and minimum points . symmetry | " | ||
6.8 | Graph power y = axn n=-2,-1,0, 1, 2,3 and sum of < 3 of these | " | ||||
Graphs of y = kax, a = +ve integer | " | |||||
Estimation of gradient of a curve drawing tangent | " | |||||
6.10 | Sketch y= (x - p)2 + q Y = -(x-p)2 + q Y = (x-a)(x - b) Y = (x-a)(x-b) | |||||
N7 Eqns and Inequalities | 7.1 | Concepts of Equation | " | |||
7.1 | Solving linear equations in 1 var | 7.2 | Solving linear eqn in 1 var | " | ||
7.2 | Formulating linear equation in 1 var to solve problems | 7.3 | Formulating Linear eqn in 1 var to solve prob | " | ||
7.4 | Solving linear eqn (fractional coeff) | " | ||||
7.5 | Concept/properties of inequality | " | ||||
| 7.6 | Simple inequalities ax <= b, ax >=b, ax < b and ac > b where a and be are inegers | " | |||
7.3 | Graphs of linear equations in 2 var (ax + by = c) | 7.7 | Solving simple fac equation that can be reduced to linear eqn. Eg: x/2 + (x - 2)/4 = 3 ; 3/(x - 2) = 6 | " | ||
7.4 | Solving simple fac equation that can be reduced to linear eqn. Eg: x/2 + (x - 2)/4 = 3 ; 3/(x - 2) = 6 | 7.8 | Graphs of linear equations in 2 var (ax + by = c) | " | ||
7.5 | Solving Simultaneous Eqn in 2 var by . substitution and elimination . Graphical | 7.9 | Solving Simultaneous Eqn in 2 var by . substitution and elimination . Graphical | " | ||
7.6 | Formulating a pair of linear eqn in 2 var to solve problems | 7.10 | Formulating a pair of linear eqn in 2 var to sol prob | " | ||
7.7 | Solving quad eqn in 1 var by use of formula2 | 7.11 | Solving quad egn in 1 var by . Factorisation . Use of Formula . Completing the square y = x2 + px + q . Graphical method | " | ||
7.8 | Formulating a quad equation in 1 var to solve problems | 7.12 | Solving fractional to quad eqn such as . 6/(x +4) = (x + 3) . 1/(x - 2) + 2/(x - 3) = 5 | " | ||
7.13 | Formulating quad eqn in 1 var to solve prob | " | ||||
N8 Set Lang and notation | 8.1 |
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| Use of set language and the following notation: Union A U B, A ∩ B, n(A), ∈, ∉,∅, a⊆B, A⊈B, A⊂B, A⊄B | ||
8.2 | Union and Intersect of two sets | |||||
8.3 | Venn Diagram | |||||
N9 Matrix | 9.1 | Display of info as matrix of any order | ||||
9.2 | Interpreting data in given matrix | |||||
9.3 | Product of scalar and a matrix | |||||
9.4 | Prob inv + - and x of matrices |
<< Sec 1 >> <<Sec 2>><<Sec 3/4>> | << Sec 1 >> <<Sec 2>><<Sec 3/4>> | |||||
| NT | NA | O | |||
G1 Angles, triangles and Polygons | 1.1 | Right, acute, obtuse and reflex angles | 1.1 | Right, acute, obtuse and reflex angles | " | |
1.2 | v.opp angles, angle on str line, at a point | 1.2 | v.opp angles, angle on str line, at a point | " | ||
1.3 | Angles : 2 parallel lines & transversal, corr/alt angle | 1.3 | Angles : 2 parallel lines & transversal, corr/alt angle | " | ||
1.4 | Properties of triangles and quad | 1.4 | Properties of triangles | " | ||
1.5 | Properties of P.bisector of line and angles | 1.5 | Prop of special quad / polygons (Pentagon, hexagon, octagon and decagon) incl symmetry properties | " | ||
1.6 | Construction of simple geom fig using compass, ruler, set sq and protractor where approp | 1.6 | Classifying special quad and their properties | " | ||
1.7 | 1.7 | Angle sum of interior and exterior angles of convex polygon | " | |||
1.8 | 1.8 | Construction of simple geom figs using compasses, ruler, set squares and protractors, where approp | " | |||
G2 Symmetry | 2.1 | Line and rotational symmetry of plnae figures |
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2.2 | Line of Symmetry |
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2.3 | Order of rotational Symmetry | 2.1 | Congruent figures | |||
2.4 | Congruent and similar figures | 2.2 | Similar Figures | |||
2.5 | Properties of similar triangles and qual: . Corr angles are equal . Corr sides are proportional | 2.3 | Properties of similar triangles and polygons: . Corresponding angles are equal . Corresponding sides are proportional | |||
2.4 | Enlargement and reduction of plane figure | |||||
| 2.5 | Scale drawings | ||||
Prop and construction of p.bisectors of line and angle | ||||||
2.6 | Solving simples prob : congruence and similarity | |||||
2.7 | Ratio of area/vol | |||||
G3 Circles | 3.1 | Symmetry of Properties of circles: . = chords are equidistant from centre . p.bisector of chord pass thru the centre . Tangents fr ext point are equal in length . Line joining ext pt to centre bisect angle betw tangents | ||||
| 5.2 | Angle properties of Circle: . in semicircle is right angle . betw tangent and radius is right angle . centre is twice the angle at the circum . in same segment are equal . opp segment are supplementary | ||||
3.1 | Use of Pythagoras Theorem | 4.1 | Use of Pythagoras Theorem | " | ||
G3/G4(NA) Pythagoras Trigo | 3.2 | Determine if triangle is right-angled given 3 sides | 4.2 | Determine if triangle is right-angled given 3 sides | " | |
3.3 | Use of trigo ratio of acute angle to cal unknown sides and angles in right-angled triangle (incl angles of elevation and depression) | 4.3 | Use of trigo ratio of acute angle to cal unknown sides and angles in right-angled triangle (incl angles of elevation and depression) | " | ||
3.5 | 4.4 | Extending since / cosine to obtuse angles | ||||
3.6 | 4.5 | Use of 1/2 ab sinC for triangle area | ||||
3.7 | 4.6 | Use of sine and cosine rule for any triangle | ||||
3.8 | 4.7 | Prob in 2/3 dimension (incl elevation/ depressions/bearing) | ||||
G4/G5(NA) Mensuration | 4.1 | Area of triangle 1/2 x base x height |
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4.2 | area of cir of circle |
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4.3 | Area of parallelogram and trapezium | 5.1 | Area of parallelogram and trapezium | " | ||
4.4 | Prob inv perimeter/area of composite figure | 5.2 | Prob inv perimeter and area of comp plane figs | " | ||
4.5 | Vol and surface area of cube and cubiod | 5.3 | Volume and surface area of prism and cylinder | " | ||
4.6 | Conversion cm2-m2, cm3-m3 | 5.4 | Conversion between cm2-m2,cm3-m3 | " | ||
4.7 | Prob inv vol and surface area of comp. solids | 5.5 | Prob inv vol and surface area of comp solids | " | ||
4.8 | Volume and surface area of prism and cylinder | 5.6 | Vol and surface area of pyramid, cone and sphere | |||
4.9 | Conversion cm2-m2, cm3-m3 | 5.7 | Arc Length and sector area as fractions of cir/area of circle | |||
4.10 | Prob inv vol and surface area of comp. solids | 5.8 | Area of segment | |||
4.11 | Vol and surface area of pyramid, cone and sphere | 5.9 | Radian measure of angle(conversion radian and degree) | |||
4.12 | Conversion cm2-m2, cm3-m3 | 5.10 | Problem - arc length, sector area of circle and segment | |||
4.13 | Arc Length and sector area as fractions of cir/area of circle | |||||
G6 (NA) Coordinate Geometry | 6.6 | 6.1 | Finding gradient given coordinate of 2 points | |||
6.7 | 6.2 | Finding length of line segment given coordinate of end points | ||||
6.3 | Finding equation of straight line y = mx + c | |||||
6.4 | Geometric prob with use of coordinates | |||||
G7 Vectors | 7.1 |
| Use of notations | |||
7.2 |
| Representing vector as directed segment | ||||
7.3 | Translation by a vector | |||||
7.4 | Position Vectors | |||||
7.5 | Magnitude of a vector | |||||
7.6 | Use of sum and diff of 2 vectors | |||||
7.7 | x of vector by a scalar |
<< Sec 1 >> <<Sec 2>><<Sec 3/4>> | << Sec 1 >> <<Sec 2>><<Sec 3/4>> | |||
| NT | NA/O | ||
S1 Data Handling and Analysis | 1.1 | Simple Concepts in collecting, classifying and tabulating data | 1.1 | Simple Concepts in collecting, classifying and tabulating data |
1.2 | Analysis and interpretation of: . Tables . Bar graphs . Pictograms . Line graphs . Pie charts | 1.2 | Analysis and interpretation of: . Tables . Bar graphs . Pictograms . Line graphs . Pie charts | |
1.3 | Purposes and uses, advantages and disadvantages of the different forms of statistical representations | 1.3 | Purposes and uses, advantages and disadvantages of the different forms of statistical representations | |
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| 1.4 | Explaining why a given statistical diagram leads to misrepresentation of data | |
1.4 | Analysis and interpretation of: . Dot diagrams . Histograms with equal class intervals | 1.5 | Analysis and interpretation of: . Dot diagrams . Histograms . Stem-and-leaf diagrams | |
1.5 | Purpose and uses of mean, mode and median | 1.6 | Purposes and uses, advantages and disadvantages of the different forms of statistical representations | |
1.6 | Purpose and uses of mean, mode and median | 1.7 | Explaining why a given statistical diagram leads to misrepresentation of data | |
1.7 | Calculation of the mean, mode and median for a set of ungrouped data | 1.9 | Mean, mode and median as measures of central tendency for a set of data | |
1.8 | Percentiles, quartiles, range and interquartile range | 1.10 | Calculation of the mean for grouped data | |
1.9 | Analysis and interpretation of cumulative frequency diagrams | 1.11 | Quartiles and Percentiles | |
1.12 | Range, interquartile range and standard deviation as measures of spread for a set of data | |||
1.13 | Analysis and interpretation of: . Cumulative frequency diagrams . Box-and-whisker plots | |||
1.14 | Purposes and uses, advantages and disadvantages of the different forms of statistical representations | |||
1.15 | Calculation of the standard deviation for a set of data (grouped and ungrouped) | |||
Using the mean and standard deviation to compare two sets of data | ||||
S2 Probability |
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2.1 | Probability as a measure of change | 2.1 | Probability as a measure of change | |
2.2 | Probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability) | 2.2 | Probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability) | |
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| 2.3 | Probability of simple combined events (including using possibility diagrams and tree diagrams) | |
2.4 | Addition and Multiplication of probabilities (Mutually exclusive events and independent events) |
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