Sec Maths Topics Link

Maths Syllabus (For Reference Only) 

(1) Numbers/Algebra

(2) Geometry / Measurement

(3) Statistics/Probability

(1) Number/Algebra



<< Sec 1  >> <<Sec 2>><<Sec 3/4>>


<< Sec 1  >> <<Sec 2>><<Sec 3/4>>




 

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N1 

Number and 

Operation

1.1

Negative Numbers and Prime

1.1

Primes and prime factorisation

"

Link

1.2

Integers and four operations

1.2

Finding HCF/LCM/Square/cubes/sq roots/cube roots by prime factorisation

"

Link

1.3

Four operations on fractions and decimals

1.3

-ve no, integers, rational, real nos and their 4 operations 

"

Link

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

"

Link

1.6

Use of < > ,,

1.6

Use of < > ,,

"

Link

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

"

Link

1.8

Use of index notation for integer powers


Use of index notation for integer powers


Link

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


Link



1.9

+ve, -ve, zero and fractional indices


Link



1.10

Laws of Indices


Link

N2

Ratio 

and 

Proportion

2.1

Comparison between 2 or more qty by ratio

2.1

Ratios involving rational numbers

"

Link

2.2

Diving a qty in a given ratio

2.2

Writing ratio in its simplest form

"

Link

2.3

Ratios involving fractions and dec

2.3

Problems involving ratio

"

Link

2.4

Equivalent Ratio

 

 


Link

2.5

Writing ratio in its simplest form

 

 


Link



 

 


Link

2.6

Direct and Inverse Proportion

2.4

Direct and Inverse Proportion

"

Link

2.7

Map scale (Distance and area)

 


"

Link

N3

%age

3.1

Expressing percentage as a fraction or dec

3.1

"

"

Link

3.2

Finding whole given a % part

3.2

Comparing 2 qties by percentage

"

Link

3.3

Expressing 1 qty as a % of another

3.3

% greater than 100%

"

Link

3.4

Comparing 2 qty given % and the other qty

3.4

Increase/Decr  a qty by given % (incl concept of % point)

"

Link

3.5

% greater than 100%

3.5

Reverse %

"

Link

3.6

Find 1 qty given % and the other qty

3.5

Problems involving %

"

Link

3.7

Increasing/dec a qty by a given %

3.6

 


Link

3.8

Finding % increase/decr

3.7

 


Link

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

"

"

Link

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

"

Link

5.3

Evaluation of algebraic expressions and formulae

5.3

"

"

Link

5.4

Recognising no. seq (incl eval nth term like n + 3 and 2n + 1)

5.4

"

"

Link

5.5

Real-world situation into algebraic expression (words prob)

5.5

"

"


5.6

Addition and Subtraction of linear Expression

5.6

"

"

Link

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

"

Link

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


Link

5.13

Factorisation of l.exp ax + kay

5.10

Use brackets / extract common factors

"

Link

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)

"

Link

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

"

Link



5.12

Factorise ax2 + bx + c

"

Link

5.12

Find value of unknown qty in a given formula

5.17

Find value of unknown qty in a given formula

"

Link

5.11

Changing subject of a simple formula

5.16

Changing subject of a formual

"

Link



5.14

Factorise ax + bx + kay +kby

"

Link



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

"

Link

N6 Functions

and 

Graphs

6.1

Cartesian coordinates in 2 dimensions

6.1

"

"

Link

6.2

Graph of set of ordered pairs as rep of relationship betw 2 variables

6.2

"

"

Link

6.3

Linear Functions y = ax + b

6.3

"

"

Link

6.4

Graph of linear functions

6.4

"

"

Link

6.5

Gradient of linear graph as ratio of vertical chg to hori chg (+ and - type)

6.5

"

"

Link

6.6

Quadratic functions (y = ax2 + bx + c) <sec 4>

6.6

Quadratic functions (y = ax2 + bx + c) 

"

Link

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

"

Link



6.8

Graph power y = axn n=-2,-1,0, 1, 2,3 and sum of <  3 of these

"

Link




Graphs of y = kax, a = +ve integer

"

Link




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

"

Link

7.1

Solving linear equations in 1 var

7.2

Solving linear eqn in 1 var

"

Link

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)

"

Link



7.5

Concept/properties of inequality

"

Link


 

7.6

Simple inequalities ax <= b, ax >=b, ax < b and ac > b where a and be are inegers

"

Link

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

"

Link

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

"

Link

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

 


 

Use of set language and the following notation:

Union A U B, A  B, n(A), ,, aB, AB, AB, AB


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




(2) Geometry and Measurement



<< Sec 1  >> <<Sec 2>><<Sec 3/4>>


<< Sec 1  >> <<Sec 2>><<Sec 3/4>>




 

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G1

Angles, triangles and Polygons

1.1

Right, acute, obtuse and reflex angles

1.1

Right, acute, obtuse and reflex angles

"

Link

1.2

v.opp angles, angle on str line, at a point

1.2

v.opp angles, angle on str line, at a point

"

Link

1.3

Angles : 2 parallel lines & transversal, corr/alt angle

1.3

Angles : 2 parallel lines & transversal, corr/alt angle

"

Link

1.4

Properties of triangles and quad

1.4

Properties of triangles

"

Link

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

"

Link

1.7


1.7

Angle sum of interior and exterior angles of convex polygon

"

Link

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

 




2.2

Line of Symmetry

 




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

"

Link

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

 


"

Link

4.2

area of cir of circle

 


"

Link

4.3

Area of parallelogram and trapezium

5.1

Area of parallelogram and trapezium

"

Link

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

"

Link

4.6

Conversion cm2-m2, cm3-m3

5.4

Conversion between cm2-m2,cm3-m3

"

Link

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


Link

4.9

Conversion cm2-m2, cm3-m3

5.7

Arc Length and sector area as fractions of cir/area of circle


Link

4.10

Prob inv vol and surface area of comp. solids

5.8

Area of segment


Link

4.11

Vol and surface area of pyramid, cone and sphere

5.9

Radian measure of angle(conversion radian and degree)


Link

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


Link

6.7


6.2

Finding length of line segment given coordinate of end points


Link



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



(3) Statistics and Probability



<< 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

 

 

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

 

 

 


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)

 

 

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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