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F F O T
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I [ nwnI 4 I
Unit 'I
I
- Welat~ens
a% Funct~uns
-
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-
.-
- 1
Unit 1 - Directed Numbers
Unit 2 - Rational Numbers
Urnit 2
- Products & Factors
o
3 taots, one on unik I 2 , one on ur\\!C
Unit 3 - Measurement
4 and the other on ursilt 5 The tebk
Unit 4
- G~akhernalical
Shorthand 'I
Unit 3 -- Logar~thrns
shoalld be of at least 35 rnln~lter,
duration each
Untt 4 - 7ngcaraomeluy (wrth PgrtEuagorlis)
ca
2 student xssxksheetsl workshsets,
Unit 5- Coordinates I
Un~i
5 - Properties of Shapes 2
one on unit 3 and hhe other on umhs G
!Jail 6 - Social FvPaQhematicsZ
8
r
Unit 7 - Statistics 1
Unit 6
- MathemaliceP SB~orthearnd 2
Unit 8 - Properties of Shapes 1
e Gonsts ucti&sw$lDssiqn
Un~t
7 - Coord~nabes 2
1 asks rrr 1 errn 3 covet lrlg unrts 8 to 12
Ter~si
3
(Details on these are prov~ded ou-o a
Unai 8 - Social Malf~emaliles
2
qepasate sheet)
Unit 9 - Translations asad Vecbrs
Unit 40 - Rcfiecbis~ns
Unat 9 - Stabstrcs 2
-- B ill@ interlea& assscsments will be
Unit 11 - Rslaticar-ss
worth 50% 06. &he FJG mark.
Unit 12 - Enlargement 8 Similarity
Unit 10 - Probabal~Py

3 ~ 3 PREAMBLE
t.1
The Fiji Junior Cevtificate hJathematics course provides opportunities for sluderlts lo olejrelop further a broad range of sltilis ar~cl ealcurdrayeb;
them to be creative and good problem solvers in their daily lives.
- -
1.2
1 eachers need to note that the understanding of w~alllerr~atical
concepts irluolves more than learning a set of rules or i~sirlg
a formula. It
involves knowing what method 10 choose, Row to use it and why iE works irr a particular sii.ualioi.r.
1.3
mathevlatical processes include problem solving, togical reasoning, analytical thinking, communication, rnaitirlg co~~neclioris
and using
mathematical tools. Calculators as tools will feature prcrninenlly irr the new course. These should be developed withirt the context of the iopic::;
and emphasised "troughout the course.
1.4
Flriathema"tcs at this level lays the foundation for mathematics learr~ing
in Form 5
2.0
AIMS AND OBJECTIVES
2.3
AIMS
--
I he FJC Matli~ensatics
course aims to develop:
(a)
in students a sound undefsland~ng
of, and the abiliiy lo use ru?;aihemaficdl concepts and processe:>
(b)
students' mathematical skills and abilities to think and reason logically, and lo cnrnrnanicaie rnaiklemaiicai ideas av?d e:cperier~ce:;,
orally and in writing
jc)
sktadents' knowledge and skills, and the understanding recju~ied
for everyday i ~ v ~ n g ,
atlid for- i-iiilhe~
learning Iri niaihem-ii~cs 3rd oliie;
suE3Jects

(el
sfr.~der~ls'
abi!ilies t'u conileef mathematics to everyday siiuaiicins, to sShcer topics within vnattjcanaatics 3rd to otlier'
eb!s
b
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( i')
ir: slilcki-~ts
favourable aittit'udss ts\\~ards,
and continuing int@re:;l in matl.len-rahics
(g)
iis stlr.rci~:rlts
she abiPi'iy f.o recogi'lise and appreciate the mathematics in et~eryday
situaiior~s
(h)
sti~deslts'
i:orifidence and ability to do mathenlatics
QE,,JEc]'lVES
On conipi~iing
the i3ji d u r ~ i ~ r
Ceri~.[~cate
course, pupils seaauld have
2.2."1
develc~psd
ihe kna:jwledge and undea-shdding re q t l i ~ ~ d
to:
)
use wilh increasing cos'lfidence problem-solvirsg approaclles "l investigate and tlrrderstand xnaV~ematEcat cos~ler-lt
!
recognise arid 'Tor~.slulate
problems fsrarn siiuai~cafss within and outside rnatklemalics
jc)
develop arid apply a variety of skdtegies &o
solve problems wikhil-s and G;~w~s~c"~F:
~ l a i h e ~ ~ a i i c s
(..\\I
" i
:?pisly mathema"lical patterras and re:latiionships to everyday situations
(f)
make conrtectinns with other Bopics within Mathematics, with otkrer subjects and with tire oukside world
(gj
zppPy rnlathematics to everyday life


2.2
3
dc~elopad
the" values arad attliudes wliic!~
17eip them 10.
(a)
appreciate Mathem:=~tics
as ark infere~k~ng,
enjoyable and cha!lenga~lg
subjee:i
&I)
develop the skills of ~nquiry, investigation, discovery and verificals~n
which afe cS:ssei\\$saB lor the Iearrlli~g
of I~AaiiB~errii~il~"~
(cj
appreclafe Mathematics as a creative, relevarat ar~d
i~seful
activity in daily iivislg
jcZj
galn conf~deni:e
in their abelrty lo learn and practice self assessm~wt
s&w!%s
in
mb-sfi\\emat~cu
(e)
show confidence in using tileer own Iciirguage and the larlguage of li~iatRe~18ties
to express mellrematicai 3de72s
f )
vxerc!se self d~scepllne and be resourcafaal in engaging ila maAemeatical activodss
(g)
work co-operalively w~Eh others alld padicipade in group d~seusslsr~s
(h)
appreciate that Matkrematscs is useful to the learning sf other subjects and for job opporaunsi~es.

o;a
Estirnaking arid approximatiu~g
~r
Personnel
Q
Recognising and using patterns and relationships
+ a
6 f 3 l l ~ ~ ~ d
1
Organising information b r mathematical analysis
o Rc:i1reser-n2atioun and irrterpietatnbr-a
/ _
Preser~tc~ti~~n
__
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TQQLS AND 6biANAGBNG RESOURCES
Problem soiving plannir~g
a
6s'l:ikr~~ent~
8
Problem soivialg strategies
o
Calculators
Modelling
e
Corr-ep~iters
BlAanagiwg t ~ r r ~
h/las.naging mlsraey
o
Managiw~GI~er
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resources
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I . Categorising and interpreting
I 6. MAKING CONNf:Glti"iiObJS
s
VVitPrlin ma"6tlenlatics
Recognising and working with patterns
e Other eun-ieu6iarn areas
ca
Reasoning
Everyday life
inferring
o General
Proving -
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GENERAL PUMS
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i\\Aer completing this unit, stkade~rts
r;hauid be able to
e
To revise and extend Ihe use OF
1. (a) ideniify the basic uirits of measurermni used in\\ the rnetric system.
rn~irrc
units for measurements
(b) stale itle values for commonly used metric prefixes.
(c) convert frorn one uoil to another with She relevant prefixes
o
To discuss the accuracy of
(d) wrile a gi\\ien number in standard form and \\iice."vessa.
measurements
2. (a) estimate comrvlonly used dimension such as length, mass, area,
o
To Interpret and draw scale
\\colurne, and Eiaae
dragrams
(b) measure objects to the nearest units required
(6) write a measurement correct Bca the ~aearesl
unit required
To measure ci~rect~ons
by idsrng
(d) slate Ihe smallest and largest possible measurements for ail object
compass bearlngs
whose recorded measurement is given;
Classify tiie dislinr::iion betweer1
(e) wrile an inequality for the aciual measure o.1 al: object wl-ien given a
mass and weight. Ci.g. A mass
recorded meascnre for it.
of 511 kg has a weighi of diO0 N.
o
To revlse and extend idects of
areas and volurne
3. (a) interpret the: scale of a drawing as the ratio of Ieinylh 01 the drawri object
to the length of Phe actual ok~ject;
(h) calculate lengtlls of objects from a scale dsawirig;
(c) draw scale diagramis to a given scale;
(d) measure angles of elevation and depression using a ciio~orneher.
I.
(a) case a magneiic cornpass to give the bearing of an objeci from where the
student stands;
Irv'uric or1 rsvnljiems deaiing wit!]
(b) determine the bearings of points usirrg a map or diagram, and 3
elevation-\\ anrl depressinri are io
protractor;
be 1%ea9t
\\~~,vith as part oi the iilrori;
(c) draw sdale diagrenls where the directions or' lines, or the direction frorr~
or1 Trigonometry.
one point BC'I another, are given as beauings.
5. (a) apply and manipulate, formulac for tire area of e redangle, square,
parallelogram, triangle, rhombus and taapeziusr~.
(b) Calccrlale the circosrslerence and area of a circle and relate these b
the area and are length sf a sector
(c) Calculate approximate ereas for irregular figures by using Irapeziurn;
(d) Calanlo'ce the surface area of sirnple cuboids, cylinders ar~d
spl-seres.
5. Apply and nlarsi[~uleke,
forimuias for the wolurne of prisms, g~yran~ids
and
sphc!ses.

After corr~pleting this urrii, sluderrts should be able lo :
I
MATHEMATI&
0
'fo introduce stlidenis lo a 1 (a) e;cpiarn the difference between rrumerals and pronumerals,
SHORTHAND 4
I
nlaihematical language oftell
called algebra.
(b) narlrie different types of algebraic expressions on the basics or" the
number of terms in each - monownial, birroru,ial, trinomial only;
(c) difierenliaie between "lilie" and "unlike" terms and then add and
subtract polynomials;
To
practise
rnanipulaiii~g
(d) multiply and divide rnonon-iials, including those wv~lh powers
pronumeral terms, expressior~s
and fractions, solving linear
equations and inequations, and 2. (a) relate numerical fractions to algebraic fractions
using operators.
(b) add, subtraci, multiply and divide s~mple
algebraic fractions.
3. (a) explain the coileepl of an operator,
I
(b) know the meaning of the terms "inverse operator'' and "self-inverse
operator";
(c) solve problems involviiig operators, their inverses, arid combination o i
two operators.
4. solve simple linear equations, such as
2x -4 117; &o($ = 2 ; ,ti2 - x/:3 -. 0
4
5. (a) use set-buiider notation;
(b) determine the soli~tion
set of an ii?equation, and graph it on an
appropriate number line.

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After cornpietirig this unit, siudr:nis should be zble lo :
1-0 revise and extend the work
'1. (a) give rational i~umber
coordinates for potrrls
on coordinates
platted on a number line and vice versa,
e
To draw graphs of sets of
numbers and inequalities in one
variable, on a number line
(b)
graph inequalities on a ilurnber line, using irrlegers or real nurnbers as
replacement set:
All work era graphs o'i Einc\\iir
Ga
To draw graphs of lines parallel
to the axes on a Cartesian
(i) graph ail real numbers greater ihan 5.
equaiicjns okkrer than tilose
plane.
parailel io the x or the y-mi:,,
(ii) Graph
eq~eaticiils of
grrapi~; a ~ t i i
)( < 3 6 , x E real number
irnecio~aiities
associated wit11 line
(ii!) Graph all integers where -2s
x < 8
graphs is ext:lalded at this skigo.
1 (c) descnbe sets sl pomrs graphed on d wunlber fine
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2. (a) give integer coordinates for points plotled on a Cartesian plane and vi;:e
versa;
(b) Determine ilie coordinates OF points and graph the lines of the ~faliovvin~g
types of equations :
e.g. x = 2 , B/ =: 5
'
7
y ==

x = .I4
(c) m~ie
down ihe equation of a givers line that is parallel Ica one oi iCle
axes

After completing this unit, sludents sbio~~ld
be able 10:
1-0 revise and exierad students'
1. peiform simple money (;alculaiions for domestic pilrcklases;
SOClAL M A T H E M A W /
knowledge and use of money
01 t''fo ohle(:tsl
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calculations and percentages,
2. (a) write a ratio to coi~qpare tiis corres~or!aincj ~ i ~ a ~ l J ~ e
(b) deiermine the larger (or ~irialitr)
o l iwo objecis cornpared in a rail0
w
To inlroduce stadenls to the
and if the measure of one o i the objects is given, calc;ulate ihe
concepts of ratio, proportion and
measure of tile other object;
rate and
apply these in
(c) identi@ ratios that are eqvivaleni;
everyday situations.
(d) simplify ratios;
(el apply ratios to incita.;lng or decreasing u i quarrliiies, and lo tiivlsion
into parts;
I
3. ( 8 ) identify when two variable qi~aiitiias
are proportinrial, and lo explali~
why they are proportional;
(b) perform sirlapie calculations involving two variables ?hat are
proportional;
4. (a) calculate a rate or ail average sale;
(b) perform simple calculaiions in\\~olving
rakes or average sates;
5. (a) convert a traction or decimal irilo a percentage, arid vice versa;
The use of calculraiors to \\h1oldf d, i!
on percentages \\ ~ l \\ i greatly 1
(b) express one quantity as a percentage o i another;
reduce h e tiroe ieyirire:!
io 1
solve problems.
1 I
(c) calcuiaie the percentage of a cluairliiy;
il
1
1
I
i (d) increase or decrease a quantity by a given percentage;
i
ii
(8) pe&rm sirnple calcl;laiions iil\\/oIvis;lcj percentages, inc:l~.idincj
~ ~ r o t l i
2ild
loss calculations
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GENERAL AIMS
SDAECBF'If.; OBJECTIVES
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At the end o i this unit, skwde!>Ps shoi~ld
be able io :
In this unit, siuder~ls
will loo/( at
1. (a) draw charts lo represerii tables of slalisticai data usirig pie charts,
piciograms, bar-graphs and line gr-aplis
represeriling statistical data in
graphical or chart form;
(b) comment on the irverall Isends illinsirated in a graph of staiistii:al data
and also read vaiues from it:
computing R e mean, median,
mode and range for a given
(c) decide when, and how, a chart coi~ld
be used l o critically analyse
sample
coriclusions drawn from statistical data;
C"..jc
/ . . f
, a l u ii 01 work on siaiislicai
2.
firndions is r~oi
necessary ;,i tliis
0
organising data from a sample
caiciilale the range, mode, median arrd mean for a given set of nurneric~;I
into a frequency distribution and
data.
si3ge.
representing this by a
frequency line graph or
3. (a) organise numerical data irrto a frequency table, where equal width
hislogmm.
class intervals are given, and draw a frequency line graph.or a
(:aicul;-aiioris of the rnear) \\rtil! riiii
histogram lo illustrate ii;
in\\!oive using grouped ciala as ir.1
a Giequency table.
(b) when given nul-uerical data i i ~
the lonn ol a
freqirerscy table or a frequency lirle graisii or a histogram, delermirre
the i-anye, Ihe mode or khe rnodal class, and the median;
(c) read off a freques~cy lirle graph or a histagraurr, record the data in a
irequency labie, and answei questions related ko the graph and ",he
table.

After completing this unit, students shocild be able to:
TBIS unit has been pill %o:~,cV~~cr
with units on transl'orrnatioils to
a
10 exterid students' knouiledge
of the angie and symmetry
enable siadents lo relaie move
properties
of
krangles,
1. (a) classify iriangies as equilateral, isosceles or scalene, and as obiuse-
easily io puoperlies .it figures
quadrilaterals, polygons and
angled or acute-angled:
airld ihe iransic~mmaiiorrs ?hey
clrcies
undergo.
o
To explore the angles i o ~ ~ r ~ e
by d
(b) stale and use in simple problems, the property of the sum of llie
a transversal on tho parallel
knterior angles of a triangle, and the property or' the exterior angle of a
i~nes
tri~anglr?;
a
To construct, examine and draw
two-drmens~onal pictures
of
(c) draw the lines of symmetry For eyt;ilai'eual, isosceles and scalene
some solrd objecis
triangles and state ihe order of rotational symmetry for them;
To shaw the applrcafion of
properties of shapes in real-l~le
(d) use the symmetry of a triangle to make deductions about the sizes of
s ~ t ~ ~ a l ~ o n s
its sides and angles;
je) decide whether a triangle can be drawn from the inforrnaliori given
about its sides and angles;
(f) make an accurate drawing of a given triangle.
2. (a) g!ve correct names oC polygons with 3 lo 10 sides e.g. Ir~angEe,
quadrilaleral, penlagon, i~exagon
etc.
(b) calculate, and use irr sirnple problems, the sum of the lriter~or angles of
a polygon.
(c) know, and use the properly of the sum o i the exlerlor angles or' a
polygon
(d) skate the number of axes of symmetry and !he order of rotational
symmetry of a regular polygon, and show these on diagram of the
iegiliar polygon;

SPECIFIC OBJEGP'YVES
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3. (a) name from a diagram pails of alternate, allied, corresponding,
vertically opposite, adjacent, cowrplenaenl'ar'y and supplerrlentary
angles;
(b) give the cornplernenl, and supplement of a given angle;
(e) use in si~mple
numerical problems, the properties of verCcalEy opposite
angles, the :ium of tile angles OPI
straight line, and the sum of Ike
angles around a point.
(d) stale, and use, Ilhe properties of alternate, allieti, and correspondirng
angles, when lines are parallel;
je) stale a definition of parallel lines;
(f) identify parallel lines arrd non-parallel lines
( g ) draw a line parallel to another, and th~ough
a given point, by ~rsing
a
st& square and straigllt edge.
4. (a) identify avrd name trapeziums, parallelograi~~s,
rectangles, rhombus,
squares, kites and arrowheads
(b) for the quadrilaterals in (a), indicate Vieir syrnrneir'ies arid use !lien.\\ to
deduce lengths and arigierj of given cquadriialerals;
(c) state, and use, ihe basic side, angle and diagonal preperhes of the
quadrilaterals in (a) above
5. (a) state tlrnat a circle is syn~metsical about any ciiaaneler;
(b) use the properly that the mediator of a chord is a diarneler of the circle
(c) construct toe centre ol the circle by using a straight edge and a
compass
jd) define a cyclic qldk3diifat@r~u/;
(e) racogr~ise
when a quadrilateral is cyclic;
(9 recognise, and use, the follu~diiing angie properties:

(g) identify the axes of syrnmeivy in diayrarr~s
showing ohe or two
langeruis %o
circle;
(hj use symmekvy to deduce the sizes sf angles and line segmerrl;, n
d~agrarns
showing one or two tangents ?o c~ucle,
6 . (a) slate the difierence between pyramids and prisms;
(b) idenliiy prisms and pyramids frovu\\ a colledon of solids;
(c) name prisms and pyuaulids, e.g. triaiigular prism, cuboid, square
pyramid.
(d) ident~fy
atlci coiiiil edges, faces, and vertices when given a prism:,
square, pyramid etc;
(e) recognise possible r~els
for cubes and cuboids,
(f) draw nets fgr simple solids sucil as cubes, cuboids, triangular prism,
square pyramids elc.
r
h!
/
(g) consirlrci a solid objsci given its net:
(h) draw p:c%uues
d
cubes, cubo~ds,
l~yiirzs
bdsed on cubo~ds,
and
rectangular pyrarnrds

After completing this topic, students should be able to.
To introduce simple translation
properties and 2-component
7 . (a) identify lrasrslalions used in patterns where some basic shape is
The General A1111 has been
vectors to students.
repeated, in one or. two dimensions
~rodiiieid.
Po show the application of
(b) desigrr their own patterns by banslating some basic sihape;
translation and
(c) stale the basic translation properties;
vectors to everyday
(d) use the notation A - -* A" P13Q -+ AB;
situations.
2. (a) descnbc a trscssiabon by giving us vector lu? the Eoxrn
(b) pe~.forrn
a translalio~a
when given the image of orie point, or when givesa
the translation veclor;
(c) draw an arrow vector for the G ~ ~ L B W I W
vector
3. (a) combine trailslations by pedorming one lmnslatisn afler arlolher
($) add two vectors algebraically, and draw their addition rdiagsal~?;
(c) wile down the inverse of a translation vector, and give the prhapefiies
of a vector and its inverse;
jci) givs the position vector for one ol~ject
relative lo anotl-rar.
4. (a) pedc~rn-,
transiztions when ail operator symbol is 1ar;ed.
(b) perform the translation i",B where and B are operator syalrbois for
transiations.

a
To revise and extend s i ~ l p l e
After ~ o r n ~ l e l i n g
this topic, students shoaloi be all1e
to:
Unit -lO
reflection properties.
1. (a) show that the n~irror
line is tkie mediator of Ihe line segnient joining a
RE&L.EC%IBNS
e
TO show the application of
point and its image;
reflections to everyday
situations.
(b) const~uct
the image given 2n object (point, line, line segment, etc.) and
the mirror line!,
jc) construct the mirror lirre, and lo state [hat this is an axis of symmetry;
given an object and its image,
All ;niasic on l~jore
I h a ~i ~ o
combined ir;dnsformal,ion::; i:.
(d) shovv Cial an object and its Image are congiuent and therefore length,
angle and area measures are ~ n v a r ! a ~ ~ t ,
/ (el show that sense or olionhiion is changed in reflectiol~,
jf) identify puirels arld lines that are invariant in a reflection
2, (a) carry out s~~ccessive
reflections in two yawilc4 mirror lines, and specify
the equivalent translation;
($1 carry oui successive refiecliorls in two inteiseciiilg mirrors and speciiy
the equivaierrl rotation;
i! is expected that graph paper
3. use operator symbols for refeelions rand cornhinations of refiedons;
and lo a lesser exteill,
coordinatcs will bz ust?d.
4. carry out giver) cornb~nakiorls of reflecilorls and translations

_
-_______-Y_."-w-X
_-svxe.-"
-.-T,w-<.s%--m>%.
~ &
a
,
.

"v-
V-CY-^.I-"~I~----
_sj_i___-v-,
SPEciFjC OB J$CTIVE%
-*--.,
~ .
.
-
,
L
-
,
A
*
-
n
,
m
s
*
a
-

--.a,--mAa
.m*-#*,-.*7
*.-.-- - - u - w . - A . S
>----*a
.a
,fter completing inis iopic, students should be able 20:
-ro revise and extend simple
. (a) use the c~nventiow
oB positive rotation (anti- cBodtwise) and negative
rotation properties
rotation (clock-vjise) to cor~strucl
the image given an object (point, line,
line segment, etc.), centre arid angle of roklian,
8
To show the application of
rotations to everyday
/b) find the cenlie of roldtion and skate the angle of rotation given an okajech
situations.
and its image;
To show the me of rotation in
(6) slate that an object and its irnaye under rotation are gwc.@fij and
obtaining 'ine properties of
therefore length, angle and area measures are invariant;
some common shapes.
(d) identify the point that is invariant in a ro'cateon and stale that it. is Itle
cerltre of roeation.
I.
(a) identify figures which )lave rutalinruai syi~rmeiry and give tlie ovdeu of
rotational symmetr)?;
(bj identify figures ifi~hich
have point syrnn3eki.y
3. use operator syvrrbols far ~o&aii~ou;s
and combinahesns of rotalaoul5,
4. (a) iderrl.ify khe "Iransformskios; used; choosrng froin [tra~~sBalion,
retlection,
\\Miirk on hnoee llaan l!*vis
rotatbnj. when given an ok1jea:t and its image,
transf(irnlrlriicjns are ex~;8mded.
(h) carry out given cornbination ot rslations, refections and transiaiions,
and to describe the single Iransfe~r.rnat9op-r
choosing from {transltrtion,
reflection, and rslakion] that wokrid sr~ip
the object to its fsnai image.
(cp elst? o~~erators
10 carry
successive Isansiormations of Grapaslalihans,
reflections arld rotations.
-
m*-z---w---t-r--
_- _
_
m-m=.
___s,l__i
_"
" _ l ~ _ l i I ~ " - . i ' ~ i i l i X - . i i e - ~
j_____jIj.-Ta.

--
--
-.- --
/AaY/-A
I
_
I
Y
I
L
A

L - i
l
l
-

2 %
SPk-elFB(; OBJEbGTlVE S
---
---"
- -
%
-
-
=

__-mLY
I"
<*--
_I L
M A + -M"
o
To introduce students to the
After complehng Erlrs unit, shwdene should be able ro
transformation of
ENLAWGEMEM AKD
enlargement, and to the idea
1 (a) identify blrllei-~
oile objecl is related to auaoihei by an enParge!nenl,
SIMILARITY
-
of similar figures
jb) make sirrsple er:iargemenls of figures drawn un gap11 paper, giveiz ikte
centre of the enlargernewt and %he
scale factor, {or posib!ve scele
factors,
(c) ident~fy
the centre and the scale factor, whei3 given an c~aldrgcmeiit
of
figures drawn on paper,
(d) use the scale fa~kor
when calcuialing lengths on correspoird~ng 31des 117
an enlargemeiit,
(e) use a symbol as an eniasgemer~t
operator,
jf) give the a i m scale Factors when rile ierrqIl\\ scale factor of dn
\\jiIork oil more 1P!a1i t\\tiln
enlargemerri is given, and use these in elenlentary problems,
consecutive
rdr'js3ornlaiions aie ni?l
2 (a9 carry 0148 com$iwatioi-r$ of tha transforrnat~ons
of refltacitoils, rotations
studied.
i ~ n d
translations with enlargement, thus obtaining s~rn~lar
figures,
(b) identify pass~ble
Irranslormai~orns
used in Pnapplng from one figure to a
similar figuee,
(c) ~denuty
corresponding verbces, angles and line stlgrnewls given kviw
ssrniiar figures
(d) calculate the length scale factor and use t l ~ ~ s
lo
calculate orhee lengths
of given sin-soilar figures
(el rdea-atdy pars @a figures as sim~lai or nor
3. @-se~!ct a pantograph, given ihe ~nskructiou-i;
Ass6 g ~ g
li,
to enlarge simple pictizres
------sa-
7-
,?---->-A
---=--A
b-
-.a-"-m
.---*-

--
- -- - s - - - - ~ - - ~ ~ = = = - " - -
UWlT TITLE
1
GENERAL AIMS
SF3EGIFilC OE$&IECTIVES
_ __UY----
--I--=~---I-----
-I--I--1-~---~------
-----L-=~-Y-I---.-~%=-
a
a
~
9
1 ~

After comp!eZ~ny this umt, sludcriils should bc able to
RELATlONS AND
--
or
Po lormalrse tile csneepk o?f
FUNCTIONS
a relat~on as gainng of
1. (a) draw a graph o.l a rdaiion giver) in vmrd ic~rm-pl
EIY

given 241; a set
elements of one set, or of
of ordered pairs of elements. Suitable types of graphs are
elements of one set \\mf!th
given belavv.
elements of another.
-
I:; - .(J
o
i o introduce furec"njons as
-"-
special types of relations.
..__
- -=.-
(b) !ist the ordered pairs sf
a relation given as a gra~,A%
or as a
rule, with domain;
(e) geb~erate ordered pairs of a relation given in the form
-+3x or ((rc, 3 ~ ) )
or y = 3x, each wit11 its donaaiird;
Id) listhe dornaila and rarlge ~ i /
a s-ela1:sous;
(e) dsavw the graph (I$ tkse inverse of the relation, given its graph;
jt) list the ordered pairs of the inverse relation, given a relation as
a set o.! olderecj pairs of elernenis.
2. (a) recsgnise 'al~:.st for a furletion, aaclh clerrsent 6m
tile domain or" the relation is w~apped 'eo orsly
silt? element of the range;
(b> differentiate
betbveen a function arsd a rron-.Function
(a;)
calculate the values of a fsrraclio~
using ns%ations such as:
if "f : x -+ 2x, evaluate f 7 ; and
,if r - 2
3, find the value (;of npJ.
-
.,.~-*,r-=ser-,,-.-~~~*A--~,#>
,
u-L.-

'
,L--.u.=,a"
==.-asE
b .
L -
* &
~ n
s ~ ~ d . . . - - ~ . ~ ~ - ~ !
-->=.
-
.
.
.
-
.
%
.

,

----
'"".""
T-i-l-="--..--""
-
"
-
a
-w-mv------=--"
-
L
-
-
*
l

[
UCIB ;:TL.i:
p r ' <I r
akRiU2AL
AIMS
i
AAer corn[dleting ihis topic, students shreould be able tow:
To apply khe distributive prspedy to the
PWODLICTS ANQ
-
product of two polynomial expressions
1.
express a given movlomial expression in kenns of fiad.ors and
FACTORS
and the corresponding factorasation
vice versa,
Example: 3 a $ - = 3 x a b = 3 a : i b = 3 x a x $
I 0
To introduce $Re use of factors ID salv~ng
polynomial equations and in simpBif\\flng
I
ratsonal algebraic expressrrans
2 . use the distributive law Do write producls of iactoors as
sums of terms
4. sirr~piify
rational algebraic expressions such as:
by usirng common factors

Afes compleling this iogsic, steadca~ls
should be able io:
To begin the steady of logarithms,
espedaE1y those using base 2
and base
10.
1. (a) write najrnbers iia base-index form and vice-.versa
(b) simplify index expressiesrrs for positive, zero,
and negative indices,
2
(a) use the expouuential grdphs y ;: 2"arld
y:lO~>
xr R, to write wiimbers as powers of 2
or "10,
and vice versa;
(b) use ihe graphs of y=2x and y:-'!Was appropiatr? to
express rgiurnbers ;as ps~vers;
(c) express the base-index forrrr of a slt~rntper in Bogaiiilarn fweal
and vice-versa
eg. giver] 32 = z5, the12 log232 = 5 and
given R0g,~49 = "1.98,
then 4.9 = 101 98
3 (a) use ca1cuIators tc~ iliir~d Iogarifhm~s
0%
r ~ i ~ ~ n b e ; ~ ~
(b) case ca8ea1lats%rs
Is fend a number, gwcn its logar~~ilrn
-
-
-
-
i

I
--"."-C>
I - L Y S I U _ a % -
c r
J
-1
- X L E
&CI
,
-
-
a
C
Y

" _

GENEIqhL AIMS
SPECIFBC OB$ECTBVE,S '
_
,,*_l_l_
YI_UVIY__a.a.-7-,ma-ssa&%
- w , - - , ~ ~ ~ - ~ ~ , ~ ~ ~ - - ~ - - " ~ - - - . ~ - - - - =
LY-
J.m.LP_
.
l
a
_
,
.
-
-
-

~ . - ~ Y U ~ ~ U ~ ~ . s m . m ~ ~ . * 3 * = " - , - - - .
Tx'{er oon.ipisti.~g f:i>is l~ p i c ,
sttide~;k
sk:auid be able lo:
I
i
1 . Use calc~a$al~:~rr,
to find squares and srguare rdds d
[\\umbers
I
correct "r~
either one or %WJO decir~lal
places.
v
on
B
3-0 use calculabrs tra firid squares a i d
2.
(a) state the f~rmula
for the Pytklagoras' Theorem far any given
square roots.
' C ~ ~ O Y G " ~
is part ui' lkie
re'gtlt-angled triangle;
'I'rigos?oanelry
I$)
calc~slate
the length of a side sf a riglit-angled triangle when
To introduce and apply the theorem of
ii
Ine lengths of the other Bifiso sides are giver) as natural
Pythagoras.
numbers; and the square n'r
side to be eaicetialed is not
I
1
greater thaur 100;
I
Q
To introduce the basic sine, cosine and
(c) sfats whether a triangle is right-angled or not, by using the
1
tangent functions.
concept of pythagorean lriatis (restricted to natural
speciiic, obeciiw? 5,
t">? 1
numbers).
B
pupil does not Irave io b;r
e
I!
; ident~ky
the lengths of tile sides of fight-angled tria~syie in ferrlas
able lo solve the hypoiesriisn "
length lisiilg tl-~c-:
1
of r CosO rsirtd r Sin0 given the hypdenuse (r) and angle O
i
Brigsnomciric fur'ictioris.
j/
4. Identify the side whose Eeng'rh is :c tar! 8,
for nilvnerical vr;lues 0.i
b
x and 63; given a side x (which is not the hypotenttse) arid an
/
angle 0 sf a righi- angled triangle,
"ihs use rii calcuiaio!~
will
I
ease
1
\\ , i . v 1
r&U,
ii 081
1
5. For a given right angled iriangle, select the appropriate f~liwction irigonurfielry iur'lcticuls.
11
(sine, cosine or tangent) and use it k3 solve the size of the
r
i;
required angle or side
1 i
6. Use calculators to delermlr~e
!he sine, cosine and iariyenl
values fog3: given angles
7 . Skelch the graphs of sine, cosine and tangent fo:or, arlgles from
0" to 360"
8. Identify the sine, cosine and tangent graphs for arlgles irowi 0"
lo 360" frorm a selection of graphs
9. Use a clinometei' lo uzeastdrc? arrgies of elewation and
deprc;ssion and make subsequent calculaiica~?~
for heights.

After completing this topic, students sho~sld be able b:
~3
2
study
couipass
and
ruler 1. (a) construct, Zfae bisectclr sf an angle, mid.-point 04' a
PROPERTIES QF
constructions, simple loci, centres of a
Bine seygmenl, the rr~edialor
of a line segnsent and
SHAPES 2
----
tuianyle, and intersecting ckb~rds of a
avlgles of 90°,
6OU, 45", 30" at a point on a gi~~en
circle.
line, usirlg ruler and compass.
(a) %:onstruct the centroid, srlhoceniue, circ;u~~ceraQre
asxd
circuml-,irt;Re, ineenfie and incircle of a triarpigie and rdentiiy
these i:~
given diagrams;
2. crsnstnsck, or iderslify on a given diagram, sets of points based
sn the follw~ing
loci:
Ihs locus of psivats equidestant from a .fixed point, or ~ W C B
.filled poiills;
13
;
she l~scus
uf points equidistan.! from a given line, or froren tWo
given lines;
3
state and usc it1 problems, the prcjpeny of the anple
subteraded at the cenlrtt (of a circle being "awice thc sire of tl~e
areqle subtended al the csrcas~nfcresoce
by &he
same asc,
4
slak end use in sample wumernf:a! calculaiions, the propedy QI
chords inte~eciing
itnissde or suBsde a elrcle, and the special
case of the tauagents

_
---
-.--
--
Y Z _ ,
Y Y _ _ _ ~ ~ _ _ ^ _ _ l _ , ~ - s = - ~ - I k - I I X I Y . I M I - L ,
-",.
L--IY
- *
L_i
- - - - - - B
UNIT TI"FLE
F
GENERAL AIMS
SPECIFIC OBJECTiVES
F-
__--
-- _--
------ -
----
*w----x^.--;a_uru-=r;u;r-
-==--*-=--i
'"
-
-=*--=*--
-=
-&-
-*
!
illis $pic has to be giv;:ii 1
ffi
l o practise manEp~n9akion of algebraic
After csmple~ng
tlr~,is
"rppi, S~IEC!B;~I$S
S ~ P O U ! ~
be able to:
expressjonr; and formulae, and solve
greater em[~hasis becaiise cf ;I
algebraic equations.
1. (a) substilute values inlo algebraic expressisns;
tile nee! ii reinlorcn s i ~ s i n b i '
1
(kz) add and s~rbtrac'r
polynomials
aiglsbnic sltiiis -- a prsi~lem c
examples:
encoiirllewd by sitrdeniv in lini: 1
latier school years. li. i:i
aniicipaied
i;ilai
1
iifiar,
iniiod~ced
at Forri; 7 i e ~ d
wili 1
b(+ ic,',*r,?
*..,(j ,'
.;->I nr;)Kt . I ~ Q
$ K I ~ I ~ ~~S ~
r S
i
(1
h
solving rc;al
pro\\,lsm% !I 1
(6)
pe,'~f~$rm
the bur basic erperations (-b-,..p:;,-f-)
v~ijt!u
arithmetic and zigebraic; fractions,
necessitates t17j0&, ijb'i f~~rrji':{j
1
examples :
cqwfons arid liiidirig soiutioiii; I
io eqtn:dions so !omed.
i
2. I-ind solutions sB 8&1c: follomflfing types 0
8
equatia~is:
-
gi) 2~
-2- 1 5~ - - fj
(ii) E . J - ~
2 3
(EiA) x' ~ 4 "
()(1.9)2=9,
jx',:
3) z
(i%$> (x-4) (~-2.2)
($4)
2 0
3. (a) substit~lle
valeres into a giver) iormuia and give
the answer it-] the sirnp9esl form;
(b) ckafige the stjbjesk. of a given lownul;t.
estampls: Make v 1he scrb,jec:t o'i ihe fornr~~la
d=x~~Iv;
(c) se~!ve problevns by translating flrOin verbal sf wrhtters
slater~ent
into nrathematical eqgatior~s or forrflula

AAer comralcting this kogric, students should be able li?:
o
1-0 dra\\czr glaphs of simple linear
equations and inequaticarls in t ~ 8
1. (a) slate the intercepts on Bhe axes and Ike yradierrd
vauiables on a ca~esian
plane, and
or slope of a giver1 liree sais tb~e cadesian plane, sr
introduce the ideas of iw"hrcepls and
of a line brrl-sose equation is given.
slopes.
2. drawl grap81s ow a e;,ari.k:sian plane Po sb~aw
pairits tisat
saiisfy given inequatio~ts
such as:.
y - KI]X + k:

.Aficr c~rnpleting
this topic, sludenis sbesuld be able to.
1. (a) verify enb'ies made in savings bank accoua-lls;
SOCIAL
e
1 TJ look a! Sdvirlgs Bank Accounts, i+re
Purchase or Credit Accourats, and Tax
Ccsracepis iir this topic are aiso
MATHEMATICS
---- 2
Returns as examples of scrcsal uses ra8
(b) calculat~
the tolal amouni as be paid, and ihe s~i~v~ngs
641 Bosses
elementaq mathematrcs.
ancurred, when goods are bought on hfre-gsirrcha"ic:, credit Beoms, Economics
n! Papbuy
(c) ccamplek a tdx return,
gwcn !Re aelevdnl ~nfomfat~on,
-
i o apply pei-centages in problems sisck 2 (a) increase or decrease quantities by a given b~cucentage;
as ir1teres.i earned on lending and
in?resting money, and compou12d groba~tarth
(b) calculaie the ancaunt afiii\\ieresi receivable and payable annually,
of a town's populajion
given the principal and the rake of interest; when money is
loaned, interested or borrovved at simpie inferesl
(c) slate She differe~ace
$elween sianple and cniinpourrd Enteresi;
(d) calculate the amoa.sb-~f:
and the interest earned, or' paid when the
phncipal, rate and period of time is given when money is loaned,
invest,ed or borrowed at compn~ne~
interest
(el snse tables Chat give ssmsple and cspi~gaa~~lnd
sntercs!. on $'I for
grvem ~ntebesk
rales and numbes crf years,
(0 apply tire compound g1~3wBh vnodel io ot81er praci~cal examples
S F I C ~
as pspula8oias, and deprec;~aticlan of values

In this unit of work students wvil1 Book
1. (a) calculat6: the anlhrnebc i;neai%
Posn a kaequency table, by elsi1168
further at cornpeeting sb;atisties such as
She rnsd-laalkses 691 !he class intervals (wb\\ere necessay)
mean, median, upper and lower
qua~iles
and infer--:-quaflplile
range.
(b) solve bimpYe prc~bleans related to !Re mean value
-.
VV&gs..k on frcxgtsar~cy
potygows and ct~~rrruialiu~e
frcif~uenn;y is exa;lud~:ii.
2
determsne the med~an,
the upper and Bower quahlles, and tire ~rste;iu-
qr~arfile
range for a last of scores, and for sa:o#es in 8 frequer~c~y
table (without class rnten!als)
3
apply the statistical correepk learnt in this topic Po real-lik
situations.

PRORABlhiSY
--
1
1, (a) perform simple s%atir;tical experim-rrerits, and trorn tRc?sc
I
TO ~ntroda~ce
elementary ideas of
B
1
1
probability
determine the relative R'equeixy of a particular orrkcomo
examples : tossing a coin, rolli~g
a dice, di-aw~iny
a card;
(b) (i) recognise Ilaa'i as the number- of times Ihe
e~iperiment
pedocrrrned increases, the relative
fsecquencies approach a particular value (limit)
jii) estinrra8@
this paiqicular value (limit); and
jiii) use this limit as a probability, eg in tossing a
coin.
2.
(a) explaii? the meaning ok Il-re terms s i ~ h
as "rarjdon
event", "equally like outccornes", '"fair", "biased"
jb) (leterrnine the probability of each outcome of an
experinser~t,
where the oulcomes are eqeiaily
likely io occur, or where Ihc outcomes can be
easily related to eqli?ally likely oukcomes, eg. in
ilra~jiing
colonred balls f w m a box;
(c) explain why the sum (1% the probabilities of an experimerrt I:; orre,
and that the probability of an event is-betweeurn zero and one,
ineiusive;
(e!) calculate the probability of an evcl-it;
3. determine ,the expeclc;d svurnber ol occesi-rences of an event giver1
ih pprobabilihi, and i . 8 ~
nutpabes of trials io he carried out..
/ apply the probability ccsncepks ~,eal-i~t:: !;ikuatinns

FORM 3 UNITS
- -.
-- - --
-- -
---

.
-

-
.
--
TASK
, % r ~ j ~
~ l , t
F ~ ~ R I ~ ~ - I O ~ ~
Y.
a , ,
3 1 1
I
_ - -
Iisrw units i and 3
-
_
-
/ (Vlieei: 7 of 'I eri-ai 1)
-
- - - - _ - -
- - - -
-_
--
-
- -
-
--
-
--
1
I
2
35 msnutes
k:nd of Unit n
Paper avad pen 8ssl ~~\\lei-rng
objcct~~es
--
- 4
I
1
(lingeek l 4 of -lerm "1)
flsrn u n l l 4
-
_ - - -- - - - -
I
._
- _
_-
_ - -_ _.
-
- - -
-
--
- -
-- -
-
3
35 mineii tes
End sf \\$(sit 5
Papel and Pen &ash coverir~g skalec:tivt:l;
I
be l~rovided
co Illat students could c.oiTrgrfip1
-
-
- -
11
I
I
frelri7 ilxg~ii 5
-
I
.
-
_
--
- -
_
- - - _-
-
- -
lei:
!
par! of the tasks aPer scllool ur during weekc~ds.
- -
-
-- - -
No more hlsan 3
pei.isds
End of Unit ?
I
F<cfc:r Po %11e
sample
(Wet;lk 9
sf 1 err!
I - - - - - .- -- -- - - - - -
E r ~ d
of Unii 3
$?,I8 sthaden& swill be rec11nirc.d to follow CI
(Weel; 9
of "I errn I)
task sln~ilar
lo lhf: .;a~nplc provided.
Studeii~ls
wil! klave to subn~i"ekie
csrripleted !ask sl~eet The: wsarksng
crilersa sl~ould
be cliscussed with the
students in adjsanee,
9)
('Te3c;her.s are rerrsjdczij n c ~ t
to use tlie
same task year after year)
.
-.
-
_
.

Activity 1 : 2
per~ods Activity I
r\\Mk 4 of 'l"ern1
"l"hese activities will Cie desigraed %cs
,4etivity 2: 2 -3
3
a ~ 5
,,,
ohjd~cfi~~es
COVC:T~I.II~
sjnits 8
to 'I 2.
,
L
>
, 4 c e "
weeks
Activities 2 8[ r.3: \\ A h "10
Refer to the ~:?i.ampde:;~ proltiided.
Acliviv 3:
"periods
'Tern 3

w2
rO-
,=-
< B
2%
cn
4 3

0
5
a-
$2 *
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1.
'The
'fst'a3a.t of r &je
exalminati~n
paper for FJG s&ri;Ai
remaiiil as it is, '['&re
I1,J&; k4a%l1err1a&#esc
paper vwil! be !-ja:;ed an Fofm?j;
4
units O S P B ~ .
2.
fak3ie 65:8uw
sasmmarises the weightibag of the uni,%s
in1 the e x a r n i n a t paper
3.
\\[iA1-8ie the er:ariiiiii.-tatiu2r1
will have a few knowledge type questions, the errlpk~asls
vvill be on wand pra;~blersas
arid ~ : ~ r n i ~ ~ i a t ~ t : ~ i r ~
2nd a p p l i c : .type c~l;,.ecstltsras.




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