yearly plan maths F3 2011

8/7/2019 yearly plan maths F3 2011

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1. LEARNING AREA: LINES AND ANGLES II

WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIES

LEARNING OUTCOMES POINTS TO NOTE VOCABULARY

1

Students will be taught to:

1.1 Understand and useproperties of anglesassociated withtransversal and parallellines.

Explore the properties ofangles associated withtransversal using dynamicgeometry software, geometrysets, acetate oerlays or tracingpaper.

Discuss when alternate andcorresponding angles are notequal.

Discuss when all anglesassociated with transversals areequal and the implication on itsconverse.

Students will be able to:

i. Identify:

a) transversalsb) corresponding anglesc) alternate anglesd) interior angles

ii. Determine that for parallel lines:

a) corresponding angles areequal

b) alternate angles are equalc) sum of interior angles is 180 .

iii. Find the values of:

a) corresponding anglesb) alternate angles

c) interior angles associatedwith parallel lines.

iv. Determine if two given lines areparallel based on the properties ofangles associated withtransversals.

v. Solve problems involving

The interior angles on thesame side of thetransversal aresupplementary.

parallel lines

transversal

alternate angle

Iiterior angle

associated correspondangle

intersecting lines

supplementary - 180

acetate overlay

1

SEKOLAH MENENGAH KEBANGSAAN TUN MUTAHIR

SCHEME OF WORK MATHEMATICS FORM 3 YEAR 2011


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properties of angles associatedwith transversals.

Limit to transversalintersecting parallel lines.

2. LEARNING AREA: POLYGONS II



1


2.1 Understand the concept ofregular polygons.

Use models of polygons andsurroundings to identify regularpolygons.

Explore properties of

polygons using rulers,compasses, protractors, gridpapers, templates, geo-boards,flash cards and dynamicgeometry software.

Include examples of non-regular polygons developedthrough activities such asfolding papers in the shape ofpolygons.

Relate to applications inarchitecture.


i. Determine if a given polygon is aregular polygon.

ii. Find:a) the axes of symmetryb) the number of axes of

symmetry of a polygon.

iii. Sketch regular polygons.

iv. Draw regular polygons by dividingequally the angle at the centre.

v. Construct equilateral triangles,squares and regular hexagons.

Limit to polygons with amaximum of 10 sides.

Construct usingstraightedges andcompasses.

Emphasise on the accuracyof drawings.

polygon

regular polygon

convex polygon

axes of symmetry

straightedges angle

equilateral triangle

square

regular hexagon

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2. LEARNING AREA: POLYGONS II



2


2.2 Understand and use theknowledge of exterior andinterior angles of polygons.

Explore angles of differentpolygons through activities suchas drawing, cutting and pasting,measuring angles and usingdynamic geometry software.

Investigate the number oftriangles formed by dividing apolygon into several triangles byjoining one chosen vertex of the

polygon to the other vertices. Include examples fromeveryday situations.


i. Identify the interior angles andexterior angles of a polygon.

ii. Find the size of an exterior anglewhen the interior angle of apolygon is given and vice versa.

iii. Determine the sum of the interiorangles of polygons.

iv. Determine the sum of theexterior angles of polygons.

v. Find:

a) the size of an interior angleof a regular polygon giventhe number of sides.

b) the size of an exterior angleof a regular polygon giventhe number of sides.

vi. Solve problems involving anglesand sides of polygons.

Interior angle

Exterior angle

ComplementaryAngle

sum

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3. LEARNING AREA: CIRCLES II



3


3.1 Understand and useproperties of circles involvingsymmetry, chords and arcs.

Explore through activities such astracing, folding, drawing andmeasuring using compasses,rulers, threads, protractors, filterpapers and dynamic geometrysoftware.


i. Identify a diameter of a circle asan axis of symmetry.

ii. Determine that:

a) a radius that is perpendicularto a chord divides the chordinto two equal parts and viceversa.

b) perpendicular bisectors oftwo chords intersect at thecentre.

c) two chords that are equal inlength are equidistant fromthe centre and vice versa.

d) chords of the same lengthcut arcs of the same length.

iii. Solve problems involvingsymmetry, chords and arcs ofcircles.

Diameter

axis of symmetry

chord

perpendicularbisector

intersect

equidistant

arc

symmetry

centre

radius

perpendicular

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3


3.2 Understand and useproperties of angles incircles.

Explore roperties of angles in acircle by drawing, cutting andpasting, and using dynamicgeometry software.


i. Identify angles subtended byan arc at the centre and at thecircumference of a circle.

ii. Determine that angles subtendedat the circumference by the samearc are equal.

iii. Determine that angles subtended:

a) at the circumference

b) at the centre by arcs of thesame length are equal.

iv. Determine the relationshipbetween angle at the centre andangle at the circumferencesubtended by an arc.

v. Determine the size of an anglesubtended at the circumferencein a semicircle.

vi. Solve problems involving angles

subtended at the centre andangles at the circumference ofcircles.

Include reflex anglesSubtended at the centre.

Angle subtended by an arcis the same as anglesubtended by thecorresponding chord.

angle

subtended

semicircle

circumference

arc

chord

reflex angle

centre

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3


3.3 Understand and use theconcept of cyclicquadrilaterals.

Explore properties of cyclicquadrilaterals by drawing, cuttingand pasting and using dynamicgeometry software.


i. Identify cyclic quadrilaterals.

ii. Identify the interior oppositeangles of cyclic quadrilaterals.

iii. Determine the relationshipbetween interior opposite anglesof cyclic quadrilaterals.

iv. Identify exterior angles and thecorresponding interior oppositeangle of cyclic quadrilaterals.

v. Determine the relationshipbetween exterior angles andthe corresponding interioropposite angle of cyclicquadrilaterals.

vi. Solve problems involving anglesof cyclic quadrilaterals.

vii. Solve problems involving circles.

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4. LEARNING AREA: STATISTICS II



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4.1 Represent and interpret datain pie charts to solveproblems.

Use everyday examples fromsources such as newspapers,magazines, reports and theinternet.

Use calculators and computersoftware in constructing pie charts.


i. Obtain and interpret informationfrom pie charts.

ii. Constuct pie charts to representdata.

iii. Solve problems involving piecharts.

iv. Determine suitable representationof data.

Relate the quantities of thedata to the size of angles ofthe sectors.

A complete pie chart shouldinclude:

i. The titleii. Appropriate labels for

the groups of data.

Pie charts are mainlysuitable for categoricaldata.

Include pictograms, barcharts, line graphs and piechart.

Discuss that representationof data depends on the typeof data.

sector

pie chart

angle

suitable

representation

construct

size of sector

quantity

data

size of angle

label

title

pictograms

bar chart

pie chart

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4. LEARNING AREA: STATISTICS II



4


4.2 Understand and use theconcept of mode, medianand mean to solve problems.

Use sets of data from everydaysituations to evaluate and toforecast.

Discuss appropriate measurementin different situations.

Use calculators to calculate themean for large sets of data.

Discuss appropriate use of mode,median and mean in certainsituations.


i. Determine the mode of:

a) sets of data

b) data given in frequencytables.

ii. Determine the mode and therespective frequency frompictographs, bar charts, linegraphs and pie charts.

iii. Determine the median for setsof data.

iv. Determine the median of datain frequency tables.

v. Calculate the mean of:

a) sets of data

b) data in frequency tables

vi. Solve problems involving mode,

median and mean.

Involve data with more thanone mode.

Limit to cases with discretedata only.

Emphasise that moderefers to the category orscore and not to thefrequency.

Include change in thenumber and value of data.

data

mode

discrete

frequency

median

arrange

odd

even

middle

frequency table

mean

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5 LEARNING AREA: INDICES



5


5.1 Understand the conceptof indices.

Explore indices using calculatorsand spreadsheets.


i. Express repeated multiplicationas a and vice versa.

ii. Find the value ofa .

iii. Express numbers in indexnotation.

Begin with squares andcubes.

a is a real number.

Include algebraic terms.

Emphasise base andIndex.

a x a x . a = an

n factors

a is the base, n is theindex.

Involve fractions andDecimals.

Limit n to positive integers.

indices

base

index

power of

index notation

index form

express

value

real numbers

repeated multiplication

factor

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5. LEARNING AREA: INDICES



5


5.2 Perform computationsinvolving multiplication ofnumbers in index notation.

5.3 Perform computationInvolving division of numbersIn index notation.

Explore laws of indices usingrepeated multiplication andcalcul tors.


i. Verify am x a = am+n

ii. Simplify multiplication of:a) numbers

b) algebraic terms

expressed in index notationwith the same base.

iii. Simplify multiplication of:

a) numbers

b) algebraic terms

expressed in index notation withdifferent bases.

i. Verify am an = am-n

ii. Simplify division of:

a) numbers

b) algebraic terms

expressed in index notation withthe same base.

Limit algebraic terms to oneunknown.

Emphasise a = 1

multiplication

simplify

base

algebraic term

verify

index notation

indices

law of indices

unknown

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5


5.4 Perform computationsinvolving raising numbersand algebraic terms in indexnotation to a power.


i. Derive (am ) =amn

ii. Simplify:

a) numbers

b) algebraic termsexpressed in index notationraised to a power.

iii. Simplify multiplication and divisionof:

a) numbers

b) algebraic terms

expressed in index notation withdifferent bases raised to a power.

iv. Perform combined operationsinvolving multiplication, division,and raised to a power on:

a) numbers

b) algebraic terms

(am ) =amn

m and n are positiveintegers.

Limit algebraic terms to oneunknown.

Emphasise:

(am x b )p = ampx b

pam= ampbn bnp

raised to a power

base

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5


5.5 Perform computationsinvolving negative indices.

Explore using repeatedmultiplications and the law ofindices.


i. Verifya - = 1a

ii. Statea - as 1and vice versaa

iii. Perform combined operations ofmultiplication, division andraising to a power involvingnegative indices on:

a) numbers

b) algebraic terms

1

i. Verifya = a .

1

ii. Statea as a and viceversa.

1

iii. Find the value ofa .

miv. Statea as:

1 1a) (am) or (a )m .

b) a or ( a ) m

n is a positive integer..

Begin with n = 1.

a and n are positiveintegers.

Begin with n = 2

verify

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5.7 Perform computationinvolving laws of indices.


v. Perform combined operationsof multiplications, division andraising to a power involvingfractional indices on

a) numbers

b) algebraic terms

mvi. Find the value ofa

i. Perform multiplication, division,raised to a power or combinationof these operations on severalnumbers expressed in indexnotation.

ii. Perform combined operations ofmultiplication, division and raisedto a power involving positive,negative and fractional indices.

Limit to positive integralroots.

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6. LEARNING AREA: ALGEBRAIC EXPRESSIONS III



6


6.1 Understand and use theconcept of expandingbrackets.

Relate to concrete examples.

Explore using computer software.


i. Expand single brackets.

ii. Expand two brackets.

Begin with linear algebraicterms.

Limit to linear expressions.

Emphasise:

(a b) (a b)

= (a b)

Include:

(a + b) (a + b)

(a b) (a b)

(a + b) (a b)

(a b) (a + b)

linear algebraic terms

like terms

unlike terms

expansion

expand

single brackets

two brackets

multiply

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6


6.2 Understand and use theconcept of factorisation ofalgebraic expression tosolve problems.

Explore using concrete materialsand computer software.


i. State factors of an algebraic term.

ii. State common factors and the aHCFfor several algebraic terms.

iii. Factorise algebraic expression:

a) using common factor

b) the difference of two squares

Emphasise the relationshipbetween expansion andfactorisation.

Note that 1 is a factor forall algebraic terms.

The difference of twosquares means:

a - b

= (a b) (a b) .

Limit to four algebraicterms.

ab ac = a(b c)

e - f = (e + f) (e f)

x+ 2xy + y = (x + y)

Limit answers to

(ax + by)

ab + ac + bd + cd

= (b + c) (a + d)

factorisation

square

common factor

term

highest common factor(HCF)

difference of twosquares

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6 Students will be taught to:


6.3 Perform addition andsubtraction on algebraic

fractions.



Relate to real-life situations


iv. Factorise and simplify algebraicfractions.


i. Add or subtract two algebraicfractions with the samedenominator.

ii. Add or subtract two algebraicfractions with one denominatoras a multiple of the otherdenominator.

iii. Add or subtract two algebraicfractions with denominators:

a) without any common factor

b) with a common factor

Begin with one-termexpressions for thenumerator anddenominator.

Limit to factorisationinvolving common factorsand difference of twosquares.

The concept of LCM maybe used.

Limit denominators to onealgebraic term.

numerator

denominator

algebraic fraction

factorisation

common factor

lowest commonmultiple (LCM)

multiple

denominator

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6


6.4 Perform multiplication anddivision on algebraicfractions.



i. Multiply two algebraic fractionsinvolving denominator with:

a) one term

b) two terms

ii. Divide two algebraic fractionsinvolving denominator with:

a) one term

b) two terms

iii. Perform multiplication and divisionof two algebraic fractions usingfactorisation involving commonfactors and the different of twosquares.

Begin multiplication anddivision withoutsimplification followed bymultiplication and divisionwith simplification.

simplification

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7. LEARNING AREA: ALGEBRAIC FORMULAE



8


7.1 Understand the concept ofvariables and constants.

7.2 Understand the concept offormulae to solve problems.

Use example of everydaysituations to explain variablesand constants.


i. Determine if a quantity in a givensituation is a variable or aconstant.

ii. Determine the variable in agiven situation and represent itwith a letter symbol.

iii. Determine the possible values of

a variable in a given situation.


i. Write a formula based on agiven:

a) statement

b) situation.

ii. Identify the subject of a givenformula.

Variables include integers,

fractions and decimals.

quantity

variable

constant

possible value

formula

value

letter symbol

formulae

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7. LEARNING AREA: ALGEBRAIC FORMULAE



Students will be taught to: iii. Express a specified variable asthe subject of a formulainvolving:

a) one of the basic operations:+, -, x,

b) powers or roots

c) combination of the basicoperations and powers or

roots.

iv. Find the value of a variable whenit is:

a) the subject of the formula

b) not the subject of the formula

v. Solve problems involvingformulae.

Symbols representing aquantity in a formula mustbe clearly stated.

Involve scientific formulae.

subject of a formula

statement

power

roots

formulae

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8. LEARNING AREA: SOLID GEOMETRY III



8

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8.1 Understand and use theconcept of volume of rightprisms and right circularcylinders to solve problems.

Use concrete models to derive theformula.

Relate the volume of right prismsto right circular cylinders.


i. Derive the formula for volume of:

a) prisms

b) cylinders.

ii. Calculate the volume of a rightprism in cubic units given theheight and:

a) the area of the base

b) dimensions of the base.

iii. Calculate the height of a prismgiven the volume and the area ofthe base.

iv. Calculate the area of the base ofa prism given the volume andthe height.

Prisms and cylinders referto right prisms and rightcircular cylindersrespectively.

Limit the bases to shapesof triangles andquadrilaterals.

derive

prism

cylinder

right circular cylinder

circular

base

radius

volume

area

cubic units

rectangle

triangle

dimension

height

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10 Students will be taught to: Students will be able to:

v. Calculate the volume of acylinder in cubic units given:

a) area of the base and theheight.

b) radius of the base and theheight

of the cylinder.

vi. Calculate the height of a

cylinder, given the volume andthe radius of the base.

vii. Calculate the radius of the baseof a cylinder given the volumeand the height.

viii.Convert volume in one metricunit to another:

a) mm3, cm3 and m3

b) cm3 , ml and l

ix. Calculate volume of liquid in acontainer.

x. Solve problems involving volumeof prisms and cylinders.

Limit the shape ofcontainers to right circularcylinder and right prisms.

cubic metre

cubic centimetre

cubic milimetre

mililitre

litre

convert

metric unit

liquid

container

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10


8.2 Understand and use theconcept of volume of rightpyramids and right circularcones to solve problems.

Use concrete models to derivethe formula.

Relate volume of pyramids toprisms and cones to cylinders.


i. Derive the formula for thevolume of:a) pyramidsb) cones.

ii. Calculate the volume ofpyramids in mm3 , cm3 and m3 ,given the height and:a) area of the baseb) dimensions of base.

iii. Calculate the height of a pyramidgiven the volume and thedimension of the base.

iv. Calculate the area of the base ofa pyramid given the volume andthe height.

v. Calculate the volume of a conein mm3 , cm3 and m3 , given theheight and radius of the base.

vi. Calculate the height of a cone,

given the volume and the radiusof the base.

vii. Calculate the radius of the baseof a cone given the volume andthe height.

viii.Solve problems involving volumeof pyramids and cones.

Inclue bases of differenttypes of polygons.

pyramid

cone

volume

base

height

dimension

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8.3 Understand and use theconcept of volume of sphereto solve problems.

8.4 Apple the concept of volumeto solve problems involvingcomposite solids.

Use concrete models to formcomposite solids.

Use examples from real-lifesituations.


i. Calculate the volume of a spheregiven the radius of the sphere.

ii. Calculate the radius of a spheregiven the volume of the sphere.

iii. Solve problems involving volumeof spheres.

i. Calculate the volume ofcomposite solids.

ii. Solve problems involvingvolumes of composite solids.

Include hemisphere

Composite solids arecombinations of geometricsolids.

sphere

hemisphere

solid

composite solid

combination

volume

radius

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9. LEARNING AREA: SCALE DRAWINGS



11-12


9.1 Understand the concept ofscale drawings.

Explore scale drawings usingdynamic geometry software, gridpapers, geo-boards or graphpapers.

Relate to maps,graphics and architecturaldrawings.


i. Sketch shapes:

a) of the same size as theobject

b) smaller than the object

c) larger than the object

using grid papers.

ii. Draw geometric shapesaccording to scale 1 : n , wheren = 1, 2, 3, 4, 5, 1 , 1 .

2 10

iii. Draw composite shapes,according to a given scale using:a) grid papersb) blank papers.

iv. Redraw shapes on grids ofdifferent sizes.

v. Solve problems involving scaledrawings.

Limit objects to two-dimensional geometricshapes.

Emphasise on the accuracyof the drawings.

Include grids of differentsizes.

Emphasise that gridsshould be drawn on the

original shapes.

sketch

draw

objects

grid papers

software

scale

geometrical shapes

composite shapes

smaller

larger

accurate

size

redraw

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10. LEARNING AREA: TRANSFORMATIONS II



13


10.1 Understand and use theconcept of similarity.

Involve examples from everydaysituations.


i. Identify if given shapes aresimilar.

ii. Calculate the lengths of

Emphasise that for atriangle, if thecorresponding angles areequal, then the

shape

similar

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10.2 Understand and use theconcept of enlargement. Explore the concept of

enlargement using grid papers,concrete materials, drawings, geo-boards and dynamic geometrysoftware.

Relate enlargement to similarity ofshapes.

unknown sides of two similarshapes.

i. Identify an enlargement.

ii. Find the scale factor, giventhe object and its image of an

enlargement when:

a) scale factor > 0b) scale factor


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object. b) lengths of the side of theimage

c) length of the side of theobject

of an enlargementvii. Determine the relationship

between the area of the image

and its object.

viii.Calculate the:

a) area of image

b) area of object

c) scale factor

of an enlargement

ix. Solve problems involvingenlargement.

Include negative scalefactors.

11. LEARNING AREA: LINEAR EQUATIONS II

WEEK LEARNING OBJECTIVES SUGGESTED TEACHING ANDLEARNING ACTIVITIES LEARNING OUTCOMES POINTS TO NOTE VOCABULARY

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11.1 Understand and use theconcept of linear equationsin two variables.

11.2 Understand and use the

concept of twosimultaneous linearequations in two variablesto solve problems.

Derive linear equations in twovariables relating to real-lifesituations.

Explore using graphic calculators,dynamic geometry software andspreadsheets to solve linearequations and simultaneous linearequations.

Use trial and improvement

method.

Use examples from real-lifesituations.


i. Determine if an equation is alinear equation in two variables.

ii. Wrtie linear equations in two

variables from given information

iii. Determine the value of a variablegiven the object variables.

iv. Determine the possible solutionsfor a linear equation in twovariables.

i. Determine if two given equations

are simultaneous linearequations.

ii. Solve two simultaneous linearequations in two variables by

a) substitution

b) elimination

iii. Solve problems involving twosimultaneous linear equations intwo variables.

Include letter symbols other

than xand yto representvariables.

equation

variable

linear equation

value

possible sollution

linear equation

variable

simultaneous linearequation

solution

substitution

elimination

12. LEARNING AREA: LINEAR INEQUALITIES



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15


12.1 Understand and use theconcept of inequalities.

Use everyday situations toillustrate the symbols and the useof > , or b isequivalent to b < a.

> read as greater than.


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15


12.2 Understand and use theconcept of linearinequalities in oneunknown.


i. Determine if a given relationshipis a linear inequality.

ii. Determine the possible solutionsfor a given linear inequality in

one unknown:

a) x> h;

b) x< h;

c) x h;

d) x h.

iii. Represent a linear inequality:

a) x> h;

b) x< h;

c) x h;

d) x h.

on a number line and vice versa.

h is a constant, xis aninterger.

relationship

linear

unknown

number line




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12.3 Perform computationsinvolving adding,subtraction, multiplicationand division on inequalities.

Involve examples from everydaysituations.


iv. Construct linear inequalitiesusing symbols:

a) > or


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Students will be taught to: Students will be able to:

iii. Construct inequalities

a) x + k > m + k

b) x k > m - k

c) kx > km

d) x > mk k

from given information.

Information given from real-life situations.

Include also


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12.4 Perform computations tosolve inequalities in onevariable.

Explore using dynamic geometrysoftware and graphic calculators.


i. Solve a linear inequality by:

a) adding a number

b) subtracting a number

on both sides of the inequality.

ii. Solve a linear inequality by

a) multiplying a number

b) dividing a number

on both sides of the inequality

iii. Solve linear inequalities in onevariable using a combination ofoperations.

Emphasise that for asolution, the variable iswritten on the left side ofthe inequalities.

add

subtract

multiply

divide




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12.5 Understand the concept ofsimultaneous linearinequalities in one variable


i. Represent the common values oftwo simultaneous linearinequalities on a number line.

ii. Determine the equivalentinequalities for two given linearinequalties.

iii. Solve two simultaneous linearinequalities.

Emphasise the meaning ofinequalities such as:

i. a < x < b

ii. a x b

iii. a x < b

iv. a < x b

Emphasise that forms suchas:

i. a > x < b

ii. a < x b

iii. a < x > b

are not accepted.

determine

common value

simultaneous

combining

linear inequality

number line

equivalent

13. LEARNING AREA: GRAPH OF FUNCTIONS



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13.1 Understand and use theconcept of functions.

13.2 Draw and use graphs offunctions.

Explore using function machines.


i. State the relationship betweentwo variables based on the giveninformation.

ii. Identify the dependent andindependent variables in a givenrelationship involving twovariables.

iii. Calculate the value of thedependent variables, given thevalue of the independentvariable.

i. Construct tables of values forgiven functions.

ii. Draw graphs of functions usinggiven scale.

iii. Determine from graph the valueofy, given value ofxand viceversa.

iv. Solve problems involving graphsof functions.

Involve functions such as:

i. y = 2x + 3

ii. p = 3q2 + 4q 5

iii. A = B3

iv. W = 1Z

Limit to linear, quadraticand cubic functions.

Include cases when scalesare not given

function

relationship

variable

dependent variable

independent variable

ordered pairs

coordinate plane

table of values

origin

graph

x-coordinate

y-coordinate

x-axis

y-axis

scale

14. LEARNING AREA: RATIOS, RATES AND PROPORTIONS II



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13.2 Understand and use theconcept of speed.

Use examples from everydaysituations.


i. Identify the two quantitiesinvolved in speed.

ii. Calculate and interpret speed.

iii. Calculate:

a) the distance, given thespeed and the time

b) the time, given the speedand the distance.

iv. Convert speed from one unit ofmeasurement to another.

v. Differentiate between uniformspeed and non-uniform speed.

Moral values related totraffic rules should beincorporated.

Include the use of graphs.

speed

distance

time

uniform

non-uniform

differentiate

14. LEARNING AREA: RATIOS, RATES AND PROPORTIONS II



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14.3 Understand and use theconcept of average speed.

14.4 Understand and use theconcept of acceleration.

MID YEAR EXAMINATION

Use examples from dailysituations.

Discuss the difference between

average speed and mean speed.


i. Calculate the average speed invarious situations.

ii. Calculate:

a) the distance, given theaverage speed and thetime.

b) the time, given theaverage speed and thedistance.

iii. Solve problems involvingspeed and average speed.

i. Identify the two quantitiesinvolved in acceleration.

ii. Calculate and interpretacceleration.

Include cases ofretardation.

average speed

distance

time

acceleration

retardation

15. LEARNING AREA: TRIGONOMETRY



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15.1 Understand anduse tangent of an acuteangel in a right-angledtriangle.


Understand and use sine ofan acute angle in a right-angled triangle

Use right-angled triangles with realmeasurements and developthrough activities.

Discuss the ration of the oppositeside to the adjacent side when theangle approaches 90.

Explore tangent of a given anglewhen:

a) The size of the triangle variesproportionally.

c) The size of angle varies.

Explore sine of a given anglewhen:

a) The size of the trianglevaries proportionally.

b) The size of the angle varies


i. Identify the:

a) hypotenuse

b) the opposite side and theadjacent side with respectto one of the acute angles.

ii. Determine the tangent of anangle.

iii. Calculate the tangent of anangle given the lengths ofsides of the triangle.

iv. Calculate the lengths of sidesof a triangle given the value oftangent and the length of

another side.Students will be able to:

i. Determine the sine of an angle.

ii. Calculate the sine of an anglegiven the lengths of sides of thetriangle.

iii. Calculate the lengths of sides ofa triangle given the value of sineand the length of another side

Use only right-angledtriangle.

Tangent can be written as

tan .

Emphasise that tangent is aratio.

Limit to opposite andadjacent sides.

Include cases that requirethe use of PythagorasTheorem.

Sine can be written assin .

right-angled triangle

angle

hypotenenuse

opposite side

adjacent side

ratio

tangent

value

length

size




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15.2 Understand anduse consine of an acuteangle in a right-angledtriangle.

Explore cosine of a given anglewhen:

a) The size of the triangle

varies proportionally.

b) The size of the angle varies.


i. Determine the cosine of anangle.

ii. Calculate the cosine of an anglegiven the lengths of sides of thetriangle.

iii. Calculate the lengths of sides ofa triangle given the value ofcosine and the length of anotherside.


Cosine can be written ascos .


ratio

right-angled triangle

length

value

hypotenuse

opposite side

size

constant

increase

proportion




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15.4 Use the values of tangent,sine and cosine to solveproblems.


i. Calculate the value of othertrigonometric ratios given thevalue of a trigonometric ratio.

ii. Convert the measurement ofangles from:

a) degrees to degrees andminutes.

b) degrees and minutes todegrees.

iii. Find the value of:

a) tangent

b) sine

c) cosine

of 30, 45 and 60 without usingscientific calculator.

iv. Find the value of:

a) tangent

b) sine

c) cosine

using scientific calculator.

Include angles expressedin:

i. Degrees

ii. Degrees and minutes.

degree

minute

tangent

sine

cosine

15. LEARNING AREA : TRIGONOMETRY

WEEK LEARNING OBJECTIVES SUGGESTED TEACHINGAND


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LEARNING ACTIVITIESStudents will be taught to: Students will be able to:

v. Find the angles giventhe values of:

a) tangent

b) sine

c) cosine

using scientificcalculators.

vi.Solve problems involvingtrigonometric ratios.

angle

degree

minute

tangent

sine

cosine

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yearly plan maths F3 2011

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Transcript of yearly plan maths F3 2011