SECONDARY SCHOOL LEVEL FORMS 1-4 · · 2019-07-08Introduction The critical documents assist you the teacher in delivering Mathematics effectively and guide learners in handling

ZIMBABWE

MINISTRY OF PRIMARY AND SECONDARY EDUCATION

MATHEMATICS

FORMS 1-42015-2022

TEACHER’S GUIDE

Curriculum Development Unit P.O.BOX MP133 Mount PleasantHarare

© All Rights ReservedCopyright 2015

CURRICULUM DEVELOPMENT AND TECHNICAL SERVICES

SECONDARY SCHOOL LEVEL

Mathematics Teachers’ Guide 2015-2022 Forms 1-4

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ACKNOWLEDGEMENTS

The Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued contribution in the production of this teacher’s guide:

z Curriculum Development and Technical Services (CDTS) Staff z The National Mathematics panel z United Nations Children’s Fund (UNICEF) for funding


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CONTENTS PAGE

Acknowledgements ..........................................................................................................2

Organisation of the guide .................................................................................................4

Critical Documents ...........................................................................................................4

UNIT 1: Curriculum framework for Zimbabwe Primary and Secondary Education ...........5

UNIT 2: Syllabus Interpretation ........................................................................................6

UNIT 3: Scheme of work...................................................................................................8

UNIT 4: Lesson Plans .....................................................................................................10

UNIT 5: Record Keeping .................................................................................................14

PART B: Curriculum Delivery ..........................................................................................15

UNIT 6: Scope of the guide ............................................................................................19

Annexure ........................................................................................................................21


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1.0 ORGANISATION OF THE GUIDE

In developing the Mathematics Teachers’ Guide, attention was paid to the need to further the teachers’ understanding and interpretation of the national syllabus. This teachers’ guide was cre-ated to guide you the teacher as you embark on teaching of Mathematics from form 1-4 in the new curriculum. The teachers’ guide provides progression from one level to another and also to link the developmental stages of learners and their learning abilities to relevant competencies and methodologies. This Teachers’ Guide will be divided into two sections;

Part A: critical documents Part B: curriculum delivery.

2.0 PART A: CRITICAL DOCUMENTS

Introduction

The critical documents assist you the teacher in delivering Mathematics effectively and guide learners in handling this new learning area.

You should have access the following Critical Documents: z Curriculum Framework z National Syllabus z School syllabus z Schemes of Work/Scheme Cum Plan z Lesson Plan z Records

Rationale

It is imperative that learners acquire necessary mathematical knowledge, skills and develop a positive attitude. This will enable learners to be creative thinkers, problem solvers and communi-cators with values of unhu/vumunhu/Ubuntu such as discipline, integrity and honesty. The knowl-edge of mathematics enables learners to develop mathematical skills such as accuracy, research, logical and analytical competencies essential for sustainable development in life. The importance of mathematics can be under pinned in inclusivity and human dignity and is a universal language that cuts across all boundaries and unifies diverse cultures. Mathematics plays a pivotal role in careers such as enterprise, education, medicine, agriculture, meteorology and engineering.This teachers’ guide promotes innovativeness confidence and self-actualisation. It is designed to cover Mathematics at Ordinary Level. The guide assists you as a teacher in planning your work.

Objective

This Guide was developed for the teacher to understand the importance and use of the critical documents in the new curriculum delivery.


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UNIT 1

CURRICULUM FOR PRIMARY AND SECONDARY EDUCATION 2015-2022

Introduction

This is a policy document that outlines underpinning principles, national philosophy, learning are-as, the description and expectations of MOPSE at policy level. It prescribes what the government expects you to deliver as you go about your duties. The document outlines the issue of skill-based approaches in every learning area. The document also clearly explains the aspiration of the Min-istry of Primary and Secondary Education, which is to enable all learners to develop their capac-ities as successful learners confident individual, responsible citizen and effective contributors to Zimbabwe.

Objectives

z interpret the national syllabuses and translate them into meaningful and functional school syllabuses, schemes of work and record books

z prepare relevant daily teaching notes z appreciate and understand the need to keep and maintain useful, comprehensive and up to

date class records z make and use relevant teaching and learning materials in the delivery of your lessons z acquire and use effective teaching techniques suitable for the subject and level of learners z acquire and demonstrate skills of setting reliable and valid test/ examination questions z cope with specific problem areas in language teaching z design appropriate strategies for problem solving z manage your class effectively z be resourceful z guide learners to study effectively on their own z objectively evaluate your own teaching and the learners’ progress

Key Elements

z Background z Principles and Values Guiding the Curriculum z Goals of the Curriculum z Learning Areas z Teaching and learning Methods z Assessment and Learning z Strategies for effective implementation z The Future


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UNIT 2

SYLLABUS INTERPRETATION

Introduction

Syllabus interpretation is the process of making sense of the syllabus. Interpretation is about find-ing meaning. It is the process of unpacking the syllabus, analysing it and synthesising it.

Objectives

The following are objectives for syllabus interpretation

z To help the teacher to share the same meaning with the developer. z To put the teachers’ at the same level. z To assist the teacher to implement the new curriculum z To achieve the assessment objectives. z To assist the teacher in scheming and planning.

Types of Syllabuses

There are two types of syllabuses namely z National Syllabus z School syllabus

National Syllabus

It is a policy document that outlines and specifies the learning area philosophy, aims and objec-tives, Learning/teaching concepts and content, suggested methodology and assessment criteria at every grade level. As a teacher you should always have it and use it to guide you in your day to day teaching and learning activities.

It is a major curriculum document which prescribes what government would like to see taught in all schools as spelt out in the curriculum framework and outlines the experiences that learners should undergo in a particular course of study: infant, junior, secondary.

Elements

The national syllabus consists of: z Preamble z Presentations of syllabus z Aims z Objectives z Topics z Methodology z Time Allocation z Scope and sequence z Competency Matrix z Assessment z Appendix


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Content

z Real Numbers z Sets z Financial Mathematics z Measures and Mensuration z Graph z Variation z Algebra z Geometry z Statistics z Trigonometry z Vectors z Matrices z Transformation z Probability

2.2 School Syllabus

It is a breakdown of the national syllabus which is drafted at school level with experts from the learning area by reorganising content taking into account local factors.

Factors Influencing drafting:

In coming up with the school syllabus the following should be taken into consideration z Level of learner performance (Knowledge they already have) z Availability of resources z Time allocation in the official syllabus z Attitudes and values of some topics by learners and teachers z Education technology

Elements

The School syllabus consists of: z Preamble z Presentations of syllabus z Aims z Objectives z Topics z Methodology z Time Allocation z Scope and sequence z Competence Matrix z Content Matrix z Assessment z Appendix


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UNIT 3

Scheme of work

This is a document that you as a teacher should draw from the national and school syllabus. You should outline the Week ending/cycle ending, Topic/Content, Objectives, Competencies/Skills/Knowledge, Sources of Material/Media, Suggested Resources, Methods or Activities and Evalua-tion. It’s a weekly breakdown of activities which should enable you to organise teaching activities from the topics which are set in the syllabus. You as a teacher should draw your scheme of work /Scheme-cum plan two weeks ahead of lesson delivery date. (USE OF ICT IN DRAWING THE DOCUMENTS IS ENCOURAGED).

A well-prepared Scheme of work does the following: z Give an overview of the total course content z Provide for a sequential listing of learning tasks z Show a relationship between content and resource materials z Provide a basis for long range planning and evaluation of the learning area

COMPONENTS

The components of a scheme of work include the following aspects:

z Level of learners Form 3 z Learning Area : Mathematics z Aims (Extract from the national syllabus) z Week ending: dd/mm/year z Topic/Content: Content from simple to complex z Objectives: Should be SMART (Specific ,Measurable, Accurate, Result Oriented and Time

framed z Competencies/skills/Knowledge: Any skill that the learner has to achieve z Source of material /media: eg Reference of national syllabus ,textbooks z Suggested Resources: eg ICT tools z Methods/Activities: z Evaluations

EXAMPLE FORM 3 SCHEMES OF WORKLearning area: MathematicsAims: By the end of the term learners should be able to:

z develop an understanding of mathematical concepts and processes in a way that encourages confidence, enjoyment and interest

z further acquire appropriate mathematical skills and knowledge z develop the ability to think clearly, work carefully and communicate mathematical ideas

successfully z apply mathematics in other learning areas and in life z develop an appreciation of the role of mathematics in personal, community and national

development z engage, persevere, collaborate and show intellectual honesty in performing tasks in

mathematics, in the spirit of Unhu/ Ubuntu/Vumunhu z use I.C.T tools to solve mathematical problems


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UNIT 4

Lesson Plan

This is a detailed daily plan of what you intend to deliver during the lesson. This is to be used in the event of you having drawn a scheme of work rather than a scheme- cum plan.

DETAILED LESSON PLAN

CLASS: Form 3

LERANING AREA: Mathematics

DATE: 16 Feb 2016

TIME: 1030hrs – 1110hrs

NUMBERT OF LEARNERS:35

TOPIC: Inequalities

Content

z Simultaneous inequalities z Graphs of inequalities

S.O.M /MEDIA

- Mathematics Form 1-4 National syllabus Page 55 ,relevant text,Talking books/software

ASSUMED KNOWLEDGE:

Learners are able to solve linear equations and linear inequalities, be familiar with inequality signs as well as number line and Cartesian plane

LESSON OBJECTIVES

During the lesson learners will: z solve simultaneous linear inequalities in one variable z represent solution set on line graph solve simultaneous linear inequalities graphically


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STAGE CONTENT ORGANISATION COACHING POINTS

Introduction (5 min)

Lesson development (30min)

Conclusion (5min)

LESSON EVALUATION:

Strength: ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

Weaknesses: ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................Way forward: ................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

-Teacher introduces the lesson by asking ques-tions on the assumed knowledge-Learners answer ques-tions, give examples as well as asking questions if they have

-individual

-Illustration on the white-board by the teacher-Class discussion-Solving simultaneous linear inequalities in one variable be learners-Learners to discuss and represent inequalities on a number line

-in pairs learners solve si-multaneous linear inequali-ties-group discussion on rep-resenting inequalities on a number line

- group present their discus-sions whilst the whole class assist them

-learners to recall that divid-ing or multiplying both sides of an inequality by a nega-tive number reverses the sign

-concepts learnt -feedback by learners and teacher


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UNIT 5

RECORD - KEEPING

Records are critical documents about the teaching – learning process, which you must keep as a teacherThey include:

- Syllabuses (National and School)- Staff (for HOD’s) and pupil details- Continuous assessment and examination mark lists- Stock control registers- Attendance register

TYPES OF RECORDS

- Official syllabuses- School syllabuses- Attendance Register- Records of staff details- Records of learner details- Supervision records- Files, circulars, handouts, past exam papers- Minutes of meetings- Inventory of resource materials- Stock control registers- Learner Profiles

CONCLUSION

Critical Documents are a must that you as a teacher must have for effective teaching and learning to take place .You need to be familiar with the requirements of the New Curriculum by reading the Curriculum Framework for Primary and Secondary Education and not by just having it. As a teach-er you need to scheme, plan and prepare for your lessons well in advance to show preparedness and commitment to work.


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PART B CURRICULUM DELIVERY

Introduction

This section comprises of the objectives, content, methodology, teaching-learning materials, class management, evaluation and assessment. These assists you as a teacher in lesson delivery.

OBJECTIVES (EXAMPLES)

By the end of this unit, you should be able to:- select appropriate teaching methods for your lessons - design meaningful and effective instructional material- use a variety of learner-centred approaches- plan and organise educational tours- help pupils carry-out projects or experiments - make good quality aids from available resources

(Types: charts, chalkboard, whiteboard, computers slides, films, videos, flannel graph, textbooks )

CONTENT

The following is the content you should cover: z Real Numbers z Sets z Financial Mathematics z Measures and Mensuration z Graphs z Variation z Algebra z Geometry z Statistics z Trigonometry z Vectors z Matrices z Transformation z Probability

METHODOLOGY

As a teacher it is important for you to use problem solving and learner–centred approaches. You are the facilitator and the learner is the doer. You should select appropriate teaching methods for your lessons. They should be varied and motivating. You should select one or several methods depending on:

z The subject matter z Instructional objectives z The learner z Your personality z Learners level of development (cognitive, affective and psychomotor)) z Content to be covered z The time z Learning material


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z The environment z Competencies to be developed

Teaching methods can be grouped under three main categories:

a) Cognitive development methods

These are mainly: z Discussion Method z Socratic (Question and answer) z Team Teaching Method z Self-activity/independent learning z Educational tours Method z Group work z Problem solving

b) Affective development methods

z Modelling Method z Simulation Method z Observation z Exposition z Lecture

c) Psychomotor development methods

z Inquiry z Interactive e-learning z Guided Discovery z Demonstration and illustration Method z Experimentation Method z Programmed Learning Method z Assignment Method z Research z Project Method z Microteaching Method

CROSS CUTTING ISSUES

z Life skills z Enterprise skills z Financial literacy z ICT z HIV and AIDS z Environmental issues z Disaster Risk management z Collaboration


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TEACHING - LEARNING MATERIALS

These are materials which help the learner to learn effectively, faster, capture learners’ interest and create virtual reality.

EXAMPLES

z ICT tools z Geo-Board z Environment z Relevant texts z Braille materials and equipment z Talking books z Charts z Whiteboard or Chalkboard z Videos

ASSESSMENT AND EVALUATION

Is the measure of success or failure in the teaching-learning process and provides feedback on the acquisition of knowledge and skills by learners as well as attitude.

EXAMPLES

Tests and exercisesAssignmentsExaminationsProjectsPresentations

CLASS MANAGEMENT

This is a process of planning, organising, leading, controlling classroom activities and maintaining discipline to facilitate an effective learning environment hence motivating learners.

Organisational skills for effective learning

This covers classroom organization from:

z Physical environment

- Classroom to be clean, tidy and airy - Safety considerations when arranging furniture- Teaching aids to be visible to learners.

z Emotional environment

- You need to be pleasant, firm but friendly. - set the right tone- tell learners what you expect from them.


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z Grouping- You may group your learners according to needs, abilities, and be gender sensitive. - Encourage them to share ideas in groups.

z Class control and discipline

- be prepared for the lesson- Be familiar with the schools policy on discipline. - Be firm but fair- Acknowledge good behaviour- Punishments must be corrective and to the benefit of the child. - create an atmosphere of trust and honesty

z Motivation

- Make your learners feel important through recognizing and rewarding achievements- encouraging those who are lagging behind to continue working hard.- Knowing learners by their names creates good rapport. - Be a role model to your learners

. z Supervision

- Always check learners’ work in order to guide and correct them.- Give immediate feedback in order to motivate learners.


19

UNIT 6

SCOPE OF THE GUIDE

TOPICS The following topics are to be covered from form 1-4

z Real Numbers z Sets z Financial Mathematics z Measures and Mensuration z Graphs z Variation z Algebra z Geometry z Statistics z Trigonometry z Vectors z Matrices z Transformation z Probability

TOPIC (breakdown)

GEOMETRY

z Points, lines and angles z Bearings z Polygons and circles z Similarity and congruency z Constructions and loci z Symmetry

CONTENT ACTIVITIES METHODOLOGY MATERIALS EVALUATIONSGeometry

z Triangles z Quadrilaterals

z Constructing triangles and quadrilaterals

z Solving problems using construction of tri-angles and quadri-laterals

z Problem solving

z Discussion z Problem solving z Experimentation z Demonstration

and illustration z Interactive

e-learning

z ICT tools z Maths set z Environment z Relevant texts z Braille material

and equipment z Talking books z Talking soft-

ware

Should show strength and weaknesses of methodology, and whether objectives were achieved. Map the way forward.


20

TEACHABLE UNIT: CONSTRUCTION AND LOCI (hints)

NB . break down all the topics using the format above

FORM 1 FORM 2 FORM 3 FORM 4

Real numbers Real numbers Real numbers

Sets Sets Sets

Financial mathematics Financial mathematics Financial mathematics Financial

mathematics

Measures and Measures and Mensuration Mensuration

mensuration mensuration

Graphs Graphs Graphs Graphs

Variation Variation Variation

Algebra Algebra Algebra Algebra

Geometry Geometry Geometry Geometry

Statistics Statistics Statistics Statistics

Trigonometry trigonometry

Vectors Vectors Vectors

Matrices Matrices

Transformations Transformations Transformations Transformations

Probability Probability Probability

CONCLUSION

This part on curriculum delivery assists you the teacher on expectations during lesson delivery eg classroom management and breaking down of topics. The guide might not have exhausted everything that is essential for curriculum delivery hence you are allowed to exploit more.


21

31

SC

OP

E A

ND

SE

QU

EN

CE

7.

1 R

eal n

um

ber

s

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Num

ber

Con

cept

s an

d O

pera

tions

Num

ber

type

s

Fac

tors

and

m

ultip

les

D

irect

ed n

umbe

rs

F

ract

ions

and

pe

rcen

tage

s

Ord

er o

f ope

ratio

ns

F

acto

rs a

nd

mul

tiple

s

Squ

ares

and

squ

are

root

s

Cub

es a

nd c

ube

root

s

O

rder

of o

pera

tions

Irra

tiona

l num

bers

Num

ber

patte

rns

App

roxi

mat

ions

and

es

timat

ions

R

ound

off

num

bers

Dec

imal

pla

ces

S

igni

fican

t fig

ures

Est

imat

ions

Sig

nific

ant f

igur

es

E

stim

atio

ns

Li

mits

of a

ccur

acy

Rat

ios,

rat

es a

nd

prop

ortio

ns

R

atio

s

R

atio

s

Pro

port

ions

Rat

ios

R

ates

Pro

port

ions

Ord

inar

y an

d st

anda

rd

form

Larg

e an

d sm

all

num

bers

Num

bers

in

stan

dard

form

Ope

ratio

ns in

st

anda

rd fo

rm

Num

ber

base

s

Num

ber

base

s in

ev

eryd

ay li

fe

P

lace

val

ues

C

onve

rtin

g nu

mbe

rs

from

one

bas

e to

an

othe

r

O

pera

tions

in

num

ber

base

s

Sca

les

and

sim

ple

map

pr

oble

ms

S

cale

mea

sure

men

t

Sca

le d

raw

ing

S

cale

s

Leng

th fa

ctor

Are

a fa

ctor

AN

NE

XT

UR

E 1

: SC

OP

E A

ND

SE

QU

EN

CE

TOP

ICS

FO

R E

AC

H L

EV

EL


22

32

7.2

Set

s

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

S

ets

Set

s an

d S

et

nota

tion

T

ypes

of s

ets

T

ypes

of s

ets

V

enn

diag

ram

with

tw

o su

bset

s

S

et B

uild

er N

otat

ion

V

enn

diag

ram

s w

ith

thre

e su

bset

s

7.3

Fin

anci

al M

ath

emat

ics

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Con

sum

er a

rithm

etic

Hou

seho

ld b

ills

P

rofit

and

loss

Dis

coun

t

Hou

seho

ld b

udge

ts

C

orpo

rate

bill

s

P

rofit

and

loss

Sim

ple

inte

rest

Hire

pur

chas

e

Sm

all s

cale

en

terp

rise

budg

ets

B

ank

stat

emen

ts

C

ompo

und

inte

rest

Com

mis

sion

Hire

pur

chas

e

F

orei

gn e

xcha

nge

S

ales

and

inco

me

tax

rate

s (P

ay a

s yo

u ea

rn (

PA

YE

))

V

alue

add

ed ta

x (V

AT

)

Cus

tom

s an

d E

xcis

e D

uty


23

33

7.4

Mea

sure

s an

d M

ensu

rati

on

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Mea

sure

s

Uni

ts o

f :

- T

ime

- M

ass

- Le

ngth

-

Tem

pera

ture

-

Cap

acity

Uni

ts o

f: - A

rea

- V

olum

e -

Cap

acity

-

Den

sity

Men

sura

tion

Per

imet

er o

f pla

ne s

hape

s

Are

a of

pla

ne s

hape

s

P

erim

eter

of p

lane

sh

apes

Are

a of

pla

ne s

hape

s

Vol

ume

of c

uboi

ds

P

erim

eter

of

com

bine

d sh

apes

Are

a of

com

bine

d sh

apes

Vol

ume

of

cylin

ders

A

rea

and

volu

mes

of

sol

id s

hape

s

Sur

face

are

a

Den

sity

7.5

Gra

ph

s

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Fun

ctio

nal G

raph

s

C

arte

sian

pla

ne

S

cale

Co-

ordi

nate

s

C

arte

sian

pla

ne

T

able

of v

alue

s

Line

ar g

raph

s

Sca

le

F

unct

iona

l Not

atio

n

Li

near

gra

phs

Q

uadr

atic

gra

phs

C

ubic

gra

phs

In

vers

e gr

aphs

Tra

vel G

raph

s

Dis

tanc

e tim

e gr

aphs

Dis

tanc

e tim

e gr

aphs

Dis

tanc

e tim

e gr

aphs

Spe

ed-t

ime

grap

hs

D

ispl

acem

ent t

ime

grap

hs

V

eloc

ity-t

ime

grap

hs


24

34

7.6

Var

iati

on

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Var

iatio

n

D

irect

var

iatio

n

D

irect

var

iatio

n

Inve

rse

varia

tion

Jo

int v

aria

tion

P

artia

l var

iatio

n

7.7

A

lgeb

ra

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Alg

ebra

ic M

anip

ulat

ion

B

asic

arit

hmet

ic

proc

esse

s in

lette

r sy

mbo

ls

S

ubst

itutio

n of

va

lues

Alg

ebra

ic

expr

essi

ons

S

ubst

itutio

n of

va

lues

Alg

ebra

ic

expr

essi

ons

A

lgeb

raic

frac

tions

Qua

drat

ic

expr

essi

ons

F

acto

risat

ion

A

lgeb

raic

frac

tions

Hig

hest

Com

mon

F

acto

r (H

CF

) an

d Lo

wes

t Com

mon

M

ultip

le (

LCM

) of

al

gebr

aic

expr

essi

ons

Q

uadr

atic

ex

pres

sion

s

Fac

toris

atio

n

A

lgeb

raic

frac

tions

Qua

drat

ic

expr

essi

ons

F

acto

risat

ion

Com

plet

ing

the

squa

re

Equ

atio

ns

Li

near

equ

atio

ns

E

quat

ions

with

br

acke

ts

E

quat

ions

with

fr

actio

ns

C

hang

e of

sub

ject

of

form

ulae

Sim

ulta

neou

s lin

ear

equa

tions

S

imul

tane

ous

equa

tions

Qua

drat

ic e

quat

ions

Cha

nge

of s

ubje

ct in

fo

rmul

ae

Sub

stitu

tion

of

valu

es

C

ompl

etin

g th

e sq

uare

Qua

drat

ic fo

rmul

ae


25

35

Q

uadr

atic

equ

atio

ns

Ineq

ualit

ies

Line

ar in

equa

litie

s

Line

ar in

equa

litie

s

Num

ber

line

C

arte

sian

pla

ne

S

imul

tane

ous

ineq

ualit

ies

G

raph

s of

in

equa

litie

s

Li

near

pro

gram

min

g

Indi

ces

and

Log

arith

ms

Inde

x fo

rm

La

ws

of in

dice

s

Hig

hest

Com

mon

F

acto

r (H

CM

) an

d Lo

wes

t Com

mon

M

ultip

le (

LCM

) in

in

dex

form

Squ

ares

and

squ

are

root

s

Cub

es a

nd c

ube

root

s

In

dice

s

Lo

garit

hms

The

ory

of

loga

rithm

s

Equ

atio

ns

invo

lvin

g in

dice

s an

d lo

garit

hms


26

36

7. 8

G

eom

etry

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Poi

nts,

line

s an

d an

gles

Poi

nts

Line

s

A

ngle

s

A

ngle

s

Par

alle

l and

T

rans

vers

al li

nes

A

ngle

s of

ele

vatio

n an

d de

pres

sion

Bea

ring

Car

dina

l poi

nts

T

hree

figu

re b

earin

g

Com

pass

bea

ring

T

hree

figu

re

bear

ing

C

ompa

ss b

earin

g

Pol

ygon

s

P

olyg

ons

Pro

pert

ies

of p

olyg

ons

(tria

ngle

s an

d qu

adril

ater

als)

P

rope

rtie

s of

po

lygo

ns

A

ngle

s an

d pr

oper

ties

of

poly

gons

Num

bers

of s

ides

of

poly

gons

C

ircle

theo

rem

s

Sim

ilarit

y an

d C

ongr

uenc

y

S

imila

r an

d co

ngru

ent

figur

es

C

ases

of c

ongr

uenc

y

A

reas

of s

imila

r fig

ures

Vol

ume

and

mas

s of

si

mila

r so

lids

Con

stru

ctio

ns a

nd L

oci

C

onst

ruct

ion

of

lines

and

ang

les

C

onst

ruct

ion

of a

ngle

s

Bis

ectin

g lin

es a

nd

angl

es

C

onst

ruct

ion

of

tria

ngle

s an

d qu

adril

ater

als

C

onst

ruct

ion

of

diag

ram

to a

sca

le

Lo

ci

Sym

met

ry

Line

sym

met

ry in

two

dim

ensi

ons

Rot

atio

nal s

ymm

etry

in

two

dim

ensi

ons


27

37

7.9

Sta

tist

ics

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Dat

a C

olle

ctio

n,

Cla

ssifi

catio

n an

d R

epre

sent

atio

n

D

ata

colle

ctio

n

Dat

a cl

assi

ficat

ion

Dat

a co

llect

ion

C

lass

ifica

tion

of

ungr

oupe

d da

ta

C

olle

ctio

n an

d cl

assi

ficat

ion

of

grou

ped

data

Fre

quen

cy ta

ble

P

ie c

hart

His

togr

am

F

requ

ency

pol

ygon

F

requ

ency

tabl

e

Fre

quen

cy

poly

gon

C

umul

ativ

e fr

eque

ncy

tabl

e

Cum

ulat

ive

freq

uenc

y cu

rve

Mea

sure

s of

Cen

tral

T

ende

ncy

Mea

n

Mod

e

Med

ian

A

ssum

ed m

ean

M

ean,

med

ian

and

mod

e of

gro

uped

da

ta

A

ssum

ed m

ean

M

edia

n fr

om

cum

ulat

ive

freq

uenc

y cu

rve

Mea

sure

s of

Dis

pers

ion

Qua

rtile

s

Inte

r qu

artil

e ra

nge


28

38

7.10

Tri

go

no

met

ry

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Pyt

hago

ras

The

orem

Pyt

hago

ras

theo

rem

Pyt

hago

rian

trip

ple

Trig

onom

etric

al R

atio

s

Trig

onom

etric

al

ratio

s of

acu

te

angl

es:

- si

ne

- co

sine

-

tang

ent

T

rigon

omet

rical

ra

tios

of o

btus

e an

gles

: -

sine

-

cosi

ne

- ta

ngen

t

C

osin

e ru

le

S

ine

rule

Are

a of

a tr

iang

le


29

39

7.11

V

ecto

rs

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Def

initi

on a

nd N

otat

ion

Def

initi

on o

f vec

tor

V

ecto

r no

tatio

n

Typ

es o

f Vec

tors

T

rans

latio

n ve

ctor

s

Neg

ativ

e ve

ctor

s

Equ

al v

ecto

rs

P

aral

lel v

ecto

rs

T

rans

latio

n

N

egat

ive

Equ

al

P

aral

lel

P

ositi

on

Ope

ratio

ns

Add

ition

of v

ecto

rs

S

ubtr

actio

n of

ve

ctor

s

A

dditi

on o

f vec

tors

Sub

trac

tion

of

vect

ors

sc

alar

mul

tiplic

atio

n

Mag

nitu

de

C

ombi

ned

vect

or

oper

atio

ns

V

ecto

r pr

oper

ties

of

plan

e sh

apes


30

40

7.12

Mat

rice

s

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Ord

er

Ord

er o

f mat

rices

T

ypes

of m

atric

es

Ope

ratio

ns

A

dditi

on a

nd

Sub

trac

tion

of

mat

rices

S

cala

r m

ultip

licat

ion

of m

atric

es

M

ultip

licat

ion

of

mat

rices

Det

erm

inan

ts

D

eter

min

ants

of

Mat

rices

S

ingu

lar

and

non-

sing

ular

mat

rices

Inve

rse

Mat

rix

In

vers

e of

mat

rix

S

imul

tane

ous

linea

r eq

uatio

ns in

2

varia

bles


31

41

7.13

T

ran

sfo

rmat

ion

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Tra

nsla

tion

T

rans

latio

n of

pla

ne

figur

es

T

rans

latio

n ve

ctor

to

mov

e a

poin

t

tran

slat

ion

vect

or to

m

ove

a pl

ane

figur

e on

Car

tesi

an p

lane

Ref

lect

ion

R

efle

ctio

n of

pla

ne

figur

es

R

efle

ctio

n of

pla

ne

figur

es o

n a

Car

tesi

an p

lane

in

the

x-ax

is, y

-axi

s,

lines

of t

he fo

rm y

=a

and

x=b

R

efle

ctio

n of

pla

ne

figur

es in

any

line

an

d us

e of

mat

rices

Rot

atio

n

R

otat

ion

of p

lane

fig

ures

in a

C

arte

sian

pla

ne b

y dr

awin

g

R

otat

ion

of p

lane

fig

ures

by

draw

ing

and

use

of m

atric

es

Enl

arge

men

t

Enl

arge

men

t abo

ut

the

orig

in u

sing

a

ratio

nal s

cale

by

draw

ing

E

nlar

gem

ent u

sing

m

atric

es a

nd a

bout

an

y po

int u

sing

a

ratio

nal s

cale

Str

etch

O

ne-w

ay a

nd tw

o-w

ay s

tret

ch u

sing

m

atric

es a

nd

geom

etric

al m

etho

ds

She

ar

She

ar u

sing

mat

rices

an

d ge

omet

rical

m

etho

ds


32

42

7. 1

4 P

rob

abili

ty

TO

PIC

F

OR

M 1

F

OR

M 2

F

OR

M 3

F

OR

M 4

Pro

babi

lity

Def

initi

on o

f pr

obab

ility

term

s

Exp

erim

enta

l pr

obab

ility

E

xper

imen

tal

prob

abili

ty

T

heor

etic

al

prob

abili

ty

S

ingl

e ev

ents

C

ombi

ned

even

ts

A

pplic

atio

n of

pr

obab

ility