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ZIMBABWE
MINISTRY OF PRIMARY AND SECONDARY EDUCATION
ADDITIONAL MATHEMATICS
SYLLABUS
FORMS 5 - 6
2015 - 2022Curriculum Development and Technical Services
P. O. Box MP 133Mount Pleasant
Harare
© All Rrights Reserved2015
Additional Mathematics Syllabus Forms 5 - 6
i
ACKNOWLEDGEMENTSThe Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued contribution in the production of this syllabus:
• National Mathematics panel• Zimbabwe School Examinations Council (ZIMSEC)• United Nations International Children’s Emergency Fund (UNICEF)• UnitedNationsEducationalScientificandCulturalOrganisation(UNESCO)• Representatives from Higher and Tertiary institutions
ii
Additional Mathematics Syllabus Forms 5 - 6
CONTENTSACKNOWLEDGEMENTS .............................................................................................................i
CONTENTS ...................................................................................................................................ii
1.0 PREAMBLE ............................................................................................................................1
2.0 PRESENTATION OF SYLLABUS ..........................................................................................1
3.0 AIMS....................................................................................................................................... 1
4.0 OBJECTIVES ..........................................................................................................................1
5.0 METHODOLOGY AND TIME ALLOCATION ..........................................................................2
6.0 TOPICS ...................................................................................................................................3
7.0 SCOPE AND SEQUENCE ......................................................................................................4
8.0 COMPETENCY MATRIX .........................................................................................................15
FORM FIVE (5) ..............................................................................................................................15
FORM SIX (6) ................................................................................................................................29
9.0 ASSESSMENT ........................................................................................................................50
1
1.0 PREAMBLE
1.1 INTRODUCTION
The Form 5 – 6 Additional Mathematics syllabus builds on the Form 3 - 4 Additional Mathematics syllabus and is designed to cater for the needs of post Form 4, mathematically outstanding learners. The teaching and learning that is based on the syllabus provides further opportunities for such learners to enjoy doing and using mathematics and, in the process developing a deeper appreciation and understanding of the nature of mathematics, its pivotal role in Science, Technology, Engineering and Mathematics (STEM) and life in general and hence promoting sustainable development. The intentionistoprovideafirmbasisonwhichtopursuefurther studies in mathematics and related areas which are critical for national development and global compet-itiveness in the 21st century. In addition to providing a firmbase,thelearningareaisalsoexpectedtoenhancelearners’confidenceandsenseofselffulfilment,collegiality and intellectual honesty, hence contributing to their growth in the acquisition of Unhu/Ubuntu//Vumunhu values.
1.2 RATIONALE
In its socio-economic transformation agenda, Zimbabwe has embarked on an industrialisation development strategy, where high level mathematical knowledge and skills are a prerequisite. To this end, Additional Math-ematics learners are expected to emerge with a solid basis for further studies in STEM, and with enhanced mathematical competencies. These include abstract and analytical thinking, logical reasoning, designing algorithms, communicating mathematical information effectively, conjecturing and proving conjectures, modelling life phenomena into mathematical language in order to better understand those phenomena and to solve related problems and applying mathematics in a wide variety of contexts. It is from the pool of individuals with such competencies that some of Zimbabwe’s most creative thinkers, innovators, inventors and mathemati-cally literate entrepreneurs are expected to emerge. This is critical for sustainable development.
1.3 SUMMARY OF CONTENT
The Form 5- 6 Additional Mathematics syllabus will cover the theoretical concepts and their applications. This two year learning area consists of Pure Mathematics, Mechanics and Statistics.
1.4 ASSUMPTIONS
The syllabus assumes that the learner:
• hasatalentinmathematics• hasahighpassinMathematicsorapassineither
Pure Mathematics or Additional Mathematics at Form 4.
• IsexcellinginPureMathematicsatForm5
1.5 CROSS- CUTTING ISSUES
The following are some of the cross cutting themes catered for in the teaching and learning of Additional Mathematics:-
• Businessandfinancialliteracy• Disasterandriskmanagement• Communication• Teambuilding• Problemsolving• Environmentalissues• Enterpriseskills• InformationCommunicationandTechnology(ICT)• HIV&AIDS
2.0 PRESENTATION OF SYLLABUSThe Additional Mathematics syllabus is a single document covering Form 5–6. It contains the preamble, aims, objectives, syllabus topics, scope and sequence, competency matrix and assessment procedures. The syllabus also suggests a list of resources to be used during the teaching and learning process.
3.0 AIMSThe syllabus will enable learners to:
3.1 further develop mathematical knowledge and skillsinawaythatpromotesfulfilmentanden-joymentandlaysafirmfoundationforfurtherstudies and lifelong learning
3.2 acquire an additional range of mathematical skills, particularly those applicable to other learning areas and various life contexts, in-cluding enterprise
3.3 enhanceconfidence,criticalthinking,innova-tiveness, creativity and problem solving skills for sustainable development
Additional Mathematics Syllabus Forms 5 - 6
2
3.4 develop a greater appreciation of the role of mathematics in personal, community and na-tional development in line with Unhu/Ubuntu/Vumunhu
3.5 further develop an appreciation for and ability to use I.C.T tools in solving problems in math-ematical and other contexts
3.6 develop the ability to communicate mathemati-cal ideas and to learn cooperatively
4.0 OBJECTIVESThe learners should be able to:
4.1 use mathematical skills and techniques that are necessary for further studies
4.2 use mathematical models to solve problems in life and for sustainable development
4.3 use I.C.T tools in solving problems in mathe-matical and other contexts
4.4 demonstrate expertise, perseverance, coop-eration and intellectual honesty for personal, community and national development
4.5 interpret mathematical results and their impli-cations in life
4.6 communicate mathematical results and their implications in life
4.7 draw inferences through correct manipulation of data
4.8 conduct research projects including those related to enterprise
4.9 apply relevant mathematical notations and terms in problem solving
4.10 present data through appropriate presenta-tions
4.11 apply mathematical skills in other learning areas
4.12 conduct mathematical proofs
5.0 METHODOLOGY AND TIME ALLOCATION
5.1 Methodology
A constructivist based teaching and learning approach is recommended for the Form 5 – 6 Additional Mathematics Syllabus. The theoretical basis for this approach is that: in a conducive environment with appropriate stimuli, learners’ capacity to build on their pre-requisite knowledge and create new mathematical knowledge is enhanced. A conducive environment in this context is one that encourages creativity and originality; a free
exchange of ideas and information; inclusivity and respect for each other’s views, regardless of personal circumstances (in terms of, for example: gender, ap-pearance, disability and religious beliefs); collaboration and cooperation; intellectual honesty; diligence and persistence; and Unhu/ Ubuntu /Vumunhu. This is particularly important in a learning area like mathematics, given the negative attitudes associated with its teaching and learning.
Providing appropriate stimuli has to do with posing rel-evant challenges that excite learners, and help to make learningAdditionalMathematicsanenjoyable,fulfillingexperience. Such challenges could be posed in the form of problems that encourage learners to create new mathematical ideas in line with the teacher expectations and even beyond. New knowledge acquired in such a manner tends to be deep rooted and meaningful to learners, hence enhancing their ability to apply it within thelearningareaandinlife.Definitelyspoonfeedingisnot and cannot be an appropriate stimulus, as it does not help learners to develop critical thinking, creativity, and the ability to think outside the box, which are critical for self-reliance, national sustainable development and global competitiveness. Thus learners need to be active participants and decision makers in the Additional Mathematics teaching and learning process, with the teacher playing the facilitator’s role.Pre-requisite knowledge and skills refers to what the learners should already know and can do, which can form a strong basis on which to construct the expected new knowledge. Thus the Additional Mathematics teacher needs to carefully analyse the new concepts and principles he/she intends to introduce, identify the relevant pre-requisite knowledge, assess to identify any gaps,andtakeappropriatestepstofillsuchgaps.The following, is a list of teaching and learning approach-es that are consistent with, and supportive of the above approach:
5.1.1 Guided discovery 5.1.2 Group work5.1.3 Interactive e-learning5.1.4 Problem solving5.1.5 Discussion5.1.6 Modelling5.1.7 Visual tactile
The above suggested methods should be enhanced through the application of multi-sensory (inclusive) approaches.
Additional Mathematics Syllabus Forms 5 - 6
3
5.2 Time Allocation
10 periods of 35 minutes each per week should be allocated. Learners are expected to participate in the following activities:-
- MathematicsOlympiads- Mathematics and Science exhibitions- Mathematics seminars- Mathematical tours to tertiary and other institu-
tions
6.0 TOPICSThe following topics will be covered from Form 5 - 6
6.1 Pure Mathematics
6.1.1 Algebra6.1.2 Series6.1.3 Trigonometry 6.1.4 Mathematical Induction6.1.5 Geometry and Vectors
6.1.6 Calculus
6.2 Mechanics
6.2.1 Particle dynamics6.2.2 Elasticity6.2.3 Energy, work and power6.2.4 Circular motion6.2.5 Simple harmonic motion
6.3 Statistics
6.3.1 Probability 6.3.2 Random Variables6.3.3 Sampling and estimation6.3.4 Statistical inference6.3.5 Bivariate data
Additional Mathematics Syllabus Forms 5 - 6
4
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
10
7.0
SC
OPE
AN
D S
EQU
ENC
E 7.
1 PU
RE
MAT
HEM
ATIC
S
TOPI
C 1
: ALG
ERB
RA
TOPI
CS
FORM
5
FORM
6
RAT
ION
AL F
UN
CTI
ON
S
Parti
al F
ract
ions
Oblique
Asy
mpt
otes
G
raph
s
MAT
RIC
ES A
ND
LIN
EAR
SPA
CES
Line
ar e
quat
ions
Sp
aces
and
sub
spac
es
GR
OU
PS
Pr
oper
ties
Orderofelements
Si
mpl
e su
bgro
ups
La
Gra
nge’
s th
eore
m
St
ruct
ure
of fi
nite
gro
ups
Is
omor
phis
m
7.0
SCO
PE A
ND
SEQ
UEN
CE
7.1
PUR
E M
ATH
EMAT
ICS
TOPI
C 1
: ALG
ERB
RA
4 5
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 2
: SER
IES
11
TOPI
C 2
: SER
IES
SUB
TOPI
C
FORM
5
FORM
6
SUM
MAT
ION
OF
SER
IES
St
anda
rd re
sults
(∑
𝒓𝒓,∑𝒓𝒓𝟐𝟐
,∑𝒓𝒓𝟑𝟑
)
Met
hod
of d
iffer
ence
s
Su
m to
infin
ity
TOPI
C 3
: TR
IGO
NO
MET
RY
12
TOPI
C 3
: TR
IGO
NO
MET
RY
SUB
TOPI
C
FORM
5
FORM
6
HYP
ERB
OLI
C F
UN
CTI
ON
S
Six
hype
rbol
ic fu
nctio
ns
Id
entit
ies
In
vers
e no
tatio
n
6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 4
: MAT
HEM
ATIC
AL
IND
UC
TIO
N
TOPI
C 5
: GEO
MET
RY A
ND
VEC
TOR
S
13
TOPI
C 4
: MAT
HEM
ATIC
AL IN
DU
CTI
ON
SUB
TOPI
C
FORM
5
FORM
6
MAT
HEM
ATIC
AL IN
DU
CTI
ON
Proo
f by
indu
ctio
n
C
onje
ctur
e
14
TOPI
C 5
: G
EOM
ETR
Y AN
D V
ECTO
RS
SUB
TOPI
C
FORM
5
FORM
6
POLA
R C
OO
RD
INAT
ES
C
arte
sian
and
pol
ar c
oord
inat
es
Po
lar c
oord
inat
es c
urve
s
Ar
ea o
f a s
ecto
r
VEC
TOR
GEO
MET
RY
Tr
iple
sca
lar p
rodu
ct
C
ross
pro
duct
Eq
uatio
ns o
f lin
es a
nd p
lane
s
6 7
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 6
: CA
LCU
LUS
14
TOPI
C 5
: G
EOM
ETR
Y AN
D V
ECTO
RS
SUB
TOPI
C
FORM
5
FORM
6
POLA
R C
OO
RD
INAT
ES
C
arte
sian
and
pol
ar c
oord
inat
es
Po
lar c
oord
inat
es c
urve
s
Ar
ea o
f a s
ecto
r
VEC
TOR
GEO
MET
RY
Tr
iple
sca
lar p
rodu
ct
C
ross
pro
duct
Eq
uatio
ns o
f lin
es a
nd p
lane
s
8
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
7.2
MEC
HA
NIC
S
TOPI
C 1
: PA
RTI
CLE
DYN
AM
ICS
16
7.2
MEC
HAN
ICS
TOPI
C 1
: PAR
TIC
LE D
YNAM
ICS
SUB
TOPI
C
FORM
5
FORM
6
KIN
EMAT
ICS
OF
MO
TIO
N
Mot
ion
in a
stra
ight
line
Ve
loci
ty
Ac
cele
ratio
n
Displacem
ent-
tim
e ve
loci
ty-ti
me
and
acce
lera
tion-
time
grap
hs
Eq
uatio
n of
mot
ion
for c
onst
ant l
inea
r acc
eler
atio
n
Ve
rtica
l mot
ion
unde
r gra
vity
M
otio
n an
d co
nsta
nt v
eloc
ity
NEW
TON
’S L
AWS
OF
MO
TIO
N
N
ewto
n’s
law
s of
mot
ion
- M
otio
n ca
used
by
a se
t of f
orce
s
- C
once
pt o
f mas
s an
d w
eigh
t
M
otio
n of
con
nect
ed o
bjec
ts
MO
TIO
N O
F A
PRO
JEC
TILE
Pr
ojec
tile
M
otio
n of
a p
roje
ctile
8 9
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 2
: ELA
STIC
ITY
17
Ve
loci
ty a
nd d
ispl
acem
ents
R
ange
on
horiz
onta
l pla
ne
G
reat
est h
eigh
t
M
axim
um ra
nge
C
arte
sian
equ
atio
n of
a tr
ajec
tory
of a
pro
ject
ile
18
TOPI
C 2
: EL
ASTI
CIT
Y
SUB
TOPI
C
FORM
5
FORM
6
ELAS
TIC
ITY
Prop
ertie
s of
ela
stic
stri
ngs
and
sprin
gs
W
ork
done
in s
tretc
hing
a s
tring
El
astic
pot
entia
l ene
rgy
M
echa
nica
l ene
rgy
C
onse
rvat
ion
of m
echa
nica
l ene
rgy
10
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 3
: EN
ERG
Y, W
OR
K A
ND
PO
WER
TOPI
C 4
: CIR
CU
LAR
MO
TIO
N
19
TOPI
C 3
: EN
ERG
Y, W
OR
K A
ND
PO
WER
SUB
TOPI
C
FORM
5
FORM
6
ENER
GY,
WO
RK
AN
D P
OW
ER
Ener
gy
- G
ravi
tatio
nal p
oten
tial
- El
astic
pot
entia
l
- Ki
netic
W
ork
Po
wer
Pr
inci
ple
of e
nerg
y co
nser
vatio
n
20
TOPI
C4:
C
IRC
ULA
R M
OTI
ON
SUB
TOPI
C
FORM
5
FORM
6
CIR
CU
LAR
MO
TIO
N
(Ver
tical
and
Hor
izon
tal)
Angu
lar s
peed
and
vel
ocity
H
oriz
onta
l and
ver
tical
circ
ular
mot
ion
Ac
cele
ratio
n of
a p
artic
le m
ovin
g on
a c
ircle
M
otio
n in
a c
ircle
with
con
stan
t spe
ed
C
entri
peta
l for
ce
R
elat
ion
betw
een
angu
lar a
nd li
near
spe
ed
C
onic
al p
endu
lum
Ba
nked
trac
ks
10 11
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 5
: SIM
PLE
HA
RM
ON
IC M
OTI
ON
7.3
STAT
ISTI
CS
TOPI
C 1
: PR
OB
AB
ILIT
Y
21
TOPI
C 5
: SIM
PLE
HAR
MO
NIC
MO
TIO
N
SUB
TOPI
C
FORM
5
FORM
6
SIM
PLE
HAR
MO
NIC
MO
TIO
N
Basi
c eq
uatio
n of
sim
ple
harm
onic
mot
ion
Pr
oper
ties
of s
impl
e ha
rmon
ic m
otio
n
22
7.3
STAT
ISTI
CS
TOPI
C 1
: PR
OB
ABIL
ITY
SUB
TOPI
C
FORM
5
FORM
6
PRO
BAB
ILIT
Y
Ev
ents
- In
depe
nden
t
- M
utua
lly e
xclu
sive
- Ex
haus
tive
- C
ombi
ned
C
ondi
tiona
l pro
babi
lity
Tr
ee d
iagr
ams
Outcometables
Ve
nn d
iagr
ams
Pe
rmut
atio
ns a
nd c
ombi
natio
ns
12
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 2
: R
AN
DO
M V
AR
IAB
LES
23
TOPI
C 2
: R
AND
OM
VAR
IAB
LES
SUB
TOPI
C
FORM
5
FORM
6
RAN
DO
M V
ARIA
BLE
S (d
iscr
ete
and
cont
inuo
us)
Prob
abilit
y di
strib
utio
ns
Ex
pect
atio
n
Va
rianc
e
Pr
obab
ility
dens
ity fu
nctio
ns (p
df) a
nd c
umul
ativ
e
dist
ribut
ion
func
tions
(cdf
)
M
ean,
m
edia
n,
mod
e,
stan
dard
de
viat
ion
and
perc
entil
es
DIS
TRIB
UTI
ON
S
Bino
mia
l di
strib
utio
n
Po
isso
n d
istri
butio
n
N
orm
al d
istri
butio
n
St
anda
rd n
orm
al ta
bles
C
ontin
uity
cor
rect
ion
Li
near
com
bina
tions
of n
orm
al a
nd P
oiss
on
dist
ribut
ions
12 13
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 3
: SA
MPL
ING
AN
D E
STIM
A-
TOPI
C4:
ST
ATIS
TIC
AL
INFE
REN
CE
24
TOPI
C 3
: SA
MPL
ING
AN
D E
STIM
ATIO
N
SUB
TOPI
C
FORM
5
FORM
6
SAM
PLIN
G T
ECH
NIQ
UES
AN
D
ESTI
MAT
ION
Pr
obab
ility
sam
plin
g te
chni
ques
N
on-p
roba
bilit
y sa
mpl
ing
tech
niqu
es
Es
timat
ion
of p
opul
atio
n pa
ram
eter
s
C
entra
l lim
it th
eore
m
C
onfid
ence
inte
rval
s
25
TOPI
C4:
ST
ATIS
TIC
AL IN
FER
ENC
E
SUB
TOPI
C
FORM
5
FORM
6
HYP
OTH
ESIS
TES
TIN
G
Nul
l hyp
othe
sis
Al
tern
ativ
e hy
poth
esis
Te
st s
tatis
tics
Si
gnifi
canc
e le
vel
H
ypot
hesi
s te
st (1
-tail
and
2-ta
il)
Ty
pe 1
and
type
2 e
rrors
z-
test
s
t –
test
s
ch
i-squ
ared
test
s
14
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 5
: BIV
AR
IATE
DAT
A
25
TOPI
C4:
ST
ATIS
TIC
AL IN
FER
ENC
E
SUB
TOPI
C
FORM
5
FORM
6
HYP
OTH
ESIS
TES
TIN
G
Nul
l hyp
othe
sis
Al
tern
ativ
e hy
poth
esis
Te
st s
tatis
tics
Si
gnifi
canc
e le
vel
H
ypot
hesi
s te
st (1
-tail
and
2-ta
il)
Ty
pe 1
and
type
2 e
rrors
z-
test
s
t –
test
s
ch
i-squ
ared
test
s
14 15
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
8.0
CO
MPE
TEN
CY
MAT
RIX
FOR
M F
IVE
(5)
PUR
E M
ATH
EMAT
ICS
TOPI
C 1
: A
LGEB
RA
27
8.0
CO
MPE
TEN
CY
MAT
RIX
FORM
FIV
E (5
)
PUR
E M
ATH
EMAT
ICS
TOPI
C 1
: AL
GEB
RA
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
RAT
ION
AL F
UN
CTI
ON
S
ex
pres
s ra
tiona
l fun
ctio
ns in
parti
al fr
actio
ns
de
term
ine
key
feat
ures
of
ratio
nal f
unct
ion
grap
hs,
incl
udin
g o
bliq
ue a
sym
ptot
es
in c
ases
whe
re d
egre
e of
num
erat
or a
nd d
enom
inat
or
are
at m
ost
two
Pa
rtial
Fra
ctio
ns
ObliqueAsymptotes
G
raph
s
Ex
pres
sing
ratio
nal f
unct
ions
in
parti
al fr
actio
ns
Ex
plor
ing
and
dete
rmin
ing
key
feat
ures
of r
atio
nal f
unct
ion
grap
hs, i
nclu
ding
obl
ique
asym
ptot
es in
cas
es w
here
degr
ee o
f num
erat
or a
nd
deno
min
ator
are
at m
ost
two
IC
T to
ols
R
elev
ant t
exts
G
eo-b
oard
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
16
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
28
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
sk
etch
gra
phs
of ra
tiona
l
func
tions
so
lve
prob
lem
s in
volv
ing
ratio
nal f
unct
ions
Sk
etch
ing
grap
hs o
f rat
iona
l
func
tions
, inc
ludi
ng th
e
dete
rmin
atio
n of
obl
ique
asym
ptot
es
So
lvin
g p
robl
ems
invo
lvin
g
ratio
nal f
unct
ions
MAT
RIC
ES A
ND
LIN
EAR
SP
ACES
defin
e th
e sy
stem
s of
line
ar
equa
tions
de
term
ine
cons
iste
ncy
or
inco
nsis
tenc
y of
sys
tem
s of
linea
r equ
atio
ns
in
terp
ret g
eom
etric
ally
the
cons
iste
ncy
or in
cons
iste
ncy
of s
yste
ms
of li
near
equ
atio
ns
re
late
to s
ingu
larit
y th
e
corre
spon
ding
squ
are
mat
rix
of a
sys
tem
of l
inea
r
equa
tions
so
lve
linea
r equ
atio
ns o
f
cons
iste
nt s
yste
ms
so
lve
prob
lem
s in
volv
ing
Li
near
equ
atio
ns
Sp
aces
and
sub
spac
es
Discussingthesystem
soflinear
equa
tions
Discussinganddeterm
iningthe
cons
iste
ncy
or in
cons
iste
ncy
of
syst
ems
of li
near
equ
atio
ns
In
terp
retin
g ge
omet
rical
ly th
e
cons
iste
ncy
or in
cons
iste
ncy
of
syst
ems
of li
near
equ
atio
ns
R
elat
ing
to s
ingu
larit
y th
e
corre
spon
ding
squ
are
mat
rix o
f a
syst
em o
f lin
ear e
quat
ions
So
lvin
g lin
ear e
quat
ions
of
cons
iste
nt s
yste
ms
So
lvin
g pr
oble
ms
invo
lvin
g
syst
ems
of li
near
equ
atio
ns
IC
T to
ols
R
elev
ant
text
s
En
viro
nmen
t
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
16 17
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
29
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
syst
ems
of li
near
equ
atio
ns
de
fine
a lin
ear s
pace
and
a
sub-
spac
e
so
lve
prob
lem
s in
volv
ing
linea
r spa
ces
and
sub-
spac
es
Discussingpropertiesoflinear
spac
es a
nd s
ub-s
pace
s
So
lvin
g pr
oble
ms
invo
lvin
g li
near
spac
es a
nd s
ub-s
pace
s
GR
OU
PS
de
fine
a gr
oup
de
term
ine
whe
ther
or n
ot a
give
n st
ruct
ure
is a
gro
up
de
fine
the
orde
r of t
he g
roup
and
elem
ents
of a
gro
up
de
fine
a su
bgro
up
de
term
ine
whe
ther
or n
ot a
give
n st
ruct
ure
is a
sub
gro
up
in s
impl
e ca
ses
st
ate
the
LaG
rang
e’s
theo
rem
ap
ply
the
LaG
rang
e’s
theo
rem
con
cern
ing
the
orde
r
Pr
oper
ties
Orderofelements
Si
mpl
e su
bgro
ups
La
Gra
nge’
s th
eore
m
St
ruct
ure
of fi
nite
gro
ups
Is
omor
phis
m
Discussinggroupsand
dete
rmin
ing
whe
ther
or n
ot a
give
n st
ruct
ure
is a
gro
up
Determiningtheordero
fagroup
and
the
orde
r of e
lem
ents
of a
grou
p
Discussingsubgroupsand
dete
rmin
ing
whe
ther
or n
ot a
give
n st
ruct
ure
is a
sub
grou
p in
sim
ple
case
s
Discussingandapplyingthe
LaG
rang
e’s
theo
rem
con
cern
ing
IC
T to
ols
R
elev
ant
text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
18
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
30
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
of a
sub
grou
p of
a fi
nite
grou
p
de
fine
a cy
clic
gro
up
de
mon
stra
te fa
milia
rity
with
the
stru
ctur
e of
a fi
nite
gro
up
up to
ord
er 7
de
fine
isom
orph
ism
bet
wee
n
grou
ps
de
term
ine
whe
ther
or n
ot
give
n fin
ite g
roup
s ar
e
isom
orph
ic
so
lve
prob
lem
s in
volv
ing
grou
ps
the
orde
r of a
sub
grou
p of
a fi
nite
grou
p
Discussingandfindingexamples
of c
yclic
gro
ups
Ex
plor
ing
prop
ertie
s of
stru
ctur
es
of f
inite
gro
ups
up to
ord
er 7
Discussinganddeterm
ining
whe
ther
or n
ot g
iven
fini
te g
roup
s
are
isom
orph
ic
So
lvin
g pr
oble
ms
invo
lvin
g
grou
ps
18 19
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 2
: SE
RIE
S
31
TOPI
C 2
: SE
RIE
S
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
SUM
MAT
ION
OF
SER
IES
us
e th
e st
anda
rd re
sults
to
find
rela
ted
sum
s
de
rive
the
met
hod
of
diffe
renc
es
fin
d th
e su
m o
f fin
ite s
erie
s
usin
g m
etho
d of
diff
eren
ces
de
term
ine
the
sum
to in
finity
of a
con
verg
ent s
erie
s by
cons
ider
ing
the
sum
to n
term
s
so
lve
prob
lem
s in
volv
ing
serie
s
St
anda
rd re
sults
(∑𝒓𝒓,∑𝒓𝒓𝟐𝟐
,∑𝒓𝒓𝟑𝟑
)
Met
hod
of d
iffer
ence
s
Su
m to
infin
ity
Fi
ndin
g re
late
d su
ms
usin
g th
e
stan
dard
resu
lts
Ex
plor
ing
and
deriv
ing
the
met
hod
of d
iffer
ence
s
U
sing
met
hod
of d
iffer
ence
s to
find
the
sum
of f
inite
ser
ies
C
ompu
ting
the
sum
to in
finity
of a
conv
erge
nt s
erie
s by
con
side
ring
the
sum
to n
term
s
So
lvin
g p
robl
ems
invo
lvin
g se
ries
R
epre
sent
ing
life
phe
nom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g se
ries
and
expl
orin
g
thei
r app
licat
ions
in li
fe
IC
T to
ols
R
elev
ant
text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
20
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 3
: TR
IGO
NO
MET
RY
32
TOPI
C 3
: TR
IGO
NO
MET
RY
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
HYP
ERB
OLI
C
FUN
CTI
ON
S
defin
e th
e si
x hy
perb
olic
func
tions
in te
rms
of
expo
nent
ials
sk
etch
the
grap
hs o
f
hype
rbol
ic fu
nctio
ns
de
rive
iden
titie
s in
volv
ing
hype
rbol
ic f
unct
ions
us
e hy
perb
olic
iden
titie
s in
solv
ing
prob
lem
s
de
note
the
prin
cipa
l val
ues
of
the
inve
rse
hype
rbol
ic
rela
tions
usi
ng th
e in
vers
e
nota
tions
de
rive
hype
rbol
ic e
xpre
ssio
ns
in te
rms
of lo
garit
hms
us
e hy
perb
olic
exp
ress
ions
in
term
s of
loga
rithm
s to
sol
ve
prob
lem
s
Si
x hy
perb
olic
func
tions
Id
entit
ies
In
vers
e no
tatio
n
Discussingthesixhyperbolic
func
tions
in te
rms
of e
xpon
entia
ls
Sk
etch
ing
the
grap
hs o
f
hype
rbol
ic fu
nctio
ns
Derivingandusingidentities
invo
lvin
g hy
perb
olic
fun
ctio
ns to
solv
e pr
oble
ms
U
sing
the
inve
rse
nota
tions
to
deno
te th
e pr
inci
pal v
alue
s of
the
inve
rse
hype
rbol
ic re
latio
ns
Derivingandusinghyperbolic
expr
essi
ons
in te
rms
of lo
garit
hms
to s
olve
pro
blem
s
So
lvin
g pr
oble
ms
invo
lvin
g
hype
rbol
ic f
unct
ions
R
epre
sent
ing
life
phe
nom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g se
ries
and
expl
orin
g
IC
T to
ols
R
elev
ant
text
s
En
viro
nmen
t
R
esou
rce
pers
ons
Brai
lle
mat
eria
ls
Ta
lkin
g bo
oks
20 21
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 5
: M
ATH
EMAT
ICA
L IN
DU
CTI
ON
33
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
so
lve
prob
lem
s in
volv
ing
hype
rbol
ic fu
nctio
ns
thei
r app
licat
ions
in li
fe
TOPI
C 5
: M
ATH
EMAT
ICAL
IND
UC
TIO
N
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
MAT
HEM
ATIC
AL
IND
UC
TIO
N
de
scrib
e th
e pr
oces
s of
mat
hem
atic
al in
duct
ion
pr
ove
by
mat
hem
atic
al
indu
ctio
n to
est
ablis
h a
give
n
resu
lt
us
e th
e st
rate
gy o
f con
duct
ing
limite
d tri
als
to fo
rmul
ate
a
conj
ectu
re a
nd p
rovi
ng it
by
the
met
hod
of in
duct
ion
Pr
oof b
y in
duct
ion
C
onje
ctur
e
Discussingtheprocessesof
mat
hem
atic
al in
duct
ion
Pr
ovin
g b
y m
athe
mat
ical
indu
ctio
n to
est
ablis
h g
iven
resu
lts
C
ondu
ctin
g lim
ited
trial
s to
form
ulat
e c
onje
ctur
e an
d pr
ovin
g
it by
the
met
hod
of in
duct
ion
IC
T To
ols
R
elev
ant
Text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
33
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
so
lve
prob
lem
s in
volv
ing
hype
rbol
ic fu
nctio
ns
thei
r app
licat
ions
in li
fe
TOPI
C 5
: M
ATH
EMAT
ICAL
IND
UC
TIO
N
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
MAT
HEM
ATIC
AL
IND
UC
TIO
N
de
scrib
e th
e pr
oces
s of
mat
hem
atic
al in
duct
ion
pr
ove
by
mat
hem
atic
al
indu
ctio
n to
est
ablis
h a
give
n
resu
lt
us
e th
e st
rate
gy o
f con
duct
ing
limite
d tri
als
to fo
rmul
ate
a
conj
ectu
re a
nd p
rovi
ng it
by
the
met
hod
of in
duct
ion
Pr
oof b
y in
duct
ion
C
onje
ctur
e
Discussingtheprocessesof
mat
hem
atic
al in
duct
ion
Pr
ovin
g b
y m
athe
mat
ical
indu
ctio
n to
est
ablis
h g
iven
resu
lts
C
ondu
ctin
g lim
ited
trial
s to
form
ulat
e c
onje
ctur
e an
d pr
ovin
g
it by
the
met
hod
of in
duct
ion
IC
T To
ols
R
elev
ant
Text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
22
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 6
: G
EOM
ETRY
AN
D V
ECTO
RS
34
TOPI
C 6
: G
EOM
ETR
Y AN
D V
ECTO
RS
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
POLA
R C
OO
RD
INAT
ES
ex
plai
n th
e re
latio
nshi
p
betw
een
Car
tesi
an a
nd p
olar
coor
dina
tes
for
r
≥ 0
co
nver
t equ
atio
ns o
f cur
ves
from
Car
tesi
an to
pol
ar a
nd
vice
ver
sa
sk
etch
sim
ple
pola
r cur
ves
for
0 ≤
𝜃𝜃<
2𝜋𝜋 o
r - 𝜋𝜋
< 𝜃𝜃
≤ 𝜋𝜋
,
show
ing
sign
ifica
nt fe
atur
es
such
as
sym
met
ry, t
he fo
rm o
f
the
curv
e at
the
pole
and
leas
t/gre
ates
t val
ues
of r
C
arte
sian
and
pol
ar
coor
dina
tes
Po
lar c
oord
inat
es c
urve
s
Ar
ea o
f a s
ecto
r
Discussingtheappropriatenessof
usin
g C
arte
sian
or p
olar
coor
dina
tes
C
onve
rting
equ
atio
ns o
f cur
ves
from
Car
tesi
an to
pol
ar a
nd v
ice
vers
a
Sk
etch
ing
sim
ple
pola
r cur
ves
for
0 ≤
𝜃𝜃<
2𝜋𝜋 o
r
- 𝜋𝜋
< 𝜃𝜃
≤ 𝜋𝜋
,
show
ing
sign
ifica
nt fe
atur
es s
uch
as s
ymm
etry
, the
form
of t
he
curv
e at
the
pole
and
leas
t/gre
ates
t val
ues
of r
IC
T To
ols
R
elev
ant
Text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
22 23
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
35
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
de
rive
the
form
ula
𝟏𝟏 𝟐𝟐∫
𝒓𝒓𝟐𝟐𝜷𝜷 𝜶𝜶
d𝜽𝜽 fo
r the
are
a of
a s
ecto
r in
sim
ple
case
s
us
e th
e fo
rmul
a
𝟏𝟏 𝟐𝟐∫
𝒓𝒓𝟐𝟐𝜷𝜷 𝜶𝜶
d𝜽𝜽 fo
r the
are
a of
a s
ecto
r in
sim
ple
case
s
so
lve
prob
lem
s in
volv
ing
pola
r
coor
dina
tes
Derivingandusingtheform
ula
𝟏𝟏 𝟐𝟐∫
𝒓𝒓𝟐𝟐𝜷𝜷 𝜶𝜶
d𝜽𝜽
for t
he a
rea
of a
sec
tor
in s
impl
e ca
ses
So
lvin
g pr
oble
ms
invo
lvin
g po
lar
coor
dina
tes
R
epre
sent
ing
life
phe
nom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g po
lar c
oord
inat
es a
nd
expl
orin
g th
eir a
pplic
atio
ns in
life
VEC
TOR
GEO
MET
RY
de
term
ine
the
vect
or p
rodu
ct
of tw
o gi
ven
vect
ors
ca
lcul
ate
the
tripl
e sc
alar
prod
uct
of g
iven
vec
tors
in
terp
ret t
he tr
iple
sca
lar
prod
uct a
nd c
ross
pro
duct
in
geom
etric
al te
rms
so
lve
prob
lem
s co
ncer
ning
dist
ance
s, a
ngle
s an
d
inte
rsec
tions
usi
ng e
quat
ions
of li
nes
and
plan
es.
Tr
iple
sca
lar p
rodu
ct
C
ross
pro
duct
Eq
uatio
ns o
f lin
es a
nd p
lane
s
C
alcu
latin
g th
e ve
ctor
pro
duct
of
two
give
n ve
ctor
s
C
ompu
ting
the
tripl
e sc
alar
prod
uct
of g
iven
vec
tors
Discussingthetriplescalarand
cros
s pr
oduc
t in
geom
etric
al
term
s
So
lvin
g pr
oble
ms
conc
erni
ng
dist
ance
s, a
ngle
s an
d
inte
rsec
tions
usi
ng e
quat
ions
of
lines
and
pla
nes.
IC
T To
ols
R
elev
ant
Text
s
En
viro
nmen
t
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
24
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
36
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Rep
rese
ntin
g li
fe p
heno
men
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g ve
ctor
geo
met
ry a
nd
expl
orin
g th
eir a
pplic
atio
ns in
life
TOPI
C 7
: C
ALC
ULU
S
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
DIF
FER
ENTI
ATIO
N
AND
INTE
GR
ATIO
N
de
rive
an e
xpre
ssio
n fo
r 𝑑𝑑2𝑦𝑦
𝑑𝑑𝑥𝑥2
in c
ases
whe
re th
e re
latio
n
betw
een 𝑥𝑥
and 𝑦𝑦
is d
efin
ed
impl
icitl
y or
par
amet
rical
ly
de
duce
the
rela
tions
hip
betw
een
the
sign
of 𝑑𝑑2
𝑦𝑦𝑑𝑑𝑥𝑥
2 and
H
ighe
r ord
er d
iffer
entia
tion
C
onca
vity
R
educ
tion
form
ulae
Ar
c le
ngth
s
Su
rface
are
as o
f rev
olut
ion
DifferentiationandIntegration
of in
vers
e tr
igon
omet
ric
Derivinganexpressionfor𝑑𝑑
2 𝑦𝑦 𝑑𝑑𝑥𝑥2
in
case
s w
here
the
rela
tion
betw
een
𝑥𝑥 an
d 𝑦𝑦i
s de
fined
impl
icitl
y or
para
met
rical
ly
Ex
plor
ing
and
dedu
cing
the
rela
tions
hip
betw
een
the
sign
of
IC
T To
ols
R
elev
ant
Text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
36
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Rep
rese
ntin
g li
fe p
heno
men
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g ve
ctor
geo
met
ry a
nd
expl
orin
g th
eir a
pplic
atio
ns in
life
TOPI
C 7
: C
ALC
ULU
S
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
DIF
FER
ENTI
ATIO
N
AND
INTE
GR
ATIO
N
de
rive
an e
xpre
ssio
n fo
r 𝑑𝑑2𝑦𝑦
𝑑𝑑𝑥𝑥2
in c
ases
whe
re th
e re
latio
n
betw
een 𝑥𝑥
and 𝑦𝑦
is d
efin
ed
impl
icitl
y or
par
amet
rical
ly
de
duce
the
rela
tions
hip
betw
een
the
sign
of 𝑑𝑑2
𝑦𝑦𝑑𝑑𝑥𝑥
2 and
H
ighe
r ord
er d
iffer
entia
tion
C
onca
vity
R
educ
tion
form
ulae
Ar
c le
ngth
s
Su
rface
are
as o
f rev
olut
ion
DifferentiationandIntegration
of in
vers
e tr
igon
omet
ric
Derivinganexpressionfor𝑑𝑑
2 𝑦𝑦 𝑑𝑑𝑥𝑥2
in
case
s w
here
the
rela
tion
betw
een
𝑥𝑥 an
d 𝑦𝑦i
s de
fined
impl
icitl
y or
para
met
rical
ly
Ex
plor
ing
and
dedu
cing
the
rela
tions
hip
betw
een
the
sign
of
IC
T To
ols
R
elev
ant
Text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
TOPI
C 7
: C
ALC
ULU
S
24 25
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
37
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
conc
avity
de
term
ine
the
poin
ts o
f
infle
xion
usi
ng 𝑑𝑑2
𝑦𝑦𝑑𝑑𝑥𝑥
2
de
rive
the
deriv
ativ
es o
f
inve
rse
trigo
nom
etric
and
hype
rbol
ic fu
nctio
ns
ap
ply
the
deriv
ativ
es o
f
inve
rse
trigo
nom
etric
and
hype
rbol
ic fu
nctio
ns in
prob
lem
sol
ving
fin
d de
finite
or i
ndef
inite
inte
gral
s us
ing
appr
opria
te
trigo
nom
etric
or h
yper
bolic
subs
titut
ion
in
tegr
ate
ratio
nal f
unct
ions
by
mea
ns o
f dec
ompo
sitio
n in
to
parti
al fr
actio
ns
de
rive
redu
ctio
n fo
rmul
ae fo
r
the
eval
uatio
n of
def
inite
inte
gral
s in
sim
ple
case
s
fin
d de
finite
inte
gral
s us
ing
func
tions
and
hyp
erbo
lic
func
tions
𝑑𝑑2𝑦𝑦
𝑑𝑑𝑥𝑥2
and
conc
avity
Fi
ndin
g po
ints
of i
nfle
xion
usi
ng
𝑑𝑑2𝑦𝑦
𝑑𝑑𝑥𝑥2
Ex
plor
ing
and
deriv
ing
the
deriv
ativ
es o
f inv
erse
trigo
nom
etric
and
hyp
erbo
lic
func
tions
Ap
plyi
ng th
e de
rivat
ives
of i
nver
se
trigo
nom
etric
and
hyp
erbo
lic
func
tions
in p
robl
em s
olvi
ng
Fi
ndin
g de
finite
or i
ndef
inite
inte
gral
s us
ing
appr
opria
te
trigo
nom
etric
or h
yper
bolic
subs
titut
ion
In
tegr
atin
g ra
tiona
l fun
ctio
ns b
y
mea
ns o
f dec
ompo
sitio
n in
to
parti
al fr
actio
ns
Ex
plor
ing
and
deriv
ing
redu
ctio
n
form
ulae
for t
he e
valu
atio
n of
defin
ite in
tegr
als
in s
impl
e ca
ses
Fi
ndin
g de
finite
inte
gral
s us
ing
26
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
38
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
redu
ctio
n fo
rmul
a
fin
d ar
c le
ngth
s fo
r cur
ves
with
equ
atio
ns in
Car
tesi
an
coor
dina
tes
incl
udin
g us
e of
a
para
met
er o
r in
pola
r for
m
fin
d th
e ar
ea o
f sur
face
of
revo
lutio
n w
hen
an a
rc is
rota
ted
abou
t one
of t
he
coor
dina
te a
xes,
giv
en th
at
the
equa
tion
of th
e cu
rve
cont
aini
ng th
e ar
c is
in
Car
tesi
an o
r par
amet
ric fo
rm
so
lve
prob
lem
s in
volv
ing
diffe
rent
iatio
n an
d in
tegr
atio
n
redu
ctio
n fo
rmul
a
Fi
ndin
g ar
c le
ngth
s fo
r cur
ves
with
equa
tions
in C
arte
sian
coor
dina
tes
incl
udin
g us
e of
a
para
met
er o
r in
pola
r for
m
Determiningtheareaofsurfaceof
revo
lutio
n w
hen
an a
rc is
rota
ted
abou
t one
of t
he c
oord
inat
e ax
es,
give
n th
at th
e eq
uatio
n of
the
curv
e co
ntai
ning
the
arc
is in
Car
tesi
an o
r par
amet
ric fo
rm
So
lvin
g pr
oble
ms
invo
lvin
g
diffe
rent
iatio
n an
d in
tegr
atio
n
R
epre
sent
ing
life
phe
nom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g di
ffere
ntia
tion
and
inte
grat
ion
and
expl
orin
g th
eir
appl
icat
ions
in li
fe
DIF
FER
ENTI
AL
EQU
ATIO
NS
fin
d th
e ge
nera
l sol
utio
n of
a
first
ord
er li
near
diff
eren
tial
equa
tion
by m
eans
of a
n
Fi
rst o
rder
diff
eren
tial
equa
tions
Se
cond
ord
er d
iffer
entia
l
Determininggeneralsolutionsof
first
ord
er li
near
diff
eren
tial
equa
tions
by
mea
ns o
f int
egra
ting
IC
T To
ols
R
elev
ant
Text
s
26 27
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
39
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
inte
grat
ing
fact
or
de
fine
a ‘c
ompl
emen
tary
func
tion’
and
a ‘p
artic
ular
inte
gral
’ in
the
cont
ext o
f
linea
r diff
eren
tial e
quat
ions
us
e a
give
n su
bstit
utio
n to
redu
ce a
firs
t ord
er d
iffer
entia
l
equa
tion
to li
near
form
or t
o a
form
in w
hich
var
iabl
es a
re
sepa
rabl
e
fin
d th
e co
mpl
imen
tary
func
tion
of a
firs
t or s
econ
d
orde
r lin
ear d
iffer
entia
l
equa
tion
with
con
stan
t
coef
ficie
nts
de
term
ine
a pa
rticu
lar i
nteg
ral
for a
firs
t or s
econ
d or
der
linea
r diff
eren
tial e
quat
ion
in
the
case
whe
re 𝑎𝑎𝑎𝑎
+ 𝑏𝑏
or
𝑎𝑎𝑒𝑒𝑏𝑏𝑏𝑏
or 𝑎𝑎
𝑎𝑎𝑎𝑎𝑎𝑎 (𝑝𝑝𝑎𝑎
) +
𝑏𝑏𝑎𝑎𝑏𝑏𝑏𝑏
(𝑝𝑝𝑎𝑎)
is a
sui
tabl
e fo
rm.
equa
tions
C
ompl
emen
tary
func
tion
G
ener
al a
nd P
artic
ular
inte
gral
s
Su
bstit
utio
n
Pa
rticu
lar s
olut
ion
fact
ors
Discussingco
mpl
emen
tary
func
tions
and
par
ticul
ar in
tegr
als
in th
e co
ntex
t of l
inea
r diff
eren
tial
equa
tions
Ap
plyi
ng g
iven
sub
stitu
tions
to
redu
ce f
irst o
rder
diff
eren
tial
equa
tions
to li
near
form
or t
o
form
s in
whi
ch v
aria
bles
are
sepa
rabl
e
Fi
ndin
g c
ompl
imen
tary
func
tions
of fi
rst o
r sec
ond
orde
r lin
ear
diffe
rent
ial e
quat
ions
with
cons
tant
coe
ffici
ents
Determiningparticularintegrals
for f
irst o
r sec
ond
orde
r lin
ear
diffe
rent
ial e
quat
ions
in th
e ca
se
whe
re 𝑎𝑎𝑎𝑎
+ 𝑏𝑏
or 𝑎𝑎
𝑒𝑒𝑏𝑏𝑏𝑏
or
𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
(𝑝𝑝𝑎𝑎)
+ 𝑏𝑏𝑎𝑎
𝑏𝑏𝑏𝑏 (𝑝𝑝
𝑎𝑎) is
a
suita
ble
form
.
Fi
ndin
g ap
prop
riate
coe
ffici
ents
of
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
28
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
40
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
fin
d th
e ap
prop
riate
coe
ffici
ent
(s) o
f a fi
rst o
r sec
ond
orde
r
diffe
rent
ial e
quat
ion
give
n a
suita
ble
form
of a
par
ticul
ar
inte
gral
fin
d a
parti
cula
r sol
utio
n to
a
diffe
rent
ial e
quat
ion
usin
g
initi
al c
ondi
tions
in
terp
ret p
artic
ular
sol
utio
ns in
the
cont
ext o
f pro
blem
s
mod
elle
d by
diff
eren
tial
equa
tions
so
lve
prob
lem
s in
volv
ing
diffe
rent
ial e
quat
ions
first
or s
econ
d or
der d
iffer
entia
l
equa
tions
giv
en s
uita
ble
form
s of
parti
cula
r int
egra
ls
Determiningparticularsolutionsto
diffe
rent
ial e
quat
ions
usi
ng in
itial
cond
ition
s
In
terp
retin
g pa
rticu
lar s
olut
ions
in
the
cont
ext o
f pro
blem
s m
odel
led
by d
iffer
entia
l equ
atio
ns
So
lvin
g pr
oble
ms
invo
lvin
g
diffe
rent
ial e
quat
ions
R
epre
sent
ing
life
phe
nom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g di
ffere
ntia
l equ
atio
ns
and
expl
orin
g th
eir a
pplic
atio
ns in
life
28 29
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
FOR
M S
IX (6
)
MEC
HA
NIC
S
TOPI
C 1
: PA
RTI
CLE
DYN
AM
ICS
41
FORM
SIX
(6)
MEC
HAN
ICS
TOPI
C 1
: PA
RTI
CLE
DYN
AMIC
S
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
KIN
EMAT
ICS
OF
MO
TIO
N
us
e di
ffere
ntia
tion
and
inte
grat
ion
with
resp
ect t
o
time
to s
olve
pro
blem
s
conc
erni
ng d
ispl
acem
ent,
velo
city
and
acc
eler
atio
n
sk
etch
the
grap
hs o
f: (x
-t), (
s-
M
otio
n in
a s
traig
ht li
ne
Ve
loci
ty
Ac
cele
ratio
n
Displacem
ent-
tim
e ve
loci
ty-
time
and
acce
lera
tion-
time
grap
hs
Discussingdistance(x)
disp
lace
men
t(s),
spee
d,
velo
city
(v) a
nd a
ccel
erat
ion(
a)
So
lvin
g pr
oble
ms
conc
erni
ng
disp
lace
men
t, ve
loci
ty a
nd
acce
lera
tion
usin
g di
ffere
ntia
tion
IC
T to
ols
G
eo-b
oard
En
viro
nmen
t
R
elev
ant t
exts
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
30
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
42
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
t), (v
-t) a
nd (a
-t)
in
terp
ret t
he (x
-t), (
s-t),
(v-t)
and
(a-t)
gra
phs
de
rive
the
equa
tions
of
mot
ion
of a
par
ticle
with
cons
tant
acc
eler
atio
n in
a
stra
ight
line
us
e th
e eq
uatio
ns o
f mot
ion
of a
par
ticle
with
con
stan
t
acce
lera
tion
in a
stra
ight
line
to s
olve
kin
emat
ics
prob
lem
s
so
lve
prob
lem
s in
volv
ing
kine
mat
ics
of m
otio
n in
a
stra
ight
line
incl
udin
g ve
rtica
l
mot
ion
unde
r gra
vity
Eq
uatio
n of
mot
ion
for
cons
tant
line
ar a
ccel
erat
ion
Ve
rtica
l mot
ion
unde
r gra
vity
M
otio
n an
d co
nsta
nt v
eloc
ity
and
inte
grat
ion
Sk
etch
ing
(x-t)
, (s-
t), (
v-t)
and
(a-
t) g
raph
s
In
terp
retin
g th
e (x
-t),
(s-t)
, (v-
t) an
d (a
-t) g
raph
s
Derivingtheequationsofm
otion
of a
par
ticle
with
con
stan
t
acce
lera
tion
in a
stra
ight
line
So
lvin
g ki
nem
atic
s pr
oble
ms
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g ki
nem
atic
s of
mot
ion
in
a st
raig
ht li
ne a
nd e
xplo
ring
thei
r
appl
icat
ions
in li
fe
30 31
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
43
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
NEW
TON
’S L
AWS
OF
MO
TIO
N
st
ate
New
ton’
s la
ws
of
mot
ion
ap
ply
New
ton’
s la
ws
of
mot
ion
to th
e lin
ear m
otio
n of
a bo
dy o
f con
stan
t mas
s
mov
ing
unde
r the
act
ion
of
cons
tant
forc
es
so
lve
prob
lem
s us
ing
the
rela
tions
hip
betw
een
mas
s
and
wei
ght
so
lve
prob
lem
s in
volv
ing
the
mot
ion
of tw
o pa
rticl
es,
conn
ecte
d by
a li
ght
inex
tens
ible
stri
ng w
hich
may
pass
ove
r a fi
xed,
sm
ooth
,
light
pul
ley
or p
eg
m
odel
the
mot
ion
of th
e bo
dy
mov
ing
verti
cally
or o
n an
incl
ined
pla
ne a
s m
otio
n w
ith
cons
tant
acc
eler
atio
n
so
lve
prob
lem
s in
volv
ing
N
ewto
n’s
law
s of
mot
ion
M
otio
n ca
used
by
a se
t of
forc
es
C
once
pt o
f mas
s an
d
wei
ght
M
otio
n of
con
nect
ed
obje
cts
D
iscu
ssin
g th
e N
ewto
n’s
law
s
of m
otio
n
Ap
plyi
ng N
ewto
n’s
law
s of
mot
ion
to th
e lin
ear m
otio
n of
a
body
of c
onst
ant m
ass
mov
ing
unde
r the
act
ion
of c
onst
ant
forc
es
So
lvin
g pr
oble
ms
usin
g th
e
rela
tions
hip
betw
een
mas
s an
d
wei
ght
So
lvin
g pr
oble
ms
invo
lvin
g th
e
mot
ion
of tw
o pa
rticl
es,
conn
ecte
d by
a li
ght
inex
tens
ible
stri
ng w
hich
may
pass
ove
r a fi
xed,
sm
ooth
, lig
ht
pulle
y or
peg
So
lvin
g pr
oble
ms
invo
lvin
g
New
ton’
s la
ws
of m
otio
n
M
odel
ling
the
mot
ion
of a
bod
y
mov
ing
verti
cally
or o
n an
incl
ined
pla
ne a
s m
otio
n w
ith
IC
T to
ols
G
eo-b
oard
En
viro
nmen
t
R
elev
ant t
exts
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
32
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
44
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
New
ton’
s la
ws
of m
otio
n co
nsta
nt a
ccel
erat
ion
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g N
ewto
n’s
law
s of
mot
ion
and
expl
orin
g th
eir
appl
icat
ions
in li
fe
MO
TIO
N O
F A
PRO
JEC
TILE
mod
el th
e m
otio
n of
a
proj
ectil
e as
a p
artic
le
mov
ing
with
con
stan
t
acce
lera
tion
so
lve
prob
lem
s on
the
mot
ion
of p
roje
ctile
s us
ing
horiz
onta
l
and
verti
cal e
quat
ions
of
mot
ion
fin
d th
e m
agni
tude
and
the
Pr
ojec
tile
- M
otio
n of
a p
roje
ctile
- Ve
loci
ty a
nd
disp
lace
men
ts
R
ange
on
horiz
onta
l pla
ne
G
reat
est h
eigh
t
M
axim
um ra
nge
C
arte
sian
equ
atio
n of
a
traje
ctor
y of
a p
roje
ctile
M
odel
ling
the
mot
ion
of a
proj
ectil
e as
a p
artic
le m
ovin
g
with
con
stan
t acc
eler
atio
n
Ap
plyi
ng h
oriz
onta
l and
ver
tical
equa
tions
of m
otio
n in
sol
ving
prob
lem
s on
the
mot
ion
of
proj
ectil
es
C
alcu
latin
g th
e m
agni
tude
and
the
dire
ctio
n of
the
velo
city
at a
IC
T to
ols
G
eo-b
oard
En
viro
nmen
t
R
elev
ant t
exts
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
32 33
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
45
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
dire
ctio
n of
the
velo
city
at a
give
n tim
e or
pos
ition
fin
d th
e ra
nge
on th
e
horiz
onta
l pla
ne a
nd h
eigh
t
reac
hed
de
rive
form
ulae
for g
reat
est
heig
ht a
nd m
axim
um ra
nge
de
rive
the
Car
tesi
an e
quat
ion
of a
traj
ecto
ry o
f a p
roje
ctile
so
lve
prob
lem
s us
ing
the
Car
tesi
an e
quat
ion
of a
traje
ctor
y of
a p
roje
ctile
give
n tim
e or
pos
ition
Fi
ndin
g th
e ra
nge
on th
e
horiz
onta
l pla
ne a
nd h
eigh
t
reac
hed
Derivingform
ulaeforgreatest
heig
ht a
nd m
axim
um ra
nge
DerivingtheCartesiane
quat
ion
of a
traj
ecto
ry o
f a p
roje
ctile
So
lvin
g pr
oble
ms
usin
g C
arte
sian
equa
tion
of a
traj
ecto
ry o
f a
proj
ectil
e
34
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 2
: EL
AST
ICIT
Y
46
TOPI
C 2
: EL
ASTI
CIT
Y
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
:
CO
NTE
NT
(Atti
tude
s, S
kills
and
K
now
ledg
e)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
ELAS
TIC
ITY
de
fine
elas
ticity
in s
tring
s an
d
sprin
gs
ex
plai
n H
ooke
’s la
w
ca
lcul
ate
mod
ulus
of e
last
icity
so
lve
prob
lem
s in
volv
ing
forc
es d
ue to
ela
stic
stri
ngs
or
sprin
gs in
clud
ing
thos
e w
here
cons
ider
atio
n of
wor
k an
d
ener
gy a
re n
eede
d
Pr
oper
ties
of e
last
ic s
tring
s
and
sprin
gs
W
ork
done
in s
tretc
hing
a
strin
g
El
astic
pot
entia
l ene
rgy
M
echa
nica
l ene
rgy
C
onse
rvat
ion
of m
echa
nica
l
ener
gy
Discussingelasticityinstringsand
sprin
gs
Ex
plai
ning
Hoo
ke’s
law
C
ondu
ctin
g ex
perim
ents
to v
erify
Hoo
ke’s
law
C
alcu
latin
g m
odul
us o
f ela
stic
ity
So
lvin
g pr
oble
ms
invo
lvin
g fo
rces
due
to e
last
ic s
tring
s or
spr
ings
incl
udin
g th
ose
whe
re
cons
ider
atio
n of
wor
k an
d en
ergy
are
need
ed
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g el
astic
ity a
nd e
xplo
ring
thei
r app
licat
ions
in li
fe
IC
T to
ols
R
elev
ant
text
s
En
viro
nmen
t
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
34 35
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
48
TOPI
C 4
: C
IRC
ULA
R M
OTI
ON
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
CIR
CU
LAR
MO
TIO
N
(Ver
tical
and
Hor
izon
tal)
de
rive
the
form
ula
for s
peed
,
velo
city
and
acc
eler
atio
n of
a
parti
cle
mov
ing
in a
circ
le
ex
plai
n th
e co
ncep
t of
angu
lar s
peed
for a
par
ticle
mov
ing
in a
circ
le w
ith
cons
tant
spe
ed
di
stin
guis
h be
twee
n
horiz
onta
l and
ver
tical
mot
ion
ca
lcul
ate
ang
ular
spe
ed fo
r a
parti
cle
mov
ing
in a
circ
le
with
con
stan
t spe
ed
ca
lcul
ate
acce
lera
tion
of a
parti
cle
mov
ing
in a
circ
le
with
con
stan
t spe
ed
so
lve
prob
lem
s w
hich
can
be
mod
elle
d as
the
mot
ion
of a
parti
cle
mov
ing
in a
horiz
onta
l circ
le w
ith c
onst
ant
spee
d
An
gula
r spe
ed a
nd v
eloc
ity
H
oriz
onta
l and
ver
tical
circ
ular
mot
ion
A
ccel
erat
ion
of a
par
ticle
mov
ing
on a
circ
le
M
otio
n in
a c
ircle
with
cons
tant
spe
ed
C
entri
peta
l for
ce
R
elat
ion
betw
een
angu
lar
and
linea
r spe
ed
C
onic
al p
endu
lum
Ba
nked
trac
ks
Ex
plor
ing
and
deriv
ing
the
form
ula
for s
peed
, vel
ocity
and
acce
lera
tion
of a
par
ticle
mov
ing
in a
circ
le
Discussingtheconceptof
angu
lar s
peed
for a
par
ticle
mov
ing
in a
circ
le w
ith c
onst
ant
spee
d
Distinguishingbetweenthe
conc
epts
of h
oriz
onta
l and
verti
cal m
otio
n in
a c
ircle
C
ompu
ting
ang
ular
spe
ed fo
r a
parti
cle
mov
ing
in a
circ
le w
ith
cons
tant
spe
ed
C
alcu
latin
g ac
cele
ratio
n of
a
parti
cle
mov
ing
in a
circ
le w
ith
cons
tant
spe
ed
So
lvin
g pr
oble
ms
whi
ch c
an b
e
mod
elle
d as
the
mot
ion
of a
parti
cle
mov
ing
in a
hor
izon
tal
IC
T to
ols
R
elev
ant t
exts
En
viro
nmen
t
Si
mpl
e
pend
ulum
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
TOPI
C 3
: EN
ERG
Y W
OR
K
36
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
48
TOPI
C 4
: C
IRC
ULA
R M
OTI
ON
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
CIR
CU
LAR
MO
TIO
N
(Ver
tical
and
Hor
izon
tal)
de
rive
the
form
ula
for s
peed
,
velo
city
and
acc
eler
atio
n of
a
parti
cle
mov
ing
in a
circ
le
ex
plai
n th
e co
ncep
t of
angu
lar s
peed
for a
par
ticle
mov
ing
in a
circ
le w
ith
cons
tant
spe
ed
di
stin
guis
h be
twee
n
horiz
onta
l and
ver
tical
mot
ion
ca
lcul
ate
ang
ular
spe
ed fo
r a
parti
cle
mov
ing
in a
circ
le
with
con
stan
t spe
ed
ca
lcul
ate
acce
lera
tion
of a
parti
cle
mov
ing
in a
circ
le
with
con
stan
t spe
ed
so
lve
prob
lem
s w
hich
can
be
mod
elle
d as
the
mot
ion
of a
parti
cle
mov
ing
in a
horiz
onta
l circ
le w
ith c
onst
ant
spee
d
An
gula
r spe
ed a
nd v
eloc
ity
H
oriz
onta
l and
ver
tical
circ
ular
mot
ion
A
ccel
erat
ion
of a
par
ticle
mov
ing
on a
circ
le
M
otio
n in
a c
ircle
with
cons
tant
spe
ed
C
entri
peta
l for
ce
R
elat
ion
betw
een
angu
lar
and
linea
r spe
ed
C
onic
al p
endu
lum
Ba
nked
trac
ks
Ex
plor
ing
and
deriv
ing
the
form
ula
for s
peed
, vel
ocity
and
acce
lera
tion
of a
par
ticle
mov
ing
in a
circ
le
Discussingtheconceptof
angu
lar s
peed
for a
par
ticle
mov
ing
in a
circ
le w
ith c
onst
ant
spee
d
Distinguishingbetweenthe
conc
epts
of h
oriz
onta
l and
verti
cal m
otio
n in
a c
ircle
C
ompu
ting
ang
ular
spe
ed fo
r a
parti
cle
mov
ing
in a
circ
le w
ith
cons
tant
spe
ed
C
alcu
latin
g ac
cele
ratio
n of
a
parti
cle
mov
ing
in a
circ
le w
ith
cons
tant
spe
ed
So
lvin
g pr
oble
ms
whi
ch c
an b
e
mod
elle
d as
the
mot
ion
of a
parti
cle
mov
ing
in a
hor
izon
tal
IC
T to
ols
R
elev
ant t
exts
En
viro
nmen
t
Si
mpl
e
pend
ulum
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
TOPI
C 4
: C
IRC
ULA
R M
OTI
ON
36 37
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
49
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
so
lve
prob
lem
s w
hich
can
be
mod
elle
d as
the
mot
ion
of a
parti
cle
mov
ing
in a
ver
tical
circ
le w
ith c
onst
ant s
peed
fin
d th
e re
latio
nshi
p be
twee
n
angu
lar a
nd li
near
spe
ed
ca
lcul
ate
tens
ion
in a
stri
ng
and
angu
lar s
peed
in a
coni
cal p
endu
lum
so
lve
prob
lem
s in
volv
ing
bank
ed tr
acks
.
so
lve
prob
lem
s w
hich
can
be
mod
elle
d as
the
mot
ion
of a
parti
cle
mov
ing
in a
horiz
onta
l circ
le w
ith c
onst
ant
spee
d us
ing
New
ton’
s
seco
nd la
w
and
verti
cal c
ircle
with
con
stan
t
spee
d
Discussin
g th
e re
latio
nshi
p
betw
een
angu
lar a
nd li
near
spee
d
C
ompu
ting
tens
ion
in a
stri
ng
and
angu
lar s
peed
in a
con
ical
pend
ulum
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g ci
rcul
ar m
otio
n an
d
expl
orin
g th
eir a
pplic
atio
ns in
life
38
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 5
: SI
MPL
E H
AR
MIN
IC M
OTI
ON
50
TOPI
C 5
: SI
MPL
E H
ARM
INIC
MO
TIO
N
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
SIM
PLE
HAR
MO
NIC
M
OTI
ON
de
fine
sim
ple
harm
onic
mot
ion
so
lve
prob
lem
s us
ing
the
stan
dard
sim
ple
harm
onic
mot
ion
form
ula
fo
rmul
ate
diffe
rent
ial
equa
tions
of m
otio
n in
prob
lem
s le
adin
g to
sim
ple
harm
onic
mot
ion
so
lve
diffe
rent
ial e
quat
ions
invo
lvin
g si
mpl
e ha
rmon
ic
mot
ion
to o
btai
n th
e pe
riod
and
ampl
itude
of t
he m
otio
n
Ba
sic
equa
tion
of s
impl
e
harm
onic
mot
ion
Pr
oper
ties
of s
impl
e ha
rmon
ic
mot
ion
Discussingsimpleharm
onic
mot
ion
C
ondu
ctin
g ex
perim
ents
to
dem
onst
rate
sim
ple
harm
onic
mot
ion
usin
g a
pend
ulum
So
lvin
g pr
oble
ms
usin
g th
e
stan
dard
sim
ple
harm
onic
mot
ion
form
ula
Fo
rmul
atin
g di
ffere
ntia
l equ
atio
ns
of m
otio
n in
pro
blem
s le
adin
g to
sim
ple
harm
onic
mot
ion
So
lvin
g di
ffere
ntia
l equ
atio
ns
invo
lvin
g si
mpl
e ha
rmon
ic m
otio
n
to o
btai
n th
e pe
riod
and
ampl
itude
of th
e m
otio
n
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g si
mpl
e ha
rmon
ic m
otio
n
and
expl
orin
g th
eir a
pplic
atio
ns in
IC
T to
ols
R
elev
ant
text
s
En
viro
nmen
t
Pe
ndul
um
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
38 39
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
STAT
ISTI
CS
TOPI
C 1
: PR
OB
AB
ILIT
Y
52
STAT
ISTI
CS
TOPI
C 1
: PR
OB
ABIL
ITY
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
PRO
BAB
ILIT
Y
defin
e pr
obab
ility
key
term
s
ca
lcul
ate
prob
abilit
ies
of
even
ts
so
lve
prob
lem
s in
volv
ing
cond
ition
al p
roba
bilit
y
us
e tre
e di
agra
ms,
Ven
n
diag
ram
s an
d ou
tcom
e
tabl
es to
sol
ve p
robl
ems
us
e th
e no
tatio
ns n
!, n P𝑟𝑟 a
nd
(𝑛𝑛 𝑟𝑟)
de
fine
perm
utat
ions
and
com
bina
tions
so
lve
prob
lem
s in
volv
ing
perm
utat
ions
and
com
bina
tions
Ev
ents
- In
depe
nden
t
- M
utua
lly e
xclu
sive
- Ex
haus
tive
- C
ombi
ned
C
ondi
tiona
l
prob
abilit
y
Tr
ee d
iagr
ams
Outcometables
Ve
nn d
iagr
ams
Pe
rmut
atio
ns a
nd
com
bina
tions
Discussingtheimporta
nceof
prob
abilit
y in
life
C
ompu
ting
prob
abilit
ies
of a
varie
ty o
f eve
nts
Ap
plyi
ng c
ondi
tiona
l pro
babi
lity
conc
epts
in s
olvi
ng p
robl
ems
So
lvin
g pr
oble
ms
usin
g tre
e
diag
ram
s, V
enn
diag
ram
s an
d
outc
ome
tabl
es
C
arry
ing
out e
xper
imen
ts
invo
lvin
g pr
obab
ility
U
sing
the
nota
tions
n!,
n P𝑟𝑟 a
nd
(𝑛𝑛 𝑟𝑟)
Ex
plai
ning
the
mea
ning
s of
perm
utat
ions
and
com
bina
tions
So
lvin
g pr
oble
ms
invo
lvin
g
perm
utat
ions
and
com
bina
tions
IC
T to
ols
R
elev
ant
text
s
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
40
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 2
: R
AN
DO
M V
AR
IAB
LES
54
TOPI
C 2
: R
AND
OM
VAR
IAB
LES
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
RAN
DO
M V
ARIA
BLE
S (d
iscr
ete
and
cont
inuo
us)
de
fine
a ra
ndom
var
iabl
e
co
nstru
ct a
pro
babi
lity
dist
ribut
ion
tabl
e
de
fine
expe
ctat
ion
us
e th
e pr
obab
ility
dens
ity
func
tions
and
cum
ulat
ive
dist
ribut
ion
func
tions
to
calc
ulat
e pr
obab
ilitie
s
ca
lcul
ate
mea
n, m
ode,
med
ian,
sta
ndar
d de
viat
ion,
varia
nce
and
perc
entil
es
us
e in
tegr
atio
n to
cal
cula
te
cum
ulat
ive
dist
ribut
ion
func
tion
from
pro
babi
lity
dens
ity fu
nctio
n
us
e di
ffere
ntia
tion
to
calc
ulat
e pr
obab
ility
dens
ity
func
tion
from
cum
ulat
ive
dist
ribut
ion
func
tion
Pr
obab
ility
dist
ribut
ions
Ex
pect
atio
n
Va
rianc
e
Pr
obab
ility
dens
ity fu
nctio
ns
) and
cum
ulat
ive
dist
ribut
ion
func
tions
(cdf
)
M
ean,
med
ian,
mod
e,
stan
dard
dev
iatio
n an
d
perc
entil
es
Discussingexam
plesofrandom
varia
bles
C
onst
ruct
ing
prob
abilit
y
dist
ribut
ion
tabl
es
C
alcu
latin
g m
ean,
mod
e, m
edia
n,
stan
dard
dev
iatio
n, v
aria
nce
and
perc
entil
es
So
lvin
g pr
oble
ms
invo
lvin
g m
ean,
varia
nce
and
stan
dard
dev
iatio
n
Discussingthedifference
betw
een
a di
scre
te ra
ndom
varia
ble
and
a co
ntin
uous
rand
om v
aria
ble
Discussingthesignificanceof
prob
abilit
y de
nsity
func
tion
and
cum
ulat
ive
dist
ribut
ion
func
tion
of
a co
ntin
uous
rand
om v
aria
ble
C
ompu
ting
prob
abilit
ies
usin
g
both
and
cdf
IC
T to
ols
R
elev
ant t
exts
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
40 41
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
55
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
so
lve
prob
lem
s in
volv
ing
prob
abilit
y de
nsity
func
tion
So
lvin
g pr
oble
ms
invo
lvin
g pd
f
and
cdf
DIS
TRIB
UTI
ON
S
Outlinethecharacteristicsof
Bino
mia
l, Po
isso
n an
d
Nor
mal
dis
tribu
tions
ca
lcul
ate
the
mea
n, v
aria
nce
and
stan
dard
dev
iatio
n of
each
dis
tribu
tion
ca
lcul
ate
prob
abilit
ies
for t
he
dist
ribut
ions
ex
plai
n th
e ch
arac
teris
tics
of
a no
rmal
dis
tribu
tion
curv
e
st
anda
rdiz
e a
rand
om
varia
ble
us
e th
e st
anda
rd n
orm
al
tabl
es to
obt
ain
prob
abilit
ies
ap
prox
imat
e th
e bi
nom
ial
usin
g th
e no
rmal
dis
tribu
tion
Bi
nom
ial d
istri
butio
n
Po
isso
n d
istri
butio
n
N
orm
al d
istri
butio
n
St
anda
rd n
orm
al ta
bles
C
ontin
uity
cor
rect
ion
Li
near
com
bina
tions
of
norm
al a
nd P
oiss
on
dist
ribut
ions
Discussingthecharacteristicsof
Bino
mia
l, Po
isso
n an
d N
orm
al
dist
ribut
ions
C
ompu
ting
the
mea
n, v
aria
nce
and
stan
dard
dev
iatio
n of
eac
h
dist
ribut
ion
C
alcu
latin
g pr
obab
ilitie
s us
ing
the
prob
abilit
y de
nsity
func
tions
of
the
dist
ribut
ions
Discussingthecharacteristicsof
a no
rmal
dis
tribu
tion
curv
e, g
ivin
g
life
exam
ples
St
anda
rdiz
ing
rand
om v
aria
bles
Obtainingprobabilitiesusing
stan
dard
nor
mal
tabl
es
U
sing
the
norm
al d
istri
butio
n
mod
el to
app
roxi
mat
e th
e
IC
T to
ols
R
elev
ant t
exts
En
viro
nmen
t
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
42
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
56
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
whe
re n
is la
rge
enou
gh to
ensu
re th
at 𝑛𝑛𝑛𝑛
> 5
and 𝑛𝑛𝑛𝑛
> 5
and
appl
y co
ntin
uity
corre
ctio
n
us
e th
e no
rmal
dis
tribu
tion
as
a m
odel
to s
olve
pro
blem
s
us
e th
e fo
llow
ing
fact
s to
solv
e pr
oble
ms:
- E(
aX±b
) = a
E(X)
± b
and
Var(a
X±b)
= a
2 Var
(X)
- E(
aX±b
Y) =
aE(
X)±b
E(Y)
- Va
r(aX±
bY) =
a2 V
ar(X
)+
b2 Var
(Y) f
or in
depe
nden
t
X an
d Y
us
e th
e re
sults
that
:
- If
X ha
s a
norm
al
dist
ribut
ion,
then
so
does
aX +
b
- If
X an
d Y
have
inde
pend
ent n
orm
al
dist
ribut
ions
, the
n
aX +
bY
has
a no
rmal
bino
mia
l dis
tribu
tion
U
sing
the
norm
al d
istri
butio
n as
a
mod
el to
sol
ve p
robl
ems
Discussingexam
plesoflinear
com
bina
tions
C
alcu
latin
g pr
obab
ilitie
s, m
ean
and
varia
nce
of a
sum
of t
wo
or
mor
e in
depe
nden
t var
iabl
es fo
r
Pois
son
or n
orm
al d
istri
butio
n
So
lvin
g pr
oble
ms
invo
lvin
g lin
ear
com
bina
tions
and
thei
r
appl
icat
ions
in li
fe
So
lvin
g pr
oble
ms
invo
lvin
g
dist
ribut
ions
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g di
strib
utio
ns a
nd
expl
orin
g th
eir a
pplic
atio
ns in
life
42 43
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
57
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
dist
ribut
ion
- If
X an
d Y
have
inde
pend
ent P
oiss
on
dist
ribut
ions
, the
n X
+ Y
has
a Po
isso
n di
strib
utio
n
so
lve
prob
lem
s in
volv
ing
the
dist
ribut
ions
44
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 3
: SA
MPL
ING
AN
D E
STIM
ATIO
NS
58
TOPI
C 3
: SA
MPL
ING
AN
D E
STIM
ATIO
NS
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
SAM
PLIN
G T
ECH
NIQ
UES
AN
D E
STIM
ATIO
N
di
stin
guis
h be
twee
n a
sam
ple
and
a po
pula
tion
di
stin
guis
h be
twee
n
prob
abilit
y sa
mpl
ing
tech
niqu
es a
nd n
on-
prob
abilit
y sa
mpl
ing
tech
niqu
es
ap
ply
the
sam
plin
g m
etho
ds
to id
entif
y re
pres
enta
tive
sam
ples
ca
lcul
ate
sam
ple
mea
n,
varia
nce
and
stan
dard
devi
atio
n
fin
d th
e un
bias
ed e
stim
ates
of
popu
latio
n pa
ram
eter
s
st
ate
the
Cen
tral L
imit
Theo
rem
re
cogn
ize
that
the
sam
ple
mea
n ca
n be
rega
rded
as
a
rand
om v
aria
ble
Pr
obab
ility
sam
plin
g
tech
niqu
es
N
on-p
roba
bilit
y s
ampl
ing
tech
niqu
es
Es
timat
ion
of p
opul
atio
n
para
met
ers
C
entra
l lim
it th
eore
m
C
onfid
ence
inte
rval
s
Discussingthedifferencebetween
a sa
mpl
e an
d a
popu
latio
n,
prob
abilit
y sa
mpl
ing
and
non-
prob
abilit
y sa
mpl
ing
tech
niqu
es
Id
entif
ying
and
dis
cuss
ing
situ
atio
ns in
whi
ch p
roba
bilit
y an
d
non-
prob
abilit
y sa
mpl
ing
met
hods
are
used
C
arry
ing
out s
ampl
ing
in a
prac
tical
situ
atio
n
C
ompu
ting
sam
ple
mea
n,
varia
nce
and
stan
dard
dev
iatio
n
Determiningtheunbiased
estim
ates
of p
opul
atio
n
para
met
ers
DerivingtheCentra
lLimit
Theo
rem
Ex
plai
ning
how
the
sam
ple
mea
n
can
be re
gard
ed a
s a
rand
om
varia
ble
IC
T to
ols
R
elev
ant t
exts
En
viro
nmen
t
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
44 45
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
59
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
us
e th
e C
entra
l Lim
it Th
eore
m
in s
olvi
ng p
robl
ems
id
entif
y th
e im
plic
atio
ns o
f the
Cen
tral L
imit
Theo
rem
on
smal
l and
larg
e sa
mpl
es
de
term
ine
a co
nfid
ence
inte
rval
for a
pop
ulat
ion
mea
n
in c
ases
whe
re th
e po
pula
tion
is n
orm
ally
dis
tribu
ted
with
know
n va
rianc
e or
whe
re a
larg
e sa
mpl
e w
ith u
nkno
wn
varia
nce
is u
sed
de
term
ine
a co
nfid
ence
inte
rval
for a
pop
ulat
ion
mea
n
in c
ases
whe
re th
e po
pula
tion
is n
orm
ally
dis
tribu
ted
with
unkn
own
varia
nce
whe
re a
smal
l sam
ple
is u
sed
de
term
ine
from
a la
rge
sam
ple
an a
ppro
xim
ate
conf
iden
ce in
terv
al fo
r a
popu
latio
n pr
opor
tion
So
lvin
g pr
oble
ms
usin
g th
e
Cen
tral L
imit
Theo
rem
Discussingtheimplicationsofthe
Cen
tral L
imit
Theo
rem
C
alcu
latin
g co
nfid
ence
inte
rval
s
for p
opul
atio
n m
ean
in c
ases
whe
re th
e po
pula
tion
is n
orm
ally
dist
ribut
ed w
ith k
now
n va
rianc
e or
whe
re a
larg
e sa
mpl
e w
ith
unkn
own
varia
nce
is u
sed
C
ompu
ting
conf
iden
ce in
terv
als
for p
opul
atio
n m
ean
in c
ases
whe
re th
e po
pula
tion
is n
orm
ally
dist
ribut
ed w
ith u
nkno
wn
varia
nce
whe
re a
sm
all s
ampl
e is
use
d
Determining
from
a la
rge
sam
ple
an a
ppro
xim
ate
conf
iden
ce
inte
rval
for a
pop
ulat
ion
prop
ortio
n
So
lvin
g pr
oble
ms
invo
lvin
g
sam
plin
g an
d es
timat
ion
C
ondu
ctin
g fie
ldw
ork
46
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
60
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
so
lve
prob
lem
s in
volv
ing
sam
plin
g an
d es
timat
ion
inve
stig
atio
ns in
volv
ing
sam
plin
g
and
estim
atio
n
46 47
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 4
: ST
ATIS
TIC
AL
INFE
REN
CE
61
TOPI
C 4
: ST
ATIS
TIC
AL IN
FER
ENC
E
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
HYP
OTH
ESIS
TES
TIN
G
fo
rmul
ate
hypo
thes
es
di
stin
guis
h be
twee
n a
type
1
and
a ty
pe 2
erro
r
co
mpu
te p
roba
bilit
ies
of
mak
ing
type
1 a
nd ty
pe 2
erro
rs
ap
ply
a hy
poth
esis
test
in th
e
cont
ext o
f a s
ingl
e
obse
rvat
ion
from
a p
opul
atio
n
whi
ch h
as b
inom
ial
dist
ribut
ion
usin
g ei
ther
the
bino
mia
l dis
tribu
tion
or th
e
norm
al a
ppro
xim
atio
n to
the
bino
mia
l dis
tribu
tion
ap
ply
a hy
poth
esis
test
conc
erni
ng p
opul
atio
n m
ean
usin
g a
sam
ple
draw
n fro
m a
norm
al d
istri
butio
n of
kno
wn
varia
nce
usin
g th
e no
rmal
dist
ribut
ion
N
ull h
ypot
hesi
s
Al
tern
ativ
e hy
poth
esis
Te
st s
tatis
tics
Si
gnifi
canc
e le
vel
H
ypot
hesi
s te
st (1
-tail
and
2-
tail)
Ty
pe 1
and
type
2 e
rrors
z-
test
s
t –
test
s
ch
i-squ
ared
test
s
Discussinghypothesistestingin
rese
arch
C
alcu
latin
g pr
obab
ilitie
s of
mak
ing
type
1 a
nd ty
pe 2
erro
rs
Ap
plyi
ng h
ypot
hesi
s te
sts
in th
e
cont
ext o
f a s
ingl
e ob
serv
atio
n
from
a p
opul
atio
n w
hich
has
bino
mia
l dis
tribu
tion
usin
g ei
ther
the
bino
mia
l dis
tribu
tion
or th
e
norm
al a
ppro
xim
atio
n to
the
bino
mia
l dis
tribu
tion
Discussingthecharacteristicsof
a t a
nd c
hi-s
quar
ed d
istri
butio
n
Fo
rmul
atin
g an
d ap
plyi
ng
hypo
thes
is te
sts
conc
erni
ng
popu
latio
n m
ean
usin
g a
smal
l
sam
ple
draw
n fro
m a
nor
mal
dist
ribut
ion
of u
nkno
wn
varia
nce
usin
g a
t – te
st
IC
T to
ols
R
elev
ant t
exts
En
viro
nmen
t
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
48
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
62
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
de
scrib
e th
e ch
arac
teris
tics
of
a t a
nd c
hi-s
quar
ed
dist
ribut
ion
ap
ply
a hy
poth
esis
test
conc
erni
ng p
opul
atio
n m
ean
usin
g a
smal
l sam
ple
draw
n
from
a n
orm
al d
istri
butio
n of
unkn
own
varia
nce
usin
g a
t –
test
us
e a
chi-s
quar
ed te
st to
test
for i
ndep
ende
nce
in a
cont
inge
ncy
tabl
e
us
e a
chi-s
quar
ed te
st to
car
ry
out t
he g
oodn
ess
of fi
t
anal
ysis
so
lve
prob
lem
s us
ing
an
appr
opria
te te
st
us
ing
chi-s
quar
ed te
sts
to te
st fo
r
inde
pend
ence
in a
con
tinge
ncy
tabl
e
ap
plyi
ng c
hi-s
quar
ed te
sts
to
carr
y ou
t the
goo
dnes
s of
fit
anal
ysis
So
lvin
g pr
oble
ms
invo
lvin
g
hypo
thes
is te
sts
C
ondu
ctin
g re
sear
ch p
roje
cts
invo
lvin
g hy
poth
esis
test
s
48 49
Addi
tiona
l Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
TOPI
C 5
: B
IVA
RIA
TE D
ATA
63
TOPI
C 5
: B
IVAR
IATE
DAT
A
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
BIV
ARIA
TE D
ATA
plot
sca
tter d
iagr
ams
dr
aw li
nes
of b
est f
it
fin
d th
e eq
uatio
ns o
f
regr
essi
on li
nes
ca
lcul
ate
Pear
son`
s pr
oduc
t
mom
ent c
orre
latio
n
coef
ficie
nt (r
)
co
mpu
te th
e co
effic
ient
of
dete
rmin
atio
n (r2 )
so
lve
prob
lem
s in
volv
ing
regr
essi
on a
nd c
orre
latio
n
Sc
atte
r dia
gram
s
R
egre
ssio
n lin
es
Le
ast s
quar
es
Pe
arso
n`s
Prod
uct m
omen
t
corre
latio
n (r)
C
oeffi
cien
t of d
eter
min
atio
n
(r2 )
Pl
ottin
g an
d in
terp
retin
g sc
atte
r
diag
ram
s
Drawinglinesofbestfit
Fi
ndin
g th
e eq
uatio
ns o
f
regr
essi
on li
nes
C
ompu
ting
Pear
son`
s pr
oduc
t
mom
ent c
orre
latio
n co
effic
ient
(r)
In
terp
retin
g th
e va
lue
of
Pear
son`
s pr
oduc
t mom
ent
corre
latio
n co
effic
ient
Discussingthesignificanceof
coef
ficie
nt o
f det
erm
inat
ion
So
lvin
g pr
oble
ms
invo
lvin
g
regr
essi
on a
nd c
orre
latio
n
C
ondu
ctin
g in
vest
igat
ions
invo
lvin
g lin
ear r
elat
ions
hips
R
epre
sent
ing
life
phen
omen
a
usin
g m
athe
mat
ical
mod
els
invo
lvin
g bi
varia
te d
ata
and
IC
T to
ols
R
elev
ant t
exts
En
viro
nmen
t
G
eo-b
oard
Br
aille
mat
eria
ls
Ta
lkin
g bo
oks
64
SUB
TOPI
C
LEAR
NIN
G O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T (A
ttitu
des,
Ski
lls a
nd
Kno
wle
dge)
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
expl
orin
g th
eir a
pplic
atio
ns in
life
Additional Mathematics Syllabus Forms 5 - 6
9.0 ASSESSMENT
9.1 Assessment Objectives
The assessment will test candidate’s ability to:-
9.1.1 usemathematicalsymbols,termsanddefinitionsappropriately9.1.2 sketch graphs accurately 9.1.3 use appropriate formulae, algorithms and strategies to solve problems in familiar and less familiar contexts 9.1.4 solve problems in Pure Mathematics, Mechanics and Statistics systematically9.1.5 apply mathematical reasoning and communicate mathematical ideas clearly 9.1.6 conduct mathematical proofs rigorously9.1.7 make effective use of a variety of ICT tools in solving problems 9.1.8 construct and use appropriate mathematical models for a given life situation 9.1.9 conduct research projects including those related to enterprise9.1.10 draw inferences through correct manipulation of data.9.1.11 use data correctly to predict trends for planning and decision making purposes9.1.12 construct mathematical arguments through appropriate use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions9.1.13 evaluate mathematical models including an appreciation of the assumptions made and interpret, justify and present the result from a mathematical analysis in a form relevant to the original problem
9.2 Scheme of Assessment
Forms 5 to 6 Additional Mathematics assessment will be based on 30% Continuous Assessment and 70% Summative Assessment.The syllabus’ scheme of assessment is grounded in the principle of equalisation of opportunities hence, doesnotcondonedirectorindirectdiscriminationoflearners.Arrangements,accommodationsandmodificationsmust be visible in both Continuous and Summative Assessments to enable candidates with special needs to access assessments and receive accurate performance measurement of their abilities. Access arrangements must neither give these candidates an undue advantage over others nor compromise the standards being assessed.Candidates who are unable to access the assessments of any component or part of component due to disability (transitory or permanent) may be eligible to receive an award based on the assessment they would have taken.NBForfurtherdetailsonarrangements,accommodationsandmodificationsrefertotheassessmentprocedurebooklet.
a) Continuous Assessment
Continuous Assessment for Form 5 – 6 will consists of topic tasks, written tests, end of term examinations and projects to measure soft skills.
i) Topic Tasks
These are activities that teachers use in their day to day teaching. These should include practical activities, assign-ments and group work activities.
ii) Written Tests
These are tests set by the teacher to assess the concepts and skills covered during a given period of up to a month. The tests should consist of short structured questions as well as long structured questions.
50
iii) End of term examinations
These are comprehensive tests of the whole term’s or year’s work and can be set at school or district or provincial level.
iv) Project
Thisshouldbedonefromtermtwototermfive.
Summary of Continuous Assessment Tasks
Fromtermtwotofive,candidatesareexpectedtohavedonethefollowingrecordedtasks:
• 1topictaskperterm• 2writtentestsperterm• 1endoftermexaminationperterm
Term Number of Topic Tasks
Number of Written Tests
Number of End OfTermExam-ination
Project Total
2 1 2 1 13 1 2 14 1 2 15 1 2 1Actual Weight 3% 8% 9% 10% 30%
Component Skills Topic Tasks Written Tests End of Term ProjectSkill 1Knowledge&Comprehension
50% 50% 50% 20%
Skill 2Application&Analysis
40% 40% 40% 40%
Skill 3Synthesis&Evaluation
10% 10% 10% 40%
Total 100% 100% 100% 100%Actual weighting 3% 8% 9% 10%
Specification Grid for Continuous Assessment
51
Additional Mathematics Syllabus Forms 5 - 6
b. Summative Assessment
The examination will consist of 2 papers: Paper 1 and Paper 2.
69
Actual weighting
3% 8% 9% 10%
b. Summative Assessment
The examination will consist of 2 papers: Paper 1 and Paper 2.
Paper Type of Paper and Topics Marks Duration
1 Pure Mathematics 1 - 10 120 3 hours
2 Mechanics 1 – 5
Statistics 1 – 6
120 3 hours
Paper 1(120 marks)
Pure Mathematics– this is a paper containing about 14 compulsory questions chosen from topics 1 – 6.
Paper 2 (120 marks)
Mechanics and Statistics – this is a paper containing about 14 compulsory questions chosen from topics 1 – 5 of the mechanics section and topics 1 – 5 of the
Statistics section.
Detailed Summative Assessment Table
Paper 1(120 marks)
Pure Mathematics– this is a paper containing about 14 compulsory questions chosen from topics 1 – 6.
Paper 2 (120 marks)
Mechanics and Statistics – this is a paper containing about 14 compulsory questions chosen from topics 1 – 5 of the mechanics section and topics 1 – 5 of the Statistics section.
Detailed Summative Assessment Table
The table below shows the information on types of papers to be offered and their weighting.
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The table below shows the information on types of papers to be offered and their weighting.
P1 P2 Total
Weighting 50% 50% 100%
Actual weighting 35% 35% 70%
Type of Paper PURE MATHEMATICS
Section A (60 Marks)
About 10 compulsory short questions
Section B (60 Marks)
5 compulsory long questions
MECHANICS AND STATISTICS
Section A
MECHANICS-(60 Marks)
About 7 compulsory questions
Section B
STATISTICS- (60 Marks) about 7 compulsory questions
Marks 120 120
Specification Grid for Summative Assessment 52
Additional Mathematics Syllabus Forms 5 - 6
Specification Grid for Summative Assessment
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P1 P2 Total
Skill 1
Knowledge&
Comprehension
50% 36% 86%
Skill 2
Application&
Analysis
40% 36% 76%
Skill 3
Synthesis&
Evaluation
10% 28% 38%
Total 100% 100% 200%
Weighting 35% 35% 70%
9.3 Assessment Model Learners will be assessed using both Continuous and Summative Assessments.
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Additional Mathematics Syllabus Forms 5 - 6
9.3 Assessment Model
Learners will be assessed using both Continuous and Summative Assessments.
Assessment of learner performance in Additional Mathematics
100%
Continuous Assessment 30%
Continuous Assessment Mark = 30%
Final Mark 100%
Summative Assessment 70%
Summative Assessment Mark = 70%
Profiling
Profile
Exit Profile
Topic Tasks3%
Written Tests 8%
End of term
Tests 9%
Project10%
Paper 1 35%
Paper 2 35%
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Additional Mathematics Syllabus Forms 5 - 6
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