resource pack gr10-term1
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MATHEMATICSRESOURCE PACKGRADE 10 TERM 1
GRADE 10,TERM 1: REsouRcE PAck
2 Grade 10 MATHEMATICS Term 1
ALGEBRAIc EXPREssIoNs
REsouRcE 1
LESSON 1
The Real Number system
REAL NUMBERS
RATIONAL NUMBERS IRRATIONAL NUMBERS
FRACTIONS INTEGERS
NEGATIVE INTEGERS
WHOLE NUMBERS
ZERO NATURAL NUMBERS
GRADE 10,TERM 1: RESOURCE PACK
3Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
REsouRcE 2
LESSON 1
Rational
Irrational
Integers
Whole
Natural
REAL NuMBER sYsTEM
4 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
REsouRcE 3
LESSON 4 INVESTIGATION, RUBRIC AND MARKING GUIDEAL
GEBR
A IN
VEST
IGAT
ION
– GR
ADE
10
A sq
uare
with
leng
th a
is d
raw
n on
the
follo
win
g pa
ge.
Wor
k w
ith a
par
tner
and
follo
w th
e st
eps
belo
w:
PAR
T A
1.
Writ
e an
exp
ress
ion
repr
esen
ting
the
area
of t
he s
quar
e in
te
rms
of a
.2.
D
raw
a s
quar
e in
the
botto
m le
ft co
rner
of t
he la
rge
squa
re
and
call
the
leng
th b
.3.
W
rite
an e
xpre
ssio
n re
pres
entin
g th
e ar
ea o
f the
new
sq
uare
in te
rms
of b
.4.
S
hade
eve
ryth
ing
exce
pt th
e ne
w s
quar
e w
ith le
ngth
b.
5.
Writ
e an
exp
ress
ion
repr
esen
ting
the
area
of t
he s
hade
d pa
rt.
(Hin
t: us
e yo
ur a
nsw
ers
from
1 a
nd 3
)
PAR
T B
1.
Ext
end
the
line
form
ed fo
r the
top
of th
e sm
all s
quar
e (le
ngth
b) t
o th
e rig
ht u
ntil
it m
eets
the
side
of t
he o
rigin
al
squa
re. T
here
sho
uld
now
be
a re
ctan
gle
next
to th
e sm
alle
r sq
uare
.2.
W
hat i
s th
e re
ctan
gle’
s le
ngth
and
bre
adth
in te
rms
of a
and
b?
3.
Cut
out
the
smal
l squ
are
and
set i
t asi
de.
4.
Cut
out
the
rect
angl
e an
d la
y it
alon
gsid
e th
e le
ftove
r par
t to
form
a la
rger
rect
angl
e. M
ake
sure
ther
e ar
e tw
o si
des
that
ar
e th
e sa
me
leng
th a
re n
ext t
o ea
ch o
ther
. (Th
e re
ctan
gle
will
nee
d to
turn
).5.
W
hat i
s th
e N
EW
rect
angl
e’s
leng
th a
nd b
read
th in
term
s of
a
and
b?6.
W
rite
an e
xpre
ssio
n re
pres
entin
g th
e ar
ea o
f the
new
re
ctan
gle
in te
rms
of a
and
b. T
here
is n
o ne
ed to
sim
plify
–
leav
e it
in it
s or
igin
al fo
rm.
7.
Wha
t is
the
rela
tions
hip
betw
een
the
area
of t
he s
hade
d re
gion
(Par
t A s
tep
5) a
nd th
e ar
ea o
f new
rect
angl
e?8.
W
hat a
lgeb
raic
con
cept
has
bee
n pr
oven
by
this
in
vest
igat
ion?
5Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
NA
ME
S:
PAR
T A
1 3 4
PAR
T B
2Le
ngth
:B
read
th:
5Le
ngth
:B
read
th:
6 7 8
a
6 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
32
10
PAR
T A
Evid
ence
that
in
stru
ctio
ns w
ere
follo
wed
met
hodi
cally
Lear
ners
had
writ
ten
mea
sure
men
ts o
n th
eir
squa
re a
s th
ey p
roce
eded
thro
ugh
the
step
s co
rrec
tly.
Lear
ners
see
med
to p
roce
ed
thro
ugh
the
step
s ea
sily.
Lear
ners
nee
ded
som
e
assi
stan
ce
No
atte
mpt
mad
e to
follo
w
the
inst
ruct
ions
Cor
rect
use
of
mat
hem
atic
al s
ymbo
ls
and
lang
uage
All
mat
hem
atic
s w
ritte
n w
ith
no e
rror
s
An
erro
r mad
e in
the
use
of
expo
nent
s O
R th
e us
e of
subt
ract
ion
for s
tep
4.
An
erro
r mad
e in
the
use
of
expo
nent
s A
ND
the
use
of
subt
ract
ion
in s
tep
4.
No
solu
tions
Dem
onst
rate
s a
clea
r un
ders
tand
ing
of
rela
tions
hips
in A
lgeb
ra
No
erro
rs in
any
of t
he s
teps
,
parti
cula
rly s
tep
4.
Ste
ps 1
and
3 c
orre
ct b
ut
step
4 in
corr
ect
At l
east
two
step
s in
corr
ect
No
solu
tions
PAR
T B
Evid
ence
that
in
stru
ctio
ns w
ere
follo
wed
met
hodi
cally
It w
as c
lear
that
the
lear
ners
had
follo
wed
eac
h st
ep
care
fully
and
use
d kn
owle
dge
gain
ed a
s th
ey p
roce
eded
.
Lear
ners
see
med
to p
roce
ed
thro
ugh
the
step
s w
ith e
ase
Lear
ners
nee
ded
som
e
assi
stan
ce
No
atte
mpt
mad
e to
follo
w
the
inst
ruct
ions
Cor
rect
use
of
mat
hem
atic
al s
ymbo
ls
and
lang
uage
All
mat
hem
atic
s w
ritte
n w
ith
no e
rror
s
No
solu
tions
Dem
onst
rate
s a
clea
r un
ders
tand
ing
of
rela
tions
hips
in A
lgeb
ra
No
erro
rs in
any
of t
he s
teps
.
A cl
ear a
nsw
er in
ste
p 8.
No
erro
rs in
any
of t
he s
teps
but s
tep
8 w
as le
ft ou
t or
vagu
e an
d in
corr
ect.
Err
ors
mad
e in
2 o
r mor
e
step
s.
Err
ors
mad
e in
4 o
r mor
e
step
s.
7Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
MA
RK
ING
GU
IDE
PAR
T A
1a2
3b2
4a2 –
b2
PAR
T B
2Le
ngth
: a
– b
Bre
adth
: b
5Le
ngth
: a
+ b
Bre
adth
: a
– b
6(a
+ b
)(a
– b)
7Th
ey a
re e
qual
8Fa
ctor
isin
g a
diffe
renc
e of
two
squa
res
a 2 – b
2 = (a
+ b
)(a
– b)
a
b
b
a –
b
8 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
Par
t B p
oint
4:
b
a – b
a
9Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
ALGEBRAIc EQuATIoNs
REsouRcE 4
LESSON 5
Inequality sign words Open/closed dot Arrow points to the
> Greater than Open right
≥ Greater than or equal to Closed right
< Less than Open left
≤ Less than or equal to Closed left
GRADE 10,TERM 1: REsouRcE PAck
10 Grade 10 MATHEMATICS Term 1
TRIGoNoMETRY
REsouRcE 5
LESSONS 1 & 3
LESSON 1
Sine (sin) Cosine (cos) Tangent (tan)
opposite hypotenuse
SOH
adjacent hypotenuse
CAH
opposite adjacent
TOA
θ θ θ
Hypotenuse
Hypotenuse
Opp
osite
Adjacent Adjacent
Opp
osite
LESSON 3
The six trigonometric functionsbasic reciprocal
sin(θ) - ho cosecant csc(θ) =
( )sin1i
= oh
cos(θ) = ha secant sec(θ) =
( )cos1i
= ah
tan(θ) = ao cotangent cot(θ) =
( )tan1i
= oa
11Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
REsouRcE 6
LESSONS 1 & 3
90º
r = 2
x = √3̄
√3̄2
12
y = 1
x = 1x
y
60º,
,
30º
45º
0º
90º
r = 2y = √3̄
√3̄2
12
x
y
60º
30º
45º
0º
12 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
REsouRcE 7
Test Term 1
QUESTION DESCRIPTION MAXIMUM MARK ACTUAL MARK
1 Algebra 28
2 Number Patterns 6
3 Trigonometry 16
TOTAL 50
13Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
QuEsTIoN 1 28 MARks
1.1 Matcheachnumberwiththedefinitionthatfits.EachnumberonlyhasONEdefinition thatfitsBEST. (5)
a. 8 1. Natural number
b. 0,5 2. Integer
c. –3 3. Whole number
d. 0 4. Rational number
e. 2 5. Irrational number
1.2 Simplify the following:
1.2.1 ( )xx
82
3
--
(2)
1.2.2 x x
x x3 412
2
-+ - - (4)
1.2.3 .
.
27 2
6 3x
x x
x 2
2 2
-
+
(4)
1.3 Solve for x in each of the following:
1.3.1 2x2 + 2x = 12 (4)
1.3.2 2 – x 5
4
+ = x1
5
- (4)
1.3.3 2x + 3.2x + 1 = 56 (3)
1.3.4 4x – 9 < 5x + 4 (2)
QuEsTIoN 2 6 MARks
2.1 Consider the sequence: 10; 6; 2; –2; …
2.1.1 Determine the 5th and 6th terms of the sequence. (2)
2.1.2 Determine the nth term of the sequence. (2)
2.2 Consider the sequence: –1; 0; 1; –1; 0; 1; …
2.2.1 Determine the value of the 100th term. (2)
14 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
QuEsTIoN 3 16 MARks
3.1 State whether each of the following statements are True or False.
3.1.1 sin(x + 2) = sin x + sin 2 (1)
3.1.2 – cos x = cos (–x) (1)
3.2 WITHOUT using your calculator, answer the following:
3.2.1 Evaluate: º º
º º
sin cos
sin tan
90 60
30 45
-- (3)
3.2.2 If 13 sin θ + 12 = 0 and cos θ < 0, calculate the value of 5 tan θ. (4)
3.3 Usingyourcalculator,determinethevalueofθinthefollowingquestions:Note:0<θ<90
3.3.1 3 cos (θ + 10°) = 1 (3)
3.3.2 (4)
30cmA D B30cm
50cm
θ
15Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
REsouRcE 8
Memorandum Test Term 1
QUESTION DESCRIPTION MAXIMUM MARK ACTUAL MARK
1 Algebra ; Exponents; Equations
28
2 Number Patterns 6
3 Trigonometry 16
TOTAL 50
16 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
QuEsTIoN 1 28 MARks
1.1 Matcheachnumberwiththedefinitionthatfits.EachnumberonlyhasONEdefinition thatfitsBEST. (5K)
a. 8 1. Natural number {
b. 0,5 2. Integer {
c. –3 3. Whole number {
d. 0 4. Rational number {
e. 2 5. Irrational number {
1.2 Simplify the following:
1.2.1 ( )xx
82
3
--
(2R)
= ( ) ( )x x x
x2 2 4
2
2
-- + +
{
= x2 + 2x + 4 {
1.2.2 x x
x x3 412
2
-+ - - (4C)
= ( )
( ) ( )
x xx x
1
4 11{
{-
+ --
= x xx x
4 {+ -
= x4 {
1.2.3 .
.
27 2
6 3x
x x
x 2
2 2
-
+
(4R)
= . .
. . .
3 2 2
2 3 3 3x x
x x x
3 2
2 2
{{
-
= 2 x – x + 2.3 x + 2x + 2 – 3x {
= 22.32
= 36 {
17Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
1.3 Solve for x in each of the following:
1.3.1 2x2 + 2x = 12 (4R)
2x2 + 2x – 12 = 0 {
x2 + x – 6 = 0 {
(x + 3)(x – 2) = 0 {
x = –3 or x = 2 {
1.3.2 2 – x 5
4
+ = x1
5
- (4C)
40{– 5x – 25{ = 4 – 4x {
–x = –11
x = 11 {
1.3.3 2x + 3.2x + 1 = 56 (3C)
2x + 3.2x.2 = 56
2x(1 + 3.2) = 56 {
2x.7 = 56 {
2x = 8
x = 3 {
1.3.4 4x – 9 < 5x + 4 (2R)
4x – 5x < 4 + 9 {
–x < 13
x > –13 {
QuEsTIoN 2 6 MARks
2.1 Consider the sequence: 10; 6; 2; –2; …
2.1.1 Determine the 5th and 6th terms of the sequence. (2K)
–6{ and –10{
2.1.2 Determine the nth term of the sequence. (2C)
–4n + 14 { {
18 Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
2.2 Consider the sequence: –1; 0; 1; –1; 0; 1; …
2.2.1 Determine the value of the 100th term. (2P)
–1 { {
QuEsTIoN 3 16 MARks
3.1 State whether each of the following statements are True or False.
3.1.1 sin(x + 2) = sin x + sin 2 False { (1K)
3.1.2 – cos x = cos (–x) False { (1K)
3.2 WITHOUT using your calculator, answer the following:
3.2.1 Evaluate: º º
º º
sin cos
sin tan
90 60
30 45
-- (3R)
= 1
1
1
2
1
2-
-
= –1 {
3.2.2 If 13 sin θ + 12 = 0 and cos θ < 0, calculate the value of 5 tan θ. (4R)
sin θ = 12
13- {
x2 + (–12)2 = 132 {
x2 = 25
x = 5 {
5tan θ = 5 12
5-- lb { = 12
–12
–5
13
θ
3.3 Usingyourcalculator,determinethevalueofθinthefollowingquestions: Note: 0 < θ < 90
3.3.1 3 cos (θ + 10°) = 1 (3C)
cos (θ + 10°) = 13
{
θ + 10° = 70,53° {
θ = 60,53° {
19Grade 10 MATHEMATICS Term 1
GRADE 10,TERM 1: REsouRcE PAck
3.3.2 (4P)
30cmA D B30cm
50cm
θ
CB2 = 502 – 302 {
CB2 = 1 600
CB = 40cm {
tan θ = 4060
{
θ = 33,69° {