Resource Pack Gr10-Term1

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


REsouRcE 2

LESSON 1

Rational

Irrational

Integers

Whole

Natural

REAL NuMBER sYsTEM



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?



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



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.



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



Par

t B p

oint

4:

b

a – b

a



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



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



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



REsouRcE 7

Test Term 1

QUESTION DESCRIPTION MAXIMUM MARK ACTUAL MARK

1 Algebra 28

2 Number Patterns 6

3 Trigonometry 16

TOTAL 50



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)



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



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



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 {



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 { {



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° {



3.3.2 (4P)

30cmA D B30cm

50cm

θ

CB2 = 502 – 302 {

CB2 = 1 600

CB = 40cm {

tan θ = 4060

{

θ = 33,69° {

Documents

Resource Pack Gr10-Term1