Grade 11 Mathematics: Memorandum Paper 2

Mathematics(NSC)/Grade 11/ P2

MEMORANDUM

86

Exempl

ar

Grade 11 Mathematics: Memorandum Paper 2

1.1.1

1.1.2

1.1.3

1.1.4

1.2

1.3.1

1.3.2

1.4

1.5

1.6.1

1.6.2

1.7

AB

(5 2) 2

25

=5D

Bot

h poi

nt

shavet

hesamex-valuet

herefore

x = 4D

52

3

m=

= D

40 4

3

x  2D

?y

4

3

tanT

D

4

? T 36,

87 D D

2

m = 3 DD

0,

81 D

-1,

92 DD

 si

nA

DD

cosA

= -tanA D

1

t

an2x = D

3

?Referenceangl

e:18,

43¡ãD

?2x = 18,

43¡ã+ 180¡ãnD

?x = 9,

22¡ã+ 90¡ãnD n? Z D

?x = 9,

22¡ãor 99,

22¡ãor 189,

22¡ã

5

KT

DD

sin40D sin60D

? KT = 3,

71 cm D

2

2

2

PT = 7 + 5 -2(7)(5)cos30¡ãDD

? PT = 3,

66cm D

Basi

cshapeD

Mi

nimum = 10D

M edi

anandl

ower quart

i

l

eD

Upper quart

i

l

eandmaximum D

Scal

eshownD

10 11

1.8

2.1

2.2

(4 

0) 2 D

17

20

h = 12 D (Pyt

hagoras)

1 2

V = ?r h

3

1

= ?(5)?(12) D

3

3

= 314.16mm D

Di

agonal

sareequalD

Adjacentsidesareperpendicular D

AC

(21 0) 2

30

2.3

2

1

2.4

2

2

2

1

2

3.5

4

3

Copyright reserved

3.6

3

4

2

5

2

8-4 4+8

Mi

dpoi

ntofBB?i

s(2 ;2 ) = (2;

6) DD

1

mBB'  D

3

Equat

i

onofperpendi

cul

ar:

y = 3x + cD

?6= 6+ cD

?0= c

?y = 3x

Aypoi

ntofi

nt

ersect

i

on-4x = 3xD

? 7x = 0

? x = 0D

? y = 0D

? (0;0) i

st

hepoi

ntofi

nt

ersect

i

onofAA?

andBB.?

A' ' (3;5) D

B ''( 8 ;

4)D

C ''( 2;

2) D

5

3

3

4.1

5

3

2

(20

5) 2 D

(

11 10) 2 (25 

0) 2 D

3.2

3.3

3

666 D

BD

3.1

626 D

25  20 5

m AB

DD

11  0 11

20  0

m AD

2 DD

0 1 0

No

AC andBD arenotequaldi

agonal

s. D

m AB m BC zu

1 ? AB andBC arenot

perpendi

cul

ar t

oeach ot

her. D

A' (5;

3) DD

B ' (4;

8) DD

C ' (2;2) D

(-y ;x) DD

4

P ' (3;

6) D

Q' (

12;

12) D

R' (

18;

3) D

S ' (9;3) D

Li

nesofenl

argementDD

P?Q?R?S?ongraph D

7

Mathematics(NSC)/Grade 11/ P2

MEMORANDUM

4.2

PQ

4 1

P' Q '

2

3 12

2

4 2

2

6

12

87

cos 2  sin 2 TTD

1 sin 2

sin 2 TT 1  2

sin 2 T DD



13 D

2

117



7.1

7.2

D

9 13 u3 13

Area PQRS

13 u 13 = 13D

Area P?Q?R?S? 3 13 u 3 13 D

= 9¡Á13 = 117

The length of the sides of PQRS increase by

a factor of 3 to give the length of the sides of

P?Q?R?S?. D

The area of PQRS increased by a factor of 9

to give the area of P?Q?R?S? . This is 3? i.e

the square of the increase of the length of the

sides. D

5.1.2

5.2.1

5.2.2

5.3.1

5.3.2

6.1

6.2

6.3

 tan x. cos x tan x



DDDD

 sin x

 sin x

sin x cos x sin x

1

D

.

.



cos x sin x cos x sin x

cos x  1

1

1

or

D

cos x

cos x

 cos 60 D

DD

tan 45 D

1



2 DD

1

1



2

cos x (2 cos x ¨C1) D

cos x = 0 D

? x = 90¡ã + 360¡ãn or 270¡ã + 360¡ãn D n ? Z

(add on the period of the cos graph i.e.360¡ãn

to get general solution)

OR

1

cos x = 2 D

? x = 60¡ã + 360¡ãn or 300¡ã + 360¡ãnD,

n ? ZD

sin (180¡ã+58¡ã) = - sin 58¡ãD = - kD

2

2

sin 58¡ã + cos 58¡ã = 1 D

2

2

? cos 58¡ã = 1 ¨Ck

2

cos 58D

1  k?

DD

1

0,5 or 2 D

Sipho, Ray and Vishnu get - 0,17DD

Lorraine gets 0,23DD

sin 2 T

1

cos 2 T D

sin 2 T

1

cos 2 T

cos 2  sin 2 TT

D

cos 2  sin 2 TT

Copyright reserved

or cos 2 T 1 cos 2

2 cos 2 TT 1

DD

39,69 cmD

3

sin18x  D

5

Reference angle is 36,87¡ãD

18 x 216,87  360

? DDn

1

x 12  20

?DDn D

OR

18 x 323,13  360

? DDn

6

5.1.1

Exemplar

8.1

8.2

8.3

6

9.1

9.2

4

1

10.1

x 18  20

?DDn D

? x 12 , 18, 32 or 38DD

y - xDD

In ¡§PAB:

PB

5

DD

D

sin 90  x sin( y  x )

5 cos x

D

PB ?

sin( y  x )

In ¡§PBT:

PT

sin y

D

PB

5 cos x sin y

D

PT ?

sin( y  x)

1

bcsin x D

2

DA? K 360 90 90 DDD

x

6

2

3

2

1

180 D  x D

1

DAK '?

bc sin(180D  x) D

2

1

bcsin x D

2

'ABC

Sum of lengths is 42,4D

Mean length is 4,24D

3

2

10.2

5

2

3

1

4

7

Length

(cm)

3,2

3,6

5

4,1

4,3

4,7

3,4

5,2

4,6

4,3

2

xi  x

xi  x

-1,04

-0,64

0,76

-0,14

0,06

0,46

-0,84

0,96

0,36

0,06DD

1,0816

0,4096

0,5776

0,0196

0,0036

0,2116

0,7056

0,9216

0,1296

0,0036DD

4,064D

Standard deviation =

4,064

9

0,67 D

6

Mathematics(NSC)/Grade 11/ P2

MEMORANDUM

10.3

88

Length to width comparison of 10

shel

ls

W idth (mm)

4

3

2

1

0

0

1

2

3

4

5

6

Length (mm)

1

1

x  DD

2

2

Line on graph D

90, 330, 740, 940, 1000 DD

y

3

2

Length of pebble/cumulative frequency graph

Cumulative frequency

11.1

11.2

Length of pebble

11.3

D Values plotted at ends of intervals

D D Accurate points

D Accurate curve

D Labels (Length of shell, cumulative

frequency, title)

Median: 49 (47 ¨C 51) D

Upper quartile: 61 (59 ¨C 63) D

Lower quartile: 35 (33 ¨C 37) D

Copyright reserved

5

3

Exemplar

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download