Grade 11 Mathematics: Memorandum Paper 2

[Pages:3]Mathematics(NSC)/Grade 11/ P2

86

MEMORANDUM

Grade 11 Mathematics: Memorandum Paper 2

Exemplar

1.1.1 AB (5 2)2 (4 0)2 D

626 D

2.3

25 20 5

25

=5D

2

1.1.2 Both pointshavethesamex-valuetherefore

x = 4D

1

mAB 11 0 11 DD

m AD

20 0 0 1 0

2 DD

4

1.1.3

m =

5 2 40

=

3 4D

2.4 No AC andBD arenotequaldiagonals. D

?y

3 4

x

2

D

1.1.4

tan T

3 4D

mAB mBC z1u? AB andBC arenot

2 3.1

perpendicular toeach other. D A'(5;3) DD

2

B'(4;8) DD

1.2 1.3.1 1.3.2 1.4

1.5

1.6.1

?T 36,87D D

2 m = 3 DD

0,81 D -1,92 DD

sinA cosA DD

= -tanA D

tan2x

=

1 3D

?Referenceangle:18,43?D

?2x = 18,43?+ 180?nD

?x = 9,22?+ 90?nD n ZD

?x = 9,22?or 99,22?or 189,22?

KT

5

DD

sin40D sin60D

2 3.2

2 3.3 1 2

3

3.5

4

C'(2;2) D

5

(-y ;x) DD

2

M

idpointofBB?is(82-4

4+8 ;2 )

=

(2;6) DD

mBB'

1 3

D

Equationofperpendicular:

y = 3x + cD

?6= 6+ cD

?0= c

?y = 3x

5

Aypointofintersection-4x = 3xD

? 7x = 0

? x = 0D

? y = 0D

? (0;0) isthepointofintersectionofAA?

and BB?.

3

? KT = 3,71 cm D 1.6.2 PT2 = 72 + 52 -2(7)(5)cos30?DD

3 3.6 A''(3;5) D B''( 8 ;4 ) D

? PT= 3,66cm D 1.7 BasicshapeD

M inimum = 10D

3 4.1

C''( 2;2) D

3

M edianandlower quartileD

Upper quartileandmaximum D

ScaleshownD

10 11

17

20

30

5

1.8 h = 12 D (Pythagoras) V = 1 r2h 3

1 = 3 (5)?(12) D

= 314.16mm3 D

3

2.1 DiagonalsareequalD

Adjacentsidesareperpendicular D

2

2.2

AC (21 0)2 (205)2 D

P'(3;6) D Q'(12;12) D R'(18;3) D S '(9;3) D

666 D

LinesofenlargementDD

BD (11 10)2 (25 0)2 D

P?Q?R?S?ongraph D 4

7

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Mathematics(NSC)/Grade 11/ P2

87

MEMORANDUM

Exemplar

4.2 PQ 4 1 2 4 2 2 13 D P' Q ' 3 12 2 6 12 2 117

D

cos2 sin 2 TTD

1 sin 2 sin 2 TT 1 2sin 2 T DD

 or cos2 T 1 cos2 2cos2 TT1DD

7.1 39,69 cmD

1

9 13 u3 13 Area PQRS 13 u 13 = 13D Area P?Q?R?S? 3 13 u 3 13 D

7.2

sin18x

3 5

D

Reference angle is 36,87?D

18x 216,87 3?60DDn

= 9?13 = 117 The length of the sides of PQRS increase by a factor of 3 to give the length of the sides of

x 12 2?0DDn D OR

P?Q?R?S?. D

18x 323,13 3?60DDn

The area of PQRS increased by a factor of 9

x 18 2?0DDn D

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

? x 12 , 18, 32 or 38DD

6

the square of the increase of the length of the sides. D

8.1 y - xDD 8.2 In ?PAB:

2

6

PB

5

5.1.1

tan x.cos x tan x sin x sin x

DDDD

 DD

sin 90D x sin( y x)

sin x . cos x sin x . 1 D cos x sin x cos x sin x

PB ? 5cos x D

sin( y x)

3

5.1.2

1 1 cos x

or

cos x 1 cos x D

cos 60D DD

tan 45D

8.3 6

In ?PBT:

sin y

PT PB D

PT ?5cos x sin y D sin( y x)

2

1

2 1

DD

1 2

9.1

1 2

bc

sin

x

D

1

9.2

DA^ K 360 90 90DDDx

4

180D x D

5.2.1 cos x (2 cos x ?1) D 5.2.2 cos x = 0 D

1

DAK '1?bcsin(180D x) D

2

? x = 90? + 360?n or 270? + 360?n D n Z (add on the period of the cos graph i.e.360?n

1 2

bc

sin

x

D

to get general solution)

' ABC

3

OR 1

cos x = 2 D

10.1 Sum of lengths is 42,4D

Mean length is 4,24D

2

10.2

? x = 60? + 360?n or 300? + 360?nD,

n ZD

5

Length (cm)

xi x

xi x 2

5.3.1 sin (180?+58?) = - sin 58?D = - kD

2

5.3.2 sin2 58? + cos2 58? = 1 D

? cos2 58? = 1 ?k2

3,2

-1,04

1,0816

3,6

-0,64

0,4096

5

0,76

0,5776

cos58D 1 k?2 DD

3

4,1

-0,14

0,0196

6.1

0,5

or

1 2

D

1

6.2 Sipho, Ray and Vishnu get - 0,17DD

Lorraine gets 0,23DD

4

4,3

0,06

0,0036

4,7

0,46

0,2116

3,4

-0,84

0,7056

6.3

1

sin 2 cos 2

T T

1

sin 2 T cos2 T

D

5,2

0,96

0,9216

4,6

0,36

0,1296

4,3

0,06DD 0,0036DD

4,064D

cos2 sin 2 TT

cos 2

sin

2

D TT

Standard deviation = 4,064 0,67 D

7

9

6

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Mathematics(NSC)/Grade 11/ P2 MEMORANDUM

10.3

11.1 11.2

Length to width comparison of 10 shells

4

3

W idth (mm)

2

1

0

0

1

2

3

4

5

6

Length (mm)

y

1 2

x

1 2

DD

Line on graph D

90, 330, 740, 940, 1000 DD

Length of pebble/cumulative frequency graph

88

3 2

Cumulative frequency

Length of pebble

D Values plotted at ends of intervals

D D Accurate points

D Accurate curve

D Labels (Length of shell, cumulative

frequency, title)

5

11.3 Median: 49 (47 ? 51) D

Upper quartile: 61 (59 ? 63) D

Lower quartile: 35 (33 ? 37) D

3

Exemplar

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