# Mathematics Grade 11 Paper 2 KZN November 2016 Paper & Memo

> Grade 11 Mathematics Paper 2 question paper and memo from the KZN November Exam 2016, 26 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/grade-11-mathematics-2016-kzn-november-exam-question-paper-and-memorandum-paper-2/c1cf84ce-a2af-4c80-9279-cd817385cad6
- Updated: 2026-09-28
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper and memo
- Year: 2016
- Exam period: KZN November Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 26

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Mathematics · Grade 11 · KZN November Exam · 2016. Question paper and memorandum, 26 pages. Read online or download the PDF.

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### Page 1

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basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

Ao ee eS
; MATHEMATICS P2 1
iy au
i al
i NOVEMBER 2016 "
OT TTTTTTTETITrrrerrerrrerreeecrereerreeceeeee ere sd

NATIONAL

SENIOR CERTIFICATE

GRADE II

MARKS: 150

TIME: 3 hours

This question paper consists of 13 pages and a 22-page answer book.

Copyright reserved

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### Page 2

Mathematies/P2 2 DBE/November 2016

NSC ~ Grade 11

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

3.

This question paper consists of 12 questions.
Answer ALL the questions in the SPECIAL ANSWER BOOK provided.

Clearly show ALL calculations, diagrams, graphs et cetera that you used to determine
the answers,

Answers only will NOT necessarily be awarded full marks,
If necessary, round off answers to TWO decimal places, unless stated otherwise.
Diagrams are NOT necessarily drawn to scale. ¢ )

You may use an approved scientific calculator (non-programmable and
non-graphical), unless stated otherwise.

Write neatly and legibly.

Copyright reserved HRCA CAA A Please tum over

### Page 3

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Mathematics/P2 3 DBE/November 2016
NSC - Grade 11
QUESTION 1

The table below shows the number of cans of food collected by 9 classes during a charity
drive.

5 8 15 20 25 27 31 36 75

Ld Calculate the range of the data.

1.2 Calculate the standard deviation of the data.

13 Determine the median of the data.

14 Determine the interquartile range of the data.

1.5 Use the number line provided in the ANSWER BOOK to draw a box and whisker
diagram for the data above.

1.6 Describe the skewness of the data.

L7 Identify outliers, if any exist, for the above data.

QUESTION 2

The table below shows the time (in minutes) that 200 learners spent on their cellphones during
a school day.

TIME SPENT
(IN MINUTES) FREQUENCY
95 <x <105 15
105 <x <115 27
115 <x <125 43
125 <x < 135 52
135 <x <145 28.
145 <x <155 21
155 <x < 165 10
165 <x $175 4
2.1 Complete the cumulative frequency column in the table provided in the ANSWER
BOOK.
2.2 Draw a cumulative frequency graph (ogive) of the data on the grid provided.
2.3 Use the cumulative frequency graph to determine the value of the lower quartile.
24 Determine, from the cumulative frequency graph, the number of learners who used

their cellphones for more than 140 minutes.

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### Page 4

Mathematics/P2 4 DBE/November 2016

NSC ~ Grade 11

QUESTION 3

In the diagram, A(6;~—2), B(2; 15) and C(—4; 3) are the vertices of AABC.
M is the midpoint of AB. N isa point on CA such that MN || BC.

3.1

3.2

3.3

3.4

3.5

a

B(2; 15)

C4; 3)

wt

[e] |
A(6 ; -2)

Determine the coordinates of M, the midpoint of AB.

Determine the gradient of line MN,

Hence, or otherwise, determine the equation of line MN, inthe form y = mx-+e.
Calculate, with reasons, the coordinates of point N.

If ABCD (in that order) is a parallelogram, determine the coordinates of point D.

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### Page 5

Mathematics/P2

QUESTION 4

5
NSC - Grade 11

DBE/November 2016

In the diagram, Rand A are the x- and y-intercepts respectively of the straight line AR.

The equation of ARis y= ~ e+ 4. Another straight line cuts the y-axis at P(O ; 2) and

passes through the points M/k; 0) and NG ; 4).

a and £ are the angles of inclination of the lines MN and AR respectively.

ty
C)
Mc; 0) a
() 44 Given that M, P and N are collinear points, calculate the value of &.
4.2 Determine the size of 0, the obtuse angle between the two lines.

4.3 Calculate the length of MR.

4.4 Calculate the area of AMNR.

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### Page 6

Mathematics/P2 DBE/November 2016

6
NSC ~ Grade 11

QUESTION 5

51 In the diagram below, P(-8 ; 4) is a point in the Cartesian plane such that
OP = 17 units and reflex XOP=0.

(21

17

PC-8;1)

3.41 Calculate the value of f,
5.1.2 Determine the value of each of the following WITHOUT using a

calculator:
(a) cos(-)
(b) 1-sind
3.2 If sini7°= a, WITHOUT using a calculator, express the following in terms
of a;
5.2.1 tan17°
5.2.2 sin 107°
5.2.3 cos? 253° + sin? 557°

53 Simplify fully, WITHOUT the use ofa calculator:

cos(—225*), sin 135° + sin 330°
a 2 6 7

1 ~]
(cosx-+1)(cosx-1)  tan?x.cos?x

5.4 Prove the identity:
5.5 Determine the general solution for 2sin x.cos x =cos x,

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### Page 7

Mathematics/P2 7 DBE/November 2016

NSC - Grade 11

QUESTION 6

In the diagram the graphs of f(x)=cosx and g(x)=sin(x+5) are drawn for
the interval -180° <x < 90°.

()

6.1
6.2

63

6.4

() 65

AS

Write down the value of 0,
Write down the period of g.

Write down the value(s) of x in the interval -180°< x <90° for which
S(s) - g(x)=0.

For which values of x in the interval ~180°< x < 90° is sin(90°-x) > g(x)?

The graph of A is obtained by shifting f 3 units upwards. Determine the range of h.

comet YM LUUNUIIN 8

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### Page 8

Mathematics/P2 8 DBE/November 2016

NSC - Grade 11
QUESTION 7
VA In the figure below, acute-angled AABC is drawn having C at the origin.
y B
x
i A
Wd Prove that c? =a? +b? ~ 2abcosC. (6)
- 4
7A2 Hence, deduce that 1-+cosC = enter. @)
a

72 Quadrilateral ABCD is drawn with BC=235m and AB= 90,52 im. It is also
given that ADB =3 1,23°; DAB = 109,16° and CBD = 48,88°,

Determine the length of:
7.21 BD (3)
7.2.2 cD (3)

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### Page 9

Mathematics/P2 DBE/November 2016

9
NSC — Grade II
QUESTION 8
The diagram below shows a water tank which is made up of a cylinder and cone having equal

radii. The height of the tank is 1,8m and the radius is 0,5m. The angle between the
perpendicular height, AB, and the slant height, AC, of the conical section is 35,5°,

Volume of cone “5 ah
Total surface area of cone=71’ +75

4 Volume of cylinder = 77°h
t
! Total surface area of cylinder = 2a r?+2arh
H
'
1
H SC
'
1

18m
1
1
'
t
t
'
'
'
'
t
v

8.1 Calculate the perpendicular height, AB, of the cone. (2)

8.2 When the tank is full, an electric pump switches on and pumps the water from the

tank into an irrigation system at a rate of 0,52 m’/h, The pump automatically
switches off when the tank is full.

Calculate how long, in hours, the pump feeds water into the irrigation system. (4)

[6]

Comvaaenes NAMEN oe

### Page 10

Mathematics/P2 10 DBE/November 2016
NSC - Grade 11

Give reasons for your statements and calculations in QUESTIONS 9, 10, 11 and 12,

QUESTION 9
91 Complete the statement so that it is TRUE:

The angle subtended by an are at the centre of a circle is ...

9.2 O is the centre of circle TNSPR. POS=60° and PS=NT.

T
N
R
|
P ' s

Calculate the size of:
9.2.1 PRS
9.2.2 NST

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### Page 11

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Mathematics/P2 at
NSC - Grade It
QUESTION 10

D, B, F, G and Hi are points on the circumference of the circle.
G,=x+20° and H=2x+10°. DEI|FG.

10.1 Determine the size of DEG in terms of x.

10.2 Calculate the size of DHG.

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DBE/November 2016

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### Page 12

Mathematies/P2 12 DBE/November 2016
NSC. Grade If -

QUESTION 11

O isthe centre of the circle PTR. N isa point on chord RP such that ON LPR.
RS and PS are tangents to the circle at R and P respectively.

RS = 15 units; TS=9 units; RPS = 42,83°,

R
11.1 Calculate the size of NOR. (5)
11,2 Calculate the length of the radius of the circle, (4)
[9]

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### Page 13

}

Mathematics/P2

QUESTION 12

13
NSC ~ Grade 11

DBE/November 2016

12.1 Use the diagram below to prove the theorem which states that EFG = EDF.

D.

F

G (5)

12.2 In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle
at A and AE = EC.

Prove that:

12.2.1
12.2.2
12.2.3

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3
4
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AOCD isa cyclic quadrilateral (5)
DC isa tangent to the circle at C (4)
[18]

ANH

TOTAL: 150

### Page 15

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### Page 16

Mathematies/P2/Wiskunde V2 3 DBBNovember 2016
CAPS/KABV ~ Grade/Graad 11 —-Memorandum
QUESTION/VRAAG 2
ud CUMULATIVE
Tipepanpeng | FREQUENCY | FREQUENCY!
FREKWENSIE | KUMULATIEWE
(IN MINUTES/ FREKWENSIE
MINUTE) f
of Lif
95 <x <105 15 15 “first 4 comect/
105 <x<115 27 a2 eorste 4 korrek
15 <x 125 8 35. CF values
125 <x<135 52 137 KF waardes
135 <x<145 28 165, “last 4 correct CF
145 <x< 155 21 186 values/
155 <x< 165 10 196 daaste 4 korrekte KF
165 <x <175 4 200 waardes
2
22 Grounding!
OGIVE/OGIEF Aner
iow CCCP Ce TTT] — 8 points coreci/
i Le a 4 8 punte korrek
20 Peet a:
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380 +} a - ¥ Grounding!
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z 100 = crt “t 4-7 punte karrek
cot
60 + i
oF Fe cr
£ i i
= EEB AREER
Ce ee a ee
[ oO 20 40 60 80 100 1206 140 160 180 200
i Time spent on cellphone
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Mathematics/P2/Wiskunde V2 4 DBE/November 2016
CAPS/KABV — Grade/Graad 11 —~Memorandum
23 Qi= 118 ] CA
| ¥ CA answer/antw

Accept any answer between (115 and 120) : Q

24 | Number of learners / Getal leerders=200-150 i YEA 150
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EoucATION

DEPARTMENT OF BASIC

206 -i- 11

PRIVATE BAG 2896, PRETORIA BOT

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### Page 17

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### Page 18

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Mathematics/B%/Wiskande V2 Tt DBE/Noveniber 2016 Mathematics! 2/Wiskunde V2 8 ' DBE/November 2016
CAPVRABY. ~tiaite/Gioail 1 Meher asta ‘CAPS/KABV — Grade/Graad 11 Memorandum
; — -QUESTION/VRAAG 4 !
| OR/OF ai
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— v tanB=—— i
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=153,43° | |
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### Page 19

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### Page 20

Mathematics/P2/Wiskunde V2 11 DBE/November 2016
CAPS/KABV —Grade/Grand 11 —Memoraadam
=t :
S34 RHS =
tan’ x.cos’ x .
_ 1 Y tango St
=a cosx
Se xcos* x
cos?x
v
-1 simplification’ vereenv.
© sin?x
¥ identity/ identiteit
-1
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_ 1
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= LHS
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{cos x +1)(cosx—1) ¥ cos’ x-1
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=} vy sivtx cos’ x
sin? x Py
cosx
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EDUGATION

DEPARTMENT OF BASIC)

206 tt 14

PRIVATE GAG X056, PRETORIA 0004

APPROVED MARKING GUIDELINE)

PUBLIC EXANINATION

Copyright reserved/Kopiereg voorbehow

Please turn over/Blaai om assebligh, Ms

Mathematics/P2/Wiskunde V2 2° DBE/November 2016
CAPS/K ABV ~ Grade/Graad 11 —- Memorandum
i
OR/OF
RES = — 508 |
Gin? xcos? x | yl 2 tx
2 | tan?x sin? x
sin? x | vai
| in?
LHS = a 5 om
cos’ x—.
1 ¥ cos*x-1
Ll sin® x | ¥~sit x
RES = | @
|
|
\
|
|
|
|
|
|
|
55 2sinx cos x—cosx=0
cosx(2sinx—I) <0 | “factors / faktore
cosx=0 or sinz=t
2 | both equations/
' beide verg.
== 90°4360 keZ 2=30°+360°K REZ or
x= 270°+ 360°. & keZ #1504360" hkeZ VBOTH general
or solutions for
4=90°H18PEkeZ | cosx= O/
| Altwee algemene
or i oplossings vir
£=190°436PkeZ | cosx=O
i vv general solutions
i el
| for sinx= =
cerAtpecmen ‘
algemene
PRIVATE BAG xt00, PRETORIADOE| 4 splossings or
M6 -Het sing=
APPROVED MARKING GUIDELINE | V kez 2
PUBLIC EXAMINATION | © ©
l (st
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Copyright reserved/Kopiereg voorbehou | Please tum over/Blaai om asset

### Page 21

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### Page 22

Mathematics/P2/Wiskunde V2 8 . DBE/November 2016
CAPS/KABY — Grade/Graad 11— Memorandum
ORIOF etna? +?—2aboosE
2 25? i . 2 gt
e=a +8 -2abeosC costed tne
a_@ +b -? 2ab
2.cos€ = ¥ Making cos C the
2 2ab subject of the formula/
arb) ~¢ Maak cos C die
2ab onderwerp van die
formule
_@ +2ab+B? — 0?
_ 2ab
V writing asa
2a p2_ 2 difference of 2
ath -e ae
2ab Steyfas die verskil
. tussen twee vierkante
=cosC +1
Y expansion/ontwikkel
=LHS > splitting up the
OR/OF fraction / Deel die
¢? =a" +b? —2abcosC breuk in twee
2abcosC =a? +b? —c?
2ab+2abcosC =a" +2ab+b? —c?
2ab(L+-cosC)=(a+5)*-c?
(a+by?—<?
1+cosC =
2ab
“making 2zbeosC the
subject of the formula/
Maak 2abces C die
onderwerp vn die
formule
¥ adding 2ab on both
sides of equation/
tel 2ab aan beide
ante van die
vergelyking
“common factor!
gemene foktor
ins
"PRIVATE BAG X03, PRETORIA 0001 ¥ factorise the
trinomial/ faktoriseer

Copyright reserved/Kopiereg voorbehou

2016 -it- 11 die drieterm
APPROVED MARKING GUIDELINE z
= = re Try
Please tun over/Blaai om eti\

Mathematics/P2/Wiskunde V2

DBE/November 2016

i
i
|
|
16 i
CAPS/KABV — Grade/Graad 11 — Memorandum.
724 in AABD |
BD __ 90,52 Y sine sule/sinusreél
A Tay 530 |
sinl09,16°  sin31,23' | Y subst |
| |
_ 90,52xsin109,16° | |
BD= ans 23 Y answer/antw.
=164,92 m i @
72.2 | CD? =164,92? +235" —2%164,92%235xc0s48,88° | 'Y cos nile/cosinusredl
CD? =31448,4874 : Y subst
CD=17734m : CA answer/antw.
|
| @)
[16]
|
QUESTION/VRAAG 8 | :
7 ¥ subst '
B81] tn35,5°= 2% | |
AB | |
_ 0s | |
AB aaa i ¥ answev/aniw |
=0,7 m fe |
82 aden (0,5)? x07 | CA V of coneftedl
Volume of cone 3 7
=0,180* |
Volume of a cylinder = (0,5)? x1,1 |
= 3 i YCA V of cylinder!
0,86m i silinder
|
3 3
of volume==-x (0,18 + 0,86) i
4 4 i
=34¢,04)m° |
4 1
=0,78m* | 3
YCA 0,78 m
0,78? j
Timetakenby pump = 05am
=1,5hours |
| ¥CA answerlantw
4)

DEPARTMENT OF 5,

EDUCATION

206 -H- 41

Convricht reserved/Kopieree voorbehou

PRIVATE BAG X605, PRETORIA GOGT

dl

RN
case turn over/Blaai ont nai} |

### Page 23

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### Page 24

Mathematics/P2/Wiskunde V2 19
CAPS/KABV — Grade/Graad 11—Memorandum

QUESTION/VRAAG 12

A

D PEA
5

DBE/November 2016

12.1 | Construction: Draw diameter AOF. Join A to D.
FoF =90° [tan 1 diameter]
B, =F [Z'sinthe same segment]
Bb, +B, =90° [Linasemicircle]
wh =B,
EPG = FBE
ORIOF
Construction :Draw diameter AOF Join Ato E.
Fo4F, =90° [tan 1 diameter]
AEF =90°[Z'sinthesemi circle]
C+ PF =90°[sumofZ'sin AT
oR+h=C+k
but C =D [Z's inthe same segment]
nf=5,

EPG = FDE

~Constt/Kons
vs

vSYR

©)

aay Bre
EDUCATION

206 -fi- 41

PRIVATE BAG 1096, PRETORIA Gout

APPROVED MARIGNG GUIDELINE

Coovrishtreserved/Kopieres voorbehou

ASAE ACD A RAEN ECON

Y

Mathématics/P2/Wiskende V2 20 | DBE/November 2016
CAPS/KABV — Grade/Graad 11 —-Memorandum
OR/OF |
Construction: Drawradii OF and OE
Let BOF =2x |
o Box [Zatcentre=2x Lat circumference]
OFE =90°—x [sumof int. Z's of A] !
wv. EPG=x frad Ltan] |
< EPG= FDE |
i}
12.2.1 | BAC=90° [/ina semicircle] YS/R
£, =90° [line drawn from centre to midpont of chord] VSR
-. BAC=E, !
. |
BAL{OD [ comesp. 2s are equal] | YR
if
oR/or |
YSIR
BAC=90° [Lin asemicircle] | YSVR
£,=90°[Line fromcentreto midpoint of chord| | VR
BAC=E, |
i @
= BA| [OD [Ait2’s are equal] i
222 [Zax
B=x [ten—chord theorem] | YSYR
O, = x [corresp Z's equal, 4B || OD] VSVR
4=6, ; |
+. AOCDisacyelicquadritateral [conv.Z'sinthe same segment] |“ ®
OR/OF |
Let 0,=a |
€,=90°~a [int. Zs of A] ' vs
2.4, =90°—a [2 sopp =sides| |
* |
cd=a — ftan trad] | YSVR
+. AOCDis acyclic quadrilateral. (Converse 2'sinthe same segment] | ¥ R ey
|
DEPARTMENT GF BASIC
EDUCATION.
PRRATESAG Made, BRETORA OOF
2016 -1i- 41 |
Copyrightreserved/Kopiereg voorbehou APPROVED MARKEE Rees over/Blaat om assed)

### Page 25

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