# Mathematics Grade 11 P2 KwaZulu Natal June 2015 Paper & Memo

> Grade 11 Mathematics Paper 2 question paper and memo from the KwaZulu Natal June 2015, 24 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/2015-june-maths-p2-qp-and-memo/71cb684f-d9c3-4cfe-a9c3-efd5453af615
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper and memo
- Year: 2015
- Exam period: KwaZulu Natal June
- Paper: 2
- Curriculum: CAPS
- Pages: 24

Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 11](https://www.hlayiso.com/library/grade-11) › [Mathematics](https://www.hlayiso.com/library/grade-11/mathematics) › [Mathematics Grade 11 P2 KwaZulu Natal June 2015 Paper & Memo](https://www.hlayiso.com/library/2015-june-maths-p2-qp-and-memo/71cb684f-d9c3-4cfe-a9c3-efd5453af615)

## About this document

Mathematics · Grade 11 · KwaZulu Natal June · 2015. Question paper and memorandum, 24 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Document text

Text extracted from the PDF. Layout, diagrams and tables may not survive extraction.

### Page 1

Nawnloacde dc om Nia ‘a alae

Basic Education

KwaZulu-Natal Department of Basic Education
REPUBLIC OF SOUTH AFRICA

a *

' MATHEMATICS pP2 "
| rn 1”
| iW i
# COMMON TEST '
w 4
i" JUNE 2015 ‘
K ”
‘oem meen meee ene ne neem ee eee eee ene?

NATIONAL

SENIOR CERTIFICATE

GRADE 11

MARKS: 100
, TIME: 2 hours

This question paper consists of 10 pages, an information sheet and Diagram Sheets.

Copyright reserved Please turnover

### Page 2

Mathematics P2 D Oo wn | oaded feo m h | ay iSO . co (Pjamon Test June2QQis ~

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1, Answer ALL the questions.

2, Clearly show all calculations and diagrams that you have used in determining your answers.
3. You may use an approved scientific calculator (non-programmable and non-graphical).

4. If necessary round off answers to TWO decimal places, unless stated otherwise.

5. Answers only will not necessarily be awarded full marks.

6. Diagrams not necessarily drawn to scale.

7. Number the answers correctly according to the numbering system used in this question paper.

8, Write neatly and legible.

Copyright reserved Please turnover

### Page 3

ken edi

Department:
Education
KWAZULU-NATAL

Downloaded from hlayiso.com

TO: THE CHIEF INVIGILATOR(S) OF ALL CENTRES OFFERING
NATIONAL SENIOR CERTIFICATE —- COMMON TEST JUNE 2015

GRADE 11: MATHEMATICS P2

ERRATA: MATHEMATICS P2
ERROR CORRECTION
Page 3 Page 3
Question 1: Question 1:

1.1.7 inthe formof y = mx+x...

1.1.7 inthe form of y = mxtc...

QUESTION FIVE: PAGE 10

ERROR

CORRECTION

Kindly ensure that all candidates are informed of the Errata.

,

“

re.
MR R.C. PENNISTON
SENIOR MANAGER

2% | VOLS
DATE

PROVINCIAL EXAMINATION ADMINISTRATION

KWAZULU-NATAL DEPARTMENT OF EDUCATION

Postal Address; Privcite Bag X01 ° EAST END * 4018 » Republic of South Affica
Physical Address: 72 Stalwart Simeiane Sireet > Maigate Building + Durban » 4000

Tels +27 31 327 0462 9 Web:www.kzneducation.goy.za

.. Together moving South Africa forward through
quality education and skills development

### Page 4

Downloaded from hlayiso.com

©

©

### Page 5

Mathematics P2 Downloaded geom hlayiso.cakMnen Test June 2015

QUESTION ONE

1.1. In the diagram below A(0;8), B(8;2), C(2;-6) and D (x ; y) are the vertices of a

parallelogram. M is the midpoint of AC. ACB = 0.

Pe

A(0:8)

B(8:2)
j M
Dey),
8
CQ+6)
1.1.1 Calculate the lengths of AB and BC. (4
1.1.2 Determine the coordinates of M. (3)
1.1.3 Prove that BM is perpendicular to AC. (4)
h
"11.4 Prove that ABC = 90° (4)
1.1.5 What type of triangle is AABC? (2)
1.1.6 Determine the area of A ABC. (2)
1.1.7 Determine the equation of BM in the form y = mx + x. @)
1.1.8 Calculate the size of angle@. (A)
1.1.9 Determine the coordinates of D. (2)
1.2 Prove that the point (-4;11) lies on the line 3x + 4y = 32 (3)

1.3. Given the points P(6;5); Q(3;2); R (Qm ; m+ 4) and T (2 is} Calculate the

value of m if PQ is parallel to RT.
Copyright reserved

Please turnover

(4)

### Page 6

Mathematics P2 Downl oaded from h | ay iso . COGommon Test June 2015

1.4 Inthe diagram below P is a point (-3;0) and Tis (2a ; 0).The inclination of the line PR

is 108,4° and R is the y-intercept of PR.

¥

108,4°

T (2a: 0) P (-3: 0)

Calculate:

1.4.1 the gradient of PR, to the nearest integer value.

1.4.2 the equation of PR inthe form y = mx +c.

1.4.3 the coordinates of R.

14.4 If TQa;0); Q (a:b) and R lie on the same straight line.

Prove that b = =

Copyright reserved

2)
Q)
(2)

(4)

[45]

Please turnover

### Page 7

|
|
|
{
i
i

Mathematis P2 Downloaded som hlayiso. Corson ts: sune 2015
5

QUESTION TWO

2.1 Complete the following statement:
The line drawn from the centre of a circle, perpendicular to a chord » (2)

2.2 ‘In the diagram BOM is a diameter of a circle with centre O. OD is perpendicular to the
chord XY. OY= 12,5 cm and XY = 24 cm.

B
oO
: 2,5 om
D
Y
M
Calculate the lengths of:
2.2.1 MD. (4)
2.2.2 BX. (4)

[10]

Copyright reserved Please turnover

### Page 8

watemise — Downloaded fram hlayiso.cortonen tes ime 2015

QUESTION THREE
3.1 Complete the statement:

The angle subtended by an are at the centre of the circle is . (2)

3.2 Inthe diagram A, B, C and D are points on the circle with centre O. OBC = 40°,

BD=DC,
A
B 40° Cc
D
Calculate, with reasons, the value of:
3.2.1 BAC. (4)
3.2.2 BDC. (2)
3.23 DCB. (2)

[10]

Copyright reserved Please turnover

### Page 9

Mathematics P2 Downl oaded feom hlayiso. COW mon Test June 2015

QUESTION FOUR

4.1 In the diagram below, O is the centre of the circle. Use the diagram to prove the
theorem which states that : If PORS is a cyclic quadrilateral then POR + PSR =180°. (6)

P

Copyright reserved Please turnover

### Page 10

matnematsP2 Downloaded Trem hlayi$O.COrBemmon Tes tune 2015

4.2 Complete this statement:
The angle between a tangent to a circle and a chord is . (2)
4.3 Inthe diagram below, AOD is a diameter of the circle and EDF is a tangent to the

circle at D.

ADB = 62° and BC = CD,

E
Calculate, with reasons, the numerical value of:
43.1 BCD. (4)
43.2 CDF. (4)

Copyright reserved Please turnover

### Page 11

Mathematics P2 Down | oaded fee m h layiso CO Mommon Test June 2015

4.4 Inthe diagram, A, B and C are points on the circumference of a circle. PCT is a tangent
to acircle at C and also parallel to AB.

Prove that AC = BC (5)
[21]

Copyright reserved Please turnover

### Page 12

Mathematics P2 Downloaded fagom h layiso .CO amon Test June 2015
10

QUESTION FIVE

In the diagram below, PQRT is a cyclic quadrilateral. PB is a tangent. RQB is a
straight line.. PT // BOR,

PT=QTand , =x.

5.1 Write down, with teason, R in terms of x. (2)
5.2. Write down, with reasons, FIVE other angles each equal to x. (10)
5.3. Prove that QP = BP Q)
[14]
- TOTAL: 100
Copyright reserved

Please turnover

### Page 13

Mathematios P2 Downloaded fscom hlayiso.Comnon-res: une 2015
Ih

INFORMATION SHEET: MATHEMATICS
INLIGTINGSBLAD: WISKUNDE

xe ~btvb? ~4ac

2a
A=P(l+ni) A= P(l~ni) A= P(~iy" A= P(+i)"
ft yn
Mien yin ee T, =a+(n—Nd S, = @a+(n-1d)
isl dal
T, =ar™ Ss aay" al ; rel S, = -y-ler<l
"pl 1-r

me (Co | past 0+9")

i i

Va) = tim LTDA LO)
FG) = jim, h

x, +X. +
d=\(%) — x1)? +04 -y,)" Seared

2

yemxte yry =m(x—-x,) m= 222 m= tand
Lo mma |

(x-a) +(y-by¥ =r?

in AABC: 4. Fe a a* =b* +¢* —2be,cosA area MABC =~ ab.sinC
sind sinB sinc 2
sin(a + £) = sina.cos B + cosa.sin f sin(a ~ 8) = sina.cos f — cosa.sin £
cos(a + 8) = cosa.cos f - sina.sin B cos(a — 8) = cosa.cos 8 + sina.sin
cos’ @~sin? a
cos2e =41-2sin? a sin 2a = 2sina.cosa@

2cos? a -1

(x; y) > (xcos0 + ysin®@ ; ycosd— xsind) (x3 9) > (xcos@ ~ ysin 8; ycos@ + xsin 8)

x= oe = 48
n n
P(A) = iG) P(A or B) = P(A) + P(B) ~ P(A and B)

Dien 5y

Copyright reserved Please turnover

### Page 14

Mathematics P2 Downloaded firem hlayi$O.COrBmmon Test une 2015
12

DIAGRAM SHEETS

Pe

Question 1.1

A(0:8)

B(8:2)

Dey)

mx

C(2:-6)

Question 1.4

—r .

108,4°
px

T (2a: 0) P (-3; 0)

Copyright reserved Please turnover

### Page 15

Mathematics P2

Question 2.2

Question 3.2

Copyright reserved

Downloaded fisom h layiso .cCO (Bommon Test June 2015

oO
2,5 cm
D
Y
M
A
40°
Cc
D

Please turnover

### Page 16

Mathematics P2 Downloaded feo h layiso .CO Ammon Test June 2015

Question 4.1

Question 4.3

Copyright reserved Please turnover

### Page 17

Mathematics P2 Do Ww nl oad ed sero m h | ay is O. CQ@bMnon Test June 2015
Question 4.4
A
P.
B
Cc
)
T
Question 5

Copyright reserved

### Page 18

Downloaded from hlayiso.com

e

### Page 19

Downloaded from hlayiso.com

w®
Swoopess Suid, “VO OV 0} senoppuodied st Wg
yorpery L
OV Won vO AIo = oe
Wamp :v¥D AP =
£8. ova
98
£
“epnun0y werper8 ant
‘ojur onMnSqns yaLI0D WO
me .
Te = Wem ert
(© wasueweneg vo Ep =
(& <=) ewer
MORTERSGNS IaNI0 Vy “\o-8 Go) 7 NT
() fol =
2940+ (C-8) = 28
Fomstte 10L109, 7VO. “OL =
wORMASANs JoatIO 7y A AZ-8) + (8-0) =a TIT
TNOLESINO
z
SLOT eune S84 YOUOS WNONVHOWSW-OSN 2d SOREWEHREYW

“soGed g 30 s}sjsuco umpueiowiow Sy

00L :SHuVN
SLVOILLY39 YOINSS
“TWNOLLVN

F "
“ wnanveowain :
: $10z 1$3.1 NOWWOS aNnr :
: 2d SOLLWWWSHLVIN :
“Senceee wee eee mene ceceeeseeccecseeeene”

vOluaW HLNOs 40 O1anday

uoneonpz jo juaurjedag jeyen-ninzemy

uonjeonpy oiseg

### Page 20

Downloaded from hlayiso.com

(2 tamsueyant0g “vO

ORMASGNs joatIOD “y

AE =a

Ae = PRO Ue LPT

TORMASGNS SOD “VW

v1
() ‘mse yang -vD
cou
woneogiduns “yD A Cowal ue
£ s
z
ad
squarpesd omy Sopenby “WW z =I
- t-peus
dam = Gut
£1
(© “worsnjsuos “yD POUL SHH UO som (TT “y-)
uopeonydans :vD Ae = TE

ste (De + IE AT

@ wASIR SSID WD

GOotsS) FI 6TT

(%)  semsue pong =v

oes “VO

618 WO

PASE =
Cres + .618)- 081 = 8

ALES = VE

Shaz sunp yay uous

+

WNONVEONSN-OSN Za sopewelReW

) msIE AION “VO
noneourduns -yvO

wORMASqns JaHIOg “VD

(g) mst wang -¥D
woneouyduns -¥D

TORMINSGNs 199109 7¥D

(g)  samsmy yang “yvD

woneourdems yatt0y °¥O

oRmuAsqns 3981109 “YO

uo

orem ak LTT

@ mse wsxt0D “WO

woumusgns yan09 y 7 OrxXOr = By OTT
@ “sapeososy
poysueaysng Vv aysowEy psojeososy - pafsue— AMET CTT

®) woIsnJOUCD =¥O,

swapped Suda VO 706 = OGY
ne lek
vo qweIpely =v¥D a rs
9
cz 7 mw
Vvouspag Wo 8
a
so dvw rli
z3 *
e
etoz eure 801 wounes wnanveowsn-osn za sonewowen

### Page 21

ton
2) wewo
$:WO AO = a) 4.6% = AG ETE
@ Wvo
scwo A(penb onjo4) »,0€1 = IGT Tee
) WS =VO A(onu20 8.7) » 0S = OFT
woUlsg “VD A(eiiaeny 2308.7 WH) 001 = 20g
WS wv AO = 40) Ov = 290 ITE

cE

@ = Tamsuz eng -yy

AP eOHD OU Fe
‘ore sures aif Aq papuaigns oj8ue ay jo szis om 901M}

Downloaded from hlayiso.com

“dqso miuey sy

€NOLISIND
fon
(p)  wemsueyosm0g cy5
PUNE =
uoneogydang y> -00vy. = Xa
wonnusqns waLI0D -WD Ag+ Zh =

a+ CX = XE

AN =

SE+CCi= da tz

$102 ounp say uowwo

WnGNYEOWaW~OSN 2d sonewomney

() G30 WBue7 WO

dose wBuey “vO

wonnmnsqns 1oan0g -W

AC Jo ysuay -y

feIIG =
S€- SUL =n =
ASt=do >
SttlP =ao

/M)- ETD = GO
- w= AG Itt

te

(@ ~—semsae ame WW

A /IOW ap HG TZ

TNOLISIQO

Ise

() —-semsuerstI09 -vO

uoneogrding yD

sypoIpers oxy Sunenbg =yvy

PRL — GE ~ 06 + GD = QD

0-9 mn
“64a 70-9

vl

@ — semsue yosti0D WD

0) ST 7
ep CY yT

@ — tamsueyan0g :y

WORNIASQNS 3991105 7W>.

A6- %E- = K

AE+DEs0-4

uo
@ ~~ somsue panto -yO Po~ E- = &
yo = 8
wonmmsgns 1010 “WO e+ (e=0 trl
s
SLOZ @une ise) VOWED WAGNYYONSW-OSN @d SOREWEURE WY

### Page 22

,

Downloaded from hlayiso.com

w ws "vo AXpenb o4194) p EST =A IE
WS VO

ACC Jo sepsue yp) 9% = aE
ws Vv

/Gaurp) 06 = Ggy Ver
ev

(2) semsue pano0g “yy

A AMusuises spoil SBUIsIE oy UL [sue ue Oo} Eby = Ty

$402 unr psa uoUNaD

WNONVEOWSN-OSN Za sopeweReW

(9) woxsnypt09 =y

WS Vv
WS 3
uosvar poe USUISS “VV

x=u0d W

WosNpUOD -y

WORTINSGNS }oaLIOD ¥

wosval 7 meWsTEIS 7y
uosear 7g wousTes °y

woseal 7 jOWIETES “Vy

wonsMsuOD -y

PMI = Ud + UO
A(enua9 (7) X— O81 = Ud
A(wonnjoney) xZ- 09E = 'O
Aanuas3 7) xz = "9
4¥ UOT = PT
ao
P/AOBL= YOd + Wd
P7081 =UGdT + USdT
A(wounposey) .09¢ = "9+ 'O
/fonuso 18 .7) UOdt = *O
Anu 7) Udz = 'O

AAO pure gO jonNsMOD
Pu
a

s

Tr
 NOLLSANO

Shoz eunp seq vouRs0D

L
WNGNVYOWSW-OSN

Z¢ sonewoNeN

### Page 23

Downloaded from hlayiso.com

fel ,
@ woIsnpmOD dq = d6
qeuerig 7 stunod) ‘g="G es
(o1) woseay -W¥
qweuarg :y (aL|| fa 8.7 “dsanos) x = 'g = Y
e ad
uoseay VW a
yuourereg 7 (pogm) x == G
va ay
uoseary -¥
JUSUISIS VW (Penb ayjoh0 J0..7 2) x= d=6
a
uoseay “y
qwourseis :V¥ (ail @as.7 4) x= G=y
Z
noseay “y¥ _
mewaig -y (ld =10) x*="O=¥ Ts
s s
wos
meus oy Atpenb ono) A{x—.0gi}= ys
s NOLISHAD
on
G10Z eunp se UOMIED WAGNVYONEW-OSN Zd sonewanEW

Ira
worsnjoueg :y Da = Ov
uoseay :y Te tal
yuomag -y
(proqo wei) p=“
wosesy “y 4 -
weneras WV (ad Weys7m)g=9
+ ad
xo
9= OF
(3) worsnpuoy y
7E-e
uosey :y
FROSTAS “WV A(proyp —ueq) pg = 9
woseng :y :
qoounrmag y ALAS 7 AK = 2 ry
wosesy ov
® WSOISIES WD A.06 =40F) »61 = 409
woseay “YD
qewarig yD AO = 08) sel =DGE Tey
6
loz ounp 61 uous Wnanvowan-osn zg sonewauneyi

### Page 24

a)

Downloaded from hlayiso.com

%OL

ALE. YEE

WOE

%

£9

co

or

19

es

ccs

Ves

is

ia

Ewe

ht loxfes

coe

Le

Ve

aaa

*4

[x4

rrt

at

crt

Trt

£1

rag

ott

stl

Ltt

9Tt

4
4

Stl

vit

ent |

ett

cit

v

TUT

SNIATOS:
Watsdoad

X#1TdWOD ANLLAON

FOTTTMONL

¥

€ z

if

‘THART

shoz eunp ysei uouiweD

AUMVAINAS GRID SISATVNV THATT TAILINIOD

$107 ANODE Td SOILVAGELLVW Tt advaD

ub
WNGNVEOWSN-OSN

Ze sopeWoUREW

## Related documents

- [2015-JUNE-MATHS-P1-QP-and MEMO-1](https://www.hlayiso.com/library/2015-june-maths-p1-qp-and-memo-1/f578c21a-61af-4af4-81ea-2d3e974f1a07) — Mathematics · QP + Memo · 2015
- [MTH-JUNE-P2-QP and MEMO](https://www.hlayiso.com/library/mth-june-p2-qp-and-memo/118b50ee-3762-422c-bd64-83a337e7b5e8) — Mathematics · QP + Memo · 2018
- [Mathematics P2 Grade 11 Nov 2015 Eng](https://www.hlayiso.com/library/mathematics-p2-grade-11-nov-2015-eng/f50b10da-e99a-465c-876f-f906a20b49bd) — Mathematics · QP · 2015 · Eng
- [MTH-NOV-P2-QP and MEMO](https://www.hlayiso.com/library/mth-nov-p2-qp-and-memo/b42ffa5f-de39-46cb-bc3b-65780601ecdc) — Mathematics · QP + Memo · 2018
- [MATHS P1 MEMO GR11 NOV2015 EA](https://www.hlayiso.com/library/maths-p1-memo-gr11-nov2015-ea/52b2b17e-c884-403e-a909-21e71ca2ee83) — Mathematics · Memo · 2015
- [Mathematics P1 Grade 11 Nov 2015 Eng](https://www.hlayiso.com/library/mathematics-p1-grade-11-nov-2015-eng/7ea4123f-88b9-476e-af53-b5f87f9ada46) — Mathematics · QP · 2015 · Eng

## More from Grade 11 Mathematics

- [Grade 11 Mathematics P1 November 2026 Mock Memo](https://www.hlayiso.com/library/grade-11-mathematics-2026-november-mock-exam-memorandum-paper-1/470265ad-99e7-4e3e-af02-0c28a273b390) — Memo · 2026 · Eng
- [MATHS P1 MEMO GR11 NOV 2025 E+A watermark](https://www.hlayiso.com/library/maths-p1-memo-gr11-nov-2025-e-a-watermark/5af2bd74-cc9d-4651-895a-310a59d8ce25) — Memo · 2025
- [MATHS P2 MEMO GR 11 NOVEMBER 2025 (ENG & AFR) watermark](https://www.hlayiso.com/library/maths-p2-memo-gr-11-november-2025-eng-afr-watermark/6bc83e22-926c-4a81-95ea-4dee0141ce24) — Memo · 2025 · Afr
- [FS Maths Grade 11 June 2025 P1 only](https://www.hlayiso.com/library/fs-maths-grade-11-june-2025-p1-only/82015d8f-bcc0-478e-ad47-d3b295dabb01) — QP · 2025
- [FS Maths Grade 11 June 2025 P2 only](https://www.hlayiso.com/library/fs-maths-grade-11-june-2025-p2-only/5d0e7dd8-cb37-419c-8fe2-0aee27fbdc84) — QP · 2025
- [MATHS P2 ANSWER BOOK GR11 2024 ENG AFR D watermark](https://www.hlayiso.com/library/maths-p2-answer-book-gr11-2024-eng-afr-d-watermark/91fd4f6b-a252-4d30-b6b1-f8f546015336) — Addendum · 2024 · Afr

## Collection

- [Grade 11 past papers](https://www.hlayiso.com/grade-11/past-papers)

---

Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.