# Mathematics Grade 11 Paper 1 Eastern Cape November 2017 Memo

> Grade 11 Mathematics Paper 1 memorandum from the Eastern Cape November Exam 2017, 19 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/final-marking-guideline-grade-11-mathematics-p1-2017-common-examination/67badd2d-178b-4a32-8ead-5f13604b50a3
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Memorandum
- Year: 2017
- Exam period: Eastern Cape November Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 19

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## About this document

Mathematics · Grade 11 · Eastern Cape November Exam · 2017. Memorandum, 19 pages. Read online or download the PDF.

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## Document text

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### Page 1

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ale basic education

wat Department:
(GO) Basic Education

aw” REPUBLIC OF SOUTH AFRICA

NATIONAL
SENIOR CERTIFICATE/
NASIONALE
SENIOR SERTIFIKAAT
GRADE/GRAAD 11
Flannel iinet’
" MATHEMATICS P1/WISKUNDE V1 :
NOVEMBER 2017 "
" MARKING GUIDELINES/NASIENRIGL YNE :
%

MARKS/PUNTE: 150

These marking guidelines consist of 19 pages.
Hierdie nasienriglyne bestaan uit 19 bladsye.

ja\n Jaorq ru 20"7

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Mathematics/P1/Wiskunde VI 2

DBE/November 2017

CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne

NOTE:

If a candidate answered a question TWICE, mark only the FIRST attempt.
If a candidate crossed out an answer and did not redo it, mark the crossed-out answer.

e

e Consistent accuracy applies to ALL aspects of the marking guidelines.
e Assuming values/answers in order to solve a problem is unacceptable.
LET WEL:

e As 'n kandidaat 'n vraag TWEE keer beantwoord het, sien slegs die EERSTE poging na.
e As ‘n kandidaat 'n antwoord deurgehaal en nie oorgedoen het nie, sien die deurgehaalde

antwoord na.

Volgehoue akkuraatheid is op ALLE aspekte van die nasienriglyne van toepassing.
Dit is onaanvaarbaar om waardes/antwoorde te veronderstel om 'n probleem op te los.

_QUESTION/VRAAG 1
Ll (2x-3\Xx+7)=0
3
vy=l
x= > or x=-7 * 2
vx =-7
112 Te 43x-2=0
—b+,/b’ -4ac
x=
2a ¥ substitution/vervanging
————
_~8)* VG) 4-2)
27)
~3+ 65 NOTE/LET WEL:
= 414, Penalty 1 mark for
incorrect rounding ¥ answer/antwoord
x=-0,79 or x = 0,36 Penalisering 1 punt ¥ answer/antwoord
vir verkeerde
afronding
OR/ OF
x? + 3, a 0
7 7
>,3. 9 2.9 2
a oo 3) _ 65
TF" {96 7” 196 v(xe3) = 106
(ale
14 196
3 +65
xt—=
14 14
xe 3+ V65 ¥ answer/antwoord
14 ¥ answer/antwoord
x=-0,79 or x= 0,36

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Wu

2) |

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Mathematics/P1/Wiskunde VI 3
CAPS/KABV ~ Grade/Graad 11 — Marking guidelines/Nasienrighyne

DBE/November 2017

1.13 vx-14+3=x
vx-1l=x-3 Y isolate/isoleer \ sign/teken
(ve—1f =(x-3Y ¥ squaring/kwadr both sides/
x-1l=x? -6x+9 beide kante
2 ¥ std form/stand vorm
x —7x+10=0 ¥ factors/fakt
(x-2)(x-5)=0 vx=5
x#2 orlof x=5 Vx#2
(6) |
|
1.1.4 x? >3(x +6)
2 ¥ std form/vorm
x° —3x-18>0 ¥ factors/fakt
(x-6)(x +3)>0
OR/OF x<-3 or x>6xE(-~%;-3)U6; &) ¥x<-3 OR/OF (-» ; -3)
¥ x>6 OR/OF (6; ~)
— (4)
1.2 2y+x=l
x=l-2y V x=1-2y
+p 43xyt+yp=0
¥ substitution/verv

(l-2y)P +y? +3y0- 2y)+y = 0
1-4y+4y? +y? +3y-6y? +y=0
1-y’=0

(l- y)A+y)=0

y=l or y=-l

x=-lor x=3

OR/OF

% std form/stand vorm
Y factors/fakt
vy-values/wrdes
vx-values/wrdes

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Mathematics/P t/Wiskunde V1 4 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne
2y+x=l
l-x V ya lox
=—— y=
2 2
x+y? +3xypt+y=0 ¥ substitution/verv
2
wafIc®) 43, oe i120
2 2 2
2 l-2x+x? 3x-3x? 1-x
xo $+ +—=0
4 2 2
4x? +1-2x+x7 +6x—6x? +2-2x=0
~x?+2x+3=0
x? —~2x-3=0 ¥ std form/stand vorm
(x—3)(x+1)=0 ¥ factors/fakt
x=3 0 or x=-l vx-values/wrdes
y=-l or y=l vy-values/wrdes
(6)
13 3-12k? =0 ¥ 3-12k =0
1-4k? =0
a ve =4
4 1
v k=t—
k=t5 k 2
(3)
3-12k? =0 ¥3~12k =0
1-4k? =0
(1-24) 2k) = 0 ¥ (I-24Y1+2k)=0
1
ket OR/OF k=-5 Vh=ty
@)
[24]

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Mathematics/P1/Wiskunde VI

DBE/November 2017

CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne

QUESTION/VRAAG 2
2.1 gma 6.3"
m2
73 ¥ common factor/gemene fakt
7.3773
3-6 se .
=3 ¥ simplification/vereenv.
2
21
=1 ¥ answer/antw.
OR/OF
am+4 mil
arn 6.3 ¥ common factor /gemene fakt
73m
_ 3" 3*-6.3) v (3° -63)
3" (7.37)
= 3”.63 ¥ simplification/vereenv.
3” .63
=1 Y answer/antw.
(4)
2.2.1 3
x4 =8
3 v2
x4 =2°
aa “rational exponent/
x=(2°)? rasionele eksp
xy=24 Y answer in any form/ antw.
1 in enige vorm
16 (3)
OR/OF
as
xt=8 ¥use of surds/gebr van wortls
4 x? 3
~1_ 44
xta2" (2 = 4096) vxt=2
x'=2' (2* =16)
x=24 vi answer in any form/antw. in
1 enige vorm
x=— 3)
16

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Mathematics/P1/Wiskunde V1 6

DBE/November 2017

CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne

2.2.2 2?*_9* <2

NOTE/ LET WEL:
22*_2*-2=0 If answer only of x = 1: award 1/4 marks
| ~ Slegs antwoord van x = 1: gee 1/4 punte ¥ std vorm/stand vorm
io +1)2" - 2)= 0 ¥ factors/fakt |
x F If the learner writes 2x — x =1
2" #-1 or 2% =2 Breakdown: 0/4 marks vx=1
x=l1 As die leerder 2x —x =1 skryf Yo
Ontleding: 0/4 punte aed
5 (4)
. 2
(r+ yy -( 3a, atv “ substitution/very.
v2 2
| (7 }
2
_49 ¥ simplification/vereenv.
2
1
= _ | “answer/antw.
OR/OF
(x+y)? =x? +2xy+ y?
2 2
= 3-Va +2 3-Va (44a + 4+va ¥ substitution/verv.
V2 v2 v2 v2
-~6 _Ja—
=|? va+a +2) 12-Va-a + 16+8Va +a ¥ simplification/vereenv.
2 2 2
_ # 2ye*28) «(asi
= Pa +a+t2-Ja~a
1 |
= 24 | Yanswer/antw.
|
@)
2.4 'Y10 .9/64.10 .4/81.10. /4.10 Y split the surd/
skei wortel

='¥10 9/25 10 .4/3* 10. /2? 10
1 6 1 4 1

a 6 1! 4 Yo2 Lt
=10” .2° 10°. 34 104.2? 102

12
=2x3x2x10?

=120

OR/OF

v prime base/ priem basis
¥ rational exponents/

rasionele eksp
2
v 108

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Mathematics/P 1/Wiskunde V1 7 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne

¥ prime base/ priem basis
=¥2s 927s 43°25. \255 P p
Joi 7i 4 bois ¥ rational exponents/
= 212,512 2656 34.24, 54,22 5? rasionele eksp
wo 4 2
=2? x34 x5? Y exponent law/ eksp. wet
=23x3!x5! owe
=120 ¥ simpification/ vereenv
(4)
[18]
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Mathematics/P 1/Wiskunde V1 8 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne
QUESTION/VRAAG 3
3.1.1 12 17 N 22
5 5 v 5n
T,=5n+7 v47
(2)
3.1.2 Ty =5(12) +7 ¥ subst/verv
-67 ¥ answer/antw
— (2)
3.1.3. 5n+7=172 ¥ 5n+7=172
5n=165
¥ answet/antw
n=33 (2)
3.2 3 x yo 30
N\ AON 4oO™ a
x-3 vrx 30-y
x-3=y-x Yx-3=y-x
y=2x-3
3=30 30-y=y-x ¥ 30-yay-x
330-2 +3 S04 x=2y
x-3=30-2x
3x36 30+x = 2(2x—3) ¥ equating/verg.
= OR/OF 36=3x
x=12 De
y=2l = Y both /beide
ye2l x=I2and/en y=21
(4)
OR/OF
30-3 =3d Vv 30-3=3d
3d =27
d=9 vd=9
x=3+9=12 Y both /beide
y=12+9=21 x=12and/en y=21
(4)
_ 0}

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Mathematics/P 1/Wiskunde V1 9 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne
QUESTION/VRAAG 4
41
ae y, 193 \ y, Me y, 109
-51 -45 \ y, -39
6
NOTE/LET WEL:
T,=76 Calc. differences 1/2 marks ¥ ¥answer/antw.
bereken verskille: 1/2 punte 2)
42 2a=6
a=3
Vaz=3
3a+b=-51 4
33)+b=-S1
=-60 vb=-60
at+b+c=244
| 3+-60+c¢=244 ¥c=301
c=301
_ 3,2
T, =3n’ -60n+301 YT, =3n’ —60n+301
4)
43 3n* —60n+ 301 =508 ¥ equating/verg.
2 =
3n' — 60n— 207 =0 ¥ std form/stand vorm
Ww —20n-69=0
(n+3) (n—23) =0 ¥ factors/fakore
n=23or n#—3 ¥select/ kies n= 23
(4)
44 using first diff./ gebruik eerste versk
T, =6n-5S7 ¥ 6n-57
453 = 6n—57 ¥453=6n—57
510=6n
n=85
between 7,, and T,, inthe quadratic pattern Y between T,, and T,,
tussen T,, en T,, indie kwadratiese patroon tussen Ty, en Ty,
OR/OF @)
In the quadratic pattern / in die kwadratiese patroon
Tau ~T, = 453
3(n+ 1)? — 60(n-+1)+301 - (Bn? - 60n +301)= 453 y
3n* + 6n-+3— 60n— 60—3n? + 60 = 453 | (01° —60(n-+1)+ 301 ~ (Gn? ~ 60m +301) = 453
6n=510
n=85 v¥n=85
between 7,, and Ty, ¥ between 7,, and Ty.
tussen Ty, en Tye tussen Ts en Ty,
G3)

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Mathematics/P1/Wiskunde VI 10
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrigiyne

DBE/November 2017

45

T, =3n? -60n+300+1

=3(n-10) +1

(n-10) = 0 fortvir neN

3(n-10) >0

3(n-10) +1>0

All terms in the pattern are positive/al die terme in die patroon is
positief

OR/OF

Tn =3n? - 60n+301

= 3(n-10) +1

T is a minimum valued function with minimum value |
Range of T: y 21

All terms in the pattern are positive.

T is funksie met minimum waarde van I
Waardeversameling van T; y>1

al die terme in die patroon is positief

q = 3(10)? — 60(10)+ 301
=1
T is a minimum valued function with minimum value 1
Range of T: y2>1
All terms in the pattern are positive.

|

T is funksie met minimum waarde van |
Waardeversameling vanT,; y 21
al die terme in die patroon is positief

(vVT, =3(n-10) +1
|
|

¥ V argument

|
YVT, =3(n-10) +1

¥ ¥ argument

¥ p=10
¥qz=l

v “argument

(4)

(4)

[17]

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Mathematics/P1/Wiskunde VI DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne
QUESTION/VRAAG 5
5.1 -
f= 3 5H
=4 ¥ answer/antw.
|_ Q).
5.2} 4=2*-4 v¥4=2"-4
8=2* |
B=27
x=-3 ¥ answer /antw.
Q)
53 |x=2 Vy=2
y=l vy=l
Q
5.4 | y>-4 ¥ answer/antw.
q)
OR/OF
ye (4 ; 00) ¥ answer/antw.
q)

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Mathematics/P 1/Wiskunde V1? 12 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne
5.5 | y-intercept/afsnit:
=<—_ 3 1
y= 0+2 ¥ subst/verv
-1 x=0
ys
-l
. _. 1 Vv y=
y-intercept/afsnit is | 0; — 3 2
x-intercept/afsnit:
0-4 ¥ subst/verv
x+2 y=0
-l= =3
x+2
—~x-2=3 ¥ simplification/vereenv.
taal ¥x=l
x=1 (3)
x-intercept/afsnit is (1 ; 0)
5.6 | ya-x+e
1=-(-2)+e ¥ subst/verv
—l=c
ya-xl ¥ answer/antw.
(2)
OR/OF
y-l=-(x-(-2)) ¥ subst/verv
y= -x-2+1
yarxed ¥ answer/antw.
L _ = (2)

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Mathematics/P 1/Wiskunde V1 13 DBE/November 2017
CAPS/KABV ~ Grade/Graad 11 - Marking guidelines/Nasienriglyne

5.7 tf
¥ asympt/asimpt
v Shape / vorm
vx and/eny
intercepts / afsnitte
&
¥ asymptote/asimpt
v x-intercept/afsnit (-2 ; 0)
v y-intercept/afsnit (0 ; -3)
’
H
CG)
'
'
Hy
'
:
:
'
'
'
H
‘
eae ee eae we nessa co
1
H
‘
H
t
5.8 | x<-3 or -2<x<-l V¥xs-3
¥-2<x<-l
OR/OF (2)
xe(-0;-3)U (-2;-1] v¥ (-~ ;-3)
¥(-2;-1]
(2)
(21)
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Mathematics/P 1/Wiskunde V1 14
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne

DBE/November 2017

QUESTION/VRAAG 6
6.1 O=-x? -x+6 vy=0
2 ¥-6=0 ¥ standard form/vorm
( Ns ») ¥ factors/faktore
x+3}x-2)=0
x=-3 or/of x=2 “ both answers/beide antw
B(3;0) and C(2;0) @)
62 | = - ; ~ -
ar NOTE/ LET WEL:
( 1) If answer only: award 2/2 marks
x= a) Slegs antwoord : gee 2/2 punte ¥ method/metode
_!1 ¥ answer/antw.
2
2)
OR/ OF
_ x t+%
a)
¥ method/metode
_ ©3)+()
2
1 | Wanswer/antw
2 @)
6.3 1
A-3)
ly (1
1
a v 64
TP/ DP (-}: 63]
2 4
Range/waardeversameling ye (- 0 56 ] ¥ Answer/antw.
OR/OF y< 65 @)
6.4 DO; 6) ¥ coordinates/kodrdinate D —
6-4
Map = 0- C 2)
1 ¥ gradient.
- v
Equation of/vergelyking van g: g(x)=x+6 answer/antw @)

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Mathematics/P1/Wiskunde V2 15 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrighyne
[6.5 Average/Gemid. gradient = gradientof/van g
=1 v answer/antw.
ql)
6.6 1)? 25 ¥ in the form/ in die vorm
sts)=-{x+) +> Ly 25
2 4 se)={x+4) +—
14) 25 4
i(a)=[+-3) -—
2 4 5)?
5) 25 Y (+ - 5)
nfs)-[+-3] -— 2
2 4 ve. 25
4
OR/OF (3)
J (x)= -x? -x+6
A(x) = (x-3) +(x-3)-6 V h&x)=(x~-3) + (x-3)-6
h(x) = x? —5x 5
2 Vlx |
wa) =(x-3) _25 [ 2
2 4 25
vs
4
(3)
6.7 -3<x<2 ¥ v answer/antw.
(2)
OR/OF
xe (33 3 2) ¥ ¥ answet/antw.
| = _ 2)
6.8 r=-2 Yr=-2
By symmetry/deur simmetrie
p=l ¥vp=1
p-r=3 ¥ answet/antw.
OR/OF (4)
-x-x+6=4
=x? -x+2=0
x 4+x-2=0
(x + 2x - 1) =0
x=-2 orlof x=1
r=-2 vr=2
p=l ¥vp=1
p-r=3 ¥ answer/antw.
(4)
[22]

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Mathematics/P1/Wiskunde V1 16

DBE/November 2017

CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne

QUESTION/VRAAG 7
71 A =P(l-i)'
20000= 80000(1— i) ¥ substitution into correct
0,25 =(1-i) formula/ verv.in korrekte
vorm
4/0,25=1-i
i=1-4/0,25 ¥ simplification/vereenv
£=0,24214417
i= 24,21% ¥ answer/antw.
@)
72 _Y
Itig = ( vs ¥ vorm/vorm
eg, af 14.2295 ’
Fhe HEE ¥ subst/verv
ig = 0,050945336...
Effective rate = 5,09 % p.a. Y answer/antw.
(3)
73°) A=P(1+i)" vom
2x12 4x2 ¥ 300061 02)
-s000({1+°) [1.0) “2
12 2 y (1-202)
=R58 017,51 12
4x2
v [: + an 08 }
OR/OF ¥ answer/antw.
\n (4)
A=P(1+i)
0,12)" ony?
=30 ooo +) “30 oo{ + 0)
=R38092,04 Y¥ R38092,04 co
Y 38092,04 [« 2108)
0,108 4x2 2
A =38092,04{14°0°8) v answer/antw.
2 (4)
=R58 017,51

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Mathematics/P1/Wiskunde V1 17 DBE/November 2017
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienrigiyne _
74 5x12 Bld 1,512 0,18
A=25000 14018 — 800! 14.018 +400 14 018 v
12 12 12 12

Sx12
60 36 18 v O18
=25000{ 14228) — good 1+248} + a00014 248 25000( 1+
12 12 12 sas
=R52636,74 v ~ aoo0{ +238)
18
v + ao0o( 1-938)
12
v¥ Vanswer/antw.
OR/OF
2x12 018
4 -25000(1+°28 are
12

= R35 737,57
Amount in the account after the withdrawal:/Bedrag in rekening
na onttrekking
R35 737,5703—R 8000
= R 27737,5703
Amount in the account just before the deposit/bedrag in rekening
voor die deposito

1,5«12
A, = R27737,3703 [: + “3)

=R36262,45279

Amount in the account just after the deposit/Bedrag in rekening na
onttrekking

R 36262,45279 + R4000
=R 40262,45279

Amount in the account at the end of 5 years/Bedrag in rekening
aan die einde van 5 jaar

1,542
= 40262,45279(1 + 8)

12,
=R52636,74

2x12
v 25000 14 218
12

¥ 27737,57

13x12
¥ 27737,5703 ( + 1)

v 40262,45

¥ answer/antw.

(6)
[16]

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Mathematics/P 1/Wiskunde V1 18 DBE/November 2017
CAPS/KABV - Grade/Graad 11 - Marking guidelines/Nasienriglyne
QUESTION/VRAAG 8
8.1.1
| :
| 3 (BB)
¥ branches/takke
¥ probabilities/waarskynlikhede
|
| R (@;R)
¥ outcomes/uitkomste
B (R;B)
|
|
3
R (R;R) 8
8.1.2 =
P(R,B) = 2,3 NOTE/ LET WEL: 23
5 4 If answer only: award 2/2 marks Vv 7x
3 Slegs antwoord : gee 2/2 punte 5 4
=T07 0,3 v answer/antwoord
Q)
8.2.1 | P(A) =0,4
P(B) = 0,3

P(A or B) = 0,58

P(A or B)= P(A) + P(B) — P(A and B)
0,58 =0,4+0,3 —P(A and B)
P(A and B) =0,12 +0

Events A and B are not mutually exclusive/Gebeurtenis A en B
is nie onderlinguitsluitend nie

¥0,58 = 0,4 +.0,3— P(A and B)
Y P(A and B) =0,1220

YNot mutually exclusive/ nie
onderling uitsluitend nie

@G)

8.2.2

P(A andB) = 0,12
P(A) x P(B)=0,4 x 0,3
=0,12
..P(A and B) = P(A) x P(B)

Y P(A) x P(B)=0,4 x 0,3

v¥ P(A and B) = P(A)x P(B)

A and B are independent events/is onafhanklik vA and B are independenvis
onafhanklik
(3)
[11]

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G& WWW

Please turn over/Blaai om asseblief

### Page 19

Downloaded from hlayiso.com

Mathematics/P 1/Wiskunde V1 19
CAPS/KABV — Grade/Graad 11 — Marking guidelines/Nasienriglyne

DBE/November 2017

QUESTION/VRAAG 9
9.1 n(S) = 80
_ _ ¥ 14 or/of 12 or/of 15
R aa Vv
v 26—
| 26-x (14) 13-x 26x
{o> ¥ 13—x
x
| 12 15 v5
| 5 3 3
| Cc
— (5)
9.2 26-x4+144x+1245+415+13-x+3= 80 v
88-80 =x 26—x+144x4+12454154+13-x4+3
x=8 ¥ equating to/gelyk aan 80
_ 2) |
9.3 Number who chose Rugby only/aantal wat net rugby kies
=26-8
=18 ¥ answer/antw.
| (1)
94 P(At least 2 types of sports /ten minste 2 sportsoorte)
1241441548 ¥ numerator/Noemer
= a a ¥ denominator/Teller
NOTE/ LET WEL:
= 49 If answer only: award 3/3 marks ¥ answer/antw.
80 | Slegs antwoord : gee 3/3 punte GB)
OR/OF
P(at least 2 types of sport/ten minste 2 sportsoorte)
18454543 vy 18454543
a 80
¥ method/metode
31
=]-2
80
_ 49
~ 80 ¥ answer/antw.
(3)
[13] |

Copyright reserved/Kopiereg voorbehou

G yi

TOTAL/TOTAAL: 150

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