# Mathematics Grade 12 Paper 1 Limpopo Prelim 2024 Memo

> Grade 12 Mathematics Paper 1 memorandum from the Limpopo Prelim Exam 2024, 17 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/limpopo-maths-p1-memo-sept-2024/38c5429a-a558-486b-947b-5b962b5a83bc
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Memorandum
- Year: 2024
- Exam period: Limpopo Prelim Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 17

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## About this document

Mathematics · Grade 12 · Limpopo Prelim Exam · 2024. Memorandum, 17 pages. Read online or download the PDF.

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## Document text

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### Page 1

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PROVINCIAL GOVERNMENT
REPUBLIC OF SOUTH AFRICA

+, LIMPOPO

DEPARTMENT OF

EDUCATION

NATIONAL SENIOR
CERTIFICATE/NASIONALE
SENIOR SERTIFIKAAT

GRADE/GRAAD 12

SPREE RRR,

MATHEMATICS P1/WISKUNDE V1
MARKING GUIDELINES/NASIENRIGLYNE
SEPTEMBER 2024

o

PCP eee |
®ummumneent

PUPP POPP RPE REPU CUP POORER ECU RUPE REPRE REE Pee © ia

MARKS/PUNTE: 150

This marking guidelines consists of 17 pages/Hierdie nasienriglyne bestaan uit 17 bladsye

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Mathematics P1/Wiskunde V1 2

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

NOTE/NOTA:

e If a candidate answers a question TWICE, only mark the FIRST attempt/ As ‘n
kandidaat 'n vraag twee keer beantwoord, merk slegs die EERSTE poging.

e Consistent Accuracy applies in all aspects of the marking guidelines/ Konsekwente

akkuraatheid is van toepassing in alle aspekte van die nasienriglyne

QUESTION/VRAAG 1
11 [111 | y~3x4+2=0 Hh
actorization/faktore
(x-2)(x-1) =0 Vx=2
x22 orlof 2=1 ¥x=1 (3)
1.1.2 | 3x° =-2-6x
3x? +6x+2=0 ¥ standard form
7 /standard vorm
ge =(6) + Y(6) —43)(2) ¥ subst into correct
2(3) formula/subst in korrekte
“.x=-1,58  or/of x=-0,42 formule
¥ x=-1,58 (4)
¥x=-0,42
1.1.3 2x-l=Vl-x
2x-1) =(VI=x)
( ) ( ) ¥ squaring both sides/
4x°-4x+1=1-x kwadreer albei kante
4x°-3x=0 ¥ standard form
x(4x-3) =0 /standard vorm ;
3 ¥ x=Oor/of x=—
x=0 or/of x=— 4
2 x= i 4
x==
a (4)
1.1.4 | (x+3)(3-x)<0

(x+3)(x-3)>0
CV:x=-3 or/of x=3

x<-3 or/of x>3

¥ critical values/kritieke
waardes

¥¥ answer/antwoord (3)

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Mathematics P1/Wiskunde V1

3

NSC - Marking Guidelines/Nasienriglyne

Limpopo DoE/ September 2024

12, 2x=y+2 a
y-2=x°-3x (2)
y=2x-2 V y=2x-2
Subst in (2)
2x-2-2=x7-3x ¥ substitution / substitusie
2x-4=x° -3x ¥ simplification/vereenvoudig
x -5x+4=0 ¥ standard form
(x-1)(x-4) =0 /standard vorm
x=1 or/of x=4 ¥x=1 or/of x=4
y=0 or/of y=6 ¥ y=0 or/of y=6
(6)
OR/OF OR/OF
Qx=y+2 (dy
y-2=x-3x (2)
_yt2
a) Pen
subst xin (2) 2,
2 2 ¥ substitution / substitusie
y-2= yt4y+4 _ 3y-6 ¥ simplification/vereenvoudig
4 2
4y-8=y?+4y+4-6y-12
2 ¥ standard form
y -6y=0
/standard vorm
y=0 or/of y=6 Y y=0 or/of y=6
x=1 or/of x=4 ¥ x=lor/of x=4 (6)

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Mathematics P1/Wiskunde V1

4

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NSC - Marking Guidelines/Nasienriglyne

13 x=—

equate (1) and (2)
72_ 72
x ReES

+0,2

72x+360=72x+0,2x° +x
0,2x" + x-360=0

x° +5x-1800=0
(x-40)(x+ 45) =0

x=40 or/of x=-45
x=40km/h

72(x+5) = 72x+0,2x(x+5)

Pasi.
x
2
Cy
x+5

¥ substitution / substitusie

¥ standard form
/standard vorm

¥ x=40

GS)

[25]

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5

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NSC - Marking Guidelines/Nasienriglyne

QUESTIONVRAAG 2
21 214 ie A180 =D vccssmrcccsseel (Ll) ¥ a+3d =5.
Bei CASE vscsscsceivases (2) V¥ a+13d =15
10d =10 ¥ 10d =10
d=1 Y answer/antwoord
(4)
212 a=2 vY a=2
T, =a+(n-Nd
=2+(n-I)l
=n+l v T,=n+1
(2)
2.1.3 | S,= 5 [a+ (n-1)d]
22 3
= —[2(2) +(22- d)] ¥ subst into correct formula/
2 subst in korrekte formule
=11(25)
275 Y answer/antwoord (2)
2.2. x VY wa 7x
7x-13 v Ist difference// ste verskil
7x-19 v 2nd difference/2de verskil
7x—-13-6=6-(7-x) ¥ equation/vergelyking
7x-19=-1+x
6x=18
_ ¥ answer/antwoord (4)
[12]

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Mathematics P1/Wiskunde V1

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

QUESTION/VRAAG 3
31 | s =
l-r 1
Vr=—
= 3
= 1 ¥ subst into correct formula
3 /subst in korrekte formule
=3 Y answer/antwoord (3)
32 S,= a(l-r’
l-r
of (4)
S =~ 4 ¥ subst into correct formula
" 1- 1 /subst in korrekte formule
3
2) 1- i) 2) 1- i)
3 3
= v
2 2
3 3
=3 -(5] 43 1-(3]
3 3
= (2) 3)
3
Ly" LY"
3.3, | 3-3] =| >2,99 ¥ 3-3] —| >2,99
3 3
1" 0,01
z] 3 ¥ simplification/vereenvoudig
1 0.01 ¥ use of logs/gebruik logs
nlog = < log ——
8 3
0,01
log ——
n> 3
log i
3
n>5,19 ¥n>5,19
Smallest value of/Kleinste waarde van n is 5 ¥ reasoning/redenasie (5)
{11]

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Mathematics P1/Wiskunde V1

QUESTION/VRAAG 4

7

NSC - Marking Guidelines/Nasienriglyne

Limpopo DoE/ September 2024

4.1

4.1.1

f(x =-x? +x412
y — intercept/afsnit (x=0)

y=12
A(0;12)
“AF eH2=0 Y equate to 0/gelykstel 0
x’-x-12=0
(x-4)(x+3)=0
x=4  or/of x=-3 V¥x=4 or/of x=-3 (2)
B(4;0)
4.1.2 | y=mxt+k
y=mx+12 V¥k=12
Passing through/Gaan deur B (4;0)
4mrl2=0 ¥ substitution / substitusie
m=-3 v 3 4
y=-3x4+12 me~ ®)
OR/OF OR/OF
12-0
m>=—
0-4
=-3 ¥m=-3
y=mx+k
B(4;0)
0=-3(4) +k ¥ substitution / substitusie
wk=12 Vk=12
y=-3x+12 (3)
4.1.3 (a) EF =EG-FG
= (—x? +.x+12)—(-3x+12)
= [-(2)° +(2)4+12]—[-3(2) +12] ¥ substitution / substitusie
EF = 4 units / eenhede Y answer/antwoord (2)
OR/OF OR/OF
EF = (-x? +x+12)—(-3x+12)
=-x +4x
=-(2) +4(2) ¥ substitution / substitusie
.. EF = 4 units / eenhede Y answer/antwoord (2)

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Mathematics P1/Wiskunde V1 8

NSC - Marking Guidelines/Nasienriglyne

Limpopo DoE/ September 2024

Vv -~<x<4
2

(b) | Area of / Opy van AOGF
construct / konstrueer : PF//OG
= Area AAPF + Area OPFG 1
Ling 5 4 %5@)
== (2)(3)+ (6x2)
2 v (6x2)
=18 Y answer/antwoord (3)
bo Ss
OR/OF OR/OF
AOGFis a trapezium
Area / Opv = 5 (FG +AO)h
1 ¥ (6+12)
=—(6+12)2
2! , v2
=18 v answer/antwoord (3)
OR/OF OR/OF
Area of / opv van AOGF
= Area (AAOB — AGBF)
1 1 1
= = (4)(12) — —(2)(6) ¥ —(4)(12
3 ) 3 * )(12)
=18 1
v¥ ~(2)(6)
2
(3)
¥_answer/antwoord
414 C(-3:0)
f'(x)=-2x41 v f'Q)=-2x41
f'(-3)=-2(-3)+1
=7 ¥m=7
y—0=7(x+3)
y=7x+21 V y=7x+21
7x+21=-3x+12 Y¥ 7x+21=-3x+12
10x=-9
x=-0,9 v¥x=-0,9
y=14,7 v y=14,7 (6)
T ge
4.1.5 x<-3 or hegea as
2 (3)

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Mathematics P1/Wiskunde V1

9

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

4.2 4.2.1
¥ shape/vorm
¥ aymptotes/asimptote
¥ x — intercept/afsnit
vy — intercept/afsnit
(4)
4.2.2 x $29)
x+2
+220
“+2 VV x<-3or/of x>-1
x<-3 or/of x>-2 (2)
4.2.3 y-2=-x-2 v y-2=-x-2
y=-x Pegs 5 (2)
y=-(x+ p)+q
y=-(x+2)+2 VY y=-(x+2)4+2
y=-x VY y=-x (2)
OR/OF OR/OF
y=-x+e
2=-(2)+e ¥2=-(2)+e
c=0
y=-x Vv y=-x
(2)
[27]

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Mathematics P1/Wiskunde V1 10

NSC - Marking Guidelines/Nasienriglyne

QUESTION/VRAAG 5

so.com

Limpopo DoE/ September 2024

5.1

h(x) = log, x
Passing though/gaan deur (16;4 )

¥ substitution / substitusie

4=log,16
a’ =16 ¥ change to exponents/
vernader na eksponente
a=2 v answer/antwoord @)
5.2 | y=log,x
=x
x=2°
x=1
B(1;0) v B(1;0) 1e0)
5.3 | y=log, x
xelog,y v interchanging/ruil x & y
y=2"
’ Vi'(x)=2"
oA(x) = 2? Q)
5.4 | Range / waardeversameling: y >0 vy>0 (1)
OR/OF OR/OF
ye(0; ») ye(0; ~) @
[7]

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Mathematics P1/Wiskunde V1 11

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

QUESTION/VRAAG 6
0.115)" ¥ subst in correct formula
6.1 | l+ig = (: ah on) /subst in korrekte formule
: v 0,115
L+i,g =1,120055 ri
iy =0,1200
-. rate / koers =12% Y answer/antwoord @)
40
62 | A=200 000(1+145
400 ¥n=40
= R621 475,37 Y answer/antwoord (2)
6.3 | Loan amount/Lening bedrag =1 850 000-621 475,37] ¥ Loan/lening
= Rl 228 524,63 Y answer/antwoord (2)
64 P= x{l- d+) ]
I
-300
Gee) | ¥n=-300
¥ subst in correct formula
228 524,63 12 /subst in korrekte formule
1200 y 12
1 228 524,63 =94,94655125x 1200
x=12 939,12 Y answer/antwoord (4)
65 | Balance/ Balans = “1—G+#)"1
i
-120
12 sanaa|t-(14 3) vn=e120
= 1200 ¥ subst in correct formula
3 /subst in korrekte formule
= R901 863,28 Y answer/antwoord (3)
OR/OF OR/OF

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12

NSC - Marking Guidelines/Nasienriglyne

so.com

Limpopo DoE/ September 2024

Balance / Balans = A-F

180
12 939,12 (5) =f
1200

Y subst in compound
formula/vervang in
saamgestelde formule

180 Sorcritucts
=1 208 524,63 14 12 _ subst in Future value/
1200 12 vervang in toekomstige
1200 formule
v 3
= 901 863,28 answer/antwoord G3)
6.6 | Interest/Rente
=12 939,12x300-—1 228 524,63 ¥ calculation/bewerking
= R2 653 210,76 Y answer/antwoord
(2)
[16]

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Mathematics P1/Wiskunde V1 13

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

QUESTION/VRAAG 7
TL | f(x) =3x°
f (x+h) =3(xth) =3x° +6xh+3h?
f= Him f(xth)- f(x) ¥ 3x? +6xh + 3h"
=lim 3x1 + 6xh+ 3h 3x" ¥ substitution / substitusie
h>0 h
2 2
= fim Sat 3h vlim Gxh+ 3h”
h>0 h =H h
+
= fim 16%43h) V tim 2662+ 3h)
hoo h hoo h
shige ¥ lim(6x+3h)
hoo off 0
=6x ¥ answer/antwoord (5)
OR/OF OR/OF
f(x) =3x7
h)—
f'@)=lim£ e+ )-f@) -
0 h ¥ substitution / substitusie
. 3(x+hy -3x?
—
, 5 8G ¥ 3x? +6xh+3h"
. 3x +6xh+3h —3x"
ee h 6xh+3h"
, Vimo
. 6xh+3h h>0 h
a h(6x+3h)
V lim Ox)
=lim h(6x+3h) h0 h
a0, ik Y lim(6x+3h)
= lim(6x + 3h) cd (5)
= Y answer/antwoord
=6x
721 1 f(x) =(x-DOS 4+ 42448427 4+x41)
Hx t x8 ex txt tx exr tx ¥ products/produkte
—x§-x° —x4-x°-x?-x-1
=x’-1 S xh-A
fi) = 73° V 7x8 (3)

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Mathematics P1/Wiskunde V1

14

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

7.2.2 | D, 42x 44x
, x+1
=D [zee] ¥ simplification/vereenvoudig
. x+l1 P Biovee
=D, [x +x] v 2x
=2x+l v1
(4)
7 1
7.2.3 | y=¥x-—
3x ;
- s 1 vx
3 vy

dy 121, 3

six +=x 9

da 3 3 Gigs
3
1,

v=x” 4
3 (4)
[16]

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Mathematics P1/Wiskunde V1 15 Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

QUESTION/VRAAG 8
8.1 | £(3)=2(3)[)? -9(3)+24] “substitution /
substitusie
= 6 Y answer/antwoord 2)
8.2 | f(x) =2x3-18x7 + 48x
f (x) = 6x° —36x+48 ¥ derivative/afgeleide
6x° -36x+48=0 ¥ standard form
2 /standard vorm
—6x+8=0
ti ORE vx — values/waardes
(x-4)(x-2)=0 J
_ _ y — values/waardes
x=4 or/of x=2 (4)
y=32  or/of y=40
8.3 y
(2;40)
¥ shape/vorm
¥ turning points/
draaipunte
Y origin/oorsprong
x
|
G3)
8.4 32<k<40 v V answer/antwoord (2)
8.5 Maximum/Maksimum is 40 ¥ max/maks 40 (1)
[12]
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Mathematics P1/Wiskunde V1 16

Limpopo DoE/ September 2024

NSC - Marking Guidelines/Nasienriglyne

QUESTION/VRAAG 9
9.1 | A=a2R* +2’. ¥ Equation of A/
R+r=200 Vergelyking A
F=200 =Riecsxcseeceet (2) Yr subject of formula/ r
Subst (2) in (1) onderwerp formule
A=2R? +2(200-R)Y* ¥ substitution / substitusie
= R? + 2(40000—400R + R?)
= 2R’ +. 400002 — 4002R + 2R°
= 22R° — 40072 R + 400002 (3)
9.2. | At minimum aA 0 fA. 0
dR dR
4zR-400z =0 Y 4xR-4007
"te e, ¥ R=100
r= 200-R=100 oe (4)
9.3. | R=r=100, will not get the desired shape because a
shape with two equal circles touch externally/ sal nie ¥¥ valid explanation/
die gewenste vorm kry nie, want 'n vorm met twee gelyke geldige verduideliking
sirkels raak ekstern (2)
[9]

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Mathematics P1/Wiskunde V1 17

NSC - Marking Guidelines/Nasienriglyne

Limpopo DoE/ September 2024

QUESTION/VRAAG 10
10.1 | P(A or/of B)=P(A)+P(B)
= 0,45+0,25 ¥ 0,45+0,25
=0,7 Y answer/antwoord
, (2)
10.2 | 10.2.1
= 2@
49
30 c 7 Sand /en =
50
20 N v2 a oniten
49
v BU end fent
30 °
20 49
50
N
IN y
49
(3)
30. 20 20 30 30 20
10.2.2 | PONC)=( 30x22) 4/ 29.28 (2.2)
= & a) (3 | 5049
=0,41 y{ 20 30
50 49
Y answer/antwoord (3)
10.2.3 | P(CC) = 20. 29 FBig2?
50 49 50 49
=0,36 Y answer/antwoord (2)
10.3 $103.1 | 40°52 Y10xS
= 25000 Y answer/antwoord (2)
10.3.2 | 9x9x8x4x1 V¥9x9x8
= 12960 v4xl
v answer/antwoord (3)
[15]

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- [Maths Grade 12 NSC P1 QP September 2025 Afr Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p1-qp-september-2025-afr-northern-cape/f5b3a4ce-fa91-4475-96e0-0654a87e1405) — QP · 2025 · Afr
- [Maths Grade 12 NSC P2 QP September 2025 Eng Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-qp-september-2025-eng-northern-cape/4ede8207-ca82-4419-bae1-fae734498cc7) — QP · 2025 · Eng
- [MATHS P2 ANSWER BOOK GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-answer-book-gr12-june-2024-afr-english/4a71e975-4ac4-4f55-8e23-0b8155a5b0c6) — Addendum · 2024 · Eng

## Collection

- [Grade 12 past papers](https://www.hlayiso.com/grade-12/past-papers)

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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.