NATIONAL
SENIOR CERTIFICATE/
NASIONALE SENIOR
SERTIFIKAAT
SENIOR SERTIFIKAAT
GRADE/GRAAD 11
NOVEMBER 2025
MATHEMATICS P1/WISKUNDE V1
MARKING GUIDELINE/NASIENRIGLYN
MARKS/PUNTE: 150
This marking guideline consists of 21 pages.
Hierdie nasienriglyn bestaan uit 21 bladsye.
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Mathematics Grade 11 Paper 1 Eastern Cape November 2025 Memo
Grade 11 Mathematics Paper 1 memorandum from the Eastern Cape November Exam 2025, 21 pages. Read online or download the free PDF.
Mathematics · Grade 11 · Eastern Cape November Exam · 2025. Memorandum, 21 pages. Read online or download the PDF.
- Subject
- Mathematics
- Grade
- Grade 11
- Document type
- Memorandum
- Year
- 2025
- Exam period
- Eastern Cape November Exam
- Paper
- 1
- Curriculum
- CAPS
- Pages
- 21
- File size
- 680.8 KB
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This exam
Eastern Cape November Exam 2025
Questions in this paper
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2 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
NOTE/LET WEL:
• If a candidate answers a question TWICE, mark the FIRST attempt ONLY.
Indien ʼn kandidaat ʼn vraag TWEE keer beantwoord, merk SLEGS die EERSTE poging.
• Consistent accuracy applies in ALL aspects of the marking guideline.
Volgehoue akkuraatheid geld deurgaans in ALLE aspekte van die nasienriglyn.
• If a candidate crossed out an attempt of a question and did not redo the question, mark
the crossed-out attempt.
Indien ʼn kandidaat ʼn poging vir ʼn vraag deurgetrek het en nie die vraag weer
beantwoord het nie, merk die poging wat deurgetrek is.
• The mark for substitution is awarded for substitution into the correct formula.
Die punt vir substitusie word toegeken vir substitusie in die korrekte formule.
QUESTION/VRAAG 1
1.1.1 x ( 2x + 6) = 0
x = 0 or/of 2 x + 6 = 0 ✓ x=0 ✓ x = −3
x = 0 or/of x = −3
(2)
1.1.2 4 x + 3x − 9 = 0
2
Penalise 1 mark for
−b b − 4ac
2 incorrect rounding off./ standard form / standaardvorm
x= Penaliseer 1 punt vir
2a verkeerde afronding.
−3 (3) 2 − 4(4)( −9)
x=
2(4)
substitution / vervanging
−3 153
x=
8
x = 1,17 or / of x = −1,92 x = 1,17 or/of x = − 1, 92
(4)
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 3
1.1.3
x ( x − 4) + 2 ( 4 − x ) 0
x ( x − 4) − 2 ( x − 4) 0
✓ −2 ( x − 4 )
( x − 4 )( x − 2 ) 0
critical values / kritieke waardes ✓ critical values / kritieke waardes
x = 4 or / of x = 2
2 4
x 2 or / of x 4
✓✓ x 2 or x 4
(accuracy / akkuraatheid)
(4)
1.1.4 x + 14 0 ; x −2 ✓ x −14
(a) x −14 ✓ x −2
(2)
(b) x + 14 ✓ isolating surd / isoleer wortelvorm
=1
x+2
✓ square both sides /
x + 14 = x + 2 kwadreer beide kante
x + 14 = x 2 + 4 x + 4
✓ factors / faktore
x 2 + 3 x − 10 = 0
( x + 5 )( x − 2 ) = 0
✓ answer with choice /
x −5 or / of x = 2
antwoord met keuse
(–5 excluded / uitgesluit)
(4)
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4 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
1.2 x − 3 y = 1......................................... (1)
x 2 − 2 xy + 9 y 2 = 17..........................(2)
From / Vanaf (1) : x = 3 y + 1 ..........(3) ✓ x = 3y +1
(3) into/in (2) :
( 3 y + 1) − 2 y ( 3 y + 1) + 9 y 2 = 17
2
✓ substitution / vervanging
9 y 2 + 6 y + 1 − 6 y 2 − 2 y + 9 y 2 − 17 = 0
12 y 2 + 4 y − 16 = 0
✓ standard form / standaardvorm
3y2 + y − 4 = 0
✓ factors / faktore
( y − 1)( 3 y + 4 ) = 0
4
y = 1 or/of y = − ✓ y values / y-waardes
3
x = 4 or/of x = −3 ✓ x values / x-waardes
(6)
1.3 10
1+ =7
1
1+
1
1+
x
10
1+ =7 1
1 ✓
1+ x +1
x +1
x
x
10
1+ =7
1+
x x +1
✓
x +1 x
10
1+ =7
x +1+ x
x +1
10
1+ =7 2x +1
2x + 1 ✓
x +1
x +1
10 ( x + 1)
1+ =7
2x + 1
2 x + 1 + 10 x + 10 2 x + 1 + 10 x + 10
=7 ✓
2x + 1 2x +1
12 x + 11
=7
2x + 1
12 x + 11 = 14 x + 7
2x = 4 ✓ answer / antwoord
x=2 (5)
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 5
QUESTION/VRAAG 2
2.1 125 x. 54 x − 2
3 12 x + 6 x ✓ 125 x = 33 x
5 .5
3 x 2 x −1 ✓ 54 x −2 = 52 x −1 and/en
5 .5
= 4 x+2 x 3
512 x +6 = 54 x + 2
5 .5
= 53 x − x + 2 x −1− 4 x − 2
✓53x+2x-1-4x-2-x
−3
=5
1
= ✓ answer / antwoord
125
(4)
2.2.1 3
6 x = 482
3
✓ dividing by 6 / deel deur 6
x =82
2
✓ raising by reciprocal
x = (2 ) 3 3
verhef tot omgekeerde/resiprook
x = 22
✓ answer / antwoord
x=4
(3)
2.2.2 14 12
x − 3 x 4
+2=0 2
14
1
✓ x
let/laat : k = x4
k 2 − 3x + 2 = 0
1 1
( k − 2 )( k − 1) = 0 OR /OF x 4 − 2 x 4 − 1
✓ factors / faktore
k = 2 or/of k = 1
1 1 1 1
x = 2 or/of x = 1
4 4
✓ x = 2 or/of x = 1
4 4
x = 16 or/of x = 1
✓ answers / antwoord
(4)
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6 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
2.3 A = L B
16 x − 100 = L ( 4 x + 10 )
✓ substitution into area formula
L=
( 4 ) − 100
x 2 vervanging in oppervlakte formule
4 x + 10
✓ 16 x = ( 4 x )
2
L=
( 4 − 10 )( 4 + 10 )
x x
✓ factors of difference of 2 squares
4 + 10 x
faktore van verskil tussen 2
L = 4 − 10
x
kwadrate
Length = 4 x − 10
✓ answer / antwoord
(4)
2.4 Smaller integer / Kleiner heelgetal = x
next consecutive integer / opeenvolgende heelgetal = x + 1
✓ difference / verskil
Difference / Verskil : ( x + 1) − x 2 = 45
2
x 2 + 2 x + 1 − x 2 = 45 ✓ equating the difference to 45
stel verskil gelyk aan 45
2 x = 44
x = 22 ✓ x = 22
( 22 + 23) = 2025
2
✓ (sum)2 / (som)2 = 2025
(4)
[19]
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 7
QUESTION/VRAAG 3
3.1.1 d = − 0,5 ✓ 4
4 ; 3,5
✓ 3,5
(2)
3.1.2 Tn = −0,5n + 6 ✓ −0, 5n
✓ +6
(2)
3.1.3 1
− n + 6 −113,5
2 1
✓ − n + 6 −113,5
−0,5n 119,5 2
n 239
✓ answer / antwoord
n = 240 (2)
3.2.1 d =5
Tn = 5n + c ✓ Tn = 5n + c
but / maar: T38 = 192
✓ substitution / vervanging
192 = 5 ( 38 ) + c
c=2
T1 = 5 (1) + 2 = 7
First term is 7 / Eerste term is 7 ✓ answer / antwoord
(3)
[9]
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8 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
QUESTION/VRAAG 4
4.1.1 Tn = n 2 − 12n + k
✓ substitution / vervanging
3132 = ( 62 ) − 12 ( 62 ) + k
2
k = 32 ✓ answer / antwoord
(2)
4.1.2 Terms of the quadratic number pattern:
Terme van die kwadratiese patroon:
T1 = (1) − 12 (1) + 32 = 21
2
T2 = ( 2 ) − 12 ( 2 ) + 32 = 12
2
✓ terms of quadratic number pattern /
T3 = ( 3) − 12 ( 3) + 32 = 5
2
terme van kwadratiese getalpatroon
Terms of the first difference:
Terme van eerste verskille:
−9 ; −7 ; −5 ✓ answer / antwoord
(2)
4.1.3 Tn = n − 12n + 32
2
✓ method / metode
− ( −12 )
n= =6 ✓ answer / antwoord
2 (1) (2)
Tn −1 = ( n − 1) − 12 ( n − 1) + 32 ✓ simplification / vereenvoudiging
2
4.1.4
= n 2 − 2n + 1 − 12n + 12 + 32
= n 2 − 14n + 45 ✓ answer / antwoord
(2)
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 9
4.1.5 Tn − Tn −1 = 149
n 2 − 12n + 32 − n 2 + 14n − 45 = 149 ✓ Tn − Tn−1 = 149
149 = 2n − 13
✓ simplification /
n = 81 vereenvoudiging
consecutive terms are 80 and 81 /
opeenvolgende terme is 80 en 81 ✓ answer / antwoord
(3)
OR / OF
OR/OF
Tn = 2n − 11
✓ Tn = 2n − 11
149 = 2n − 11
160 = 2n
✓ equating Tn to 149
n = 80
consecutive terms are 80 and 81 /
opeenvolgende terme is 80 en 81 ✓ answer / antwoord
(3)
4.2 x 4 3x 18
4− x 3x − 4 18 − 3 x
✓ 2nd diff i.t.o x / 2de versk. i.t.v x
4x − 8 − 6 x + 22
4 x − 8 = − 6 x + 22 ✓ equating / gelykstelling
10 x = 30
x=3
✓ answer / antwoord
T3 = 9
(3)
[14]
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10 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
QUESTION/VRAAG 5
5.1 p = −3 ✓ answer / antwoord
(1)
a a
5.2 f ( x) = −1 ✓ f ( x) = −1
x −3 x −3
Subst. / Vervang: ( 4; 2 )
a ✓ substitution of ( 4;2 ) /
2= −1
4−3 vervanging van ( 4;2 )
a=3
3
f ( x) = −1 ✓ equation of f / vergelyking van f
x −3
(3)
x
5.3 g ( x) = +c
3
3
−1 = +c
3
c = −2
B (0 ; − 2)
x ✓ coordinates of B / koördinate van B
0= −2
3 ✓ g ( x) = 0
x
2=
3
x=6
A (6 ; 0) ✓ coordinates of A / koördinate van A
(3)
OR/OF OR/OF
f ( 0 ) = −2
B (0 ; − 2)
✓ coordinates of B / koördinate van B
3
0= −1
x−3
3 ✓ f ( x) = 0
1=
x−3
x−3= 3
x=6
A (6 ; 0) ✓ coordinates of A / koördinate van A
(3)
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 11
5.4 − ( x − 4) + 3 = 0 ✓ replacing x by − ( x − 4 )
−x + 4 − 3 = 0 vervang x met – (x – 4)
−x + 1 = 0
✓ x −1 = 0 / x = 1
x −1 = 0
V.A: x = 1 ✓ answer / antwoord
Domain / Gebied : x R ; x 1 (3)
OR / OF
OR/OF
3
h ( x) = −1
− ( x − 4) − 3 ✓ replacing x by − ( x − 4 )
3 vervang x met – (x – 4)
=
−x + 4 − 3
3
= −1
− ( x − 1) ✓ denominator / noemer: ( x − 1)
−3
= −1
x −1
Domain / Gebied : x R ; x 1 ✓ answer / antwoord
(3)
5.5 x 3 ,x 6
OR / OF ✓✓ answer / antwoord
3 x 6 or/of x 6
(2)
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12 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
5.6.1
1
mAB =
3
= 18, 43
ˆ = 18, 43 (Vert. opp 's / Regoorstaande e)
BOA
0−2
mEA = = −1 ✓ mAB and/en mEA
6−4
ˆ = 45
Ref. / Verwys.. : EAO
EABˆ = 63, 43 ✓ Length of EA / Lengte van EA
EA = ( 4 − 6) + ( 2 − 0)
2 2
✓ 18, 43 and/en 45
=2 2
1 ˆ
Area of ABE = EA AB sin EAB ✓ substitution in the area formula /
2
vervanging in die oppervlakte
1
( ) ( )
= 2 2 2 10 sin 63, 43
2
formule
= 8 units 2 / eenhede2 ✓ answer / antwoord
(5)
[17]
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 13
QUESTION/VRAAG 6
6.1 a = −1
6 ✓ value of a / waarde van a
x= = −3
−2 ✓ x = −3 and / en y = 9
f ( −3) = − (1) − 6 ( −3) = 9
2
✓ equation in T.P-form /
f ( x ) = − ( x + 3) + 9 Vergelyking in DP-vorm
2
OR / OF (3)
OR/OF
f ( x ) = − x2 − 6x
✓ common factor –1 /
= − ( x2 + 6 x ) gemene faktor –1
(
= − x 2 + 6 x + ( 3) − ( 3)
2 2
) ✓ completing the square ( 3) /
2
= − ( ( x + 3) − 9 ) voltooing van vierkant ( 3)
2 2
= − ( x + 3) + 9 ✓ equation in T.P-form /
2
vergelyking in DP-vorm
(3)
6.2 xTP = −3
✓ x = −3
xB + x A
= xTP
2
−5 + x A
= −3
2
−6 = − 5 + x A
x A = −1 ✓ xA = −1
f ( −1) = − ( −1) − 6 ( −1) = 5
2
✓ f ( −1)
A ( −1;5 )
(3)
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14 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
6.3 g ( x ) = x2 + 6x ✓ g ( x)
CD = g ( x ) − f ( x )
14 = x 2 + 6 x − ( − x 2 − 6 x ) ✓ g ( x) − f ( x)
14 = 2 x 2 + 12 x
2 x 2 + 12 x − 14 = 0
x2 + 6x − 7 = 0 ✓ standard form / standaardvorm
( x + 7 )( x − 1) = 0 ✓ both x − values /
x = −7 or / of x = 1 beide x-waardes
x = −7
OE = 7 units / eenhede ✓ answer / antwoord
(5)
6.4.1 k −9 ✓✓ answer / antwoord
(2)
6.4.2 −x − 6x = 0
2
x2 + 6x = 0
x ( x + 6) = 0
x = 0 or / of x = −6 ✓ x − values / x-waardes
−6 k 0 ✓✓ answer / antwoord
(3)
[16]
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 15
QUESTION/VRAAG 7
7.1.1 y = −3 ✓ answer / antwoord
(1)
7.1.2 x +1
1
−3= 0 ✓ f ( x) = 0
3
x +1
1
3=
3
−1 x +1
1 1
= OR / OF 31 = 3− x −1
3 3
x + 1 = −1
x = −2 ✓ x = −2
0 +1
1
y = −3
3
8 8
= − −2, 7 ✓ y=−
3 3
(3)
7.1.3
✓ shape / vorm
✓ x and y intercepts /
x- en y-afsnitte
✓ asymptote / asimptoot
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16 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
7.1.4 x −2 ✓✓ answer / antwoord
(2)
7.2 y = a.k + rx
y = a.k x − 2
✓ y = a.k x − 2
Subst./ Vervang: ( 0 ; 0 )
0 = a.k 0 − 2
2=a
✓ a=2
6 = 2k 2 − 2
8 = 2k 2 ✓ substitution of ( 2;6 ) /
4 = k2 vervanging van ( 2;6 )
k = 2
k = 2 ;k 0
h ( x ) = 2.2 x − 2 ✓ equation h / vergelyking h
(4)
[13]
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 17
QUESTION/VRAAG 8
8.1 A = P (1 − i ) n ✓ i=6
= 250 000 (1 − 13% )
6
✓ substitution / vervanging
= R108 406,55
✓ answer / antwoord
(3)
n
i
8.2 1 + 7,5% = 1 + nom
4
✓ substitution / vervanging
43 inom
4 = 1 +
40 4
43 i
4 − 1 = nom
40 4
✓ inom subject of equation /
43
inom = 4 4 − 1 inom onderwerp van formule
40
inom = 0, 07297.....
irate = 7,30% ✓ irate
(3)
24
7% 6 2 ✓ n = 24 ; 6 and / en 2
4% 7%
8.3 A = 25 000 1 + + 10 000 1 + − 5000 1 +
24
12 2 2 4%
✓ 25 000 1 +
A = R 40 222,91 12
24
4%
✓ +10000 to 25 000 1 +
12
✓ subtracting 5000 with its interest /
aftrekking van 5000 met rente
✓ answer / antwoord
(5)
OR / OF OR/OF
✓ n = 24 ; 4 and/en 2
4% 7%
24 4
7% 2 24
A = 25 000 1 + + 10000 1 + − 5000 1 + 4%
✓ 25 000 1 +
12 2 2 12
A = R 40 222,91
24
4%
✓ +10000 to 25 000 1 +
12
2
7%
✓ P 1 +
2
✓ answer / antwoord
(5)
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18 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
8.4 Option 1 : annual compounding
* Amount after 2 years: x (1 + 0,12 ) ✓ x (1 + 0,12) − 5 000
2 2
*Brian pays 5 000, leaving : x (1 + 0,12 ) − 5 000 and/en x (1 + 0,06) − 3 000
2 2
(
*Amount after another 2 years: x (1 + 0,12 ) − 5 000 (1 + 0,12 )
2
) 2
( )
✓ x (1 + 0,12 )2 − 5 000 (1 + 0,12 )2
Option 2 : semi - annual compounding
* Amount after 1 year: x (1 + 0,06 )
2
*Brian pays 3 000, leaving : x (1 + 0,06 ) − 3 000
2
( )
✓ x (1 + 0, 06 )2 − 3 000 (1 + 0, 06 )4
(
*Amount after another 2 years: x (1 + 0,06 ) − 3 000 (1 + 0,06 )
2
) 4
Times lines for both options
( x (1 + 0,12) − 5000) (1 + 0,12) = ( x (1 + 0,06) − 3000 ) (1 + 0,06)
2 2 2 4 ✓ equating both options /
gelykstel van opsies
( x (1,12) − 5000) (1,12) = ( x (1,06) − 3000 ) (1,06 )
2 2 2 4
✓ distribution by / uitbreiding
(1,12) and / en (1,06)
2 2
x (1.12 ) − 5000 (1,12 ) = x (1,06 ) − 3000 (1,06 )
4 2 6 4
−5000 (1,12 ) + 3000 (1,06 ) = x (1,06 ) − x (1,12 )
2 4 6 4
−2484,56912 = −0,1550002477 x ✓ answer /antwoord
(6)
x = R16029, 45
[17]
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(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 19
Opsie 1 : jaarliks saamgestel
* Bedrag na 2 jaar: x (1 + 0,12 ) ✓ x (1 + 0,12) − 5 000
2 2
*Brian betaal 5 000, dit laat: x (1 + 0,12 ) − 5 000 and/en x (1 + 0,06 ) − 3 000
2 2
(
*Bedrag na 'n verdere 2 jaar: x (1 + 0,12 ) − 5 000 (1 + 0,12 )
2
) 2
( )
✓ x (1 + 0,12 )2 − 5 000 (1 + 0,12 )2
Opsie 2 : half - jaarliks saamgestel
* Bedrag na 1 jaar: x (1 + 0, 06 )
2
*Brian betaal 3 000, dit laat : x (1 + 0, 06 ) − 3 000
2
( )
✓ x (1 + 0, 06 )2 − 3 000 (1 + 0, 06 )4
(
*Bedrag na 'n verdere 2 jaar: x (1 + 0, 06 ) − 3 000 (1 + 0, 06 )
2
) 4
Tydlyne vir beide opsies:
( x (1 + 0,12) − 5000) (1 + 0,12) = ( x (1 + 0,06) − 3000 ) (1 + 0,06)
2 2 2 4 ✓ equating both options /
gelykstel van opsies
( x (1,12) − 5000) (1,12) = ( x (1,06) − 3000 ) (1,06 )
2 2 2 4
✓ distribution by / uitbreiding
(1,12) and / en (1,06)
2 2
x (1.12 ) − 5000 (1,12 ) = x (1,06 ) − 3000 (1,06 )
4 2 6 4
−5000 (1,12 ) + 3000 (1,06 ) = x (1,06 ) − x (1,12 )
2 4 6 4
−2484,56912 = −0,1550002477 x ✓ answer /antwoord
x = R16029, 45 (6)
[17]
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20 MATHEMATICS P1/WISKUNDE V1 (EC/NOVEMBER 2025)
QUESTION/VRAAG 9
9.1.1 NO / NEE ✓ NO / NEE
P ( A ) ×P ( B ) = 0,3 0, 6
✓ valid reason /
= 0,18 geldige rede
P ( A and / en B ) = 0,18 0 (2)
9.1.2
✓ 0,18
✓ 0,12 and/en 0,42
✓ 0,28
(3)
9.1.3 P ( not A and not B) = P not ( A or B) = 0, 28
✓✓ answer / antwoord
P(nie A en nie B) = [nie(A of B)] = 0,28
(2)
9.2.1 42 21
=
106 53 ✓ answer / antwoord
(1)
56
9.2.2 P ( Enjoy jogging/Geniet draf ) =
106
42
P ( Male/Manlik ) =
106
56 42
P ( Enjoy jogging/Geniet draf ) P ( Male/Manlik ) =
106 106 ✓
= 0, 20932... P ( Enjoy jogging ) P ( Male ) /
26
P ( Enjoy jogging and Male/Geniet draf en Manlik ) = P (Geniet draf) x P (Manlik)
106
= 0, 24528... ✓ answer / antwoord
P ( Enjoy jogging and Male/Geniet draf en Manlik )
✓
P ( Enjoy jogging/Geniet draf ) P ( Male/Manlik ) P ( Enjoy jogging and Male ) /
Events are not independent. / Gebeurtenisse is nie P (Geniet draf en Manlik)
onafhanklik nie.
✓ conclusion / slotsom
(4)
Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief
(EC/NOVEMBER 2025) MATHEMATICS P1/WISKUNDE V1 21
9.3.1
Sunny / Sonnig -S
Not Sunny / Nie Sonnig nie - S
Use Sunscreen / Gebruik Sonskerm - U
Not using Sunscreen / Gebruik nie
sonskerm nie - U
✓ First branches i.e. S and S /
S Eerste takke dws S en S
✓ Second branches i.e. U and U /
Tweede takke dws U en U
✓ outcomes / uitkomste
U
(3)
9.3.2 0, 7 x + 0, 06 x = 0, 62 ✓ 0, 7 x + 0, 06 x
0, 76 x = 0, 62 ✓ = 0, 62
x = 0,82 ✓ answer / antwoord
(3)
[18]
TOTAL / TOTAAL: 150
Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief
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