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Graad 12 Wiskunde (WISK) November Vraestel 2 en Memo 2023 R50,00
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Exam (elaborations)

Graad 12 Wiskunde (WISK) November Vraestel 2 en Memo 2023
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Graad 12 Wiskunde November Vraestel 2 en Memo: Totaal:  150 punte. Hierdie Vraestel dek die volgende werk: Euklidiese Meetkunde. | Analitiese meetkunde. | Trigonometrie. | Statistiek. Hierdie is 'n oefenvraestel met memorandum bedoel om die leerling se kennis te toets, en sal nie dieself...

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  • November 24, 2023
  • 20
  • 2022/2023
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GRAAD 12 WISKUNDE
NOVEMBER EKSAMEN VRAESTEL 2

VRAAG 1
Die volgende frekwensietabel wys die aantal doele van die Protea netbal span in 50 wedstryde
in 2018.

Aantal doele Frekwensie Kumulatiewe frekwensie

5< x ≤10 6 b
10< x ≤15 a 14
15< x ≤20 13 27
20< x ≤25 9 c
25< x ≤30 7 43
30< x ≤35 d 48
35< x ≤ 40 e 50

1.1 Bepaal die waardes van a tot e. (5)
1.2 Bereken die gemiddelde aantal doele in 2018. (2)
[7]


VRAAG 2
Die tabel hieronder toon die polsslag per minuut vir 10 mans. Hulle polsslag is gemeet voor
hulle fiets gery het vir 10min (x) en na daarna ( y ).

1 2 3 4 5 6 7 8 9 10

Polsslag voor 65 50 125 80 85 112 53 118 85 130

Polsslag na 95 100 155 125 135 145 90 175 150 190



2.1 Stel die data voor op die spreidingsdiagram . (3)

2.2 Bereken die gemiddelde polsslag voor EN na oefening. (2)

2.3 Bepaal die formule vir die kleinste regressielyn tot 4 desimale plekke. (2)


1|Page www.summariessa.co.za Wiskunde
Graad 12 November Vraestel 2

,2.4 Bereken die korrelasiekoëffisient tot 4 desimale plekke EN lewer kommentaar op die
sterkte daarvan. (2)

2.5 Teken die kleinste kwadrate regressielyn op jou spreidingsdiagram (1)
[10]


VRAAG 3
Die tabel hieronder wys die afstande (in kilometers) wat deur ‘n verkoopsman afgelê vir 21
werksdae in ‘n sekere maand.




3.1 Bereken die gemiddelde afstand afgelê deur die verkoopsman. (2)

3.2 Skryf die vyf-getal opsomming van die data neer. (4)

3.3 Teken die snor-en-baard diagram vir die datastel. (2)

3.4 Bereken die standaardafwyking van afstand gereis. (2)
[10]



VRAAG 4
4.1 Die diagram toon P,A,Q,R en S lê op die omtrek van die sirkel met middelpunt O.
SB is ‘n raaklyn by S en RW=WP. AOWS en RWP is reguitlyne.




Bewys dat:
4.1.1 SB∥ RP (4)
4.1.2 SR2=WS . AS (5)
RW 2
4.1.3 AS= +WS (4)
WS
2|Page www.summariessa.co.za Wiskunde
Graad 12 November Vraestel 2

, 4.2 AB is die deursnee van die sirkel. D en C is punte op die omtrek van die sirkel met DE ⊥
AB. DE en AC kruis by T. Met ^ ^
D 1 =C 2




Bewys dat:
4.2.1 DA 2= AT . AC (5)
[18]



VRAAG 5
Die diagram toon ‘n sirkel met middelpunt M(1;2). TS is ‘n raaklyn aan die sirkel met T(-1;-2) ‘n
punt op die sirkel.




5.1 Bepaal die vergelyking van die sirkel emt middelpunt M in die vorm:
(x−a)2 +( y−b)2=r 2 (3)

5.2 Bepaal die vergelyking van TS. (5)
5.3 Die twee sirkels met middelpunte R en M ontmoet ekstern by punt T.TS is ‘n raaklyn
aan beide sirkels by punt T. As MT:TR = 1:4, bepaal die koördinate van punt R, indien
die sirkel met middelpunt R in die 3de kwadrant lê. (8)
3|Page www.summariessa.co.za Wiskunde
Graad 12 November Vraestel 2

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