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SENIOR CERTIFICATE EXAMINATIONS/
SENIORSERTIFIKAAT-EKSAMEN
NATIONAL SENIOR CERTIFICATE EXAMINATIONS/
NASIONALE SENIORSERTIFIKAAT-EKSAMEN
MATHEMATICS P2/
WISKUNDE V2
MARKING GUIDELINES/NASIENRIGLYNE
2021
MARKS: 150
PUNTE: 150
These marking guidelines consist of 23 pages
...
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Mathematics P2/Wiskunde V2
2
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
NOTE:
If a candidate answers a question TWICE, only mark the FIRST attempt
...
Consistent accuracy applies in ALL aspects of the marking memorandum
...
Assuming answers/values in order to solve a problem is NOT acceptable
...
As 'n kandidaat 'n antwoord van 'n vraag doodtrek en nie oordoen nie, sien die
doodgetrekte poging na
...
Hou op
nasien by die tweede berekeningsfout
...
GEOMETRY
A mark for a correct statement
(A statement mark is independent of a reason)
S
'n Punt vir 'n korrekte bewering
('n Punt vir 'n bewering is onafhanklik van die rede)
A mark for the correct reason
(A reason mark may only be awarded if the statement is correct)
R
'n Punt vir 'n korrekte rede
('n Punt word slegs vir die rede toegeken as die bewering korrek is)
Award a mark if statement AND reason are both correct
S/R
Ken 'n punt toe as die bewering EN rede beide korrek is
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Mathematics P2/Wiskunde V2
3
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
QUESTION/VRAAG 1
1
...
1
...
1
...
1
...
1
...
2
Wind speed
in km/h (x)
Temperature
in °C (y)
2
6
15
20
25
17
11
24
13
22
28
26
22
22
16
20
24
19
26
19
1
...
1
a 29,35
b 0,46
yˆ 29,35 0,46 x
a
b
equation
1
...
2
y = 25,20 °C (calculator)
answer
(3)
(2)
OR
yˆ 29,35 0,46(9)
y = 25,21 °C
1
...
3
b 0 , indicating that as the wind speed increases the
temperature decreases
...
1
Number of learners
34
45
98
43
7
3
Cumulative frequency
34
79
177
220
227
230
Modal class: 10 ≤ x < 15
answer
(1)
2
...
3
answer
230 learners
(1)
2
...
5
The median is at position 115
...
1
3
...
3
mLQ 2 1
mLQ
subst N and Q or N
and Q or Q and S into
gradient formula
answer
(2)
[LQ NS]
1
2
mLQ
1
8 (4) c OR
2
c 6
1
y 8 ( x 4)
2
1
y 8 x2
2
substitution of Q
calculation of c or
simplification
1
y x6
2
(3)
3
...
5
mRM mLQ
1
4 (6) c
2
1
2
[RM || LQ]
1
y 4 ( x 6)
2
1
y4 x3
2
OR
c 1
1
y x 1
2
T(0 ; 1)
3
...
7
area of PTMQ = area of TSM – area of PSQ
1
1
=
...
hM
...
hQ
2
2
1
1
= (15)(6) (10)(4)
2
2
= 45 – 20
= 25 square units
area of TSM –
area of PSQ
area TSM = 45
area PSQ = 20
answer
(4)
OR
TM 45 3 5 6,71
TM 3 5
MQ 20 2 5 4,47
MQ 2 5
PQ 20 2 5 4,47
PQ 2 5
area of trapezium PTMQ =
1
5 5 2 5
2
= 25 square units
=
1
3 52 5 2 5
2
area of trapezium =
1
2
(sum of ||sides)(height)
substitute into formula
answer
(4)
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Mathematics P2/Wiskunde V2
7
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
OR
MQ 20 2 5
PQ 20 2 5
TP 5
area of PTMQ area of ΔMTP area of ΔPQM
area of MTP +
area of PQM
area of PTMQ 10 15 25
1
5 6 1 2 5 2 5
2
2
area MTP = 10
area PQM = 15
area of PTMQ
answer
(4)
[19]
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Mathematics P2/Wiskunde V2
8
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
QUESTION 4
y
W
B
P(–3 ; 4)
C
V(k ; 1)
T
4
...
2
x 6 x y 8 y 15 0
2
2
y-intercepts: (0) 2 6(0) y 2 8 y 15 0
( y 3)( y 5) 0
y C 3 or y B 5
BC = 2 units
x=0
factors
both values
answer
(4)
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Mathematics P2/Wiskunde V2
9
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
4
...
1
DBE/2021
3 1
0 (2)
=1
tan 1
45
substitution into
gradient formula
mTC
tan 1
answer
(3)
OR
y mx 3
1 m(2) 3
mTC 1
substitution into
equation of a line
tan 1
45
tan 1
answer
(3)
4
...
2
ˆ V 135
BC
ˆ B 45
VW
[ext of /buite v ]
ˆ V 135
BC
[opp s of cyclic quad/teenoorst
...
4
...
4
...
4
...
1
tan x
...
sinx 180 1
tan x
...
sin(180 x) 1
sin x
...
( sin x) 1
cos x
sin 2 x 1
–tan x
–sin x
sin x
cos x
sin 2 x 1
cos 2 x
answer
(5)
5
...
1
cos 215°
= –cos 35°
= –m
reduction
answer
(2)
5
...
2
sin 20°
co-function
= cos 70°
= cos 235
double angle
expansion
= 2 cos 2 35 1
= 2m 2 1
answer in terms of m
(3)
OR
= sin (55° – 35°)
= sin55°cos35° – cos55°sin35°
compound angle
expansion
= m
...
1 m 2
= m2 1 m2
cos 55 1 m 2 or
sin 35 1 m2
answer in terms of m
(3)
= 2m 2 1
5
...
cos x sin 4 x
...
k
...
k
...
360
x 44,81 k
...
360
x 75,19 k
...
120°; k Z
(4)
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Mathematics P2/Wiskunde V2
11
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
5
...
cos 2 x 2 cos 4 x
...
cos x
tan 2 x
sin 4 x
...
sin 2 x
sin 2 x
cos 2 x
cos 2 x
sin(4 x 2 x)
sin 2 x
cos 2 x
LHS
sin 2 x
sin 2 x
cos 2 x
sin(4 x 2 x)
cos 2 x
cos x sin x
2
2
LHS = RHS
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(4)
[18]
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12
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
QUESTION/VRAAG 6
6
...
360
or x 330 k
...
360
sin x 1
1
2
–150° and –30°
90° (A)
(6)
x 150 or x 30 or x 90
OR
cos 2 x sin x
cos 2 x cos(90 x)
co-functions
2 x 180 (90 x) k
...
360
x 90 k
...
360
2 x 270 x k
...
120
x 150 or x 30 or x 90
OR
2x in quadrant 2
2x in quadrant 3
both general
solutions
–150° and –30°
90° (A)
(6)
cos 2 x sin x
cos 2 x cos(90 x)
2 x 90 x k
...
360
co-functions
or
or
2 x 360 (90 x) k
...
360
x 90 k
...
360
co-functions
or
x 30 k
...
360
x 270 k
...
2
y
f
A
B
180° x
0°
g
6
...
1
6
...
2
A(–150°; 0,5) B(–30°; 0,5)
AB = –30° – (–150°)
AB = 120°
Answer only: Full marks
AB = –30° – (–150°)
answer
x (0; 90) or x (90; 180)
x (0; 90) x (90; 180)
(2)
(2)
OR
0 x 90 90 x 180
0 x 90 or 90 x 180
(2)
6
...
3
cos 2x k 3
k 3 1 or k 3 1
k 2 or k 4
Answer only: Full marks
k 3 1 or k 3 1
k<2 k >4
(3)
OR
x
4
y = cos2x + 3
2
graph of y = cos2x + 3
O
k 2 or k 4
y
Answer only: Full marks
Copyright reserved/Kopiereg voorbehou
k<2 k >4
(3)
[13]
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Mathematics P2/Wiskunde V2
14
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
QUESTION/VRAAG 7
A
B
D
30°
C
x
2x
E
7
...
sin30
tan x
DC
sin 2 x
BC
sin x
DC
4 sin x cos x cos x
BC
DC
4 cos 2 x
correct use of sine rule
CE
BCsin30
sin 2 x
correct trig ratio
Subst CE
2 sin x cos x
sin x
cos x
(6)
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Mathematics P2/Wiskunde V2
15
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
7
...
sye
v reghoek]
BC 3AB
= (AB)(BC)
= (AB)(3AB)
=3AB2
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substitution into area
formula
(3)
[9]
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Mathematics P2/Wiskunde V2
16
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
QUESTION/VRAAG 8
8
...
1
...
1
...
1
...
= 2× omtreks ]
S R
(2)
[s in the same segment/e in dieselfde S R
sirkel segment]
OR
ˆ N 180 138
M
1
1
ˆ
M 21
1
(2)
[sum of s in ∆/e v ∆ ]
[s opp equal sides/e teenoor gelyke sye]
S R
(2)
8
...
4
ˆ 42
O
2
Pˆ 42
ˆ 48
M
2
OR
ˆ Rˆ 21
N
2
S
[alt s; NO || PR/Verw
...
e, NO || PR]
[sum of s in ∆/e v ∆]
[ s opposite equal sides/e teenoor gelyke sye] S
[sum of s of Δ NMR//e v ∆NMR]
S
(4)
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Mathematics P2/Wiskunde V2
17
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
DBE/2021
8
...
2
ˆ 4x
D
1
ˆ
D 2 180 4 x
ˆ 5x
B
[ext of /buite v ∆]
S/R
[s on a str line/e op ´n reguitlyn]
S
[ext of /buite v ]
S
ˆ D
ˆ
B
1
2
[ext of cyclic quad/buite v kvh]
S R
1
180 4 x 5x
9x 180
x 20
answer
(6)
OR
ˆ 3x
C
1
ˆ 4x
B
2
Cˆ 1 Cˆ 3 3x
ˆ 5x
D
2
4 x 5x 180
x 20
[ext of cyclic quad/buite v kvh]
[ext of /buite v ]
SR
S
[vert opp s]
S
[ext of /buite v ]
[opp of cyclic quad/teenoorst
...
1
A
h2
h1
D
E
B
C
9
...
2
M
B
A
Q
1
4
2
x
3
2
1
C
1 2
3
R
P
9
...
1
ˆ x
A
1
ˆB x
ˆ x
A
[corresp s; PQ || CA/ooreenkomstige e, PQ || CA]
SR
[s opp equal sides/e teenoor gelyke sye]
[tan-chord theorem/ tussen raaklyn en koord]
S/R
Pˆ x
[alt s; PQ || CA/verw
...
2
...
2
...
2
...
2
...
2
...
2
...
2
...
2
...
1
...
sirkel; midpt koord]
[converse: in semi circle/
Omgekeerde: in halwe sirkel]
S/R
[tan rad/raaklyn radius]
[converse: tan rad/Omgekeerde:
raaklyn radius ]
S R
R
(3)
TM MQ
ˆ 90
M
2
SQ is a diameter
R
(3)
OR
SQ QP
SQ is a diameter
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Mathematics P2/Wiskunde V2
23
SC/SS/NSC/NSS – Marking Guidelines/Nasienriglyne
10
...
2 In RTQ and ΔRQP
ˆ
Tˆ Q
3
ˆ Q
ˆ 90
Q
1
2
ˆ Q
ˆ Pˆ 90
Q
1
2
ˆ
ˆ
R R
1
2
DBE/2021
[tan-chord theorem/ tussen raaklyn
S R
en koord]
[co-interior s, MS || QR/ko-binne e, S
MS || QR]
or [ in semi circle/ in halwe sirkel ]
S
[s of /e van ]
S
RTQ ||| ΔRQP
RT RQ
RQ RP
ratio
(6)
RQ 2
RT
RP
OR
In RTQ and ΔRQP
ˆ
Tˆ Q
3
ˆ Q
ˆ 90
Q
1
2
[tan-chord theorem tussen raaklyn
en koord]
[co-interior s, MS || QR/ko-binne
e, MS || QR]
or [ in semi circle/ in halwe sirkel ]
ˆ Q
ˆ Pˆ 90
Q
1
2
RTQ ||| ΔRQP
10
...
stelling]
S R
[Pythagoras/Pythagoras]
S
RP = 12
RT
RT
answer
(6)
[15]
TOTAL/TOTAAL: 150
Copyright reserved