# Mathematics Grade 11 KwaZulu Natal June 2021 Paper & Memo

> Grade 11 Mathematics question paper and memo from the KwaZulu Natal June 2021, 11 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/maths-grade-11-june-2021-qp-and-memo/d96d4a1b-fa32-4893-a8e6-a3322a104d0e
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 11
- Document type: Question paper and memo
- Year: 2021
- Exam period: KwaZulu Natal June
- Curriculum: CAPS
- Pages: 11

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## About this document

Mathematics · Grade 11 · KwaZulu Natal June · 2021. Question paper and memorandum, 11 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Document text

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### Page 1

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\ KWAZULULNAT

EDUCATION
REPUBLIC OF SOUTH AFRICA

NATIONAL
SENIOR CERTIFICATE

MATHEMATICS

COMMON TEST

JUNE 2021

This question paper consists of 6 pages and 1 diagram sheet.

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Mathematics 2 Common Test June 2021

NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

10.

This question paper consists of 5 questions.
Answer ALL the questions.

Number the answers correctly according to the numbering system used in this
question paper.

Clearly show ALL calculations, diagrams, graphs, etc. which you have used in
determining your answers.

Answers only will NOT necessarily be awarded full marks.

You may use an approved scientific calculator (non-programmable and
non-graphical), unless stated otherwise.

If necessary, round off answers correct to TWO decimal places, unless stated
otherwise.

Diagrams are NOT necessarily drawn to scale.

A DIAGRAM SHEET for QUESTION 3.2 is attached at the end of this question
paper. Detach the DIAGRAM SHEET and hand it in together with your ANSWER
BOOK.

Write neatly and legibly.

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Mathematics 3 Common Test June 2021
NSC

QUESTION 1

The first three terms of a quadratic number pattern are 50; 35 and 24.

1. Write down the next two terms in this number pattern.

1.2 Determine the general term of this number pattern in the form 7), = an’ +bnt+c.
8) Calculate the value of the 30" first difference of this number pattern.
QUESTION 2

Given: f(x)=-2x? —4x+30

2.1 Determine the x-intercepts of f

2.2 Determine the equation of the axis of symmetry of f

2.3 Determine the range of f.

2.4 Graph g is obtained by reflecting graph fin the x-axis and then translating it 4 units to the

right. Determine the equation of graph g, in the form g(x) = a(x + py +q.

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(2)
(4)
(3)
19]

Q)
(2)
(2)

(3)

{10}

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Mathematics 4 Common Test June 2021
NSC

QUESTION 3

The diagram below shows the graph of hyperbola f passing through the point - 334) and having
asymptotes intersecting at (— 2;1).

(2:1)
3.1 Determine the equation of fin the form f(x) Ss q- (3)
x+pD

3.2 The graph fis drawn on the grid on the diagram sheet. On the same grid, sketch the graph of

g(x)= 2~*-—-4. Clearly label all the intercepts that g makes with the axes and show any

asymptotes of g. (5)
3.3 If itis given that f and g intersect at (-3;4) and (-1;- 2), determine the values of x for

which g(x)> f(x). (3)

[11

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Mathematics 5 Common Test June 2021
NSC

QUESTION 4

4.1 P(—4;3)and Q(2;k) are two points in the Cartesian plane such that the gradient of PQ is

positive and the distance PQ is2V10 units.

y]
Q2 sh)

P(-4 ; 3)

a1 Show that k =5. GB)

4.1.2 Determine the equation of PQ. (4)

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Mathematics 6 Common Test June 2021
NSC
4.2 In the diagram A(-1 ; 4) and C(4 ; -1) are points in a Cartesian plane. B is a point on the x-

axis such that BAC = 54,46".

A134) y

54,46°

>
B x
C(4 3-1)
y
4.2.1 Calculate the size of (0), angle of inclination of AC. (3)
4.2.2 Calculate the coordinates of B. (4)
[14]
QUESTION 5
Consider the following equation: 3sin? x +cos* x-5=7sinx.
5.1 Show that the equation 3sin? x + cos? x5 =7sinx can be written as
2sin? x—7sinx—4=0. a)
5.2 Hence, or otherwise, determine the general solution of 3sin* x +cos* x-5 =7sinx. (5)
[6
TOTAL: 50

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3
N
5
&
:
S 7:
oO >
VY
fo}
a
>=
S
cS
Eg .
= 2
(ra
nN
me) 4
Zz
s S
iS S
3
Se
2 &
D =
& a
E 2 3
= Ze

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AdO UVAL

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Mathematics 2 Common Test June 2021
GRADE 11
Marking Guideline
QUESTION 1
KWAZULU-NATAL PROVINCE
REPUBLIC OF SOUTHAFRICA 7 2 ] 7 iu
~~ i ~~ < N\ : 4
~ | A ~~ 4
NATIONAL 17 14 v17
SENIOR CERTIFICATE : a C
12 2a=4
a=2 v value ofa
3a+b=-15
3(2)4+b=-15
¥ value of b
at+b+c=50
- 2+(-21)+c=50 a
o : “ % c= 69
. MATHEMATICS: ‘a 7, =2n? -21n+ 69 vt,
a 2 1" (4)
.
i COMMON‘ TEST ” 13 First —— pattern:
i fo Pel Poet
: : heme
a n=
: JUNE 2021 : 7 416 v 7, =4n-19
‘ 4
A MARKING GUIDELINE : T, =4(30)-19 Y substitution
7 ane 7 =101 v answer
Pritt Q)
[9]
MARKS: 50
This marking guideline consists of 7 pages.
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Mathematics 3 Common Test June 2021
GRADE I1
Marking Guideline
QUESTION 2
Pl For x-intercepts, substitute 7 =0 :
y=~2x? —4x 430
2x? -4x+30=0 ¥ substitute y=0
x? +2x-15=0
(x +5x-3)=0 Y factors
x=—-5 or x=3 Y both answers
@)
22 ait
: 2a
one) Y substituti
2-2) substitution
=-1 v answer
(2)
OR OR
~ substitution
v answer
Q)

23 fE1)=-2(-1) -4(-1)+30
=32

Range: y<32 OR Y&(—00 32]

Y substitute y=—1

Y y<32 OR ye (-«:32]
Q)

24 S(x)=-2x +1)? +32
— f(z) = 2x41) -32
e(x)=2(x+1-4) -32
e(x)=2(x-3)? -32

S(x)=-2(e +1)? +32

Y for reflection in x-axis

¥ translation of 4 units right
Y g(x)=2(x-3)? -32

@)
OR OR
Tuming point of f (-1;32)
Turing point of g: (3 ;—32)
: Y for a=2
© 9x) 2x-3P -32
g(x)=2(e-3P va es)
Y for minimum value of
-32
(3)
[10] ]

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Mathematics 4 Common Test June 2021
GRADE II
Marking Guideline
QUESTION 3
3.1 a
ya 49
xtp
a
=—L41
are)
Substitute (-3;4)
4-41
-342
-3
V y= 41
if x42
(3)
32 For x-intercept, substitute y= 0:
0=2%-4
a*=4 Vv x=2
¥ shape
g
Indicating the:
Y x-intercept
v y-intercept
f Y asymptote
C2)
24 I
()
23) xS-3 or -2<xs-l ¥xs-3
vv -2<xs-l
(3)
OR OR
xe(-0;-3] U-2;-1] ¥ (-0:-3]
vv(-2,-1]
3)
(1)

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Mathematics 5 Common Test Sune 2021
GRADE 11
Marking Guideline
QUESTION 4
4] 2i0= Va = a) +O. F
2V10 = RT| 2-(-4)F +(k-3 Y substitution
40 =(k-3) +(2+4)* ¥ squaring both sides
40 =k? —6k +9436
ik? -6k4+5=0
(k-1fk~-5)=0 ¥ factorisation
kelork=5
412 &
: aaa
x-%
¥ substitution
. Y value of m
y—y =m(x-x,) yemxtc
Substitute (— 4:3) and m= ; :
1 i
ada’ (x-C4)) OR 3= re 4)+e | v substitution
14 13
-3ssx42 apt
y cae ce
i 3 ie v
Saxe ee answer
ir) aD 4)

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Mathematics Gg Common Test June 2021
GRADE i!
Marking Guideline
42.1
Y tig =-1
Reference angle: 45° v reference angle: 45°
Angle of inclination =180° — 45° = 135° v answer: 135°
GB
4.2.2 | Angle of inclination of AB =135° —54,46°
= 80,54" ¥ 80,54"
os mtgg = tan80,54°
=6 Y my =6
Y equating
“2
3
(4)
OR OR
Angle of inclination of AB = 135° —54,46°
= 80,54" ¥ 80,54"
J. Mg = tan80,54°
=6 Y yy =6
Equation of AB: y==6x+¢
Substitute (— 1,4):
¥ equation of AB
Substitute y = 0:
5
wean V xen :
Af 5 0)
U3 (4)
{14}
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Mathematics 7 Common Test June 2021
GRADE 11
Marking Guideline

QUESTION 5
SA 3sin? x + 00s? x—
3sin? x+1—sin? x-5=7sinx Y cos’ x=1-sin? x
2sin? x—7sinx—-4=0
a)
$2 2sin? x-7sinx-4=0
(2sin x +1Xsinx-4)=0 Y factors
: v = et inx=4
sinx=—5 or sinx=4 sinx=—> or sinx
Ref. 2: 30° no solution ¥ no solution
x= 180° +30° +4.360° (third quadrant)
= 210° +4360"
or
x= 360° —30° +%.360° (fourth quadrant) ¥ x=210° or x=330"
= 330° + 4.360" ¥ +k360° :keZ
keZ (3)
[6]
TOTAL: 50

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