# Mathematics Grade 12 P2 NSC June 2021 Question Paper (Eng)

> Grade 12 Mathematics Paper 2 question paper from the NSC June Exam 2021 (English), 15 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/mathematics-p2-may-june-2021-eng/1c10b088-6189-4086-b599-13b67b34c17e
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2021
- Exam period: NSC June Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 15

Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 12](https://www.hlayiso.com/library/grade-12) › [Mathematics](https://www.hlayiso.com/library/grade-12/mathematics) › [Mathematics Grade 12 P2 NSC June 2021 Question Paper (Eng)](https://www.hlayiso.com/library/mathematics-p2-may-june-2021-eng/1c10b088-6189-4086-b599-13b67b34c17e)

## About this document

Mathematics · Grade 12 · NSC June Exam · 2021. Question paper, 15 pages. Read online or download the PDF.

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

## Document text

Text extracted from the PDF. Layout, diagrams and tables may not survive extraction.

### Page 1

basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

SENIOR CERTIFICATE EXAMINATIONS/
NATIONAL SENIOR CERTIFICATE EXAMINATIONS

MATHEMATICS P2

2021

MARKS: 150

TIME: 3 hours

This question paper consists of 14 pages pages, 1 information sheet
and an answer book of 24 pages.

Copyright reserved Please turn over

### Page 2

Downloaded from hlayiso.com

Mathematics/P2 2 DBE/2021

SC/NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

This question paper consists of 10 questions.
Answer ALL the questions in the SPECIAL ANSWER BOOK provided.

Clearly show ALL calculations, diagrams, graphs, etc. that 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.
An information sheet with formulae is included at the end of the question paper.

Write neatly and legibly.

Copyright reserved Please turn over

### Page 3

Downloaded from hlayiso.com

Mathematics/P2 DBE/2021
SC/NSC

QUESTION 1

Ll Sam recorded the amount of data (in MB) that she had used on each of the first

15 days in April. The information is shown in the table below.

26/133 | 18 | 12 | 34 24 | 58 | 16 10 | 15 | 69 | 20 | 17 | 40

1.1.1 Calculate the:
(a) Mean for the data set (2)
(b) Standard deviation for the data set qd)

1.1.2 Determine the number of days on which the amount of data used was greater
than one standard deviation above the mean. (2)

1.1.3. Calculate the maximum total amount of data that Sam must use for
the remainder of the month if she wishes for the overall mean of April to be

80% of the mean for the first 15 days. (3)
1.2 The wind speed (in km per hour) and temperature (in °C) for a certain town were
recorded at 16:00 for a period of 10 days. The information is shown in the table
below.
WIND SPEED
IN km/h (x) 2 6 15 | 20 | 25 17 11 24 13. | 22
TEMPERATURE
IN °C () 28 | 26 | 22 | 22 16 | 20 | 24 19 | 26 19
1.2.1 Determine the equation of the least squares regression line for the data. (3)

1.2.2 Predict the temperature at 16:00 if, on a certain day, the wind speed of this

town was 9 km per hour. (2)
1.2.3. Interpret the value of 4 in the context of the data. qd)
[14]

Copyright reserved Please turn over

### Page 4

Mathematics/P2

QUESTION 2

Downloaded from hlayiso.com

DBE/2021

The number of days that Grade 8 learners were absent at a certain high school during a year was
recorded. This information is represented in the table below.

2.1

2.2

2.3

2.4

2.5

NUMBER OF DAYS ABSENT NUMBER OF LEARNERS
0<x <5 34
po 5<x<10 45
10< x <15 | 98
: 15< x <20 43
20< x <25 7
25< x <30 3

Write down the modal class for the data.

How many learners were absent from school for less than 15 days?

How many Grade 8 learners are at the school?

Draw a cumulative frequency graph (ogive) to represent the data above on the grid

provided in the ANSWER BOOK.

Use the cumulative frequency graph to determine the median number of days the

Grade 8 learners were absent.

Copyright reserved

Please turn over

(1)
(1)
(1)

(4)

(2)
19]

### Page 5

Downloaded from hlayiso.com

SC/NSC

Mathematics/P2 DBE/202]

QUESTION 3

In the diagram, S(O ; -16), L and Q(4 ; -8) are the vertices of ASLQ having LQ
perpendicular to SQ. SL and SQ are produced to points R and M respectively such that
RM || LQ. SM produced cuts the x-axis at N(8 ; 0). QM=MN. T and P are the
y-intercepts of RM and LQ respectively.

yy
R
0 [ ,
N(8 ; 0) x
LD T
M
P
QG ;-8)
S(O ; -16)
3.1 Calculate the coordinates of M. (2)
3.2 Calculate the gradient of NS. (2)
3.3 Show that the equation of line LQ is y= -3x —6. (3)
3.4 Determine the equation of a circle having centre at O, the origin, and also passing
through S. (2)
3.5 Calculate the coordinates of T. (3)
. LS
3.6 Determine —. 3
er ins RS (3)
3.7 Calculate the area of PTMQ. (4)

{19]

Copyright reserved Please turn over

### Page 6

Downloaded from hlayiso.com

SC/NSC

Mathematics/P2 DBE/2021

QUESTION 4

In the diagram, P(-3 ; 4) is the centre of the circle. V(k; 1) and Wé are the endpoints
of a diameter. The circle intersects the y-axis at B and C. BCVW isa cyclic quadrilateral.

CV is produced to intersect the x-axis at T. ofC=a.

x

41 The radius of the circle is J10. Calculate the value of & if point V is to the right

of point P. Clearly show ALL calculations. (5)
42 The equation of the circle is given as x*+6x+y?—8y+15=0. Calculate the

length of BC. (4)
43 If k=—2, calculate the size of:

43.1 a (3)

43.2 VWB (2)
44 A new circle is obtained when the given circle is reflected about the line y= 1.

Determine the:

4.4.1 Coordinates of Q, the centre of the new circle (2)

4.4.2. Equation of the new circle in the form (x-a)’ +(y—b)? =r? (2)

4.4.3 Equations of the lines drawn parallel to the y-axis and passing through the

points of intersection of the two circles (2)
[20]

Copyright reserved Please turn over

### Page 7

Downloaded from hlayiso.com

Mathematies/P2 DBE/2021
SC/NSC
QUESTION 5
5.1 Simplify the expression to a single trigonometric term:
tan(— x).cos x.sin(x —180°)-1 (5)
5.2 Given: cos 35° =m

Without using a calculator, determine the value of EACH of the following in

terms of m:

5.2.1 cos 215° (2)

5.2.2 sin 20° (3)
5.3 Determine the general solution of:

cos 4x.cosx + sin x.sin4x = —0,7 (4)
3.4 Prove the identity: sin 4x.cos 2x —2.cos4x.sin x.cosx* _ cos’ x—sin? x (4)

tan 2x
[18]

Copyright reserved Please turn over

### Page 8

Downloaded from hlayiso.com

SC/NSC

Mathematics/P2 DBE/202]

QUESTION 6

In the diagram below, the graphs of f(x)=cos2x and g(x)=~—sinx are drawn for the
interval x €[-180° ; 180°] A and B are two points of intersection of f and g.

¥
f
A
—180° ae 180° *
&

6.1 Without using a calculator, determine the values of x for which cos2x =-sinx

in the interval x €[-180° ; 180°]. (6)
6.2 Use the graphs above to answer the following questions:

6.2.1 How many degrees apart are points A and B from each other? (2)

6.2.2 For which values of x in the given interval will f’(x).g/(x) > 0? (2)

6.2.3. Determine the values of & for which cos2x+3=4 will have no solution. (3)

[13]

Copyright reserved Please turn over

### Page 9

Downloaded from hlayiso.com

Mathematics/P2 9 DBE/2021
SC/NSC

QUESTION 7

Points B, C and E lie in the same horizontal plane. ABCD is a rectangular piece of board.
CDE is a triangular piece of board having a right angle at C. Each piece of board is placed
perpendicular to the horizontal plane and joined along DC, as shown in the diagram. The

angle of elevation from E to D is x. BEC =2x and EBC =30°.

A D
B [|
30° e
x
2x,
E
Al Show that DC = BC (6)
4cos” x
72 If x= 30°, show that the area of ABCD = 3AB?. (3)

19]

Copyright reserved Please turn over

### Page 10

Downloaded from hlayiso.com

Mathematics/P2 10 DBE/2021
SC/NSC

QUESTION 8

8.1 In the diagram, MP is a diameter of a circle centered at O. MP cuts the chord NR

at T. Radius NO and chords PR, MN and MR are drawn. R, = 69°.

Determine, giving reasons, the size of:

8.11 R, (2)
8.1.2 6, (2)
813 M, (2)
8.1.4 ML, ifitis further given that NO || PR (4)

Copyright reserved Please turn over

### Page 11

Downloaded from hlayiso.com

Mathematics/P2 DBE/2021
SC/NSC
8.2 In the diagram below, ABCD isa cyclic quadrilateral. AB and DC are produced
to meet at E. AD and BC are produced to meet at F. AFB=2x, DAB=3x
and AED =x.
Determine, giving reasons, the value of x. (6)

[16]

Copyright reserved Please turn over

### Page 12

Downloaded from hlayiso.com

Mathematics/P2 DBE/2021
SC/NSC
QUESTION 9
9.1 In the diagram, ABC isa triangle. D and E are points on sides AB and AC
respectively such that DE || BC.
A

Cc

Use the diagram above to prove the theorem which states that a line drawn parallel

to one side of a triangle divides the other two sides proportionally, i.e. prove that

AD _ AE

DB EC’ (6)

Copyright reserved Please turn over

### Page 13

Downloaded from hlayiso.com

Mathematics/P2 13 DBE/2021
SC/NSC
9.2 In the diagram, M is the centre of the circle. A, B and C are points on the circle

such that AC= BC. PA isa tangent to the circle at A. PQ is drawn parallel to CA
to meet BA produced at Q. BC produced meets PQ at R and AR is drawn.

Let Q=x.
Qs
9.2.1 Determine, giving reasons, FOUR other angles EACH equal to x. (6)
9.2.2 Prove that ABPR is a cyclic quadrilateral. (2)
92.3 Prove that BA_ BE .
BQ QR (3)

[17]

Copyright reserved Please turn over

### Page 14

Downloaded from hlayiso.com

Mathematics/P2 14
SC/NSC

QUESTION 10

DBE/2021

In the diagram, TSR is a diameter of the larger circle having centre S$. Chord TQ of the
larger circle cuts the smaller circle at M. PQ is a common tangent to the two circles at Q.

SQ is drawn.
RP 1 PQ and MS || QR.

T
Ns
1 2\3
M 2
1
2
1
2 2 c
Q P
10.1 Prove, giving reasons that:

10.1.1 SQ is the diameter of the smaller circle

2
10.12 rT=RQ
RP

10.2 If MS = 14 units and PQ= +640 units, calculate, giving reasons, the length of the

radius of the larger circle.

Copyright reserved

TOTAL:

(G3)

(6)

(6)
[15]

150

### Page 15

Downloaded from hlayiso.com

Mathematics/P2 DBE/2021
SC/NSC
INFORMATION SHEET
_ -b +b? —4ac
2a
A = P(1+ni) A = P(1=ni) A=P(-3)" A=P(1+i)"
T, =a+(n-ld S, =F Ra+@-pa]
T, =ar"" Ss OO) a1 S,=—4-;-1er<l
a r—l l-r
paxl+" 1 p=2i- d+"
i i
lp) = fin LOE AD= FX)
f°(%) = lim h
oe +x, Wty.
d= \(x,-x,) +(,-9,F om 5 a 2 |
y=mxte Yr y, =m(x—-x,) m= 22% m=tan@
XX
(x-a)’ +(y-bY =r?
In AABC: ab _¢
sn A sinB sinc
a’ =b? +0 —2be.cos A
area AABC = jab.sin
sin(a + #) = sin a cos 8 + cosa sin B sin( & — 8) = sin a cos B — cos asin B
cos(a@ + #) = cos acos § -sinasin B cos(@ — 8) = cos acos # +sin asin
cos’ a —sin’ a
cos2a=| 1-2sin’a sin 20 = 2sinacosa
2cos? a -1
_ Dx DG, - x)
x= 2 _ it
n C=
n
n(A)
P(A) AS) P(A or B) = P(A)+ P(B)— P(A and B)
n
DG -x\y-y)
—_ pa een
p=atbx > @-3

Copyright reserved

## Related documents

- [Mathematics P2 Nov 2020 ANSBK Afr Eng (2) final](https://www.hlayiso.com/library/mathematics-p2-nov-2020-ansbk-afr-eng-2-final/199754f9-9f9b-4bd9-8890-beebee25863f) — Mathematics · QP · 2021 · Eng
- [Mathematics P2 SEPT2021 ANSBK SESOTHO ENG DM](https://www.hlayiso.com/library/mathematics-p2-sept2021-ansbk-sesotho-eng-dm/ae538fae-90db-4237-9a93-c7eb83053862) — Mathematics · QP · 2021 · Sesotho
- [Mathematics P2 Sept2021 QP SESOTHO ONLY D](https://www.hlayiso.com/library/mathematics-p2-sept2021-qp-sesotho-only-d/4d50cd68-a960-4bf3-b891-1fcbcd8ce495) — Mathematics · QP · 2021 · Sesotho
- [Mathematics P2 May June 2018 Eng](https://www.hlayiso.com/library/mathematics-p2-may-june-2018-eng/4f3d38e9-a707-40ca-beee-fea324344ead) — Mathematics · QP · 2018 · Eng
- [Mathematics P2 May June 2016 Afr](https://www.hlayiso.com/library/mathematics-p2-may-june-2016-afr/20642c71-2f52-482d-8724-47218c4d339c) — Mathematics · QP · 2016 · Afr
- [Mathematics P2 June July 2015 Eng](https://www.hlayiso.com/library/mathematics-p2-june-july-2015-eng/f0dc57ae-b1ff-4f0d-8e51-76a1a169619f) — Mathematics · QP · 2015 · Eng

## More from Grade 12 Mathematics

- [MATHS P1 ANSWER BOOK GR12 SEPT 2025 English Afrikaans watermark](https://www.hlayiso.com/library/maths-p1-answer-book-gr12-sept-2025-english-afrikaans-watermark/d78c3fd3-dcd5-4f3f-911b-e5635b4686cc) — Addendum · 2025 · Afr
- [MATHS P2 MEMO GR12 SEPT 2025 E+A watermark](https://www.hlayiso.com/library/maths-p2-memo-gr12-sept-2025-e-a-watermark/838d50ea-fdac-4e70-8d62-e365a012252f) — Memo · 2025
- [Maths Grade 12 NSC P2 MEMO September 2025 Eng Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-memo-september-2025-eng-northern-cape/f00a552e-132c-4871-bf72-c887cfc67272) — Memo · 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
- [MATHS P2 MEMO GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-memo-gr12-june-2024-afr-english/4a5f997e-e38d-4abb-b726-8b72e6672832) — Memo · 2024 · Eng
- [MATHS P1 GR 12 MEMO SEPT 2024 English+Afrikaans](https://www.hlayiso.com/library/maths-p1-gr-12-memo-sept-2024-english-afrikaans/f0eedb8f-ec6f-4f46-9885-3933cd274781) — Memo · 2024 · Afr

## Collection

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

---

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.