# Mathematics Grade 12 P2 NSC June 2012 Question Paper (Eng)

> Grade 12 Mathematics Paper 2 question paper from the NSC June 2012 (English), 25 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/mathematics-p2-hg-english-june-2012-qp/76d355e7-67c8-4d53-8001-c12bc0485452
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Language: English
- Document type: Question paper
- Year: 2012
- Exam period: NSC June
- Paper: 2
- Curriculum: CAPS
- Pages: 25

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## About this document

Mathematics · Grade 12 · NSC June · 2012 · English. Question paper, 25 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.

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basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

SENIOR CERTIFICATE EXAMINATION

MATHEMATICS P2

HIGHER GRADE

2012

MARKS: 200

MATHEMATICS HG: Paper 2 TIME: 3 hours

3011E
30112E
This question paper consists of 13 pages, 1 formula sheet and a diagram sheet |
consisting of 4 pages.
X05 |
capri reson NA 00 0 ae

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Mathematics/HG/P2 2 DBE/2012

SCE

INSTRUCTIONS AND INFORMATION

L

2.

10.

This question paper consists of TEN questions.
Use the formula sheet to answer this question paper.

Detach the diagram sheets from the question paper and place them inside your
ANSWER BOOK.

The diagrams are NOT drawn to scale.
Answer ALL the questions.

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

Show ALL the necessary calculations.
You may use non-programmable calculators, unless stated otherwise.

The number of decimal digits to which answers must be rounded off will be stated in the
question, where necessary.

Write neatly and legibly.

a FAIA ON IAEA A diab

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Mathematics/HG/P2 3 DBE/2012
SCE

ANALYTICAL GEOMETRY

NOTE: - USE ANALYTICAL METHODS IN THIS SECTION.
= CONSTRUCTION AND MEASUREMENT METHODS MAY NOT
BE USED

QUESTION 1

In the diagram alongside, Ay
AG; 9) and D(5 ; 1) are points in a AG; 9)
Cartesian plane. B and C are points on
the y-axis such that

ABD=ACD = 90°

DS; 1)

Ve

11 Show that (0 ; 6) are the coordinates of B. (6)
1.2 Hence, or otherwise, find the coordinates of C. (2)
1.3 Calculate the coordinates of M, the midpoint of AD. (2)

1.4 Calculate the length of the radius of circle ABD.
Leave your answer in simplified surd form. (3)

15 Will circle ABD pass through point C? Give a reason for your answer. (2)

1.6 Calculate the size of BDA , rounded off to the nearest degree. (7)
1.7 Find the equation of the straight line which is parallel to BD and which passes

through point A. (4)
[26]

aia FIO TAO A Please turn over
GAUTENG

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Mathematics/HG/P2 4 DBE/2012
SCE

QUESTION 2

2.1.‘ In the diagram alongside,
diameter AB of circle ACB
in a Cartesian plane is given. ACI; 8)

The coordinates of A and B

are (— 1; 8) and (5; 0)

respectively.

C isa point on the x-axis.

v

c B(5 ; 0)

2.1.1 Determine:
(a) The equation of circle ACB (5)
(b) The coordinates of C (3)
(c) The equation of the tangent to the circle at C (5)
2.1.2 Another circle with equation x? —4x+ y? —-8y—29=0 is given.
(a) Determine whether the two circles are concentric. (4)

(b) Determine, with reasons, whether this circle lies inside or outside

circle ACB (2)
2.2 Determine the equation of the locus of P(x ; y) which is equidistant from point
A(1 ; 3) and the line x = —2 (6)
[25]

Coil re 1 Pes moe
GAUTENG

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Mathematics/HG/P2 5 DBE/2012
SCE

TRIGONOMETRY
QUESTION 3
YOU MAY NOT USE A CALCULATOR IN THIS QUESTION.
SHOW ALL CALCULATIONS.
3.1 In the diagram alongside, P is a point in the :

first quadrant of a Cartesian plane such that y

13cos6 —-5=0

R(k ; 10) is a point in the second quadrant Pp

such that POR =90° R(k; 10)

8 x
>
oO

Determine the numerical value of:

3.1.1 tan 0 (3)

3.1.2 k (4)
32 Simplify the following expression:

cos (90°—x) . cosec(90° + x) . cos(—22°)
tan(360°—x) . sin 34°. cos 34°. sec(540°— x) (9)

3.3 If sin 24°= m, find the following in terms of m:

3.3.1 cos 114° (2)

3.3.2 cos (—156°) (2)

[20]

Cori rsa AN Pose tmove
GAUTENG

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Mathematics/HG/P2 6 DBE/2012

SCE

QUESTION 4
Given: f(x) = tanx and g(x) = sin2x for x © [-90° ; 180°]
4.1 Determine the solution of the equation

tanx = sin2x for x © [-90° ; 180°]

4.2 Use the set of axes provided on DIAGRAM SHEET 1 to draw sketch graphs of the
curves of f and g forx € [-90° ; 180°]. Clearly show all intercepts with the axes,
coordinates of all turning points and end points of both curves. Indicate the
asymptotes by using dotted lines.

4.3 Use the graphs drawn in QUESTION 4.2 and the solution obtained in
QUESTION 4.1 to determine the value(s) of x © [—90° ; 180°] for which:
43.1 f@)<g)
4.3.2 g (x) increases as x increases

43.3 f(x).g(x) = 1

QUESTION 5
5.1 Solve for x €(0°; 90°):
i+ tan? x = cosec(2x + 30°)
5.2 Given the identity: cos*A — sin’ A =cos 2A
5.2.1 Prove the identity.
5.2.2 Hence, or otherwise, find the general solution of the equation

3cos'A —3sin'A =1

Give your answer rounded off to ONE decimal digit.

Copied NN Pes oe
GAUTENG

(8)

(10)

(4)
(3)

(3)
[28]

(6)

Q)

i)
[16]

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Mathematics/HG/P2 Zz DBE/2012
SCE

QUESTION 6

6.1.1 Use the diagram on DIAGRAM
SHEET 2 or redraw the diagram in A
your ANSWER BOOK to prove
that in AABC:

B= a@ + c-2a\(c)cos B c

a (6)

6.1.2 In the diagram alongside,
ASRT is given. 8
SR = s units
RT = 2s units and
ST = runits

Show that ” = ./5—4cosR (4)
s

a FADIA AU A Please tan over
GAUTENG

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Mathematics/HG/P2 8 DBE/2012
SCE
6.2 In the diagram alongside, LM represents

a vertical mast. It is constructed so that
M isat the same level as the foundations L
of a thatched house. Points B and C are
on the perimeter of the property.

B, C and M lie in the same horizontal
plane.

BM = MC

LM = A units

MBC=30°
a is the angle of elevation from C to L.

6.2.1 Express MC in terms of hand a. (2)
6.2.2 Show that distance BC = 3 h .cota@ (4)
_ If it is further given that 4 =25 metres and a = 43°, calculate rounded off
to ONE decimal digit:
(a) The distance BC (2)
(b) The areaof ABCM (5)
[23]

Coigh roeme NH Pes am oe
GAUTENG

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Mathematics/HG/P2 9 DBE/2012
SCE

EUCLIDEAN GEOMETRY

NOTE: — DIAGRAMS FOR PROVING THEORY MAY BE USED ON THE

DIAGRAM SHEETS OR REDRAWN IN YOUR ANSWER BOOK.

— DETACH THE DIAGRAM SHEETS FROM THE QUESTION PAPER
AND PLACE THEM IN YOUR ANSWER BOOK.

— GIVE A REASON FOR EACH STATEMENT, UNLESS OTHERWISE
STATED.

QUESTION 7

In the diagram below, two concentric circles with centre at M and with radii 5 cm and

8,5 cm are given. PQRS isa chord of the larger circle cutting the smaller circle at Q and R.
MYS isa straight line with Y on the smaller circle.

QR=6cm

Calculate, with reasons, the length of PS. (7]

Co rceme A A Pe oe
GAUTENG

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Mathematics/HG/P2 10 DBE/2012
SCE

QUESTION 8

8.1 In the diagram alongside, O is the centre
of circle EBD.

Use the diagram on DIAGRAM SHEET 2

or redraw the diagram in your ANSWER

BOOK to prove the theorem which states

that: D

If BC is a tangent to the circle, then
DBC=E

(7)

STA) AUN QUO AD AU Please arn over

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Mathematics/HG/P2 Ti DBE/2012
SCE
8.2 In the diagram below, PA and PBS are tangents to circle BCA with centre M.

AC is produced to R.

AB and PR are produced to Q.
BC=AC and PQ || CB.

PC is drawn.

Let Ai=x

Prove that:

8.2.1 Po =Ps (6)
8.2.2 ABRP is a cyclic quadrilateral (4)
8.2.3 PRQ is a tangent to circle BCR at R (4)

[21]

Copyrigt reserved HUNAN. AE Please urn over
GAUTENG

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Mathematics/HG/P2 12 DBE/2012
SCE

QUESTION 9

9.1 In the diagram alongside, A ABC is A

given. M and N are points on
AB and AC such that MN || BC.

Use the diagram on

DIAGRAM SHEET 4 or redraw the
diagram in your ANSWER BOOK to
prove the theorem which states that:

M > N
If MN || BC then AM _ AN
AB NC
B > Cc
7)
9.2 In the diagram alongside, ABCD is a parallelogram
with diagonals AC and BD intersecting at F. S
P isapointon AD.
CP and BA are produced to S.
FK || BC with K on CP.
BA _2
BS 5
A P D
B id c
9.2.1 Show that K is the midpoint of PC. (4)
9.2.2 Determine, with reasons, the value of the ratio KC: SP. (4)
9.2.3 If BC = 15 cm, calculate the length of AP. (4)
[19]

Cog cen A Pe oe
GAUTENG

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Mathematics/HG/P2 iE DBE/2012
SCE

QUESTION 10

In the diagram below, AOB is the diameter of semi-circle ADB with O the centre.
ADC is a straight line.

CB isa tangent at B.

OK 1 DB with K on DB.

OK produced cuts CB at S.

10.1 Prove that:

10.1.1 OS |] AC 3)
10.1.2 A ABC ||| AADB ||| A BDC 6)
10.1.3 AB? = AD.DC (2)
10.2 Calculate the numerical value of Area of A ABC 5
Area of AOSB 118

TOTAL: 200

Comrise NAN

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Mathematics/HG/P2 DBE/2012
SCE

Mathematics Formula Sheet (HG and SG)

_ ~b+vb? —4ac

2a

n n n
T,=a+(n-1)d 8,-7@+,) S.-7@+9 S, = 5 Bat (a —1)d]
T, =ar"-! S, = a(1-r") (r #1) s, <8 =D xy
1-r r-1

S, = a (\r| <1)
A=P(1+i5) OR A=p(1-i5]

100 100

f"(x)=lim f(x+h)-f@)
h>0 h

d=, -x,) +(y, -y,)

y=mx+e

y-y, =m(x-x,)

m=227%1
x, —Xy
m = tanO
xX,+x +
ty =r

(x-p)’ + (y-q)* =r?

- £F
snA sinB_ sinC

In A ABC:

a’ =b’ +c? —2be.cosA

area A ABC = tab.sinC

Cori reed 0 A A

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basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

SENIOR CERTIFICATE EXAMINATION/SENIORSERTIFIKAAT-EKSAMEN
MATHEMATICS HG/WISKUNDE HG
PAPER 2/VRAESTEL 2
2012

DIAGRAM SHEET/DIAGRAMVEL

INSTRUCTION

This DIAGRAM SHEET must be handed in with your ANSWER BOOK. Ensure that your details
are complete.

INSTRUKSIE

Hierdie DIAGRAMVEL moet saam met jou ANTWOORDEBOEK ingelewer word. Maak seker
dat jou besonderhede volledig ingevul is.

EXAMINATION NUMBER
EKSAMENNOMMER

CENTRE NUMBER
SENTRUMNOMMER

Copyright reserved/Kopiereg voorbehou LIMA WU HALAL Please turn over/Blaai om asseblief

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Mathematics/HG/P2/Wiskunde/HG/V2

2,

DBE/2012

SCE — Diagram sheet/Diagramvel

DIAGRAM SHEET 1/DIAGRAMVEL 1

QUESTION 1/VRAAG 1

QUESTION 2.1/VRAAG 2.1

ty y
poe A(-1 ; 8)
Cc
[e} xy
CN B(S ; 0)
D6; 1)
a
oO
QUESTION 4.2/VRAAG 4.2
~~
y
34
24
1+
—
-90 45 45 90 135 180
-l-
24+
3-4
Copyright reserved/Kopiereg voorbehou | HTT WII nT | lll Ill Please turn over/Blaai om asseblief
GAUTENG

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Mathematics/HG/P2/Wiskunde/HG/V2 3

DBE/2012

SCE — Diagram sheet/Diagramvel

DIAGRAM SHEET 2/DIAGRAMVEL 2
QUESTION 6.1.1/VRAAG 6.1.1

A

QUESTION 6.2/VRAAG 6.2
L

50°)

B 3 Cc
B
QUESTION 6.1.2/VRAAG 6.1.2
S
r
Ss
T
R 2s
QUESTION 7/VRAAG 7
M
y
P Q T R .

Copyright reserved/Kopieregvoorbehiou IIIT IIIT
GAUTENG

QUESTION 8.1/VRAAG 8.1

Please turn over/Blaai om asseblief

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Mathematics/HG/P2/Wiskunde/HG/V2 4 DBE/2012
SCE — Diagram sheet/Diagramvel

DIAGRAM SHEET 3/DIAGRAMVEL 3

QUESTION 8.2/VRAAG 8.2

Copyright reserved/Kopiereg voorbehou (Wi TUMHAUAULUL AH Il lll ll Hil Please turn over/Blaai om asseblief

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Mathematics/HG/P2/Wiskunde/HG/V2 3 DBE/2012
SCE — Diagram sheet/Diagramvel
DIAGRAM SHEET 4/DIAGRAMVEL 4

QUESTION 9.1/VRAAG 9.1 QUESTION 9.2/VRAAG 9.2
S

A

QUESTION 10/VRAAG 10

Cc
Déy
: s
K
2
14 1
A Oo B

Coprigu reek voicow {MN

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