# Mathematics Grade 12 Paper 1 NSC June 2013 Question Paper

> Grade 12 Mathematics Paper 1 question paper from the NSC June 2013, 9 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/mathematics-p1-sg-2013-qp/2944743e-c7cd-41de-94ff-939546aa5ed0
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2013
- Exam period: NSC June
- Paper: 1
- Curriculum: CAPS
- Pages: 9

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## About this document

Mathematics · Grade 12 · NSC June · 2013. Question paper, 9 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

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basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

SENIOR CERTIFICATE EXAMINATION

MATHEMATICS P1
STANDARD GRADE

2013

MARKS: 150

TIME: 3 hours

MATHEMATICS SG: Paper 1
3012E

30121E

This question paper consists of 8 pages and 1 formula sheet.

X@5

IMM

Copyright reserved

GAUTENG Please turn over

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Mathematics/SG/P 1 2 DBE/2013

SCE

INSTRUCTIONS AND INFORMATION

Read the instructions below carefully before answering the questions.

1.

2

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

Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in
determining the answers.

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

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

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

Diagrams are not necessarily drawn to scale.
A formula sheet is included at the end of the question paper.

Write neatly and legibly.

Copia A Pe oe

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Mathematics/SG/P 1 é} DBE/2013
SCE

QUESTION 1
1.1 Solve for x:

11d 3x? =5x-2 (3)

1.1.2 x? +5x-—4=0 (Correct to ONE decimal place) (4)

13 vx+17 =x-3 (5)
1.2 Solve for x and y if they satisfy the following equations simultaneously:

2y+x=3 and

2x? +xy-y? =0 (8)

[20]
QUESTION 2
; oe 2

7 Determine the roots of the equation x" = 16° (1)
2.2 Determine the nature of the roots of 6x” —7x—3=0 without solving the equation. (4)
2.3 Find the values of k for which the equation x” + (2k +4)x+9k =0 has equal roots. (5)
2.4 When x? +mx?—5x+4 is divided by x+2, the remainder is 8. Determine the

value of m. (4)
25 Factorise x° — 6x? +11x—6. (6)

[20]

Copied 0 0 Pes en oe
GAUTENG

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Mathematics/SG/P1 4 DBE/2013
SCE
QUESTION 3
3.1 y
-

px

The sketch above, not drawn to scale, shows the graphs of a parabola
f(x) =2(x-1) ~18 and a circle g(x)=+4vr? —x’ . The graph of f has a tuming
point at D, intersects the y-axis at C and cuts the x-axis at A and B. The graph of
g passes through B.

Determine:

3.1.1 The coordinates of A, B, C and D

3.1.2 The coordinates of E if CE// AB

3.1.3 The range of f

3.1.4 The equation of the circle g

Copyright reserved CAANY ANA UGA deaaidaaiidea
GAUTENG

(8)
(4)
(2)
(2)

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Mathematics/SG/P1 5 DBE/2013
SCE

3.2

v

The straight line g cuts the hyperbola f for x>0 at D (2; 6), the y-axis at C and
the x-axis at B (1 ; 0). The line y=x cuts the graphs of f and g at E and A

respectively.
3.2.1 Find the equations of f and g. (5)
3.2.2 Determine the coordinates of C, A and E. (5)
[26]
QUESTION 4
2x-1 @3x+2
4.1 Show that Tye = 2
. , (6)
4.2 Simplify the following without using a calculator:
427-13
4.2.1 (2)
V3
log16+log4
4.2.2 log16—log4 3)

Corer Ag Penne
GAUTENG

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Mathematics/SG/P 1 6 DBE/2013
SCE
43 Solve for x, without using a calculator:
4.3.1 2.3% =45-3""1 (4)
4.3.2 get aset (3)
43.3 log, (2x-—3)—log, 5=2 (3)

44 Solve for x:

5 =10 GB)
[24]
QUESTION 5
5.1 The first term of a sequence is 2. The fifth term is 162. Determine the numerical value

of the third term in each of the following cases:

a If the sequence is arithmetic (4)

ee If the sequence is geometric (4)
5.2 The geometric series 16+8+4+... has 12 terms. Calculate the sum of the series

correct to TWO decimal places. (4)
53 Determine 1 if > (6k -1)=320 (6)

k=l

5.4 John's starting salary is R150 000,00 p.a. His annual increase is R7 500,00. After how

many years will he reach his maximum salary of R262 500,00 p.a.? (4)
5.5 The value of a car costing R169 999,00 depreciates at 12% per year, compounded
annually. What is the value of the car after 5 years? (4)
[26]

Cop res A gq Pe tow

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Mathematics/SG/P1 Ze DBE/2013
SCE

QUESTION 6
6.1 The height s (in metres) attained by a shell fired vertically upwards t seconds after

release, is given by s(t)=100t—5St?. What is the average speed of the shell between

the second and the fourth seconds? (3)
6.2 Determine f’(x) from first principles if f(x) ara (5)
6.3 Differentiate the following with respect to x:

vx
6.3.1 a(x) =~ — 2x

(3)
xe+x?-1
[15]
QUESTION 7
71 The diagram below shows the graph of f(x) =—x° + ax” + bx.
A and B (3 ; 0) are the turning points of f. T is the point of contact of a tangent to
the graph of f.
Fé
BG ; 0)
« 7 oO >x
‘y
v
gil Show that a=6 and b=-9. (3)
712 Determine the coordinates of A. (4)
7.13 T has an x-coordinate of 2. Find:
(a) The y-coordinate of T (2)
(b) The equation of the tangent to the graph at T (5)

Copyright reserved FART AOO GA Please um over
GAUTENG

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Mathematics/SG/P 1 8 DBE/2013
SCE
7.2 The sketch below, not drawn to scale, shows the graphs of a parabola
f(x) =-x? +2x+3 anda straight line g(x)=—2x+8. P isapointon g and Q is
a point on f
y
nf
P
Q
&
< 0 \ mx
7
Y
Determine the shortest vertical distance PQ between the graphs of f and g. (5)

[19]

TOTAL: 150

Copsright reserved FIC AQAN TOCA UAT A

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Mathematics/SG/P 1 DBE/2013
SCE

Mathematics Formula Sheet (HG and SG)
Wiskunde Formuleblad (HG en SG)

ae —b+Vb? —4ac

2a
T,=a+(n-1)d Sy= 5 (a+ Ty) or/of Sy =F(a+4)

ce =5 [2a + (n -1)d]

n a
T,=ar"-! Sy = ah-"") Guns, -te N40

1-r
a

Sop = ("\<7)

1-r

n n
A= P| 1+—— or/of A = P| 1-——
100 100

PG = lim LEAM= FO)
h>0

>! h

d= (x2 - 41) +02-n)P

y=mxte

Y-Yy = M(x - 2)

m=22771
x2 — xy
m = tanO
Xy +X. i+ V2
CPA
(x3393) ( 2 ’ 2 }
veya?

(x-pY +(y-gP =r?

In AABC: ab _€
snA sinB sinC

a® =b* +c? -2bc.cosA

area AABC = Jab.sin Cc

ae CUI AUTO
GAUTENG

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