IEB Assessment Matters National Senior Certificate Examination Mathematics 2013

NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II – INFORMATION SHEET Page i of ii

INFORMATION SHEET


–b ± b 2 – 4ac
x =
2a

n n
n (n + 1)
∑1 = n
i =1
∑i
i =1
=
2

n
Tn =a + (n − 1)d S=
n [2a + (n − 1)d ]
2

−1 a(r n − 1) a
Tn = ar n= Sn ;r ≠1 =
S∞ ; −1 < r < 1
r −1 1− r


f ( x + h) − f ( x )
f ′ ( x ) = lim
h →0 h



=
A P (1 + n i ) =
A P (1 − n i )


=
A P (1 + i ) n =
A P (1 − i ) n

 (1 + i )n − 1 1 − (1 + i )− n 
F =
x  P =
x 
 i   i 




 x + x2 y1 + y 2 
= ( x2 – x1 ) 2 + ( y 2 – y1 ) 2 M 1 ;
2 
d
 2

=
y mx + c y – y1 = m ( x – x1 )

y 2 – y1
m = m = tanθ
x2 – x1

( x – a )2 + ( y – b )2 =
r2




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,NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER II – INFORMATION SHEET Page ii of ii

a b c
In ∆ABC: = =
sin A sin B sin C

a=
2
b 2 + c 2 – 2 b c.cos A

1
area ∆ ABC = a b.sinC
2

sin(α=
+ β) sin α .cos β + cos α .sin β sin(α – β ) = sin α .cos β – cos α .sin β

cos(α + β ) =
cos α .cos β – sin α .sin β =
cos(α – β ) cos α .cos β + sin α .sin β

cos2 α − sin2 α

cos 2 α
= 1 − 2 sin α
2
sin2 α = 2sin α .cos α
2cos2 α − 1



n
∑ ( xi − x )
2
∑ fx
x= σ2 =i = 1
n n

n ( A)
P ( A) = =
P ( A or B) P ( A) + P (B ) – P ( A and B )
n (S )

∑ ( x − x )( y − y )
ŷ= a + bx b=
∑ (x − x )
2




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, NATIONAL SENIOR CERTIFICATE EXAMINATION
NOVEMBER 2013



MATHEMATICS: PAPER I

Time: 3 hours 150 marks


PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

1. This question paper consists of 9 pages, an Answer Sheet of 2 pages (i – ii) and an
Information Sheet of 2 pages (i – ii). Please check that your paper is complete.

2. Read the questions carefully.

3. Answer all the questions. Question 5 should be answered in the Answer Sheet provided.
Ensure that you write your examination number on this Answer Sheet and submit it with
your other answers.

4. Number your answers exactly as the questions are numbered.

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

6. Round off your answers to one decimal digit where necessary.

7. All the necessary working details must be clearly shown.

8. It is in your own interest to write legibly and to present your work neatly.




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, NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER I Page 2 of 9

SECTION A

QUESTION 1

(a) Solve for x:

(1) ( x  2) 2  3 x( x  2)
giving your answers correct to one decimal digit. (5)

(2) x 2  9 x  36. (4)

(3) 3x  3x  2  72. (4)

(b) Given: (2m  3)( n  5)  0.

Solve for:

(1) n if m  1. (1)

(2) m if n  5. (1)

(3) m if n  5. (2)
[17]



QUESTION 2

6
2 k 1
(a) Evaluate: 
k 2 k
. (3)


(b) The number of members of a new social networking site doubles every day.
On day 1 there were 27 members and on day 2 there were 54 members.

(1) Calculate the number of members there were on day 12. (2)

(2) The site earns half a cent per member per day. Calculate the amount of
money that the site earned in the first 12 days.
Give your answer to the nearest Rand. (4)

(c) Gina plans to start a fitness programme by going for a run each Sunday.
On the first Sunday she runs 1 km and plans to increase the distance by
750 m each Sunday. When Gina reaches 10 km, she will continue to
run 10 km each Sunday thereafter.

(1) Calculate the distance that Gina will run on the 9th Sunday. (3)

(2) Determine on which Sunday Gina will first run 10 km. (2)

(3) Calculate the total distance that Gina will run over the first 24 Sundays. (4)
[18]

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