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
IEB Copyright © 2021
, NATIONAL SENIOR CERTIFICATE EXAMINATION
SUPPLEMENTARY EXAMINATION MARCH 2016
MATHEMATICS: PAPER I
Time: 3 hours 150 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 9 pages 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.
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.
9. Please hand in this question paper.
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, NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER I – SUPPLEMENTARY Page 2 of 9
SECTION A
QUESTION 1
2 x 2 + 11x − 13
(a) (1) Simplify . (2)
x −1
2 x 2 + 11x − 13
(2) Hence, solve for x if = x2 .
x −1
Leave answers in simplest surd form. (3)
83 x.43 x
(b) (1) Simplify 15 x− 2 . (4)
2
83 x.43 x
(2) Hence solve for m if 2 = 15 x− 2 .
m
(2)
2
3
(c) In the diagram below, the graph of h=
( x) + 1 has been sketched.
x+2
y
x
(1) Write down the equations for the asymptotes of h( x) . (2)
(2) Write down the new equation for h( x) if h(x) is shifted horizontally so that
point A is at the origin. (3)
[16]
QUESTION 2
The sequence 3; p; 25 is a quadratic sequence. The sequence of first differences is 9; q; …
(a) Calculate p and q. (4)
(b) Determine the nth term of the quadratic sequence. (5)
[9]
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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
IEB Copyright © 2021 PLEASE TURN OVER
,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
IEB Copyright © 2021
, NATIONAL SENIOR CERTIFICATE EXAMINATION
SUPPLEMENTARY EXAMINATION MARCH 2016
MATHEMATICS: PAPER I
Time: 3 hours 150 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 9 pages 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.
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.
9. Please hand in this question paper.
IEB Copyright © 2016 PLEASE TURN OVER
, NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER I – SUPPLEMENTARY Page 2 of 9
SECTION A
QUESTION 1
2 x 2 + 11x − 13
(a) (1) Simplify . (2)
x −1
2 x 2 + 11x − 13
(2) Hence, solve for x if = x2 .
x −1
Leave answers in simplest surd form. (3)
83 x.43 x
(b) (1) Simplify 15 x− 2 . (4)
2
83 x.43 x
(2) Hence solve for m if 2 = 15 x− 2 .
m
(2)
2
3
(c) In the diagram below, the graph of h=
( x) + 1 has been sketched.
x+2
y
x
(1) Write down the equations for the asymptotes of h( x) . (2)
(2) Write down the new equation for h( x) if h(x) is shifted horizontally so that
point A is at the origin. (3)
[16]
QUESTION 2
The sequence 3; p; 25 is a quadratic sequence. The sequence of first differences is 9; q; …
(a) Calculate p and q. (4)
(b) Determine the nth term of the quadratic sequence. (5)
[9]
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