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 2017
MATHEMATICS: PAPER I
Time: 3 hours 150 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 8 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.
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, NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER I – SUPPLEMENTARY Page 2 of 8
SECTION A
QUESTION 1
(a) Solve for x:
(1) 4− 2− x =
3x (6)
(2) 2(5)9− x = 1 250 (3)
(b) The graph of f(x) = 3 ( x + 1)( x − 3) , not drawn to scale, is sketched below.
y
A B x
C
D
(1) Determine the coordinates of A, B, C, and D. (6)
(2) Hence, or otherwise solve for x: 3 ( x + 1)( x − 3) ≥ 0 . (2)
(c) If one root of the equation x 2 + tx + 18 =
0 is greater than the other root by 3,
determine a possible value of t . (5)
(d) Solve for x and y simultaneously in the following set of equations:
3x + y = 2 and =
y 2 2 x 2 − 1. (7)
[29]
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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 2017
MATHEMATICS: PAPER I
Time: 3 hours 150 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 8 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.
IEB Copyright © 2017 PLEASE TURN OVER
, NATIONAL SENIOR CERTIFICATE: MATHEMATICS: PAPER I – SUPPLEMENTARY Page 2 of 8
SECTION A
QUESTION 1
(a) Solve for x:
(1) 4− 2− x =
3x (6)
(2) 2(5)9− x = 1 250 (3)
(b) The graph of f(x) = 3 ( x + 1)( x − 3) , not drawn to scale, is sketched below.
y
A B x
C
D
(1) Determine the coordinates of A, B, C, and D. (6)
(2) Hence, or otherwise solve for x: 3 ( x + 1)( x − 3) ≥ 0 . (2)
(c) If one root of the equation x 2 + tx + 18 =
0 is greater than the other root by 3,
determine a possible value of t . (5)
(d) Solve for x and y simultaneously in the following set of equations:
3x + y = 2 and =
y 2 2 x 2 − 1. (7)
[29]
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