IEB Assessment Matters National Senior Certificate Examination Mathematics 2018

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
SUPPLEMENTARY EXAMINATION – MARCH 2018



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. All necessary working details must be clearly shown. Answers only will not
necessarily be awarded full marks.

7. Diagrams are not necessarily drawn to scale.

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 and y: 3x + y = –1

9x2 = y2 (5)

(b) Solve for x:

4 x 2  163 x +4 = 0 (3)


(c) (1) Show that the roots of 2 x 2  5 x = 3 are real and rational. (3)

(2) Determine the value that must be added to the negative root so that
the roots are equal. (3)
[14]



QUESTION 2

Given: f (x) = (x – 3)(x + 1)

(a) Rewrite f (x) in the form f (x) = a(x + p)2 + q. (4)

(b) Sketch the graph of f (x). Show the turning point and the intercepts with the
axes. (4)

(c) Write down the range of f (x). (2)

(d) Determine the equation of the line that passes through the negative
x-intercept and the y-intercept. (3)
[13]




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