HERZLIA SENIOR HIGH SCHOOL
"Ifyouwill il, it is no legend"
MARKS:
150
TIME:
3 TIOURS
.
This question paper consists of lL pages, L diagram sheet and 1 information sheet.
.,
INSTRUCTIONS AND INFORMATION
questions'
Read the following instructions carefully before answering the
1.
This question paper consists of 11 pages with 1 1 questions.
2.
Answer ALL the questions.
3.
used in this question
Number your answers correctly according to the numbering system
paper.
4.
used in determining
Clearly show ALL calculations, diagrams and graphs that you have
your answers.
5.
Answers only will not necessarily be awarded full marks.
6.
It is in your own interest to write legibly and to present your work neatly'
7.
An approved scientific calculator (non-programmable and non-graphical)
may be used, unless stated otherwise'
8.
If necessary, answers should be rounded off to TWO decimal places, unless
stated
otherwise.
g.
Diagrams are NOT necessarily drawn to scalb'
10.
11'3 is attached at
oNE diagram sheet for answering QUESTTON 2.2 7nd QUESTION
provided and insert the
the end of this question paper. Wiite your name in the space
sheet inside the back cover of your ANSWER BOOK'
1
1.
An information sheet, with formulae, is included
at the end of the question paper'
3
QTIESTTON
1
The following set of data shows the individual travelling times, in minutes, thatz}
leamers took to get to school one morning.
40 21 23 27 20 29
18 36 t7 19 39 2s
35
27
t9 20
22 2t
45
17
1.1
Calculate the mean time it took for a learner to get to schooi on this
particular moming.
(2)
LZ
Calculate the standard deviation of the above set of data.
(z)
1.3
The teacher says that all learners took about the same time to get to school.
Do you agree with the teacher? Give a reason for your answer.
(2)
I6I
QIIESTION 2
The price of 95-octane unieaded petrol in Gauteng for the period January 2007 to
July 2008 is shown below. The price is in South African cents per litre.
Janusw l00?
Auritr 20CI7
Juiv f00?
CI*tober ](l*?
598
Fehruarl'i007
575
il,{arch 30S?
599
fi6:
i16
Xv'Iav
3007
701
Jure f,S07
:1.1
7fl1
SeotEmber 2Ct0?
69t
704
;-+r
Decerutrer 3007
h.{arch 1008
Jwre 3CI08
i47
l[*E
Aueust 300?
l*trovetrber 2*ff7
Februarv 2006
lt,{ar'l,0GE
-Tanuarv
Apri!.3008
Julv 30*8
701
891
164
946
8.15
q96
1 0?0
[Soue ce
:
rqurr,a'^**5o1,coad
data.
(4)
2.1
Determine the median, lower quartile and upper quartile for the
2.2
DrawaboxandwhiskerdiagramonDIAGRAMSHEET
2.3
The box and whisker diagram for the price of diesel for the same period as
above is shown below. The lower quartile is 600 and the upper quartile is 800.
1.
55il 60CI 65CI 700 750 S00 850 9S0 950 I 000 1 050
How many data points are there, strictly between 600 and 800?
(2)
100 1 1s0
(2)
t8l
4
QUESTTON 3
a laboratory' The results are
The lifetime of electric light bulbs was measured in
shown in the cumulative frequency diagram beiow'
Cumulativt frequeucl: cttrte strrorviug Xifetime sf
€xeftrit light lrdhs
ss0
500
}\
{r
&
408
*)
IL
E,
)r
308
IH
E 2OCI
(J
100
0
500 ts00 1500 2000 2500 3000
3500
n-ifttime of etrettrit fight bnlbs (tleurs)
following:
use the above cumulative frequency curve to determine the
(1)
3.1
How many light bulbs were tested
3.2
The median lifetime of the electric light bulbs tested
3.3
The interquartile range
3.4
of between 1 750 and
The number of electric light bulbs with a lifetime
2 000 hours
(2)
3.5
If the cost of
purchasing
light bulb is R5,00, determine the amount spent on
the light bulbs that lasted longer thanZ 500 hours'
(2)
one
a)
(2)
tel
5
QUESTTON 4
B(-3;5)' c(-1;-5) andD(9;-7)'
ABCD is a quadrilateral with vertices A(5;1)'
\
i
\
t\
\
1
\
1
I
1
{-{_
4.1
Ir
(2)
Calculate the gradient of AC'
(2)
4.2Hence,determinetheangleofinclinationformedbyACwiththex-axis.
4.3
y
Determine the equation of AC in the form
: '"
(3)
(3)
4.4Hence,orotherwise,showthatthemidpointMofBDliesonAC'
4.5
Show that
4.6
Calculate the area
AIiIB = 90
of AABC'
(3)
(5)
t18l
PLEASE TURN OVER
6
QUESTION s
Consider the following points in the Cartesian plane: A(1;2), B (3;1) ,C(-3;k)
and D (2;-3). Determine the value(s) of ,t if:
5.1 ABICD
(3)
5.2
A, B and C are collinear
(3)
5.3
CD
(5)
=5Ji
[11]
6.1
rdinates of the image of point
Write doud
undergone the followtn
6.1.1
Translation of 3
ection about the x-axis
A(-5;3) afterf
to the right
(2)
(2)
wise direction through
A point P(3;-a) is rotated abo
an angle of 150 to obtain P'.
Ie of a calculator, the coordinates of P'
Calculate, w
QUESTTON 8
8.1
In the Cartesian plane below, the point A(-12;5) and the angle 0 are shown'
At-1f
: 5]
Determine, writing your answer as a single fraction:
8.1.1
(1)
tan9
(4)
8.1.2 cosdsind
8.2
Simplify the following to a single trigonometric ratio:
sin(90 -x)tan(360"
cos(I 80' - x)
8.3
-x)
(4)
Simplify completely, without the use of a calculator:
cos(-60')+tan135
tan 315 + cos 660
(4)
of
sin x sin 2x + cosZx =
8.4
Find the general solution
8.5
Findthevalue fotx, xe[0';i80
sequence.
(7)
1.
] if cos' ; sinx ; t6sinx
isageometric
(3)
t23I
9
QUESTTON 9
g.1 If sin 24 -- p , express the following in terms ofp, without the use of a
calculator:
9.1.1
cos24
(2)
9.1.2
sin12 cosl2 -sin(-66 )tan204
(6)
g.2
Prove
Zsinx
rnu, 2sinx+sinzx 4+3cosx -cosZx 5-2cosx
(o
9.3
Consider cos(x + 45' ) cos( x
- 45 ) .
9.3.1 Showthat cos(x+45 )cos( x-45 ) =f2 cor2r.
g.3.2
Hence, determine the value of x in the interval
cos(x
g.4
+45 )cos(x - 45 ) is a minimum'
Given AABC. Show that tan(A + B) =
-tanC.
(4)
0' < x < 1 80' for which
(3)
(3)
124l
PLEASE TURN O\rER
10
QUESTION 10
10.1
Sketched below is a plot of land with AB
AD :280 m ara
:200 m, BC -- 120 m, CD :
70 m,
fi :110".
Calculate
(3)
10.1.1
The length of AC
t0.t.2
The size of D
(3)
10.1 .3
The area of the plot of land
(3)
A
T0.2 In APQR, Q:150',
QR =
p, PR - q and PQ =..
P
ap
Show,
without the use of a calculator, that sin P =
p
(3)
2q
ltzl
11
QUESTTON
The graph
of
1.1
f (x) = sinlx for - 180" < x < 90' is shown in the sketch below.
1--
/i
/ ii
*--
i
---i---"1--
I
j
I
I
I
I
I
I
I
I
11.1
Write down the range
off
(2)
tt.2
Determine the period
f[1r).
"f "\2
)
(2)
11'3
Drawthe graph of g(x) = cos(.r-30') for -180" < x <90" on the system of
axes on DIAGRAM SHEET 1. Clearly label ALL x-intercepts and turning
'
(4)
points.
11.4
Hence, or otherwise, determine the values of x in the interval
for which
11.5
/(x).g(x) < 0.
-180'
< x < 90'
(4)
Describe the transformation that graphfhas to undergo to form
(2)
y=sin(Zx+60').
11.6
Determine the general solution of sin 2x = cos(x
- 30')'
(6)
[20]
TOTAL
:
150
HERZLIA SENIOR HIGH SCHOOL
DIAGRAM SHEET
12
GRADE MATHEMATICS PAPER 2
MoNDAY l*'JUNE zo13
(PLEASE PLACE IN YOUR ANSWER BOOK)
DIAGRAM SHEET
QUESTTON 2.2
F*?rul
1