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GRADE 10 MATHEMATICS
CURRO NATIONAL PAPER
NOVEMBER EXAMINATION
PAPER 2
Date: November 2015

Total: 100 Marks

Time: 2 Hours

Name: ______________________________________________

Mathematics Teacher: ______________________________________________

_______________________________________________________________________________________

Instructions

1. This is a ‘write-on’paper. The questions are to be answered on the question paper.

This question paper consists of 20 pages.
2. Set your work out neatly.

3. Show all relevant working out.

4. Calculators may be used unless otherwise stated.

5. Ensure your name is written on the first page.

6. Diagrams are not drawn to scale

7. Round to 1 decimal place unless otherwise stated.

_________________________________________________________________________________________

Formula Sheet: This sheet is on page 19 and 20. You may remove this sheet.

RESOURCES:

Various Past Papers

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Question 1: Multiple choice. Highlight your choice of answer in each of the following:

1.1 Which equation best describes the following graph?

A. y  2 sin x
B. y  cos x  1
C. y   cos x  1
D. y   sin x  2

1.2 The period of the graph alongside is:

A. 450o
B. 360o
C. 270o
D 180o

1.3 Determine which graph is the graph of y  tan 2 x for 0o  x  360o

A. B.

C. D.
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1.4 The graph of y  5 cos 2 x for 0 o  x  360 o is:

A. B. C. D.

180o 360o 180o 360o

1.5 Study the graph below and answer the questions that follow:
For  360 o  x  360 o , which one of the following statements is correct?

A. f (x) is not symmetrical about any line.

B. f (x) is symmetrical about the x-axis
C. f (x) is symmetrical about the y-axis
D. f (x) is symmetrical about the line y  x
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Question 2:

2.1 The diagram provided shows the image of the Southern Cross in our night sky.
y

S
(-4;16)

(17;3)
Q T
(-8;2)
R x
0

A
(-3;k)

If the quadrilateral STAR forms a kite;

2.1.1 Write down just the missing word in the following statement:
The diagonals of a kite intersect at _______ o (1)
2.1.2 Determine the value of k. (3)

2.1.3 Give the co-ordinates of Q. (3)

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2.2 Refer to the map of South Africa provided below when answering the questions that follow:
A quadrilateral joining Nelspruit (3;4), Hluluwe (4;-2), Bloemfontein (-4;-3) and Mafikeng (-5;3) is
shown.

2.2.1 Determine the direct distance between Mafikeng and Hluluwe. (3)

2.2.2 Prove that the quadrilateral resulted from connecting Nelspruit (3;4), Hluluwe (4;-2), Bloemfontein
(-4;-3) and Mafikeng (-5;3) is a parallelogram. (3)
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2.3 The co-ordinates of the endpoint of AB are A(-6;-5) and B(4;0). Point P is on AB .
Determine graphically the co-ordinates of P, such that AP:PB is 2:3.

(3)

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Question 3:

3.1 Given that 13 sin   5  0 and 0 o    270 o , determine the following:

3.1.1 tan  (3)

3.1.2 12 sec (3)

3.2 If A  51,3o and B  38,7 o ; find the value of

3.2.1 2 sin( A  B) (2)

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3.2.2  3 sin 2 (3B) (2)

3.3 Use your calculator to solve for x in the following for 0 o  x  90 o :

3.3.1 tan x  8,35 (2)

3.3.2
1
2
 
sin 2 x  15 o  0,25 (4)

3.4 Simplify the following WITHOUT the use of a calculator:

tan 45 o. cos 60 o. sin 60 o

(4)
cos 30 o
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3.5 Use the picture and storyline provided to answer the following question:

Once upon a time a King’s son came across a tower where Repunzel had spent most of her life. He
dearly wanted to meet the young lass and shouted “ Repunzel, Repunzel, let down your hair”. Repunzel
did as she was asked and as her hair was so long, it touched the ground. The angle of depression from
Repunzel to the prince who rode on horseback was 15°. He was 500 m away from the foot of the castle
tower. His line of sight was 8 metres above the ground.

How long was Repunzel’s hair (h)? ( rounded off to the nearest metre)

(4)

15°

8 metres 500 metres

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Question 4: The water tower in the picture below is modelled by the two-dimensional figure beside it.
The water tower is composed of a hemisphere, a cylinder and a cone.
Let C be the centre of the hemisphere and let D be the centre of the base of the cone.

4.1 Give the length of BC. (1)

4.2 Determine the slant height of the cone ie: EF. (3)
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4.3 Calculate the surface area of the cone (the lid of the water tower) (2)

4.4 Calculate the volume of water that the tower can hold if the water reaches the top of the cylinder.
(5)

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Question 5: ABEF is a parallelogram.

A F
x

2x 7x
B R E

If SA = SF, calculate
y
5.1 x S (3)

STATEMENT REASON

5.2 y (3)

STATEMENT REASON

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Question 6: A computer store sells 70 different kinds of games. The histogram below shows their prices and
the quantities sold. Each class interval includes the larger value.

20

16

11

7 8

5
3

R50-R100 R100-R150 R150-R200 R200-R250 R250-R300 R300-R350 R350-R400

6.1 Give the modal price of computer games sold. (1)

6.2 Complete the table below: (4)

midpoint ( xi ) f f .xi cumulative frequency

50  x  100

100  x  150

150  x  200

200  x  250

250  x  300

300  x  350

350  x  400

Total
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6.3 Show that the mean price of a computer game is approximately R199. (Correct to the nearest Rand)
(3)

6.4 Determine the median price interval of computer games bought. (3)

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Question 7: For a set of 5 data values, the following information is given:

the median is 11 cm; the mode is 13 cm; the range is 10 cm; the mean is 9 cm

Calculate the 5 data values and fill them in on the table provided below:

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Question 8: Two grade 10 classes have their pulse rate (in beats per minute) measured. The results are
Represented by the box-and-whisker plots below.

Grade 10L

Grade 10K

8.1 What is the range of the pulse rate for Grade 10 K? (1)

8.2 What does “60” represent for Gr 10 L? (1)

8.3 Which class is fitter? (i.e. generally has the lower pulse rate) (1)

8.4 How is this fact indicated? (1)

8.5 If there are 32 learners in Grade 10 K, how many have a pulse rate between 56 and
76? (2)

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B A
Question 9:

9.1 Prove that ABDE is a parallelogram 1

C
2

D E

STATEMENT REASON

(4)
9.2 In MNP, Mˆ  90 o , S is the midpoint of MN and T is the midpoint of NR.

9.2.1 Fill in the reason for : SU // MP ( _____________________________ ) (1)

9.2.2 If ST = 4 cm and the area of SNT is 6 cm 2 , calculate the area of MNR . (3)
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9.2.3 Prove that the area of MNR will always be four times the area of SNT and therefore show that the
ratio of the areas of MNR : SNT will always be 4:1
Let ST = x units and SN = y units. (3)

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Rough Work (This page will not b marked)

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MATHEMATICS
INFORMATION SHEET

–b  b 2 – 4ac
x 
2a

n n
n (n  1)

i 1
1  n i
i 1

2

  a  i  1 d   2  2 a  n  1 d 
n
i 1

n

a rn  1  

  ar
a
a ri  1  ; r  1 i 1
 ; 1  r  1 , r  0
i 1 r 1 i 1 1 r

Tn  a n 2  b n  c

Tn  T1  n  1 f 
n  1n  2 s
where f is the first term of the first difference
2
and s is the second difference

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 y  y2 
d  ( x 2 – x1 ) 2
 ( y 2 – y1 ) 2
M 1 ; 1 
 2 2 

y  mx  c y – y1  m ( x – x1 )

y 2 – y1
m  m  tan 
x 2 – x1

( x – a) 2  ( y – b) 2  r 2

2
Vhemisphere  r 3 S. Acone  rs
3
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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 . sin C
2

sin (  )  sin  . cos  cos  . sin  sin ( – )  sin  . cos – cos  . sin 

cos (  )  cos  . cos – sin  . sin  cos ( – )  cos  . cos  sin  . sin 

cos 2   sin 2 

cos 2   1  2 sin 2  sin 2   2 sin  . cos 

2 cos   1
2

x ; y   x A cos   y A sin  ;  y A cos   x A sin 

x  x x   f x
n n

n n

 x
i 1
i  x 2  x i  x 2
i 1
var  var 
n 1 n

 x
i 1
i  x 2
s.d 
n

n ( A)
P ( A) 
n (S )

P ( A or B)  P ( A)  P ( B) – P ( A and B)