may 2017 solutions edited

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1.

…

a.

Number i. Common fractions

 1 2 4  4  1    11  3 5  15

ii. Decimal operations

3.1  3.1





1.15 1.15

2

0.005



760.5

b. Buying and selling i. Price with plan A is $400  12  $65  $1180 ; 5%tax   $1134 , for the person buying it ii. Price with Plan B is $600  6  80  5%

the better deal is plan B since it costs less c.

Electricity Bill i. March Bill  3307  3011  $5.10 .10  $1509.6 09.6

ii. April Meter reading should show

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2351.1 5.1



461  3307

 3768

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a. Factorize completely 6 y

i.

2

 18xy



6 y y  3x 4m

ii.

2 2t

iii.

2



1

 2

m 1

2



m 1

 3t  

2

 t  2   2t   1

b. Write as a single Fraction

c.

5 p  2 3

3p 1



4

Formula

i.

4  29

d  

5



4.82

d 

4h 

5 4h

2

ii. Make h the subject d 



5 2

h

3. Sets and construction a.

Sets i.  M   {3,5, 7,9,11 7, 9,11} ii.

 R



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{4,9}

5d  

4



11 p  11 12

11 

 P  1 12

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iii. Draw the Venn Diagram

b. Construction

4. Functions and relations a.

Functions i.

2)  (1  2) 2)  4  f (3)  f  (3)  (1  2) 1 3

ii.

2

 x 

7

1 3  x 

iii.

 x  







5

21

 f ( x)  3  x  2  1



b. Coordinate geometry i. Gradient of line one is 2 and the gradient of line two is

1



2

ii. The equation of line one is  y  2x  1 iii. Line one is perpendicular to line two; t he product of their gradients is -1;

 

2  

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1

  1

2

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5. Geometry and transformations a.

Geometry

i.

 RQT 

ii.

PRT  PRT 

iii.

SPT  SP T 

0



28

0



90

0



39

b. Transformations i. The transformation is a 90 degree clockwise rotation about the origin ii.

………………………..

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Field 90 

2

i. Field area

90  r  360

ii. Field perimeter



14

2

7

 154m

360 90 

90   D 360

22



22

2

28

7

360



22m

22  14  14  50m

b. Triangular prism

i. The area of the triangle is 24cm2

 bh   2   length  540   ii. Length of the prism 24l  540 l  22.5cm iii. Surface area of the prism is 8  22.5  6  22.5 10  22.5  2 24

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2

 588cm

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a. .. for the interval 20  39  39  – 

i. The upper class limit is 39 ii. The class width is 20 iii. 16 vehicles passed the checkpoint at no more than 39.5 km/h b. Complete the table

c.

Draw the graph and part d

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8. Investigation a.

This part has been omitted deliberately

b. 21 dots are in the 6th c.

Complete the table

1 th

d. The figure that has 210 dots is the 20  figure 2

 x  

e. Simplified expressions

1 2

(

n n

(

n n

20

1) 1 2

f.

1)  210

The best way to show this is t o solve the equation

n

(

n n

2

1)  1000

n

 x  

2000  0  gives no whole

44.2

number solution, each iteration of the figure is a whole number. Further these are triangular numbers and 1000 is not a triangular number

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9. Algebra, Functions Relations and Graphs a. Distance time graphs i. Calculate the gradient of

a.

Gradient is

10

2

ms

25

b. Gradient of AB =0 ii. The cyclist started from rest where his velocity was 0 ms-1, and steadily

increased his velocity by

10

2

ms

25

each second during the first 25 seconds.

During the next 15 se conds his velocity remained constant, that is, his acceleration was 0 ms-2 iii. Average speed 6.875m/s b. Simultaneous nonlinear equations i. Substitute (1, 2) into both equations, the result is true for both

 x 2  2 xy



5

 x  y  3,  y  3  x substituting ii. Solving the equations gives

 x 2  2 x  3  x   5  0  x



2



6x  5  0

 x  5  x  1  0  x  5; y

 2

 x  1; y  2

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10. Measurement, Geometry and Trigonometry a. Circle theorems

SPQ

i.

0



122 PQRS is a cyclic quadrilateral, opposite angles in a c yclic

quadrilateral are supplementary

OQS 

ii.

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0



32 , triangle OQS is isosceles and SOQ is twice SRQ

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b. Bearings i. Complete the diagram

ii. ..in the diagram iii. Use the cosine rule 107km iv. First find angle BCA using the sine rule, this will be 250, the bearing is then calculated as 360  (75  25)  260

11. Vectors and Matrices a.

Matrices i.

3  5

 AB

0   18 2   4 0 3  and  BA        4   3 1   32 4   3 1  5 2 4

they are not equal

ii.

iii.

 2 1   5 3     2 2

1

 A

 AA

1

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1   0

0



1

2

12   4  4

8

  so

2

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 2 1    1    x  3   5 3   i.    5    y  5   2 2

c.

Vectors

i.

 5   20    0  0 

OS  4OQ  4    

PQ  PO  OQ ii.

 4   5  1     0    3   3      

PQ  

 RS

iii.

 RO  OS   4   5  1   4   4    3   0   3 

 RS   4 

iv. Relationships between the lines a. They are parallel b. RS is 4 times as long as PQ

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