may 2018 solutions 1

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1. Number Operations a.

Round off to TWO DP i. ii.

73.18 .18  5.23 .23  9.3 9.34  24.33 .33 3.12 6.17

.68  1.2  2.68

b. Salary question i. ii. iii.

$600  0.90  230  $807 $600  0.90n  1000 n  445

$270 $270  1.50 1.50m

iv. Salaries are equal so we need to equate the salary expressions here, n = m

$600  0.90n  $270  1.50n n  550 2. Algebra a. Factorization i. 1  4h

ii.

2

 1  2h  1  2h 

 pq  q2  3 p  3q

 q  3  p  q 

b. Solve equations

3

i.

 y  12 2  y  8

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2 x 2  5 x  3  0 ii.

 2 x  1  x  3   0  x 

1 2

, x  3

3. a. Substitution/Formula i.  F  

 F  

mv  u t  mv  u



t 

 mv  mu  Ft  mu v

ii.  Ft

m

b. 4. Construction and Transformation a. Construction – Left out b. Transformation

3  2  ( 1) 1)  1

9

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 f ( x )  i.

1 2

x  3; A1, 1, 2, 3

 f  (1)   2

1 2

 f ( x)  2 ii.

1  x  3  2 2  x  2

 

iii. Ordered pairs are  1, 2 iv. If  f ( x)  5 then

1  ,  2, 2  2

1  x  3  5 and  x  16 , 16 is not in A(1, 2, 3} so  f ( x )  5 2

b. Inequalities i.

ii.

3 x  1  11  x  4

2  3 x  1 1   x

iii. 6. Statistics a. Pie chart i.  x  221

0

ii. Percentage for cricket

94    360

45  x  40 360 1 iii. If 40 students chose tennis then  x  40 8  x  320 b. Unclosed frequency polygon i. Copy and complete # of matches # of goals

5 0

7 1

3

2

3 3

4 4

2

5

1 6

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ii. Mode =1 iii. Median = 2 iv. Mean =

54 25

 2.16

7. Measurement a. Circular disk i. Circumference of disk 2  21 2

ii. Area of disk 21



22 7

22 7

 132mm

 62  1350mm2

1cm3  1000mm3  1000 cm3  1000000 mm3 iii. Number of disks 1000000

1350  2

 370

b. Scale drawing on the globe g lobe i.

40000km 160cm

 250km / cm  so 2 cm = 500 km

ii. Distance between Palmyra and Quintec 25  250  6250 km

8. Pattern and Investigation a. Draw the 4th b. Copy and complete i

ii

n c.

figure 4 . . . 21

Number of squares 9

Perimeter of figure 20

43

88

2n  1

4n  4

Relationship between squares and perimeter 2S  2  P 

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9. Functions Relations and graphs a.

Graph  y

 3x 

1  x

i. Copy and complete x

0.1

0.2

0.5

1

1.5

2

2.2

2.5

y

10.3

5.6

3.5

4

5.2

6.5

7.1

7.9

ii. Draw the graph

b. Speed time graph i. Acceleration

25 20

 1.25m / s 2

ii. Calculate the distance by finding the area of the trapezium

20

iii.

2 40

15  40   550m  so the average speed is

2.5

 16sec

550m 20 s

 27.5m / s

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10. Geometry and Trigonometry a.

Bearings

i. Bearing of B from F is 222

0

2

32  55 55 co cos103  BG   322  552  2  32 ii. Use the cosine rule  BG 

2

 4840.83

 BG  69.6km

55 sin  A iii. Bearing of G from B first find angle A



SinA 

69.6 Sin103 55sin103

69.6

 0.77

 A  sin 1 0.77  50.4 0 Now add the 42 to get 092.4

0

b. Circle theorem i.

 ABC   320 , triangle ABC is right angled

ii.

CMB  122 0 , AMBC is a cyclic quadrilateral

iii.

 NCM   32 0

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11. Matrices vectors and transformations a.

Matrices i.

 2 1  2   7  a   2 0   3    4  b      

1 1  0  2 1  ii. This is the inverse Matrix  2    2 0  1 1   

iii. Transformation T followed by P so we need the product PT a.

Transformation Product

b. The image

 0 1   2  1  2 0   1 2   2 0    2 1       

 2 0  1       2, 6   2 1   4

1, 4   

b. Vectors i. AB and DC are parallel and  AB is

ii.

1 3

 DC 

 BC  BA  AD  DC   BC  n  2m  BL  BC  CL

iii.

 BL 

2n  m 2

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