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Page 5

4. Th e figures shown below, not drawn to scale, represent the cross sections of two circularpizzas. Both pizzas are equally thick and contain the same toppings.

(a)

(b)

Small pizzaDiameter = 15 cm

Medium pizzaDiameter = 30 cm

Is a medium pizza twice as large as a small pizza?Use calculations to support your answer. (5 marks)

A medium pizza is cut into 3 equal parts, and each part is sold for $15.95. A smallpizza is sold for 12.95.

Which is the better buy?Use calculations to support your answer. (5 marks)

Total 10 marks

(a)

(b)

(c)

On graph paper, draw the x-axis andthe y-axis. Using a scale of 1 cm to represent 1 uniton both axes, draw the triangle DE F with vertices D (1, 1), E (3, 1) and F l, 4).

(3 marks)

i Draw the image of ADEF under reflection in the line x = 4. Name the imageAD'E'F.

ii Draw the image of AD FT * underthe translation* 0

-5. Name the image D E F .

iii Name the type of transformation that maps ADEF onto hD'E'V .(5 marks)

A vertical stick of height 1.8 m casts a shadow of length 2 m on the horizontal asshown in the diagram below, no t drawn to scale.

1.8 m

Calculate, to the NEAREST degree, the angle of elevation of the sun. (4 marks)

Total 12 marks

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Page 6

6. (a) In the diagram shown below, ABCDE is a pentagon. ZBAE = 108, ZABC 90,ZAED = 80, ZADC = 57 and AE is parallel to CD.

E

D

Calculate the size of the angle marked

(i)

i i y (4 marks)

Show all steps in your calculations and give reasons for your answers.

(b) The functions an d g are definedby

fix) = ~ x + 5, g(x) x

Evaluate

(i) (3) + g(-3)

(ii) /_1(6)

iii fg( 2) (8 marks)

Total 12 marks

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Page 11

(c) Th e diagram below shows a triangular regibn bounded by the lines y - x+ 5,v = x + 5 and the line HK.J

8

: i

/1.**5****1

3:Ei::lEG

n 1 t ' 1 1 t T

3:1 I 4 V V 3B::i:} =

6

::n:4

\ \< X:

v\\ \ : . T f 1

.4... ...ii 1 \ 1 4 4frfnN

44 4*4- |:j:Ill11TT :

rifi-4444 X N JJJf 3:1:1:

. r : ...4.-4-4-4-- | -f psW

4J44. -g-rr

-M44-554...Li.4??* ...I... i-flf

tttt . 1 ; :f-i- .4.4... i 4444 11

-f 4- -4v j *] T *: 4# - 7 : *4:l: 4444- 4444-

(i) Write the equation of the line HK. (1 mark )

(ii) Write the set of three inequalities which define the shaded region GHK.(3 marks)

Total 15 marks

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