15. (a) Aoife practises her violin for at least 12 hours per week. She practises for three- quarters of an hour each session. Aoife has already practised 3 hours this week.


(i) What proportion of her weekly practice goal has she reached?


(ii) How many more sessions remain for her to meet her weekly practice goal?


(b) While practising her violin, Aoife started at point A and walked 3 m east to a point B. She then walked 4 m north to a point C and fi nally walked in a straight line back to point A.


(i) Accurately represent her path travelled, in a scaled diagram. (ii) How far did she walk from point C to point A? Give answer to the nearest centimetre.


(c) Aoife needs a new table for organising her sheet music. She purchased a circular table top that is 230 cm in diameter. Aoife’s front door is 105 cm wide and 208 cm tall. Explain one way that Aoife could get the table through the door. Justify your answer using calculations.


(d) Aoife bought a tablecloth with a design on it, which is shown opposite. |∠CBD| = 30 ° |∠ABC| = 30 ° |BC| = 140 cm


|∠BDC| = 90° |∠BAC| = 90°


(i) Find |∠ACB| Justify your answer.


(ii) Aoife thinks that ∆ ABC is congruent to ∆ BCD. Is she correct? Justify your answer.


C A


(iii) Given the area of ∆ ABC = 4 243·4 cm, fi nd the area of the blue region on this design. Give your answer to the nearest whole number.


16. (a) Sara and Adam play ice hockey. In a particular month, Sara played four more games than Adam. They played 12 games in total.


(i) By letting x be the number of games Adam played, write an equation in terms of x to represent the total number of games played.


(ii) Solve the equation formed in (i) to fi nd out how many games Sara played.


(b) An ice hockey puck is cylindrical in shape and has the following dimensions: Diameter = 75 mm Height = 25 mm


(1 cm = 10 mm)


(c) Sara purchased a pack of 50 ice hockey pucks that came in a rectangular box. The pucks were stacked in fi ves. Two stacks are placed side-by-side and fi ve stacks are placed along the length of the box, as shown.


(i) What is the minimum height of the box? (ii) What is the minimum width of the box? (iii) What is the minimum length of the box? (iv) Using the minimum dimensions above, fi nd the volume of the box. (v) What percentage of the box is empty space? Give your answer to the nearest whole number.


(d) Adam decided to roll a puck on its side. (i) How far would it travel in one full revolution? Give your answer correct to two decimal places.


(ii) How many revolutions would the puck complete if it rolled on its side for 5 km? Give your answer in the form a × 10 n


where 1 ≤ a < 10 and n ∈ ℕ. 410 Linking Thinking 1 75 mm 25 mm


(i) Draw the net of the puck. Include the dimensions on your diagram. (ii) Find the volume of rubber needed to make one puck. Give your answer to the nearest cm3


.


|CD| = 70 cm |AC| = 70 cm


B O D


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