(b) The table below shows the number of people who like each activity.


Badminton Yoga


Basketball Football Rugby Hockey


Activity Number of people 45 60 15 15 30 15


(i) How many people were surveyed?


(ii) Draw a pie chart to represent this information.


(iii) Could this data be represented by a histogram? Give a reason for your answer.


7. An artist designed this logo. It is a right triangle with a semicircle drawn on each side.


(i) Calculate the area of each semicircle, in terms of π.


5 cm 3 cm 4 cm


(ii) Add the areas of the two smaller semicircles, and compare this sum to the area of the larger semicircle. What do you notice?


(iii) One of the theorems you studied in geometry explains the relationship you found in part (ii). Name and state this theorem.


8. Mark has a design for a circular brick patio in the centre of his lawn.


(i) Find, in terms of π , the area of the brick surface if the radius of the patio is 2 m.


Mark decides to investigate the eff ect of increasing the radius of the patio on the area of the brick surface. He produces the table below.


Radius patio (m)


0 2 4 6 8


10 (ii) Copy and complete the table.


Area of brick, in terms of π (m2


)


(iii) Draw a graph to represent the data in the table. Put the radius of the patio on the x -axis and the area of brick surface on the y -axis.


(iv) What type of relationship exists between the radius of the brick patio and the area of the brick surface? Justify your answer.


(v)


If the radius of the brick patio is 3 m, use your graph to estimate the area of brick.


(vi) Is the pattern of the radius given in each case linear or non-linear? Justify your answer.


(vii) Is the pattern of the area linear or non-linear? Justify your answer.


9. (a) David has only €5 notes and €10 notes in his wallet. He has fi ve notes totalling €35.


(i) How many of each does he have?


(ii) If David selected a note at random, what is the probability it would be a €10 note?


(b) David has an annual salary of €28 000 and is entitled to a tax credit of €3 200. He is charged tax at a rate of 20%.


(i) Calculate how much tax David will have to pay (net tax).


(ii) Calculate David’s net salary (salary after tax has been paid).


(c) David is playing a video game. The game is programmed to randomly put his character somewhere on the computer screen that has a rectangular lava pit on it. If you land in the lava pit, you lose points. The screen is 25 cm by 43 cm and the lava pit is 5 cm by 14 cm.


(i) Find the area of the computer screen. (ii) Find the area of the lava pit.


(iii) What is the probability that David will land in lava on this game?


560


Linking Thinking 1


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