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WELCOME TO BTA'S

MATH TUTORING
CHALLENGE

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Produced and written by our friendly local maths tutors in
Belrose, Forestville and Mona Vale.


Who is this challenge for:
HSC (Year 12) Standard Mathematics Students (and anyone else up for the challenge!)

Relevant Syllabus Topics:
Geometry of the Earth, Rates and Ratios, Speed Distance and Time

BTA'S MATHS TUTORING CHALLENGE # 1

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Instructions

Please read the instructions and key information provided carefully.

Answer as many questions as possible, showing all working, and submit your answers in the form at the bottom. 

Introduction

Max and Rex are two quirky axolotls who are competing at the Axolotl Olympics in Tokyo.

For the first time ever, surfing will make its debut as an Olympic event.  

Max is a brown speckled axolotl who
 learnt to surf in the lake complex of Xochimilco near Mexico City, before moving to Sydney Australia to study at Belrose Tutoring Academy’s new office in Mona Vale. He received one-on-one tuition in both math and English, while refining his skills on the perfect barrels that frequently rolled along Mona Vale Beach.

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Figure 1: Image: Max the brown speckled axolotl who hangs out at our BTA Mona Vale Office (real life)
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Figure 2: Max (Artist Impression)
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Figure 3: Rex (Artist Impression)
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Figure 4: Image: Max and Rex together (BTA Mona Vale)

Rex on the other hand, is a leucistic axolotl who resides in Forestville, California. He's a quirky character who likes to wear large red loopy glasses, a disguise not to be underestimated, as once he hit the surf, he was a different beast amongst the swell.

Rex and Max knew each other from countless surfing competitions in their youth and now, at just 18 years old, they would be competing on the biggest stage of them all.

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The young axolotls would frequently do the dawn patrol of their local swells, it was always the best time to catch them firing to get in some training.

On the 22nd of July at 5:30am, Max had just finished his final training session at Mona Vale beach. He was particularly proud this morning as the waves were double overhead.

 

He paused for a moment on the beach, feeling proud of himself for his big accomplishment, but the pause didn’t last long as his attention shifted to his flight to Tokyo. It was leaving at 9AM this morning.

 

But first, some coffee...Max walks over to Golly Gosh! Café in Mona Vale and orders the usual, a small soy latte and a bacon and egg roll.

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Figure 5: Image: Golly Gosh! Cafe in Mona Vale, Sydney
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Question 1:

Total (2 Marks)

 

Max had been learning in his math class about calculating GST.

If his small soy latte cost $4.50 (incl. GST) and the tasty bacon and egg roll cost $12.90 (incl. GST), how much GST did Max have to pay in this transaction overall? 

(Note: Remember to round your answer to the nearest cent) (2 Marks)

KEY INFORMATION

The Goods and Service Tax (GST) in Australia is calculated as 10% of the purchase price.

Max (BTA Axolotl) - Calculator + Pencil

Question 2:
Total (6 Marks)


After he had gobbled his delicious breakfast, Max realised time had caught up to him and it was now 7AM. He felt relieved as he had packed everything last night, albeit reluctantly at the time.
 

Max knew he had to rush from Mona Vale to Sydney Airport to make his flight. The distance from Mona Vale to Sydney International Airport is 42km. Max knows that due to the current lockdown in Sydney, there won’t be much traffic on the road, and he will be able to travel at an average speed of 70 km/h.

Question 2 (A): How long will it take Max to get to the airport? (Note: Round your answer to the nearest minute) (2 Marks)

Question 2 (B): What time will Max arrive at the airport? 
(2 Marks)

Question 2 (C): If petrol in Sydney is $1.49 per litre and Max’s car uses petrol at a rate of 7.5L/100km, how much did Max have to pay for the petrol to get him to Sydney Airport?

(Note: Responses should be in dollars and up to 2 decimal places) (2 Marks)

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Figure 6: Route: Mona Vale to Sydney Airport

KEY INFORMATION

Time taken is measured as distance travelled divided by the average speed

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Question 3:

Total (6 Marks)

Max arrived at the airport and received an extra big hug from his parents as they waved him goodbye and wished him the very best of luck. After checking his bags and going through board-in's, Max made his way through the duty-free section before helping himself to some cheeky Maccas before heading to his gate.


Max, prompted by his maths tutoring at BTA Mona Vale just a couple of days ago, started to consider the geometry of the Earth and the math behind his journey.

 

Max had learnt in his lesson that the coordinates of Sydney Kingsford Airport are (33°S, 151°E) and the coordinates of Haneda Airport (Tokyo International Airport) is (35°N, 140°E).

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Figure 7: Map: displaying the relative positions of Sydney Airport to Haneda Airport

Max's flight to Tokyo will take 10 hours.
 

Question 3 (A): What day and time will he arrive?
(Note: The response should be in Sydney time) 
(2 Marks)

Question 3 (B): What day and time will it be in Tokyo when he arrives? (2 Marks)

KEY INFORMATION

  • Time difference concerns ONLY longitude (East & West)
     

  • Everywhere within a time zone has the same time
     

    • Positive time zone number – ahead of the UTC. ADD the time​
       

    • Negative time zone number – behind the UTC. SUBTRACT the time.

 

  • When the longitudes are in OPPOSITE directions, you need to ADD to calculate the difference
     

    • ​Example: UTC + 5 and UTC - 2 =
      5 + 2 = 7 hours time difference

 

  • When the longitudes are in the SAME direction, you need to SUBTRACT to calculate the difference
     

    • Example: UTC + 5 and UTC + 2 =
      5 – 2 = 3 hours time difference

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Question 4:
Total (8 Marks)

On the other side of the world in Forestville (California), Rex was frantically packing his suitcase to make his 7pm flight to Tokyo.

 

Currently it is 4:30pm on the 23rd of July in Forestville, California (UTC -7).
Rex's coach has already arrived in Tokyo and expects him to be there for his final training session at 2pm on the 25th of July (UTC +9).

As he runs into the airport for check in, he realizes that he has forgot his special surf wax. His flight is departing in in 45 minutes, and the next one isn't until 9am on the 24th of July (Californian time). He really needs this wax to compete at his best so he concedes and takes the flight on the 24th.

The coordinates of Forestville, California are (37°N, 114°W) and the coordinates of Tokyo are (35°N, 140°E).

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Figure 8: Map: Displaying the relative positions of Forestville, California to Haneda Airport

Question 4 (A): Calculate the time difference between California and Tokyo.

(Note: Remember to round your answer to the nearest minute) (2 Marks)
 

Question 4 (B): If the flight takes 12 hours and 30 minutes, what day and time will Max land in Tokyo?  

(Note: Remember to round your answer to the nearest minute) (2 Marks)

 

Question 4 (C): What is the average speed that Max’s flight travelled at?

(Note: Remember to answer in km/hour) (2 Marks)
 

KEY INFORMATION

  • Since Tokyo and California are in opposite directions, thus we must add their UTC’s to find the difference;

    • Tokyo’s UTC is + 9
       

    • California’s UTC is - 7 

       

  • Average speed is measured as distance travelled divided by the time taken.

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Question 5:

Total (4 Marks)

It is now 10am on the 26th of July in Tokyo, Max and Rex are making their way over to Tsurigasaki Beach for their contest which starts in two and a half hours.

All of their family and friends in Sydney and California respectively have gathered to watch them live on TV. 

Question 5 (A): In local time, when does the event start for Max’s friends and family?
(Note: Responses should include the date and time) (2 Marks) 


Question 5 (B): In local time, when does the event start for Rex’s friends and family?
(Note: Responses should include the date and time) (2 Marks) 

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Figure 9: Image: Tsurigasaki Beach, Japan
Source: https://olympics.com/tokyo-2020/en/venues/tsurigasaki-surfing-beach
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CONGRATULATIONS!
on completing
BTA's Math Tutoring Challenge # 1

(Note: Next Challenge - Year 10 Maths (8th of October 2021)

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Download the answers here - by clicking on the pdf link to see how you went.

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