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

Who is this challenge for:
Our Year 9 Mathematics Students (and anyone else up for the challenge!)

Relevant Syllabus Topics: 

Year 9 Maths (Profits & Discounts, Percentage Increase & Decrease, Circumference and perimeter of Sectors & Pythagoras' Theorem)



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Please read the instructions and key information provided carefully.


Tina is a funky green axolotl who lives on Mona Vale beach. She’s a Northern Beaches local who has been receiving maths and English tutoring at BTA for two years! Her typical morning is going for a surf, buying a coffee from Armchair Collective - Mona Vale and walking to the Academy.   

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Figure 1: Tina at the BTA Mona Vale Office

Tina is super excited to go to the annual Belrose Tutoring Academy Carnival today! The carnival is located on Kitchener Park in Mona Vale and is run by the BTA axolotls.  

As Tina arrives at the carnival, she can smell the cotton candy and hear the screams from the rollercoaster. There is so much to see and do! 

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Question 1:


Tickets to the carnival are $20 per person, however, Tina is a BTA student, so she gets a 30% discount. How much will Tina pay for entry?  

Question 2:


There are approximately 200 axolotls at the carnival. A random sample of 50 axolotls found that 35 of them receive weekly maths tutoring in Mona Vale. Based on this, how many axolotls at the carnival receive weekly maths tutoring in Mona Vale?  


Assume that there are 200 axolotls in attendance at the carnival.

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Question 3:

Upon queuing up for her turn on the Ferris wheel, Tina is astounded by how large and colourful the Ferris Wheel is. From the top of the Ferris Wheel, you can see all of Mona Vale. At the entrance to the ride, Tina sees a sign that says the radius of this wheel is 7m!

Question 3:

a) Calculate the circumference of the Ferris Wheel to the nearest metre.  

b) Calculate the area of the Ferris Wheel to the nearest metre squared.  

BTA - Ferris Wheel; Mona Vale


Circumference = 2𝝅r

Area = 𝝅𝒓²

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Figure 2: Sherry is excited that Tina is using her maths tutoring knowledge from BTA

Question 4:

While waiting in line, Tina bumps into her friendly BTA maths tutor, Sherry. Sherry is trying to figure out how many times the Ferris Wheel turns per hour. Tina and Sherry decide to see how long it takes for the wheel make the full revolution, and realise it takes one minute and thirty seconds.  

Question 4: Find out how any times the Ferris Wheel will turn (complete a revolution) in one hour?

Question 5:

Next, Tina heads towards the big Tutor Tower. Last year, Tina didn’t go on this ride because she’s scared of heights, but this year she wants to challenge herself. The axolotl who runs this ride hands her a brochure with an incomplete diagram of the Tutor Tower. She remembers from her weekly maths tutoring with Sherry on how to find the height of the tower! 

Question 5: Use the diagram to calculate the height of the Tutor Tower to one decimal place.  


Formula: 𝒂²+𝒃²=𝒄²

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Tutor Tower - Mona Vale; BTA
Figure 3: Artist Impression of Tutor Tower
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As Tina’s going up on the Tutor Tower, she can see hundreds of BTA axolotls on the ground enjoying the carnival. Before she knows it, she’s back down on the ground with all her other BTA Axolotl pals.

She feels proud of herself for facing her fear of heights! 

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on completing
BTA's Math Tutoring Challenge # 3

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

Looking for some maths tutoring?
BTA has local math tutors near you.
BTA is equipped with tutoring academies in Belrose, Forestville, Mona Vale and a range of online services.

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