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

Who is this challenge for:
Year 10 Mathematics Students (and anyone else up for the challenge!)

Relevant Syllabus Topics: Problem Solving, Right Angled Triangles, Scientific  Notation & Significant Figures, Tree Diagrams & Simultaneous Equations

Next challenge: Year 9 Math Tutoring Challenge coming 8th of November 2021


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Please read the instructions and key information provided carefully.


Sarah and Sammy are two quirky axolotls who are in a local rock band.

They have a music gig coming up this weekend at the Parkway Hotel in Mona Vale and are in a rush to get everything ready.


Sarah is a dark blue axolotl who loves living in the Northern Beaches. Her love of the Northern Beaches was derived from some of her favourite local bands; Lime Cordiale and Ocean Alley. She plays the guitar and likes to mix beats on her laptop. She also gets tutoring for music from Belrose Tutoring Academy in Mona Vale so she can brush up on her knowledge of music theory and history.  


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Figure 1: Sarah  (Artist Impression)

Sammy is a pink axolotl who lives in Belrose, on the leafy side of the Northern Beaches. She is a bubbly axolotl with bold loopy glasses, something that adds to her ‘quirky axolotl’ aesthetic. Since Primary School, Sammy has been receiving Maths & English lessons at BTA. She has always loved creative writing and poetry, as they help her in writing music.  


Sammy first met Sarah at the BTA Careers Night in Forestville RSL, where they both discussed their love of music and wanted to figure out how they would incorporate that into their career.

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Figure 2: Sammy (Artist Impression)
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Figure 3: BTA Mona Vale Beach Sign (Artist Impression)

One evening Sarah and Sammy decided to head down to Mona Vale beach to discuss their upcoming gig. 


They wanted to try to fit their whole debut album into the show but were worried that they won’t have enough time.

The staff at the Parkway Hotel in Mona Vale have told them that their set will last for 45 minutes.  
Let’s help them figure it out! 

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Question 1:


What is the full duration of their album and will it fit within the required time slot at the Parkway Hotel?


Use Figure 4 (Sammy & Sarah's) Album Cover to calculate the duration of the album

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Figure 4: Sammy & Sarah's 'I Love Maths' - Album Cover

Question 2:

Next, the girls need to work out the stage logistics. Although they are a two-person band, they have enough equipment to fill out an entire stage and more. The lovely staff at Parkway have sent them an outline of what the stage looks like, as well as the dimensions.  

Sammy remembers from her Maths tutoring at Belrose Tutoring Academy that to calculate the area of the stage (trapezium), Sammy will have to use Pythagoras theorem to calculate the height.

Question 2:  Using Pythagoras’ theorem, calculate the height of the trapezium and then calculate the area of the trapezium. 

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Figure 5: Sammy's hand drawing of the stage


Pythagoras' Theorem: a² + b² = c²

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Figure 6: Axolotl Celebration + Picnic

Question 3:

Sarah and Sammy have played at heaps of different venues around the Northern Beaches and are building up a pretty solid following.

Question 3: Currently 5218 people have bought tickets. Write this figure in scientific notation, using three significant figures.


To write numbers using scientific notation, place the decimal point after the first non-zero digit then multiply by the power of 10.

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Question 4:

Next, and most importantly, Sammy & Sarah need to plan their outfits. Initially, they were going to wear the ever-stylish BTA Hoodie, however it’s been really hot lately. Sammy has decided to wear a green button-down with denim shorts.


Sarah wants to wear something similar but isn’t certain yet.


Let’s see her options.

Question 4 (A): Create a tree diagram to calculate the total number of outfit choices, if the available options are;

  • Shirt: Green or Purple

  • Jeans: Blue or Black

  • Shoes (Airforces): Red or Yellow

Question 4 (B): What is the probability that Sarah will be wearing her blue jeans? 


Question 4 (C): What is the probability that Sarah will be wearing her blue jeans and red airforces?


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Figure 7: Sarah's Tree Diagram (Outfit Options)
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Rose 1
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Rose 1

Question 5:

Lastly, the girls want to buy some flowers for the stage. They only want one kind of flower but they are unsure about how much it costs.

The Mona Vale Florist is having a deal where you can buy three roses and five daffodils for $25, or four roses and three daffodils for $26.

Question 5: Determine the cost of each type of flower by solving the equations simultaneously

on completing
BTA's Math Tutoring Challenge # 2

(Note: Next Challenge - Year 9 Maths (8th of November 2021)

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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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