This page contains a preview of the tutorials explaining the key mathematical concepts and situations encountered in the book. Each tutorial is accompanied by a graded worksheet with a fully worked solution. To access the tutorials or worksheets, just click on the links under each heading. Clicking on the image will bring you to the tutorial.

A list of mathematical keywords and curriculum items is provided with each topic, along with page numbers in the novel where the topic is subtly covered. Normal font topics are explicitly covered in the tutorial and worksheets, while *italic font* topics can easily be covered by building on top of the existing tutorial and worksheet. If you have a certain curriculum element or keyword that you’re interested in, search the page to find it.

**We currently have:**

**26 animated tutorials and****26 sets of worksheets and worked solutions for these tutorials**

**Only the first three tutorials and worksheets are available for preview** – please consider purchasing an educational license if you would like access to all the resources including unlimited distribution within your school or education centre of the *A Question of Will e-book* and the *Complete School* Math and English package.

The worksheets are Adobe PDF files. To view the PDF files on your computer all you need is the freely available Adobe Reader software, which can be found here.

Contents

- 1 Previewable Tutorials and Worksheets
- 2 Please note the following tutorials and worksheets are only included in the paid product
- 3 Click here to order an educational license
- 3.1 Vectoring
- 3.2 Sales Discount Trickery
- 3.3 Earthquake Nuke Tremors
- 3.4 Timing Gunshot Sounds
- 3.5 Mixing Medical Supplies
- 3.6 Betting Bot
- 3.7 Overloaded Bomb Truck
- 3.8 Mobile Phone Triangulation
- 3.9 Search Grid
- 3.10 Bankroll Management
- 3.11 Fireball Radii
- 3.12 Stair Climbing
- 3.13 Leverage
- 3.14 Medication Dosages
- 3.15 Exploding Laptop Batteries
- 3.16 Door and Bomb Codes
- 3.17 Dirty Bomb Dispersal
- 3.18 Explosives Volume
- 3.19 Swinging Pendulum Escape
- 3.20 Shooting Downhill
- 3.21 Locating the Nuke
- 3.22 Falling Fire Extinguishers
- 3.23 Cracking the Code

# Previewable Tutorials and Worksheets

Each tutorial is a web-page with a mixture of animated graphics and other illustrations. On some older devices (some iOS devices for example), some of the animations may stutter slightly. The animations on this index page have been compressed – the full size animations are available on the individual tutorial pages, accessed by clicking on the animation or the “Click here for the tutorial” link.

## Escape From the Police Station

**Summary: **Will and Besra have some hard jumping choices to make if they are to escape the rampaging terrorists fighting their way up the police building below them.

**Keywords: **Falling, dynamics, velocity, gravity, acceleration

**Tutorial: **Click here for the tutorial

**Online Quiz:** Click here for the online quiz

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 34, pages 236-240

- Estimate lengths (ACMEM018)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Determine positions given acceleration and initial values of position and velocity. (ACMMM135)
- Identify common usage of rates; for example, km/h as a rate to describe speed, beats/minute as a rate to describe pulse (ACMEM014)
*Recognise features of the graph of the general quadratic y=ax2+bx+c. (ACMMM011)**Construct and interpret position-time graphs, with velocity as the slope of the tangent (ACMMM094)*

## Escape the Nuke

**Summary: **Will faces some life and death choices on how to escape the impending nuclear explosion below his feet.

**Keywords: **Time, velocity, assumptions, incomplete information

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 41, pages 293-296

- Calculate the time or costs for a journey from distances estimated from maps (ACMEM087)
- Estimate lengths (ACMEM018)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Determine positions given acceleration and initial values of position and velocity. (ACMMM135)
*Construct and interpret position-time graphs, with velocity as the slope of the tangent (ACMMM094)*

## Car Crash Investigation

**Summary: **Will and Besra discover some alarming mathematical errors in the official police report for the car crash that killed his uncle Jeff.

**Keywords: **CSI, crime scene investigation, friction, velocity, units, mistakes, estimation

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 8, pages 46-49

- Estimate lengths (ACMEM018)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Determine positions given acceleration and initial values of position and velocity. (ACMMM135)
- Identify common usage of rates; for example, km/h as a rate to describe speed, beats/minute as a rate to describe pulse (ACMEM014)
*Tell time to the minute and investigate the relationship between units of time (ACMMG062)*

# Please note the following tutorials and worksheets are only included in the paid product

# Click here to order an educational license

## Vectoring

**Summary: **Drake must calculate the direction for his helicopter that will enable him to intercept Will in the minimum time as he drives the nuke out of the city.

**Keywords: **Geometry, velocity, time

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 39, page 280

- Solve quadratic equations using the quadratic formula and by completing the square (ACMMM008)
- Review sine, cosine and tangent as ratios of side lengths in right-angled triangles (ACMMM028)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Solve problems involving bearings. (ACMEM120)

## Sales Discount Trickery

**Summary: **Will and Besra con a hapless salesperson out of $8000 by turning the store’s own deceptive sales tactics back on him.

**Keywords: **Discounting, percentages, multi-step calculation, finance, sales

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 2, pages 10-16

- Determine the overall change in a quantity following repeated percentage changes; for example, an increase of 10% followed by a decrease of 10% (ACMEM063)
- Calculate a percentage of a given amount (ACMEM011)
- Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)
- Apply percentage increases and decreases in situations; for example, mark-ups, discounts and GST. (ACMEM013)
- Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158)

## Earthquake Nuke Tremors

**Summary: **Will realizes that the Richer scale readings for the bomb tests suggest a much bigger dirty bomb than everyone originally thought.

**Keywords: **Richter scale, logarithmic scale, seismography, earthquakes, decibels, power

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 20, pages 125-128, Chapter 30, pages 210-211

- Interpret and use logarithmic scales such as decibels in acoustics, the Richter Scale for earthquake magnitude, octaves in music, pH in chemistry (ACMMM154)
- Recognise the inverse relationship between logarithms and exponentials… (ACMMM153)
*Identify contexts suitable for modelling by logarithmic functions and use them to solve practical problems. (ACMMM158)**Identify relative frequency as probability (ACMEM152)*

## Timing Gunshot Sounds

**Summary: **Drake and the other surviving member of his team are trapped under sniper fire at the port warehouse. To avoid getting incinerated, they need to fight back, but first they need to estimate how far away the sniper is.

**Keywords: **Distance estimation, speed of sound, speed of light, timing

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 1, pages 4-8

- Recognise and identify outliers (ACMEM047)
- Investigate the effect of individual data values , including outliers, on the mean and median (ACMSP207)
- Compare the time taken to travel a specific distance with various modes of transport (ACMEM082)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Estimate lengths (ACMEM018)
*Explore the variation of means and proportions of random samples drawn from the same population (ACMSP293)*

## Mixing Medical Supplies

**Summary: **Besra has to mix up some radiation medicine in a hurry but if he gets the mixture concentration wrong he’ll blow themselves up.

**Keywords: **Mixtures, liquids, dilution, concentration, percentages, fractions

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 27, page 180, Chapter 29, page 188

- Calculate a percentage of a given amount (ACMEM011)
- Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)
- Use formulas to find the volume of pyramids and spheres. (ACMEM104)
- Recognise and solve problems involving simple ratios (ACMNA173)
- Solve a pair of simultaneous linear equations, using technology when appropriate (ACMGM044)
*Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)*

## Betting Bot

**Summary: **Will and Besra use their computer bots to earn $100,000 in a night by searching online sports gambling sites for arbitrage opportunities.

**Keywords: **Gambling, finances, probability, statistics

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 14, page 87, Chapter 15, pages 91 – 94

- Describe ways of expressing probabilities formally using fractions, decimals, ratios, and percentages. (ACMEM149)
- Solve problems involving profit and loss, with and without digital technologies (ACMNA189)
- Solve a pair of simultaneous linear equations, using technology when appropriate (ACMGM044)
*Review probability as a measure of ‘the likelihood of occurrence’ of an event (ACMMM052)**Interpret commonly used probability statements, including ‘possible’, ‘probable’, ‘likely’, ‘certain’ (ACMEM148)*

## Overloaded Bomb Truck

**Summary: **Drake and Ronnie attempt to estimate the weight of the load in the back of a terrorist truck caught on video surveillance.

**Keywords: **Spring constant, estimation, weight

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 9, pages 53-54

- Review metric units of mass (and weight), their abbreviations, conversions between them, and appropriate choices of units (ACMEM098)
- Review metric units of volume, their abbreviations, conversions between them, and appropriate choices of units (ACMEM101)
- Solve problems involving linear equations, including those derived from formulas (ACMNA235)
- Estimate lengths (ACMEM018)

## Mobile Phone Triangulation

**Summary: **Ronnie and Drake try to track down the location of a policeman who might be the traitor.

**Keywords: **Triangulation, circle geometry

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 11, pages 65-66

- Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area (ACMMG197)
- Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)
- Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)
*Compare the time taken to travel a specific distance with various modes of transport (ACMEM082)*

## Search Grid

**Summary: **Will and Besra are in the unfinished rooftop garden at the top of the Skyfeller centre, trying desperately to find where the nuke has been buried.

**Keywords: **CSI, search grid, area, time

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 38, pages 264-266

- Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)
- Calculate the areas of composite shapes (ACMMG216)
- Estimate lengths (ACMEM018)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)
*Create and interpret simple grid maps to show position and pathways (ACMMG065)*

## Bankroll Management

**Summary: **Will, Besra and Drake need to get as much starting capital as they can before they let their gambling bots loose, to give them the best chance of making the $100,000 and not going bust if they have a long run of “bad luck”.

**Keywords: **Probability, statistics, likelihood, finance, gambler’s ruin, capital, repeated trials

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 14, pages 87-88, Chapter 14 page 90

- Recognise the mean or expected value of a discrete random variable as a measurement of centre, and evaluate it in simple cases (ACMMM140)
- Determine the probabilities associated with simple games (ACMEM157)
- Identify relative frequency as probability (ACMEM152)
- Identify factors that could complicate the simulation of real-world events (ACMEM153)
*Understand the concepts of a discrete random variable and its associated probability function, and their use in modelling data (ACMMM136)**Recognise uniform discrete random variables and use them to model random phenomena with equally likely outcomes (ACMMM138)*

## Fireball Radii

**Summary: **Will and Besra desperately need to stash the nuke somewhere far enough underground to contain the explosion – but how big will the fireball be?

**Keywords: **Size estimation, cube root scaling

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 21, page 131, Chapter 23, page 143, Chapter 38, pages 269-270

- Review indices (including fractional indices) and the index laws (ACMMM061)
- Use radicals and convert to and from fractional indices (ACMMM062)
- Estimate lengths (ACMEM018)
- Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)
*Creating scale drawings: understand and apply drawing conventions of scale drawings, such as scales in ratio, clear indications of dimensions, and clear labelling (ACMEM111)*

## Stair Climbing

**Summary: **The terrorists are running up the stairs to attack Will and Besra on the rooftop garden of the Skyfeller building. Will and Besra must calculate how long they have to defuse the bomb or get it out of there before the terrorists reach the roof and attack.

**Keywords: **Estimation, velocity, time

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 37, page 261

- Estimate lengths (ACMEM018)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Compare the time taken to travel a specific distance with various modes of transport (ACMEM082)
- Find the ratio of two quantities (ACMEM068)
*Tell time to the minute and investigate the relationship between units of time (ACMMG062)*

## Leverage

**Summary: **Will and Besra are trying to lift a nuke out of the hole it was buried in at the top of the Skyfeller building. Problem is, it’s much heavier than they are.

**Keywords: **Lever arm, weight, ratios

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 38, pages 268 – 269

- Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)
- Estimate lengths (ACMEM018)
- Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

## Medication Dosages

**Summary: **

**Keywords: **Dosage scaling, body weight, ratios

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 36, page249

- Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)
- Recognise the need for milligrams (ACMEM099)

## Exploding Laptop Batteries

**Summary: **In desperation, Will devises an impromptu defensive weapon from a laptop battery as the terrorists attack him, Drake, Besra and Melissa at his uncle’s house.

**Keywords: **Energy density, rates of change

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 23, pages 147 – 148

- Use units of energy to describe consumption of electricity, such as kilowatt hours (ACMEM031)
- Find the ratio of two quantities (ACMEM068)
*Convert from one unit of energy to another. (ACMEM034)*

## Door and Bomb Codes

**Summary: **The boys encounter several code-breaking situations in the book, either in passing or in a critical life and death situation. How long would it take them to crack each code using a brute force approach?

**Keywords: **Combinations, codes, cryptography, code cracking

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 3, pages 20, Chapter 29, page 192

- solve problems involving permutations (ACMSM001)
- solve problems involving permutations and restrictions with or without repeated objects. (ACMSM004)
*understand the notion of a combination as an unordered set of objects taken from a set of distinct objects (ACMMM044)*

## Dirty Bomb Dispersal

**Summary: **Tipped off that they might be dealing with a dirty radioactive bomb, Will and Drake have tracked down a professor at the local university who is an expert in terrorism. He explains that there is a trade-off when building a dirty bomb. If you build a bomb with a large amount of explosive, it will spread the radioactive material over a large area, but the concentration will be less – so the lethality from the radiation will be less severe. A smaller bomb will spread the material over a smaller area – not affecting as many people, but being much more serious for the ones it does.

**Keywords: **Radiation, density, area, square law

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 21, pages 130-132

- Investigate the relationship between features of circles such as

circumference, area, radius and diameter. Use formulas to solve

problems involving circumference and area (ACMMG197) - Recognise and solve problems involving simple ratios (ACMNA173)
- complete calculations with rates, including solving problems involving direct proportion in terms of rate. (ACMEM073)

## Explosives Volume

**Summary: **As Will, Besra and Drake desperately try to track down the dirty bomb, they need every piece of information they can get to find it. The size of the bomb the terrorists have built will determine where they can hide it and how they can transport it. A very small bomb might fit in a backpack. A larger one might fit in a car or van. A larger one again in a truck. And the actual dirty bomb in the book is crammed into 5 massive shipping containers.

**Keywords: **Radiation, density, area, square law

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 21, page 132, Chapter 26 page 170

- Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)
- Estimate volume and capacity of various objects (ACMEM029)
- Use formulas to find the volume and capacity of regular objects such as cubes, rectangular and triangular prisms and cylinders (ACMEM103)
- Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)
- Calculate perimeters of familiar shapes, including triangles, squares, rectangles, polygons, circles, arc lengths, and composites of these. (ACMEM091)
*Connect volume and capacity and their units of measurement (ACMMG138)*

## Swinging Pendulum Escape

**Summary: **Will is on a one way ride to the top of the mountain, holding on grimly to primitive lift rope pulling him up through the dark shaft. Hundreds of metres below him is a furious Danial and a nuke only minutes from exploding. In the seconds remaining he must work out how to avoid shooting up into the air at the surface only to fall back down to his death down the mine shaft.

**Keywords: **Velocity, pendulum motion, acceleration

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 40, pages 291 – 292

- Complete calculations with rates, including solving problems involving direct proportion in terms of rate. (ACMEM073)
- Determine positions given acceleration and initial values of position and velocity. (ACMMM135)
- Apply the cosine and sine ratios to find unknown angles and sides in right-angled triangles (ACMEM119)

## Shooting Downhill

**Summary: **After Drake, Will and Besra attack the construction site where the dirty bomb is hidden, they think they have cleared the area of bad guys. Unbeknownst to them, there is one bad guy left high up on a building overlooking the construction site, rifle in hand. He lines up the shot on Drake’s head and estimates the distance to his target so he can compensate with the scope. However, he forgets to take into account the fact that he is shooting downwards, rather than in a horizontal direction… and instead of hitting Drake squarely in the head, he only just nicks the top of his head. Why did the bullet go higher?

**Keywords: **Ballistics, velocity, gravity, geometry, trigonometry

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 28, pages 181 – 182

- Compare the time taken to travel a specific distance with various modes of transport (ACMEM082)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)
- Find and use the inverse trigonometric functions: arcsine, arccosine and arctangent (ACMSM119)
- Determine positions given acceleration and initial values of position and velocity. (ACMMM135)
*Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)*

## Locating the Nuke

**Summary: **Will, Besra and Drake take a number of radiation readings around a circular path in the city in order to try and locate the dirty bomb. When they examine the readings, they quickly see that the readings are much stronger on one side than the other. The radiation source they’re detecting is closer to the strongest readings and furtherest from the weakest readings.

To work out the dirty bomb’s location, they draw a line across the circle from the weakest readings towards the strongest readings and then beyond. They reason that the dirty bomb must lie somewhere along this line.

It’s only many hours later that Will realizes they may have missed something very critical – a second bomb!

**Keywords: **multiple readings, inverse square law

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 25, pages 162 – 164, Chapter 35 pages 242 – 244

- Examine examples of inverse proportion (ACMMM012)
- Solve quadratic equations using the quadratic formula and by completing the square (ACMMM008)
*Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (ACMNA214)*

## Falling Fire Extinguishers

**Summary: **At the construction site, the sniper is crawling towards the detonator for the massive 100 tonne dirty bomb. If Will doesn’t stop him, Drake, Besra, and a large chunk of Brisbane will get sprayed in fatal radiation, killing thousands. After the gunman refuses to surrender, Will is forced to try and stop him by dropping a fire extinguisher on him. The sniper’s a moving target however and he’s 7 stories below Will, so aiming will be critical…

**Keywords: **Gravity, sideways versus vertical velocity, fall duration, estimation

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 28, pages 183 – 186

- Determine positions given acceleration and initial values of position and velocity. (ACMMM135)
- Estimate lengths (ACMEM018)
- Solve quadratic equations using the quadratic formula and by completing the square (ACMMM008)
- Calculate speed, distance or time using the formula speed = distance/time (ACMEM086)

## Cracking the Code

**Summary: **After Drake, Will, Melissa and Besra repel the terrorist attack at Jeff’s house, they find a scrap of paper with what looks to be a code written on it in one of the terrorist’s pockets. They try a variety of techniques to crack it. Let’s see which one works.

**Keywords: **Codes, cryptography, frequency-based code cracking, ciphers

**Tutorial: **Click here for the tutorial

**Worksheets and Solutions:** Worksheet 1 | Solution 1

**Novel References:** Chapter 24, pages 154 – 157, Chapter 26, pages 167 – 168

- Identify relative frequency as probability (ACMEM152)
- Identify the mode (ACMEM049)
*Construct two-way frequency tables and determine the associated row and column sums and percentages (ACMGM049)**Recognise and identify outliers (ACMEM047)**Use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association (ACMGM050)*