Stage 4 NSW Maths Worksheet for 11-Year-Olds: Warhammer Theme, Probability and Statistics

Instructions

1. Read the lore snippets provided in each section to understand the tactical situation.
2. Apply your mathematical knowledge to solve the problems faced by the commanders of the 41st Millennium.
3. Use the space provided to show your working out for full credit.
4. Complete the tables by following the pattern shown in the first example row.
5. If you finish early, attempt the Challenging Chrono-Gladiator question at the end.

Section 1: The Logistics of the Astra Militarum (Ratios)

In the Imperial Guard, maintaining the correct ratio of resources to soldiers is the difference between victory and being overrun by Tyranids. Simplify the following ratios to their lowest terms to ensure the Quartermaster's records are accurate.

Section 2: Forge World Production (Percentages)

The Adeptus Mechanicus on Mars is mass-producing Bolters for the Ultramarines. However, the machine spirits are restless, and some weapons are failing inspection. Calculate the number of functional weapons for each batch.

Section 3: Tactical Movement (Rates and Speed)

A Hive Fleet is descending on a civilian settlement. You must calculate how long it will take for Imperial reinforcements to arrive. Use the formula: Time = Distance ÷ Speed.

1. A squad of Assault Intercessors is moving at a speed of 12km/h. They need to reach a bunker 3km away. How many minutes will it take them to arrive? Working Out:

2. An Ork Warbike is racing toward your lines at 60km/h. It is currently 5km away. How many minutes do your heavy weapons teams have to lock onto the target before it reaches your trench? Working Out:

Section 4: The Emperor's Will (Probability)

In the tabletop game of Warhammer 40,000, outcomes are determined by 6-sided dice (D6). Calculate the probability of the following events occurring. Express your answer as a fraction and a percentage (rounded to one decimal place).

1. A Space Marine needs to roll a 4, 5, or 6 to hit an Ork Boy with his Bolter. What is the probability of a successful hit? Fraction: Percentage:

2. A Terminator is wearing Tactical Dreadnought Armor, giving him a 2+ Save. This means he avoids damage on a roll of 2, 3, 4, 5, or 6. What is the probability he survives the shot? Fraction: Percentage:

3. A Librarian attempts to manifest a psychic power. He must roll a double 6 on two dice. What is the probability of rolling a double 6? Fraction: Percentage:

Section 5: Tactical Map Analysis

You are looking at a map of a Hive City. The scale of the map is 1:50,000.

1. On the map, the distance between the Emperor's Spire and the Power Generator is 8cm. What is the actual distance in kilometers? Working Out:

2. A group of scouts identifies a Tyranid bio-organism 4km away from their position. How many centimeters away would this appear on your 1:50,000 scale map? Working Out:

Section 6: Challenge Question (The Golden Throne)

The Golden Throne has functioned for 10,000 years. If it fails by 0.001% every year, and it started at 100% efficiency, calculate its current efficiency after 10,000 years using simple interest logic (0.001% of the original 100% per year).

Working Out:

Answer Key

Section 1: Ratios

• Chainswords: 3 : 1
• Rations: 3 : 1
• Chimera: 1 : 3
• Commissars: 1 : 20
• Vox-casters: 1 : 3

Section 2: Percentages

• Gamma: 450 functional
• Delta: 90 functional
• Epsilon: 680 functional
• Zeta: 1,470 functional

Section 3: Movement

1. 15 minutes (3 / 12 = 0.25 hours)
2. 5 minutes (5 / 60 = 1/12 hour)

Section 4: Probability

1. 3/6 (1/2) | 50%
2. 5/6 | 83.3%
3. 1/36 | 2.8%

Section 5: Map Analysis

1. 4km (8cm x 50,000 = 400,000cm = 4,000m = 4km)
2. 8cm (4,000m = 400,000cm. 400,000 / 50,000 = 8)

Section 6: Challenge

• 0.001% of 100 = 0.001.
• 0.001 x 10,000 years = 10% total loss.
• 100% - 10% = 90% efficiency remaining.