Instructions
- Read each tactical briefing carefully to understand the lore-based scenario.
- Apply your mathematical skills (fractions, percentages, probability, and geometry) to solve the problems faced by the commanders of the 41st Millennium.
- Show your working in the spaces provided to ensure the Tech-Priests can verify your logic.
- Complete the tables following the example provided in the first row.
- If you finish early, attempt the Chrono-Glitch Challenge at the end.
Task 1: The Imperial Tithe (Fractions & Percentages)
The Departmento Munitorum requires a levy of soldiers from the Hive World of Armageddon. The total draft is 1,200,000 citizens. Use your knowledge of fractions and percentages to categorize the new recruits.
| Recruit Type | Fraction/Percentage of Total | Number of Soldiers |
|---|---|---|
| Frontline Infantry | 1/2 (Example) | 600,000 |
| Armored Division | 1/4 | |
| Scout Auxiliaries | 15% | |
| Logistics & Support | 1/10 | |
| Sanctioned Psykers | 0.5% | |
| Penal Legion | (Remaining amount) |
Calculation Space:
Task 2: Tactical Probability (Dice & Ratios)
In the grim darkness of the far future, outcome is often decided by the roll of a six-sided die (D6). A Space Marine Intercessor has a Ballistic Skill (BS) of 3+, meaning they hit their target if they roll a 3, 4, 5, or 6.
-
What is the probability (as a fraction) of a single Space Marine hitting their target? Answer: __
-
If a squad of 10 Space Marines all fire their bolt rifles once, statistically, how many are expected to hit? Answer: __
-
An Ork Boy has a Ballistic Skill of 5+. What is the percentage chance that an Ork hit its target with a single shot? (Round to one decimal place). Answer: __
-
Comparison: In a shootout, a Space Marine is how many times more likely to hit than an Ork? (Express as a ratio or decimal). Answer: __
Task 3: The Emperor’s Architecture (Area and Perimeter)
A Tech-Priest is designing a reinforced Ferro-crete landing pad for a Valkyrie transport ship. The pad must be rectangular to fit within the Bastion's walls.
- Length: 45 meters
- Width: 30 meters
- Safety Border: A 2-meter wide strip of hazard stripes must be painted around the entire outer edge (inside the perimeter).
-
Calculate the Total Area of the landing pad. Answer: __
-
Calculate the Perimeter of the landing pad. Answer: __
-
If one canister of "Martian Red" paint covers 50 square meters, how many canisters are needed to paint the entire pad (excluding the hazard border)? Answer: __
Task 4: Logistic Engine (Algebraic Thinking)
The Adeptus Mechanicus uses a specific formula to calculate the fuel needed for a Leman Russ Battle Tank.
Formula: $F = (D \times 12) + 50$ (Where F is Fuel in Liters and D is Distance in Kilometers)
Calculate the fuel requirements for the following missions:
| Mission Objective | Distance (D) | Fuel Required (F) |
|---|---|---|
| Patrol Perimeter | 10 km (Example) | 170 Liters |
| Secure the Fuel Depot | 25 km | |
| Flanking Maneuver | 42 km | |
| Long Range Recon | 105 km | |
| Siege of the Hive City | 5 km | |
| Search and Destroy | 68 km |
Task 5: Chrono-Glitch Challenge (Extension)
Traveling through the Warp causes time dilation. A ship enters the Warp and travels for 3 weeks according to the ship's clock. However, when they emerge in real-space, 12 years have passed on their home planet.
-
How many days did the crew experience? Answer: __
-
How many days passed on the home planet? (Assume 365 days per year). Answer: __
-
What is the ratio of Ship Time to Planet Time? (Simplify the ratio). Answer: __
Answer Key
Task 1: The Imperial Tithe
- Armored Division: 300,000
- Scout Auxiliaries: 180,000
- Logistics: 120,000
- Sanctioned Psykers: 6,000
- Penal Legion: (1,200,000 - 600,000 - 300,000 - 180,000 - 120,000 - 6,000) = 0 (All accounted for, actually the Penal Legion is 0 in this specific calculation, or if the student calculates 1/10 + 15% + 1/4 + 1/2 + 0.5% = 100.5%, they may note the Tithe is over-subscribed! Standard subtraction from 1.2m leads to 0 or negative depending on rounding).
Task 2: Tactical Probability
- 4/6 or 2/3
- 6.66 (Accept 6 or 7)
- 33.3% (2 out of 6)
- 2:1 (Space Marine hits on 4/6, Ork on 2/6)
Task 3: The Emperor’s Architecture
- 1,350 m²
- 150 m
- Area of interior = (41 x 26) = 1,066 m². 1,066 / 50 = 21.32. Needed: 22 canisters.
Task 4: Logistic Engine
- 25km: 350L
- 42km: 554L
- 105km: 1,310L
- 5km: 110L
- 68km: 866L
Task 5: Chrono-Glitch
- 21 days
- 4,380 days
- 21 : 4,380 which simplifies to 7 : 1,460 or approx 1 : 208.5