1. Basic Arithmetic Operations โโ
Tol, foundation ng lahat ng math problems ay ang basic operations. Dapat mabilis ka mag-compute mentally!
Order of Operations (PEMDAS/BODMAS):
Parentheses/Brackets - ( )
Exponents/Orders - powers, roots
Multiplication - ร
Division - รท
Addition - +
Subtraction - โ
Example: 3 + 4 ร 2 = ?
Step 1: 4 ร 2 = 8 (multiplication first)
Step 2: 3 + 8 = 11
Fractions Operations:
| Operation | Rule | Example |
|---|---|---|
| Addition | Same denominator, add numerators | 1/4 + 2/4 = 3/4 |
| Subtraction | Same denominator, subtract numerators | 3/5 - 1/5 = 2/5 |
| Multiplication | Multiply across | 2/3 ร 3/4 = 6/12 = 1/2 |
| Division | Flip and multiply | 2/3 รท 1/2 = 2/3 ร 2/1 = 4/3 |
2. Percentage & Ratio Problems ๐
Essential sa fire damage assessment, budget calculations, at statistical reports!
Percentage Formulas:
Finding Percentage:
Percentage = (Part / Whole) ร 100
If 30 out of 50 houses burned: (30/50) ร 100 = 60%
Finding the Part:
Part = (Percentage ร Whole) / 100
What is 25% of P800,000? = (25 ร 800,000) / 100 = P200,000
Finding the Whole:
Whole = (Part ร 100) / Percentage
If P150,000 is 30% of damage: (150,000 ร 100) / 30 = P500,000
Ratio and Proportion:
Direct Proportion:
As one increases, the other increases
More hoses = More water delivery
Inverse Proportion:
As one increases, the other decreases
More workers = Less time to finish
Cross Multiplication Method:
If 5 firefighters can clear a site in 6 hours,
how long for 10 firefighters?
5 ร 6 = 10 ร x โ 30 = 10x โ x = 3 hours
3. Fire Service Math Applications ๐
Real-world math na ginagamit ng BFP personnel!
Water Flow Calculations (GPM - Gallons Per Minute):
Formula: GPM = 29.7 ร dยฒ ร โP
Where: d = nozzle diameter (inches), P = nozzle pressure (psi)
Example:
Nozzle diameter: 1 inch, Pressure: 100 psi
GPM = 29.7 ร 1ยฒ ร โ100 = 29.7 ร 1 ร 10 = 297 GPM
Friction Loss Calculation:
Formula: FL = C ร Qยฒ ร L
Where: C = coefficient, Q = flow (hundreds of GPM), L = hose length (100ft sections)
| Hose Diameter | Coefficient (C) |
|---|---|
| 1.5 inch | 24 |
| 1.75 inch | 15.5 |
| 2.5 inch | 2 |
| 3 inch | 0.8 |
Fire Damage Assessment:
Structure Value Estimation:
Total Value = Floor Area ร Price per sq.m.
Example: 100 sq.m. ร P25,000 = P2,500,000
Percentage Damage:
Damage Cost = Total Value ร % Damage
If 40% damaged: P2,500,000 ร 0.40 = P1,000,000
4. Distance, Speed & Time Problems ๐
Critical para sa response time calculations at emergency planning!
Basic Formula Triangle:
Distance
D = S ร T
Speed ร Time
Speed
S = D / T
Distance รท Time
Time
T = D / S
Distance รท Speed
Fire Service Applications:
Response Time Problem:
Fire station is 15 km away. Fire truck travels at 60 km/hr.
Response time = 15 รท 60 = 0.25 hours = 15 minutes
Coverage Distance Problem:
If maximum response time is 8 minutes at 45 km/hr speed:
Coverage = 45 ร (8/60) = 45 ร 0.133 = 6 km radius
5. Volume & Area Calculations ๐
Para sa water tank capacity, building floor area, at fire load calculations!
Area Formulas:
| Shape | Formula | Example |
|---|---|---|
| Rectangle | A = L ร W | 10m ร 8m = 80 sq.m. |
| Triangle | A = ยฝ ร b ร h | ยฝ ร 6m ร 4m = 12 sq.m. |
| Circle | A = ฯ ร rยฒ | 3.14 ร 5ยฒ = 78.5 sq.m. |
| Trapezoid | A = ยฝ ร (a+b) ร h | ยฝ ร (4+6) ร 3 = 15 sq.m. |
Volume Formulas (Water Tank Capacity):
Rectangular Tank:
V = L ร W ร H
2m ร 1m ร 1.5m = 3 cubic meters
= 3,000 liters
Cylindrical Tank:
V = ฯ ร rยฒ ร h
3.14 ร 0.5ยฒ ร 2 = 1.57 cubic meters
= 1,570 liters
Conversion: 1 cubic meter = 1,000 liters = 264.17 gallons
6. Number Series & Patterns ๐ข
Common sa aptitude tests - identify ang pattern para malaman ang next number!
Common Pattern Types:
Arithmetic (Add/Subtract constant):
2, 5, 8, 11, 14 (add 3)
20, 17, 14, 11, 8 (subtract 3)
Geometric (Multiply/Divide constant):
2, 6, 18, 54, 162 (multiply by 3)
256, 128, 64, 32, 16 (divide by 2)
Square Numbers:
1, 4, 9, 16, 25 (1ยฒ, 2ยฒ, 3ยฒ, 4ยฒ, 5ยฒ)
Fibonacci-like:
1, 1, 2, 3, 5, 8 (each = sum of previous two)
Alternating Pattern:
2, 5, 4, 7, 6, 9 (alternates +3, -1)
7. Practice Questions ๐
1. A fire truck travels 24 km in 20 minutes. What is its average speed in km/hr?
A) 48 km/hr B) 60 km/hr C) 72 km/hr D) 80 km/hr
View Answer
Answer: C) 72 km/hr
Speed = Distance / Time = 24 km / (20/60) hr = 24 / 0.333 = 72 km/hr
2. A building worth P5,000,000 sustained 35% fire damage. What is the estimated damage cost?
A) P1,500,000 B) P1,750,000 C) P2,000,000 D) P2,250,000
View Answer
Answer: B) P1,750,000
Damage = P5,000,000 ร 0.35 = P1,750,000
3. What is the next number in the series: 3, 6, 12, 24, ___?
A) 36 B) 42 C) 48 D) 30
View Answer
Answer: C) 48
Pattern: Each number is multiplied by 2. 24 ร 2 = 48
4. A rectangular water tank is 3m long, 2m wide, and 1.5m deep. How many liters can it hold?
A) 6,000 L B) 7,500 L C) 9,000 L D) 10,500 L
View Answer
Answer: C) 9,000 L
Volume = 3 ร 2 ร 1.5 = 9 cubic meters = 9,000 liters
5. If 8 firefighters can finish clearing debris in 6 hours, how long will it take 12 firefighters?
A) 3 hours B) 4 hours C) 5 hours D) 9 hours
View Answer
Answer: B) 4 hours
Inverse proportion: 8 ร 6 = 12 ร x โ 48 = 12x โ x = 4 hours
8. Exam Strategy Tips ๐ฏ
- ๐ข Memorize formulas - Distance, percentage, volume are most common
- โฑ๏ธ Practice mental math - Faster calculations = more time for hard problems
- ๐ Show your work - Even mentally, track your steps to avoid errors
- โ Check your units - Make sure answers use correct units (km, liters, hours)
- ๐งฎ Estimate first - Eliminate obviously wrong answers
- ๐ Double-check inversions - More workers = less time (inverse), not more