1. Basic Arithmetic Operations ➕➖✖️➗

Foundation ng lahat ng math problems. Dapat mabilis at accurate!

Order of Operations (PEMDAS/BODMAS):

Parentheses / Brackets - First

Exponents / Orders - Second

Multiplication & Division - Left to right

Addition & Subtraction - Left to right

Example:

5 + 3 × 2 = ?

❌ Wrong: 16 (adding first)

✅ Correct: 11 (multiply first)

2. Fractions, Decimals & Percentages 📊

Conversion between these is crucial for police statistics!

Fraction

1/4

Decimal

0.25

Percentage

25%

🔄 Conversion Formulas:

• Fraction → Decimal: Divide numerator by denominator
• Decimal → Percentage: Multiply by 100
• Percentage → Decimal: Divide by 100
• Percentage → Fraction: Put over 100, simplify

📈 Percentage Problems:

Finding Percentage:

What is 15% of 200? → 0.15 × 200 = 30

Finding the Whole:

30 is 15% of what? → 30 ÷ 0.15 = 200

Finding the Rate:

30 is what percent of 200? → (30 ÷ 200) × 100 = 15%

3. Distance, Speed, Time: The Police Triangle 🚓

Tol, pursuit situations require quick calculations!

The DST Triangle

Distance

D = S × T

Speed

S = D ÷ T

Time

T = D ÷ S

🚔 Police Scenario Examples:

Example 1:

A patrol car travels 120 km in 2 hours. What is the average speed?

S = D ÷ T = 120 ÷ 2 = 60 km/h

Example 2:

A suspect is running at 15 km/h. How far will he go in 20 minutes?

D = S × T = 15 × (20/60) = 15 × 0.33 = 5 km

Example 3:

Reinforcement is 30 km away, traveling at 60 km/h. ETA?

T = D ÷ S = 30 ÷ 60 = 0.5 hours = 30 minutes

4. Ratio and Proportion 📐

Para sa resource allocation, manpower distribution, at statistics!

Ratio:

Comparison of two quantities

Example: Police-to-population ratio

50 police : 10,000 people = 1:200

Proportion:

Equality of two ratios

a/b = c/d

Cross multiply: a × d = b × c

🎯 Practice Problem:

If 3 police officers can patrol 12 blocks, how many officers are needed for 28 blocks?

Solution

3/12 = x/28

12x = 3 × 28

12x = 84

x = 84 ÷ 12 = 7 officers

5. Crime Statistics & Data Interpretation 📊

Tol, numbers tell the story of crime trends!

Key Statistical Measures:

Mean (Average)

Sum of all values ÷ Number of values

Example: Average crimes per month

Median

Middle value when arranged in order

Example: Middle age of offenders

Mode

Most frequently occurring value

Example: Most common crime type

Range

Highest value - Lowest value

Example: Spread of response times

📈 Crime Rate Formula:

Crime Rate = (Number of Crimes ÷ Population) × 100,000

Example:

500 crimes in a city of 250,000 people

Rate = (500 ÷ 250,000) × 100,000 = 200 per 100,000

6. Work & Time Problems ⏰

Para sa task completion at resource planning!

Work Rate Formula:

Work = Rate × Time

Rate = 1/Time to complete the job

Example:

Officer A can complete a report in 3 hours.

Officer B can complete it in 6 hours.

How long if they work together?

Rate A = 1/3, Rate B = 1/6

Combined Rate = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

Time = 1 ÷ (1/2) = 2 hours

7. Age Problems 👤

Classic sa exams - mga computation ng edad!

🎯 Age Problem Tips:

• Let x = present age (usually)
• "Years ago" means subtract
• "Years from now" means add
• Set up equation based on relationship

Example:

Juan is 3 times as old as Pedro. In 10 years, Juan will be twice as old.

How old is Pedro now?

Solution

Let Pedro's age = x, Juan's age = 3x

In 10 years: 3x + 10 = 2(x + 10)

3x + 10 = 2x + 20

x = 10

Pedro is 10 years old