Written Test Prep

Area of a Rectangle

Area = Length x Width

Volume of a Box

Volume = Length x Width x Height

Average

Average = (Sum of all items) / (Number of items)

Flow Rate

Total Gallons = Gallons Per Minute (GPM) x Number of Minutes

Finding a Remainder

Amount Left = Starting Amount - Amount Used

1 Gallon of Water weighs?

8.34 pounds

To find a percentage of a number

Part = Whole x (Percentage / 100)

To find what percentage of one number is of another

Percentage = (Part/Whole) x 100

Smart 3 Step Approach to Questions

1. Identify the type of question

2. Identify the priority

3. Select the answer that best matches

Formula for Mechanical Advantage

MA = Output Force/Input Force

Example: if a tool applies 100 lbs of force with only 25 lbs of effort: MA = 100/25 = 4

The tool multiples your force by 4

Lever Mechanical Advantage

MA = Effort Arm Length/Resistance Arm Length

Example: A 6-foot effort arm and a 2-foot load arm:MA =6/2=3

A longer effort arm gives you more leverage

Law of the Lever

F1 x D1 = F2 x D2 (Torque balance on a lever: force x distance from fulcrum)

Example: 30lbs x 3ft = F2 × 1.5ft : 90 = 1.5f2 - f2 = 60

The lever is balanced when torques are equal.

Pulley System MA

MA = Number of Rope Segments Supporting the Load

Example: if 3 ropes support the load, MA = 3

Each added segment reduces the force required.

Inclined Plane MA

MA = Ramp Length/Vertical Height

Example: A 12ft ramp rising 3ft: MA = 12/3 = 4

A longer ramp makes lifting easier, but increases distance

Wheel & Axle MA

MA = Radius of Wheel/Radius of Axle

Example: Wheel = 10in, Axle = 2in - MA = 5

Larger wheel radius = more mechanical advantage

Wedge MA

MA = Length/Thickness

Example: Wedge length = 6in, thickness = 2in, MA = 6/2 = 3

A longer wedge = more cutting force.

Efficiency Formula

Efficiency = (Work Output/Work Input) x 100

Example (80/100) x 100 = 80% efficiency

Some energy is always lost to friction

Water Pressure Conversions

1ft of water = 0.433 psi

psi = Height (ft) / 2.31

Example 100ft = 100/2.31 = 43.3 psi

Gear Direction Rule

• When two gears are connected, they rotate in opposite directions.

• When you add a third gear (called an idler), the first and last gears rotate in the same direction.

• Each additional gear in the train reverses the rotation again.

• Example:

• 2 gears → Opposite

• 3 gears → Same

• 4 gears → Opposite again

• Tip: Just count the number of gear-to-gear contacts:

• Odd number of gears = First and last gears turn the same way

• Even number of gears = First and last gears turn in opposite directions

Gear Ratio Formula

Gear Ratio = Number of Teeth on Driven Gear ÷ Number of Teeth on Driver Gear

📌 Example:
Driven gear = 40 teeth
Driver gear = 20 teeth
Gear Ratio = 40 ÷ 20 = 2:1

What it means:

• The driver gear must turn 2 full rotations to turn the driven gear once.

• A higher gear ratio means more torque, but less speed in the driven gear.

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💡 Definitions:

• Driver Gear: The gear connected to the power source (e.g., motor, crank).

• Driven Gear: The gear receiving power from the driver.

How to Add Fractions

1. Find a common denominator

2. Adjust numerators

3. Add and simplify

   Example: ¼ + 2/3 - 3/12 + 8/12 = 11/12

How to Multiply Fractions

Multiply straight across

Example: 2/3 × 4/5 = 8/15

How to Divide Fractions

Flip the second fraction (reciprocal) and multiply

Example: 3/4 / 2/5 - 3/4 × 5/2 = 15/8

How to Convert a Fraction to Decimal

Divide numerator / denominator

Example: 3 / 4 = 0.75

How to Set Up a Proportion

A/B = C/D - Cross Multiply - A x D = B x C

Use this for scale/rate/volume/recipe problems

How to Solve a Ratio Word Problem

Turn the ratio into a fraction, set equal to unknown, cross - multiply

Example: 3/2 = 6:x - 3x = 12 - x = 4

How to Find a Percentage of a Number

Definition: To calculate a percentage of a given number, follow these steps:

1. Convert the percentage to a decimal: Divide the percentage by 100. For example, 20% becomes 20÷100=0.2020÷100=0.20.

2. Multiply the decimal by the number: Take the decimal value and multiply it by the whole number you are working with.

   Example: To find 20% of 60:

   0.20×60=120.20×60=12

   This method helps you find a proportional 'part' of a larger 'whole'.

Trick for 10% of Any Number

Move the decimal one place left

Example 10% of 250 = 25

Trick for 15% of Any Number

Find 10%, then add half

Example: 15% of 80 = 8 + 4 = 12

Mental Trick: Multiply 5

Multiply by 10, then divide by 2

36 × 5 - 360 / 2 = 180

Mental Trick: Divide by 0.5

Multiply by 2

Example 36 / 0.5 = 72

Mental Trick: Multiply by 25

Multiply by 100, divide by 4

Example 16 × 25 = 1600 / 4 = 400

Trick for Dividing by 5

Multiply by 2, then divide by 10

75 / 5 = (75 × 2) / 10 = 15

Trick for Estimating Decimals

Round to the nearest whole, multiply, and adjust

3.9 × 4.2 = 4 × 4 = 16

How to Estimate a Square Root

To estimate a square root:

1. Identify the number for which you want to find the square root (e.g., 5050​).

2. Find the closest perfect squares that are just below and just above your number.

   • For 5050​, the perfect square below is 72=4972=49 and the perfect square above is 82=6482=64.

3. Determine the range: Since 5050 is between 4949 and 6464, its square root will be between 77 and 88.

4. Estimate based on proximity: Since 5050 is much closer to 4949 than to 6464, the square root will be closer to 77 than to 88. A good estimate for 5050​ would be slightly more than 77, such as 7.077.07 or 7.17.1.

Fraction 1/2

Decimal 0.5

Fraction 1/3

Decimal 0.333

Fraction 1/4

0.25

Fraction 1/5

0.2

Fraction 1/6

0.166

Fraction 1/8

0.125

Fraction 2/3

0.666

Fraction 3/4

0.75

Fraction 3/5

0.6

Fraction 7/8

0.875

Fraction 5/6

0.833

What Traits Are Tested Most?

1. Judgment under stress

2. Emotional control

3. Team-first thinking

4. Respect for authority

5. Commitment to safety

Best Way to Handle Conflict

Stay calm, listen respectfully, and de-escalate the situation, follow protocol.

What If a Coworker Breaks a Rule?

Don’t ignore it. Address directly if safe, or report through chain of command.

What if a Civilian is Panicked or Angry?

Stay calm, speak clearly and simply, don’t argue or escalate.

What If a Senior Gives Unsafe Orders?

Challenge respectfully, prioritize safety, escalate if needed.

Should You Ever Ignore a Minor Rule?

No. Always follow procedures unless they directly endanger someone.

What does torque mean?

Rotational force applied around a pivot point. The farther from the fulcrum, the more torque

How does a wider wedge affect force?

A wider wedge requires more force to penetrate lower MA.

Easy trick to estimate percentage

Round the number + round the percent, then multiply

What is a Cloze Test?

A sentence with a missing word — pick the best-fit word based on context, tone, and grammar.

Common Cloze Traps

Words that look grammatically correct but don’t match tone or meaning

Fancy synonyms that are out of place

How to Use Context Clues

Look for tone words like:

However = contrast

because = cause/effect

also = continuation