Level 3: Basics
15%of exam
Level 4: Money and Time
25%of exam
Level 5: Percent and Rates
25%of exam
Level 6: Area and Multi-Step
20%of exam
Level 7: Complex Reasoning
15%of exam
Quick Facts
- Assessment
- Applied Math
- Questions
- 34
- Time
- 55 min
- Levels
- 3 to 7
- Pass
- Level 3 (Bronze)
- Calculator
- Permitted
- Formula sheet
- Provided
- Retake wait
- 30 days
- Part of
- NCRC
PEMDAS
Please Excuse My Dear Aunt Sally
P: parenthesesE: exponentsMD: multiply divideAS: add subtract
Basic Operations
- PEMDAS
- Order of operations
- Multiply fractions
- Tops times bottoms
- Divide fractions
- Flip then multiply
- Add fractions
- Common denominator first
- Decimal add
- Line up decimal points
- Mixed to improper
- Whole times denom plus top
- Fraction to decimal
- Divide top by bottom
- Rounding rule
- Depends on question context
Overtime
Over forty pays one and a half
First 40: regularExtra hours: 1.5xAdd both parts
Gross vs Net Pay
Gross
- Before deductions
- Total earnings
- Rate times hours
Net
- After deductions
- Take-home pay
- Gross minus withholdings
Before vs after deductions
Money and Time
- Regular pay
- Rate times hours
- Overtime pay
- 1.5x beyond 40 hours
- Gross pay
- Before deductions
- Net pay
- After deductions
- Minutes to hours
- Divide minutes by 60
- Elapsed time
- Use 24-hour clock
- Making change
- Count up from price
- Annual pay
- Weekly times 52
Averages
- Mean
- Sum over count
- Required total
- Mean times count
- Missing value
- Total minus known values
- Weighted average
- Weight before dividing
- Median
- Middle sorted value
Convert First
Same units before you calculate anything
Feet and inchesPounds and ouncesHours and minutes
Increase vs Decrease
Increase
- New above original
- Change over original
- Positive change
Decrease
- New below original
- Change over original
- Same base rule
Direction from the change
Operation Picker
- Total of parts→Add(Combine amounts)
- How much left→Subtract(Find difference)
- Equal groups→Multiply(Repeated add)
- Share equally→Divide(Split total)
- Part of whole→Percent(Multiply decimal)
- Two equal ratios→Cross-multiply(Solve proportion)
- Compare sizes→Unit rate(Per one unit)
- Containers needed→Round up(Partial counts)
Percentages
- Percent of
- Multiply percent by whole
- Percent change
- Change over original
- Discount
- Percent off original price
- Markup
- Added onto cost
- Commission
- Rate times sales
- Sales tax
- Added after discount
- Stacked discounts
- Multiply, do not add
- Part of whole
- Part divided by whole
Percent Change
Change divided by the original start
Original is denominatorNever use new valueTimes 100
Direct vs Inverse
Direct
- More gives more
- Ratios stay equal
- Cross-multiply
Inverse
- More gives less
- Product stays equal
- Workers times time
Same ratio vs constant product
US Unit Conversions
- 1 foot
- 12 inches
- 1 yard
- 3 feet
- 1 mile
- 5280 feet
- 1 pound
- 16 ounces
- 1 ton
- 2000 pounds
- 1 gallon
- 4 quarts
- 1 cup
- 8 fluid ounces
Metric and Temperature
- Kilo prefix
- 1000 base units
- Centi prefix
- One hundredth
- Milli prefix
- One thousandth
- 1 kilogram
- About 2.2 pounds
- 1 inch
- 2.54 centimeters
- Fahrenheit to Celsius
- Subtract 32 times 5/9
- Celsius to Fahrenheit
- Times 9/5 add 32
Proportions and Rates
- Cross-multiply
- Solve equal ratios
- Unit rate
- Amount per one unit
- Speed
- Distance over time
- Distance
- Speed times time
- Map scale
- Multiply by scale factor
- Mixing ratio
- Parts of total whole
- Inverse proportion
- More workers, less time
Round Shapes
Square the radius for round shapes
Circle: pi r squaredCylinder: add heightHalve the diameter
Area vs Perimeter
Area
- Inside region
- Square units
- Multiply dimensions
Perimeter
- Boundary length
- Linear units
- Add sides
Inside vs around
Shape and Formula Picker
- Distance around→Perimeter(Add sides)
- Flat region→Area(Square units)
- Space inside 3D→Volume(Cubic units)
- Round area→pi r squared(Use radius)
- Round boundary→pi times diameter(Circumference)
- Triangle region→Half base height(Perpendicular height)
- Box space→L times W times H(Same units)
- Tube space→pi r squared h(Cylinder)
Perimeter and Area
- Rectangle area
- Length times width
- Perimeter
- Add all sides
- Triangle area
- Half base times height
- Circle area
- pi times radius squared
- Circumference
- pi times diameter
- Area units
- Always square units
- Inner border
- Subtract 2W each dimension
Radius vs Diameter
Radius
- Center to edge
- Used in formulas
- Half diameter
Diameter
- Edge to edge
- Across the circle
- Twice radius
Halve before squaring
Volume
- Box volume
- Length width height
- Cylinder volume
- pi radius squared height
- Volume units
- Always cubic units
- How many fit
- Big volume over small
- Radius
- Half the diameter
- Fill capacity
- Volume times unit weight
Using the Formula Sheet
- Formula sheet
- Provided during exam
- No memorizing
- Know when to apply
- Match formula
- Pick then plug in
- Watch units
- Same units first
- Pi value
- Use calculator pi key
- Rearrange formula
- Isolate the unknown
Markup vs Margin
Markup
- Based on cost
- Added to cost
- Larger percent
Margin
- Based on price
- Part of revenue
- Smaller percent
Cost base vs price base
Word Problem Steps
- Start problem→Find the unknown(What is asked)
- Gather data→List givens(Note units)
- Units differ→Convert first(Same unit)
- Setup ready→Choose operation(Match to goal)
- Ready to solve→Use calculator(Avoid mental math)
- Got answer→Check placement(Verify decimal)
Multi-Step Problems
- Dilution
- C1V1 equals C2V2
- Volume pricing
- Compare total tier cost
- Rate of completion
- Fixed total work
- Profit margin
- Profit over revenue
- Combined work
- Add the rates
- Multi-step setup
- Break into ordered steps
Common Traps
Percent change base
Divide by original ≠ Not by new
Overtime hours
1.5x extra hours ≠ Not all hours
Radius vs diameter
Formulas need radius ≠ Given diameter first
Mixed units
Convert then compute ≠ Never mix units
Stacked discounts
Discounts multiply ≠ Not added together
Markup vs margin
Markup on cost ≠ Margin on price
Sales tax order
Tax the sale price ≠ Not the original
Last Minute
- 1.Level 3 earns Bronze NCRC
- 2.Convert units before calculating
- 3.Percent change over original
- 4.Overtime is time-and-a-half
- 5.Circle formulas use the radius
- 6.Volume answers are cubic units
- 7.Round up for containers needed
- 8.Check decimal placement twice
- 9.Read exactly what is asked
- 10.Use the provided formula sheet
- 11.Sales tax follows the discount
- 12.Markup on cost, margin on price
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