Data Tables and Charts
Not publishedof exam
Table AnalysisBar Chart ReadingDual Axis TrapsPie Chart AnglesCasework Output
Percentages and Growth Rates
Not publishedof exam
Percentage ChangeReverse PercentagesCompound MultipliersIndex NumbersPercentage Points
Ratios and Averages
Not publishedof exam
Part to WholeUnitary MethodWeighted AveragesWork Rate FormulasInverse Proportions
Financial and Currency Math
Not publishedof exam
VAT ExtractionCurrency SpreadBudget VarianceFTE StaffingPer Capita Rates
Quick Facts
- Administrator
- PAS publicjobs
- Target Grades
- CO EO AO HEO
- Question Volume
- Competition-specific; check candidate booklet
- Time Allowance
- Competition-specific; check assessment instructions
- Pass Standard
- Competition-specific qualifying standards
- Attempt Scope
- Follow campaign assessment rules
- Assessment Format
- Format specified by competition
- Permitted Aids
- Specified in campaign booklet
PACE Numerical Assessment Strategy
Pinpoint Ask Calculate and Eliminate
Pinpoint units and footnote contextAsk what target requiresCalculate using round estimatesEliminate distant options fast
Order of Merit vs Appointment Panel
Order of Merit
- Stage test score ranking
- Dictates batch test invitations
- Not a final job offer
Appointment Panel
- Formed after final stages
- Vacancies drawn in order
- Subject to campaign expiry
Panel follows required final stages
Chart Interpretation and Casework Strategy
- Reading stacked bar charts→Subtract boundary levels(Measure segment height only)
- Reading dual axis lines→Verify axis assignments(Not proof of numerical equality)
- Converting pie slice degrees→Divide angle by 360(Multiply by total pool)
- Information missing from table→Select cannot say option(Denominator is missing)
- Converting foreign currency invoice→Match operation to quoted units(FC/EUR divide; EUR/FC multiply)
- Purchasing foreign currency cash→Apply bank sell rate(Check currency named in table)
- Calculating staff capacity need→(Cases × hours/case)/(hours/FTE)(Convert part time FTE)
- Two workers clearing backlog→Product over sum formula(Result faster than either)
- Multiple choice options distant→Order of magnitude estimation(Eliminate distant options fast)
Table and Chart Reading Rules
- Table Headers
- Check unit multipliers firstSetup
- Footnote Modifiers
- Verify exclusions and exceptionsCaution
- Stacked Bar Value
- Top boundary minus bottom boundaryFormula
- Dual Axis Curve
- Trace curve to designated axisRule
- Pie Chart Angle
- Degrees divided by 360Formula
- Histogram Caseload
- Sum frequencies across target binsDensity × width gives frequency
- Multi Table Audit
- Match reporting years across tablesCheck
PAS Assessment Protocol and Pacing
- Pacing Target Seconds
- Total seconds divided by questionsCompetition-specific pace
- Order of Merit Ranking
- Batch ranking for stage progressionOOM
- Final Appointment Panel
- Merit list for departmental vacanciesPanel
- Marking Penalties
- Check competition instructions before guessingStrategy
- Cannot Say Rule
- Essential data or definitions missingLogic
- Order of Magnitude Check
- Round numbers to one digitCheck bounds before exclusion
- Last Digit Elimination
- Multiply end digits of numbersSpeed
GROW Percentage Change Method
Gap Relative to Original Whole
Gap between both figuresRelative arithmetic percentage differenceOriginal value in denominatorWhole multiplied by 100
Percentage Points vs Percent Change
Percentage Points
- Simple arithmetic difference
- Absolute spread between percentages
- Formula is new minus old
Percentage Change
- Relative proportional rate shift
- Scales against starting baseline
- Divide difference by original
Points subtract rates directly
Numerical Calculation Method Picker
- Finding growth over time→Percentage change formula(Divide by original value)
- Gross invoice includes23% VAT→Reverse percentage method(Divide gross by 1.23)
- Comparing two published rates→Percentage points subtraction(Direct arithmetic difference)
- Compounding multiple year rates→Sequential decimal multipliers(Multiply one plus rates)
- Comparing index to baseline→Index minus 100(Base period equals 100)
- Comparing two nonbase indices→Index difference over baseline(Treat first index baseline)
- Adjusting spend for inflation→Price deflator division(Nominal / base-100 index ×100)
- Allocating funds across ratios→Unitary part method(Divide total by parts)
- Blending unequal departmental groups→Weighted average formula(Weight times group values)
Core Percentage Formulas
- Percentage Change
- Difference divided by original baselineFormula
- Baseline Denominator
- Always divide by initial valueTrap
- Reverse Percentage
- Final value divided by multiplierFormula
- Compound Increase
- Multiply by 1 plus rateGrowth
- Compound Decrease
- Multiply by 1 minus rateDecline
- Successive Multipliers
- Multiply successive (1±r) factorsChain
- Ten Percent Mental
- Move decimal one position leftSpeed
BASE Index Number Calculations
Benchmark At Standard Equals 100
Benchmark year equals 100Adjust current over baselineScale by 100 pointsEvaluate percentage shift accurately
Percentage Points and Index Numbers
- Percentage Points
- Absolute arithmetic difference between ratesMetric
- Relative Percent Change
- Proportional shift of rate itselfMetric
- Base Period Index
- Standardized reference set to 100Base 100
- Current Period Index
- Current over base times 100Formula
- Index Percent Change
- Index change over original indexFormula
- Index Rebasing
- Old index / new-base index ×100Series
- Price Deflator Formula
- Nominal / base-100 index ×100Real Value
RATE Casework Staffing Calculations
Required Aggregate Time Divided by Effort
Required workload total volumeAggregate hours across casesTime windows in daysEffort capacity per officer
Part to Part vs Part to Whole
Part to Part Ratio
- Compares subgroup against subgroup
- Compare one group against the other
- Example four to sixteen
Part to Whole Fraction
- Compares subgroup against total
- Denominator sums both groups
- Example four over twenty
Whole includes all subgroup parts
Ratios and Proportions Reference
- Unitary Method Sum
- Add all ratio parts togetherStep 1
- One Part Value
- Total sum divided by partsStep 2
- Part to Whole Ratio
- Subset divided by combined totalFraction
- Part to Part Ratio
- Direct comparison of two subgroupsContrast
- Cross Multiplication
- Product of extremes equals meansDirect
- Inverse Proportion
- Product of variables remains constantConstant
- Harmonized Three Ratios
- Scale common term with LCMMethod
Direct vs Inverse Proportion
Direct Proportion
- Variables move together identically
- Ratio quotient stays constant
- Cross multiplication holds true
Inverse Proportion
- More workers take fewer days
- Variable product stays constant
- Divide total work by headcount
Inverse maintains constant variable product
Averages and Casework Rates
- Weighted Mean Formula
- Σ(weight × value) / ΣweightFormula
- Unweighted Mean Trap
- Distorts groups of unequal sizeCaution
- Combined Work Time
- Two constant rates: t₁t₂/(t₁+t₂)Formula
- Casework Hours Needed
- Volume times hours per caseLabor
- Staff Required Metric
- Total hours over available hoursStaffing
- Harmonic Average Speed
- Equal distances: 2uv/(u+v)Travel
- Daily Output per FTE
- Completed cases over FTE daysOutput
Bank Sell vs Bank Buy Rates
Bank Sell Rate
- Bank sells foreign cash
- You exchange domestic euros
- Applies to overseas travel
Bank Buy Rate
- Bank buys foreign currency
- You convert cash to euros
- Applies when returning home
Identify quoted currency and viewpoint
Currency Conversion and FX Spreads
- Euro to Foreign Currency
- Multiply euros by exchange rateEUR Base
- Foreign Currency to Euro
- Divide foreign amount by rateEUR Base
- Bank Sell Rate
- Bank sells foreign currency outIf quoted foreign currency
- Bank Buy Rate
- Bank buys foreign currency backCheck quoted currency
- Exchange Spread Margin
- Difference between sell and buyCost
- Stronger Currency Check
- Read quote units before comparing valuesSanity
- Foreign-per-Euro Quote
- Foreign units per one euroExplicit units govern
Favourable vs Adverse Budget Variance
Favourable Variance
- Actual costs below budget
- Retention depends on funding rules
- Indicates operational underspend
Adverse Variance
- Actual costs exceed budget
- Approved allocation breached
- Indicates departmental overspend
Underspend is not proof of performance
Public Sector Fiscal Math
- Favourable Variance
- Actual spend less than budgetUnderspend; not automatic retained funds
- Adverse Variance
- Actual spend exceeds approved budgetOverspend
- Percentage Variance
- Variance divided by budgeted amountFormula
- Unit Cost Allocation
- Total costs over output volumeCost
- Economies of Scale
- Fixed overhead spreads over volumeScale
- Capital Pro Rata Grant
- Annual budget × eligible months /12Formula
- Procurement Price Score
- Specified formula; often lowest/bid ×weightTender
VAT FTE and Conversion Rates
- Add Standard VAT
- Multiply net amount by 1.2323% Rate
- Extract Net Price
- Divide gross amount by 1.23Pre-VAT
- VAT Deduction Trap
- Never subtract 23 percent directlyTrap
- Part Time FTE Ratio
- Weekly hours over standard hoursFTE
- Total Team FTE
- Full time plus prorated staffWorkforce
- Per Capita Spending
- Total expenditure divided by populationRate
- Decimal Work Hours
- Hours plus minutes over 60Time
Common Traps
Baseline vs Final Value Denominator
Dividing change by original value ≠ Dividing change by new value
Direct VAT Deduction vs Extraction
Dividing gross amount by 1.23 ≠ Subtracting 23 percent from gross
Percentage Points vs Relative Change
Subtracting percentage rates directly ≠ Calling point differences percentage change
Dual Axis Curve Intersections
Tracing lines to designated axes ≠ Assuming line intersections equal values
Successive Percentage Summation Fallacy
Multiplying sequential decimal rates ≠ Adding percentages together directly
Stacked Bar Cumulative Values
Subtracting lower boundary from upper ≠ Reading segment tops from axis
Foreign Exchange Rate Application
Evaluating transactions from bank perspective ≠ Using customer perspective for quotes
Last Minute
- 1.Divide difference by original baseline
- 2.Divide gross by 1.23 net
- 3.Points subtract rates directly
- 4.Base year index equals 100
- 5.Multiply successive decimal multipliers
- 6.Bank quotes view bank side
- 7.Trace curves to proper axes
- 8.Part to whole sums parts
- 9.Check marking rules before guessing
- 10.Cannot say if essential data missing
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