Key Formulas You Need for LANTITE Numeracy (2026)
One of the most common questions we get is: "What formulas do I actually need for LANTITE?" Fair question. There's a lot of conflicting information out there, and nobody wants to waste time memorising things that won't show up. Below are the key formulas you'll encounter across the three LANTITE numeracy sections, organised by topic. Bookmark this page.
Quick note before we start
LANTITE is a personal literacy and numeracy test — it's testing whether you can handle the maths a teacher encounters day-to-day. That means the formulas are practical, not theoretical. You won't see university-level calculus or complex algebra. Everything here is roughly Year 9-10 Australian curriculum level.
Jump to a Section
Number & Algebra
The biggest section on the test (~45% of questions). Lots of percentages, fractions, and real-world calculations.
Percentages
Finding a percentage of an amount
Amount × (Percentage ÷ 100)
Example: 15% of $240 = $240 × 0.15 = $36
Expressing one quantity as a percentage of another
(Part ÷ Whole) × 100
Example: 18 out of 25 students passed = (18 ÷ 25) × 100 = 72%
Percentage increase or decrease
((New − Original) ÷ Original) × 100
Example: Enrolment went from 400 to 460 = ((460 − 400) ÷ 400) × 100 = 15% increase
Finding the original amount (reverse percentage)
Final Amount ÷ (1 ± Percentage/100)
Example: After a 20% discount, the price is $160. Original = $160 ÷ 0.8 = $200
Fractions & Decimals
Fraction of an amount
Amount × (Numerator ÷ Denominator)
Example: ¾ of 120 students = 120 × 0.75 = 90 students
Converting fractions to decimals
Numerator ÷ Denominator
Key conversions to know: ¼ = 0.25, ⅓ = 0.333..., ½ = 0.5, ⅔ = 0.667, ¾ = 0.75
Converting decimals to percentages
Decimal × 100
Example: 0.85 = 85%
Ratios & Proportions
Sharing in a given ratio
Each share = Total ÷ Sum of ratio parts
Example: Split $500 in ratio 2:3 → one share = $500 ÷ 5 = $100. So: $200 and $300.
Unit rate
Rate = Quantity ÷ Number of units
Example: 450 km in 5 hours = 450 ÷ 5 = 90 km/h
Unitary method (scaling)
Find the value of 1 unit, then multiply
Example: 5 books cost $45. One book = $9. So 8 books = $72
Financial Maths
GST (Goods and Services Tax — Australia's 10%)
Price including GST = Price × 1.1
Reverse: Price excluding GST = GST-inclusive price ÷ 1.1
Profit and loss
Profit (or Loss) = Selling Price − Cost Price
As a percentage: (Profit ÷ Cost Price) × 100
Discount
Sale Price = Original × (1 − Discount%/100)
Example: 30% off $80 = $80 × 0.7 = $56
Simple interest
I = P × R × T
Where: I = interest, P = principal, R = annual rate (as a decimal), T = time in years
Powers & Order of Operations
Index (exponent) laws
am × an = am+n
am ÷ an = am−n
(am)n = am×n
a0 = 1
Example: 23 × 24 = 27 = 128
Order of operations (BODMAS / BIMDAS)
Brackets → Orders (indices) → Division / Multiplication → Addition / Subtraction
Division and multiplication are done left-to-right (same priority). Same for addition and subtraction.
Rounding & Estimation
Rounding rules
Look at the digit to the right of where you're rounding. If it's 5 or more, round up. If it's 4 or less, round down.
Example: 3.7461 to 2 decimal places = 3.75 (because the third decimal is 6 ≥ 5)
Estimation
Round each number to 1 significant figure, then calculate. Great for checking if your answer is in the right ballpark.
Example: 487 × 21 ≈ 500 × 20 = 10,000 (actual: 10,227)
Measurement & Geometry
About 25% of the test. Lots of area, perimeter, volume, and unit conversions. Everything is in metric (obviously — it's Australia).
Perimeter
Rectangle
P = 2(l + w)
Square
P = 4s
Circle (circumference)
C = 2πr or C = πd
Use π ≈ 3.14159. The test usually tells you whether to use 3.14 or your calculator's π.
Tip: For irregular shapes, just add up all the sides. Watch out for missing sides — they'll give you enough info to work them out.
Area
Rectangle
A = l × w
Square
A = s²
Triangle
A = ½ × b × h
The height must be perpendicular to the base — not the slant side.
Parallelogram
A = b × h
Trapezium
A = ½(a + b) × h
For the trapezium: a and b are the two parallel sides, h is the perpendicular height between them.
Circle
A = πr²
Remember: r is the radius (half the diameter). A common trap is being given the diameter and forgetting to halve it.
Tip: Composite shapes? Break them into rectangles, triangles, and circles. Add areas together (or subtract the cut-out part).
Volume
Rectangular prism (box)
V = l × w × h
Triangular prism
V = ½ × b × h × length
That's the area of the triangular cross-section multiplied by the prism's length.
Cylinder
V = πr²h
Same idea — area of the circular cross-section multiplied by height.
Capacity conversion
1 cm³ = 1 mL 1000 cm³ = 1 L 1 m³ = 1000 L
This comes up all the time — "how many litres does the tank hold?" Just calculate volume in cm³ and convert.
Unit Conversions
Length
1 km = 1000 m | 1 m = 100 cm | 1 cm = 10 mm
Area (square the conversion factor!)
1 m² = 10,000 cm² | 1 km² = 1,000,000 m²
Also: 1 hectare = 10,000 m²
Mass
1 kg = 1000 g | 1 tonne = 1000 kg
Time
1 hour = 60 min | 1 min = 60 sec
And the classic trap: 1.5 hours = 1 hour 30 min, not 1 hour 50 min.
Angles
Angles in a triangle
Sum = 180°
Angles in a quadrilateral
Sum = 360°
Complementary angles
Sum = 90°
Supplementary angles
Sum = 180°
Angles on a straight line
Sum = 180°
Angles at a point
Sum = 360°
Vertically opposite angles
Are equal
When two lines cross, the angles opposite each other are the same.
Scale Drawings
Finding actual size
Actual = Drawing measurement × Scale factor
Example: Scale 1:200, drawing shows 3 cm → Actual = 3 × 200 = 600 cm = 6 m
Finding drawing size
Drawing = Actual measurement ÷ Scale factor
Time Calculations
Elapsed time
End time − Start time
Use 24-hour time to avoid AM/PM confusion. Count up to the next whole hour, then add remaining hours.
24-hour time conversion
PM times: add 12 to the hour (e.g. 3:30 PM = 15:30)
Time zones
Australian time zones appear often. East is ahead, west is behind.
AEST (QLD/NSW/VIC/TAS) | ACST = AEST − 30 min (SA/NT) | AWST = AEST − 2 hrs (WA)
Statistics & Probability
Around 30% of the test. Expect questions about averages, data interpretation, and basic probability — always set in teaching contexts.
Averages (Measures of Central Tendency)
Mean
Mean = Sum of all values ÷ Number of values
Example: Test scores: 65, 72, 80, 88, 95 → Mean = 400 ÷ 5 = 80
Weighted mean
Weighted Mean = Σ(value × weight) ÷ Σweights
Example: A class of 20 averaged 70%, a class of 30 averaged 80%. Combined = (20×70 + 30×80) ÷ 50 = 76%
Median
Middle value when data is ordered from smallest to largest
If there's an even number of values, average the two middle ones. E.g. {3, 5, 7, 9} → median = (5+7)÷2 = 6
Mode
Most frequently occurring value
A data set can have no mode, one mode, or multiple modes.
Measures of Spread
Range
Range = Maximum − Minimum
Interquartile range (IQR)
IQR = Q3 − Q1
Q1 = median of the lower half, Q3 = median of the upper half. The IQR tells you the spread of the middle 50% of data. Appears often on box-and-whisker plot questions.
Probability
Basic probability
P(event) = Favourable outcomes ÷ Total outcomes
Example: 8 red balls out of 20 total → P(red) = 8/20 = 0.4 or 40%
Complementary probability
P(not A) = 1 − P(A)
Example: P(rain) = 0.3, so P(no rain) = 1 − 0.3 = 0.7
Expected number of outcomes
Expected = Probability × Number of trials
Example: P(heads) = 0.5, flip 200 times → expect 100 heads
Probability from frequency tables
P(event) = Frequency of event ÷ Total frequency
These are very common on LANTITE. Read the table carefully — they sometimes use relative frequencies (already percentages).
Data Interpretation
Graphs and charts you need to read
- Bar charts and grouped bar charts
- Line graphs (including multiple lines on one graph)
- Pie charts (reading and calculating sectors)
- Dot plots and stem-and-leaf plots
- Box-and-whisker plots (median, Q1, Q3, IQR)
- Two-way frequency tables
- Scatter plots (identifying trends)
Tip: Always check the axis labels and scale. They love making bar charts where the y-axis doesn't start at zero, which can make differences look bigger than they are.
Quick Reference Cheat Sheet
Here's everything on one screen. Print this out or screenshot it for your study sessions.
Number & Algebra
% of amount: amount × (% ÷ 100)
% change: ((new−old) ÷ old) × 100
Fraction of amount: amount × (num ÷ den)
Ratio share: total ÷ sum of parts
Unit rate: quantity ÷ units
GST: price × 1.1
Simple interest: I = P × R × T
Discount: price × (1 − %/100)
BODMAS: Brackets, Orders, Div/Mult, Add/Sub
Indices: am×an=am+n
Measurement & Geometry
Rectangle P: 2(l + w)
Rectangle A: l × w
Triangle A: ½ × b × h
Circle A: πr²
Circumference: 2πr or πd
Trapezium A: ½(a+b) × h
Box V: l × w × h
Cylinder V: πr²h
Triangle angles: = 180°
Straight line: = 180°
Scale: actual = drawing × factor
1 cm³ = 1 mL | 1000 cm³ = 1 L
Statistics & Probability
Mean: sum ÷ count
Median: middle value (ordered)
Mode: most frequent value
Range: max − min
IQR: Q3 − Q1
Probability: favourable ÷ total
P(not A): 1 − P(A)
Expected: P × trials
One last thing
Don't try to memorise all of this in one sitting. Pick one section per study session, work through some practice questions using those formulas, and move on. Spaced repetition is your friend. And remember — the on-screen calculator handles the arithmetic. What LANTITE really tests is whether you can set up the calculation correctly.