NCEA Numeracy CAA Prep
Work through all 7 modules in order. Each one covers a distinct domain that appears on the CAA — from Number & Rates to Probability and Patterns — with authentic practice questions and immediate feedback.
🎯 About the Full CAA Simulator
The simulator mirrors the real CAA paper exactly: 5 themed contexts, each with 4–6 sub-questions covering all 6 domains and all 3 outcomes. Written (Outcome 3) responses get checked by AI, just like in this training programme. Complete all 7 modules first to get the most out of it.
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Module 1
Number, Rates & Percentages
Operations, ratios, rates, percentages, large numbers, and ordering. The foundation of the entire exam — these skills appear in every single context.
The Golden Rule
Before you calculate, ask: What does the question actually want? Read the question sentence — not just the numbers. Students most often fail by dividing when they should multiply, or vice versa.
I Do — Rate × Quantity (Foundational Example)
Context
Salmon costs $28.00 per kilogram at the fish market. Aroha buys 750 grams. How much does Aroha pay?
Step 1 — Identify what you need
Cost of 750g when price is given per kg. Convert grams to kilograms first, then multiply.
Step 2 — Unit conversion
$750\text{ g} = 750 \div 1000 = 0.75\text{ kg}$
Step 3 — Calculate
$0.75 \times \$28.00 = \$21.00$
Step 4 — Check reasonableness
750g is ¾ of 1kg. ¾ of $28 = $21. ✓ Makes sense.
Section A — Scalar Multipliers: "How many times?"
Rule
Convert to the same units first, then divide bigger ÷ smaller.
Worked Example — Animal Weights
Context
A tuatara weighs 1 kg. A wētā weighs 25 g. How many times heavier is the tuatara?Step 1 — Same units
1 kg = 1000 g. Now both are in grams.
Step 2 — Divide bigger ÷ smaller
$1000 \div 25 = 40$ times heavier.
Common Mistake
Dividing 1 ÷ 25 without converting → gets 0.04. Wrong because the units weren't matched first.
Section B — Large Numbers
Rule
"2.4 million" = 2,400,000. Write out the zeros before calculating.
Worked Example — Budget Division
Context
A council budget is $2.6 million. How many $1,000 grants can be awarded?Write out the number
$2.6\text{ million} = \$2,600,000$
Divide
$2{,}600{,}000 \div 1{,}000 = 2{,}600$ grants
MC Strategy
Real exam gives 5 options: 26 / 260 / 2,600 / 26,000 / 260,000. Eliminate obviously wrong answers first — if your answer is in the right ballpark, trust it.
Section C — Ratio (a:b notation)
Rule
Find total parts → divide total by total parts → multiply each part.
Worked Example — Candles
Context
Candles are made in a 5:2 ratio (mānuka:other). 84 candles total. How many are mānuka?Total parts
$5 + 2 = 7$ parts
Value of one part
$84 \div 7 = 12$ candles per part
Mānuka candles
$5 \times 12 = 60$ mānuka candles
Section D — "X is what percentage of Y?"
Rule
$(X \div Y) \times 100 = $ percentage. Distinguish: "find X% of Y" (multiply) vs "X is what % of Y?" (divide then ×100).
Worked Example — Sale Price
Context
Jeans cost $24. Original price was $120. What percentage of the original price is the sale price?Apply rule
$(24 \div 120) \times 100 = 0.2 \times 100 = 20\%$
Section E — Unit Rate from a Bill
Rule
Unit rate = total cost ÷ total quantity. Always write the units (e.g. $/m³).
Worked Example — Water Bill
Context
A water bill charges $35.96 for 24.8 m³. What is the rate per m³?Calculate
$\$35.96 \div 24.8 = \$1.45$ per m³
Section F — Fraction as Operator on Metric Measurements
Rule
Divide by denominator first, then multiply by numerator.
Worked Example
Context
Find $\frac{5}{12}$ of 48 litres.Step 1
$48 \div 12 = 4$
Step 2
$4 \times 5 = 20$ litres
Section G — Negative Numbers in Context
Contexts
Temperature, altitude, sea level. Left on the number line = more negative = further in the past / deeper below sea level.
Worked Examples
Sea level
A cliff 9 metres below sea level = −9 m.
Temperature change
Temperature rises from −3°C to 7°C. Change = $7 - (-3) = 7 + 3 = 10$ degrees.
Section H — Ordering Decimals / "Which Two Swap?"
Rule
Write numbers vertically, align decimal points, scan digit by digit. Find the two values out of sequence.
Worked Example — Player Heights
Context
Heights listed in order: 2.00, 1.77, 1.85, 1.81, 1.80, 1.90, 1.72. Two players need to swap to put them in order shortest to tallest.Write in ascending order
1.72, 1.77, 1.80, 1.81, 1.85, 1.90, 2.00
Compare to original list
1.81 and 1.80 are swapped in the original. Those two players need to swap positions.
Section I — Range Calculations (Show Both Ends)
Rule
When given a range (e.g. 6–10 eggs), always calculate BOTH the minimum and maximum. State the full range in your answer.
Worked Example — Tuatara Eggs
Context
A female lays 6–10 eggs every 4 years. How many eggs over 10 years?Minimum
$6 \div 4 \times 10 = 15$ eggs
Maximum
$10 \div 4 \times 10 = 25$ eggs
Answer
Expect 15–25 eggs over 10 years.
Common Mistake
Only using one end of the range. If the question says "6–10", you must calculate both 6× and 10× answers.
Section J — Percentage Discount + Multi-step Totals
Rule
Discount amount = price × (discount% ÷ 100). Discounted price = original − discount. For group totals: calculate the full price first, then apply the discount.
Worked Example — Group Booking
Context
6 adults buy 2-day passes online. Single day = $6 each. 15% discount on the 2-day total.Step 1 — Full price
$6 \times \$6 \times 2 = \$72$
Step 2 — Discount amount
$\$72 \times 0.15 = \$10.80$
Step 3 — Final price
$\$72 - \$10.80 = \$61.20$
🎯 Warm-up: Outcome 1 — Identify the Approach click to expand
Before calculating, you must choose the right method. Match each problem description to its approach.
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Module 4
Graphs, Tables & Statistics
Bar charts, line graphs, timetables, dot plots, histograms, pie charts, dual-axis graphs, and statistical enquiry questions. Data appears in every single CAA context.
Before Every Graph Question
(1) Read the title. (2) Read both axis labels. (3) Check the scale — what does each grid line represent? Only then read your answer.
I Do — Timetable Reading
Context
Bus timetable: Station A departs 08:15, arrives Station B 08:47. You need to arrive before 9:00 am.
Find the duration
08:47 − 08:15 = 32 minutes. The bus arrives at 08:47 — well before 9:00 am. ✓
Axis Scale Trap
If the y-axis goes 0, 10, 20, 30… a bar halfway between 20 and 30 is exactly 25 — not 22 or 28. Always read from the nearest labelled gridline, then count subdivisions.
Section A — Dual-Axis Graphs
Definition
One chart with two y-axes — e.g. left axis = rainfall in mm, right axis = temperature in °C. Bars and lines share the same x-axis but measure completely different things.
Rule
Before reading any value, identify which axis belongs to the data type you need. Left axis? Right axis? Getting this wrong means reading the wrong scale entirely.
Worked Example — Climate Graph
Context
A climate graph shows monthly bars (rainfall, left axis in mm) and a line (temperature, right axis in °C). Question: "Which season has the highest rainfall?"
Step 1 — Identify the correct axis
Rainfall = bars = left axis. Ignore the temperature line completely.
Step 2 — Read the bars only
June, July, August bars are tallest → Winter has the highest rainfall.
Common Mistake
Reading temperature values when asked about rainfall, or vice versa. The two lines/bars look similar — always check which y-axis applies before reading any number.
Section B — Histograms
How histograms differ from bar charts
- Bars touch (no gaps) — continuous data
- x-axis shows ranges (e.g. 150–155 cm)
- y-axis shows frequency (count)
- Bar width = the range interval (often equal)
How to answer "how many are above X?"
Add up the frequencies for all bars whose range is above X. Don't just read one bar — you need the total of all qualifying bars.
Common Mistake
Treating a histogram like a bar chart and reading only one bar. "How many students are taller than 160 cm?" requires adding all bars from 160 cm upward.
Section C — Pie Charts & Multiple True/False
Reading a pie chart
- Each segment = a fraction of the whole circle (360°)
- Convert segment to count: fraction × total = count
- Convert segment to percentage: (count ÷ total) × 100
- "Which two segments together add up to more than half?" → add their fractions, check if > ½
Exam Alert — Multiple True/False Format
Some questions give a list of 4–5 statements and ask you to tick ALL that are true. There may be 2, 3, or even 4 correct answers. Do not stop at the first true statement — check every single one.
Worked Example
Context
A pie chart shows sport preferences: Football 40%, Netball 25%, Swimming 20%, Other 15%.
Q: Which two sports together account for more than half?
Football + Netball = 40% + 25% = 65% > 50% ✓. Also Football + Swimming = 60% > 50% ✓. Both pairs work — if the exam gives this as a tick-all question, both pairs must be ticked.
Section D — Statistical Enquiry Questions
Task
Write a question that can be answered using the data in the given table. The question must reference variable names that are actually in the table.
| Question type | What it compares | Example |
|---|---|---|
| Summary | One variable, one group | "How heavy are the turtles?" |
| Comparison | One variable, two groups | "Are male turtles heavier than female turtles?" |
| Relationship | Two variables, one group | "Is there a relationship between shell length and weight?" |
Worked Example — Turtle Data
Table columns
Species | Gender | Weight (kg) | Shell length (mm)
Valid question ✓
"Are Green turtles heavier than Loggerhead turtles?" — uses weight and species, both in the table.
Invalid question ✗
"How old are the turtles?" — age is not in the table. Cannot be answered from this data.
Marking Requirement
The question must reference exact variable names from the table. A vague question like "Is there a pattern?" will not pass — it must name the variables.
Section E — Time Series Trends & Outcome 3
Rule
When evaluating a trend claim, you must show the arithmetic — not just describe what you see on the graph. Read two specific values, calculate the relationship, state whether it matches the claim.
Worked Example — Purchases Claim
Context
A line graph shows online purchases from 2002 to 2022. Claim: "Purchases tripled from 2002 to 2022."
Step 1 — Read the two values
2002 value ≈ 18%. 2022 value ≈ 54%.
Step 2 — Show the arithmetic
$3 imes 18\% = 54\%$. The 2022 value matches 3× the 2002 value.
Step 3 — State position and link
Agree. 18% × 3 = 54%, which matches the 2022 value, so the claim is correct.
Weak Answer (no marks)
"The line goes up a lot so it probably tripled." — No numbers. Not accepted. You must read actual values and show the calculation.
Section F — Dot Plots & Median
Reading a dot plot
- Each dot = one data point
- Dots stack vertically when values repeat
- A dotted vertical line = the median (half the data above, half below)
- Count dots to find a proportion
"What proportion are above X?"
Count all dots at or above X. Divide by total dots. Express as a fraction or percentage.
Example: 100 snapper lengths, median at 30.5 cm. "What proportion are above 30 cm?" → approximately 50 dots ÷ 100 = ½ ≈ 50%.
Section G — Timetable: Comparing Two Durations
Format
Two events share a timetable. Each event has a listed start time and the next event starts after a short break. "How much longer is Event A than Event B?"
Worked Example — Stage Performance Times
Timetable (5-minute break between performances)
Stage A: starts 1:00 pm, next act starts 1:45 pm. Stage B: starts 1:10 pm, next act starts 1:40 pm.
Duration of Stage A performance
1:45 − 1:00 = 45 min total. Subtract 5-min break = 40 min performance.
Duration of Stage B performance
1:40 − 1:10 = 30 min total. Subtract 5-min break = 25 min performance.
Difference
40 − 25 = 15 minutes longer for Stage A.
Common Mistake
Forgetting to subtract the break time before comparing. If you compare raw time slots without removing the break, your answer will be inflated by 5 minutes per slot.
🎯 Warm-up: Outcome 1 — Identify the Approach click to expand
Match the problem to the correct method before calculating.
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Module 7
Outcome 3 — Explain & Justify
The most failed question type on the CAA. You must state a position, show a calculation using real numbers, and link your result back to the original claim. AI will check your response.
Section A — The Exact Marking Criteria
NZQA checks for these three things — in order
✅
Position: A clear statement — agree, disagree, or cannot tell
✅
Calculation: Real numbers from the question, shown as working
✅
Link: Your result connected back to the claim or threshold
⚠️
If percentages are involved, you must include percentages in your answer
⚠️
Describe your calculation is not the same as showing it — write out the numbers
Any position is accepted
NZQA does not require you to find the "right" answer. Agree or disagree are both valid — as long as your calculation supports your stated position. You cannot fail by choosing the wrong side; you fail by not showing working or not linking back.
⚠️ Outcome 3 can be the very first question
Many students expect Outcome 3 at the end of a context — but the 2025 CAA Term 2 opened with one as question 1a: "Three weeks is about 30,000 minutes — is this right? Use time calculations to explain." Don't wait for a hint that it's coming. Any question with "explain your answer", "use numbers to support", or "do you agree?" is an Outcome 3, wherever it appears.
Section B — Official Exemplar: Speed (2024 CAA)
Exemplar 1 — Running Speed
Scenario
Michaela ran 1,540 m in 14 minutes. Ani claims she averaged over 100 m/min.
✅ Strong (passes)
"I agree. 1,540 ÷ 14 = 110 metres per minute. 110 > 100, so Ani's claim is correct."
❌ Weak (no marks)
"I agree because she ran fast and 1,540 m is a long way in 14 minutes." — No numbers, no marks.
Section C — Official Exemplar: Volume (2024 CAA)
Exemplar 2 — Candle Boxes
Scenario
Zion claims Option 2 maximises profit. Option 1: 4.5 × 4.5 × 8 cm. Option 2: 4 × 4.5 × 8 cm.
✅ Strong (passes)
"I disagree. Option 1 = 4.5 × 4.5 × 8 = 162 cm³. Option 2 = 4 × 4.5 × 8 = 144 cm³. Option 1 holds more wax, so Option 1 maximises profit."
❌ Weak (no marks)
"I disagree because Option 1 looks bigger." — No calculation shown.
Section D — Official Exemplar: Range Calculation (2024 CAA)
Critical Rule — Only count complete cycles
When a range question involves a repeating cycle (e.g. "every 4 years"), count only complete cycles within the time period. A half-cycle does not produce a partial result — there are no half-batches.
Exemplar 3 — Egg Laying
Scenario
A female lays 6–10 eggs every 4 years. How many would you expect in 10 years?
Find complete cycles
10 ÷ 4 = 2.5 cycles. Only 2 complete cycles fit within 10 years.
Calculate both ends
Minimum: 2 × 6 = 12. Maximum: 2 × 10 = 20.
Strong answer
"In 10 years there are 2 complete 4-year cycles. I would expect between 12 and 20 eggs (minimum 2 × 6 = 12, maximum 2 × 10 = 20)."
Official Borderline Answer (gets borderline, not strong)
A student who correctly calculates 2 complete cycles but then halves the range for the 0.5 remaining cycle gets borderline. Only count complete cycles.
Section E — Official Exemplar: Probability Claim (2024 CAA)
Exemplar 4 — Rugby 7s Finals
Scenario
NZ appeared in the Rugby 7s final 5 out of 8 World Cups. Claim: "NZ has been in the final for over 60% of World Cups."
Calculate
5 ÷ 8 = 0.625 = 62.5%
Compare and link
62.5% > 60%. Agree.
Strong answer
"I agree. 5 ÷ 8 = 62.5%. Since 62.5% is greater than 60%, the statement is correct."
Section F — Special Case: The Coin Toss (2024 CAA)
Either answer is correct
On coin-toss independence questions, NZQA accepts either heads or tails as the position. The marks come entirely from the explanation — you must state that each toss is independent and that past results have no effect.
✅ Strong (either position)
"Either. Each coin flip is an independent event — the probability of heads or tails is always ½ regardless of previous results. Getting three tails does not make heads more likely."
❌ Wrong reasoning
"Heads — because we've had three tails in a row, heads is overdue." This is the gambler's fallacy. Coins have no memory.
Section G — Four Types at a Glance
Type 1 — Speed / Rate
❌ "She ran fast so it's probably over 100." — No numbers.
✅ "1,540 ÷ 14 = 110 m/min > 100. Agree."
Type 2 — Volume Comparison
❌ "Option 1 looks bigger." — No calculation.
✅ "Option 1 = 162 cm³, Option 2 = 144 cm³. Option 1 is larger. Disagree."
Type 3 — Range / Cycle
❌ "10 ÷ 4 = 2.5 cycles → 2.5 × 8 = 20 min." — Uses partial cycle.
✅ "2 complete cycles: min = 2 × 6 = 12, max = 2 × 10 = 20."
Type 4 — Probability % Claim
❌ "They've been in most finals." — No percentage calculated.
✅ "5 ÷ 8 = 62.5% > 60%. Agree, the claim is correct."
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Module 3
Geometry & Spatial Reasoning
Symmetry, transformations, nets, 2D/3D views, scale diagrams, and formations. Usually multiple choice — but students lose marks by not reading carefully before clicking.
Foundations
Angles — Benchmarks to Know
- 90° — right angle (corner of a page)
- 45° — half a right angle
- 60° — angle in equilateral triangle
- 180° — straight line
- 360° — full rotation
Strategy: decide acute/right/obtuse/reflex first, then use benchmarks to narrow down.
Lines of Symmetry (Reflective)
A line of symmetry divides a shape so both halves are mirror images. Mentally "fold" along each possible line — if both sides match exactly, it is a line of symmetry.
Exam alert: questions may ask you to tick ALL correct lines from a numbered list — there may be 2, 3, or more correct answers.
Nets of 3D Shapes
A net folds into a 3D object. To check: count the faces (cube = 6, rectangular prism = 6), then mentally fold each face — every edge needs a matching edge to join.
Top / Front / Side Views
The top view = looking straight down. The front view = looking from the front. Only draw what is visible from that direction — hidden edges are not shown.
Section A — Rotational Symmetry
Definition
A shape has rotational symmetry if it looks identical after being rotated by less than 360°. The order of rotation = how many times it looks the same in one full 360° turn.
| Shape | Lines of symmetry | Order of rotation |
|---|---|---|
| Square | 4 | 4 |
| Rectangle | 2 | 2 |
| Equilateral triangle | 3 | 3 |
| Regular hexagon | 6 | 6 |
| Circle | ∞ | ∞ |
| Irregular / asymmetric shape | 0 | 1 (none) |
Real Exam Format (confirmed)
Questions ask two separate yes/no questions on the same design: "Does it have reflective symmetry?" AND "Does it have rotational symmetry?" — answer each part independently.
Section B — Both Symmetry Types in One Question
BOTH (equilateral triangle)
3 lines of symmetry ✓
Order 3 rotation ✓
Lines only (letter A)
1 line of symmetry ✓
No rotational symmetry ✗ — rotate it 180° and it no longer looks the same.
Rotation only (letter S)
No lines of symmetry ✗
Order 2 rotation ✓ (looks the same upside down)
NEITHER (scalene triangle)
No lines of symmetry ✗
Order 1 (no rotational symmetry) ✗
Common Mistake
Confusing "line of symmetry" with "rotational symmetry" — they are different things. A shape can have one without the other. Always answer both parts independently.
Section C — Multiple Lines of Symmetry: Tick All Correct
Exam Format
The exam may show a design with 6 numbered potential lines and ask you to tick ALL that are lines of symmetry. There will be more than one correct answer. You must find all of them — missing one costs marks.
Strategy
For each numbered line
Mentally fold the design along that line. Ask: do both halves match exactly — every part, every colour, every detail? If yes → tick it. Do this for every numbered line before submitting.
Don't stop at the first match
Even if you find one line of symmetry early, keep checking the remaining lines. A regular hexagon has 6 lines — you need all 6.
Section D — Transformations
Reflection
Flip across a line (mirror image). Every point is the same distance from the mirror line on the opposite side.
Rotation
Turn around a fixed point. Specify: how many degrees, and which direction (clockwise or anti-clockwise).
Enlargement (Scale)
Scale up or down. Scale factor = new size ÷ original size. Shape stays the same — only the size changes.
Frieze Patterns
A repeating border pattern that uses one or more transformations. Exam question format: "Which transformation(s) does this pattern use?" — MC options: reflection only / rotation only / reflection and rotation / enlargement.
Section E — Scale Diagrams as Outcome 3
Format
A scale diagram shows an object (car, bed, building) with a known real-world dimension. You calculate a real measurement from the diagram, compare it to a threshold, and take a position.
Worked Example — Parking Distance
Context
A car is parked 1.5 car lengths from a corner. Each car length is 4.5 m. The legal minimum distance from a corner is 6 m. Is the car legally parked?
Step 1 — Position
I agree — the car IS legally parked.
Step 2 — Calculation
$1.5 imes 4.5 ext{ m} = 6.75 ext{ m}$
Step 3 — Link
6.75 m > 6 m, so the car is more than the legal minimum from the corner. The car is legally parked.
Marking Requirement
You must show the multiplication (1.5 × 4.5), state whether the result is above or below the threshold, and give a clear position. A description without numbers will not pass.
Section F — Formation / Array Counting
Context
Performers are arranged in rows and columns in Formation A. They rearrange into Formation B. Both formations have the same total. Find the minimum number who need to move.
Worked Example
Context
Formation A = 4 rows of 10 (total 40). Formation B = 5 rows of 8 (total 40). Find the minimum movers.
Step 1 — Confirm totals match
$4 imes 10 = 40$ and $5 imes 8 = 40$ ✓
Step 2 — Compare row by row
Formation B needs 8 per row. Formation A has 10 in its first row. Row 1 of B can take 8 from row 1 of A — 2 must move out. Repeat for all rows.
Step 3 — Find minimum
The minimum is the number who must leave their current row because B's corresponding row needs fewer. Assume people move into rows that are short before counting who must leave rows that have too many.
Common Mistake
Saying "everyone moves." The question asks for the minimum — people who are already in the right row in Formation B do not need to move.
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Module 2
Measurement & Time
Area, volume, unit conversion, reading scales, and time calculations. These appear in nearly every CAA context — often as the core calculation inside an Outcome 3 question.
Section A — Area of Rectangles
Formula
Area = length × width. Units are always squared — write m², cm², not just the number.
Worked Example — Rugby Field
Context
A rugby field is 106 m long and 68 m wide. What is its area?
Calculate
106 × 68 = 7,208 m²
Common Mistakes
Adding instead of multiplying (106 + 68 = 174 — wrong). Forgetting to write m² in the answer.
Section B — Volume of Rectangular Prisms
Formula
Volume = length × width × height. Units are cubed — write cm³, m³. Also: 1,000 cm³ = 1 litre.
Worked Example — Candle Box
Context
A candle box is 4.5 cm × 4.5 cm × 8 cm. What is its volume?
Calculate
4.5 × 4.5 × 8 = 162 cm³
⚠ Mixed Units — Convert First
If dimensions are given in different units (e.g. 100 mm and 15 cm), convert all to the same unit before multiplying.
Example: aquarium is 100 mm × 150 mm × 200 mm.
100 mm = 10 cm, 150 mm = 15 cm, 200 mm = 20 cm.
Volume = 10 × 15 × 20 = 3,000 cm³ = 3 litres.
100 mm = 10 cm, 150 mm = 15 cm, 200 mm = 20 cm.
Volume = 10 × 15 × 20 = 3,000 cm³ = 3 litres.
Section C — Volume as Outcome 3
Format
A claim is made about which of two containers holds more. You must calculate both volumes, compare them, take a position, and justify.
Worked Example — Two Candle Options
Context
Zion claims Option 2 maximises profit. Option 1: 4.5 × 4.5 × 8 cm. Option 2: 8 × 4.5 × 4.5 cm (a different arrangement — the dimensions produce a different shape).
Option 1 volume: 162 cm³. Option 2 volume: 162 cm³. Here they are equal — so check the exact numbers given in your question.
Strong answer
"I disagree. Option 1 volume = 4.5 × 4.5 × 8 = 162 cm³. Option 2 volume = 4 × 4.5 × 8 = 144 cm³. Option 1 holds more wax, so Option 1 maximises profit."
Marking requirement
State your position + show BOTH volume calculations + state which is greater.
Section D — The 1 L Water = 1 kg Benchmark
Key Fact
1 litre of water weighs exactly 1 kilogram. This fact appeared printed on the real 2024 CAA exam. Know it.
Worked Example — Large Water Bottle
Context
A large bottle holds 15 L of water. When full it weighs 15.352 kg. How much does the empty bottle weigh?
Weight of water
15 L × 1 kg/L = 15 kg
Empty bottle weight
15.352 − 15 = 0.352 kg = 352 g
Worked Example — How Many Glasses?
Context
3 bottles, each 1.5 L. How many 300 mL glasses can be filled?
Total capacity
3 × 1.5 L = 4.5 L = 4,500 mL
Number of glasses
4,500 ÷ 300 = 15 glasses
Section E — Metric Unit Conversions
| Type | Key conversion | To convert → | To convert ← |
|---|---|---|---|
| Mass | 1 kg = 1,000 g | kg → g: × 1,000 | g → kg: ÷ 1,000 |
| Length | 1 m = 100 cm = 1,000 mm; 1 km = 1,000 m | m → cm: × 100 | cm → m: ÷ 100 |
| Capacity | 1 L = 1,000 mL = 1,000 cm³ | L → mL: × 1,000 | mL → L: ÷ 1,000 |
| Area | 1 m² = 10,000 cm² | m² → cm²: × 10,000 | cm² → m²: ÷ 10,000 |
Section F — Reading Measurement Scales
Strategy — 4 Steps
- Find the two nearest labelled marks (e.g. 29 cm and 30 cm)
- Count the number of subdivisions between them
- Calculate value per subdivision: (upper − lower) ÷ count
- Count how many subdivisions past the lower mark the arrow is pointing
Worked Example — Fish Length
Context
A ruler shows marks at 29 cm and 30 cm with 10 subdivisions between them. The arrow points 5 subdivisions past the 29 cm mark.
Value per subdivision
(30 − 29) ÷ 10 = 0.1 cm = 1 mm per subdivision
Reading
29 cm + (5 × 0.1 cm) = 29.5 cm = 295 mm
Outcome 3 connection
If the legal minimum is 300 mm, the fish measures 295 mm < 300 mm → put the fish back. Position: the fish should NOT be kept.
Section G — Time: Duration Between Two Times
Method 1 — Count Up
From 9:55, count to 10:00 = 5 min. Then count from 10:00 to 13:00 = 3 hours. Total = 3 h 5 min.
Method 2 — Column Subtraction
13:00 − 9:55. Borrow 60 minutes: 12:60 − 9:55 = 3 h 5 min. Borrow 60, not 100.
Critical Warning
There are 60 minutes in 1 hour — NOT 100. When subtracting times, if you need to borrow, borrow 60 minutes. Students who borrow 100 get consistently wrong answers.
Section H — 24-Hour Time
Conversion Rule
For pm times: add 12 to the hour (except 12:00 pm = 12:00). Midnight = 00:00.
| 12-hr | 24-hr | 12-hr | 24-hr | 12-hr | 24-hr |
|---|---|---|---|---|---|
| 12:00 am | 00:00 | 12:00 pm | 12:00 | 6:00 pm | 18:00 |
| 1:00 am | 01:00 | 1:00 pm | 13:00 | 11:00 pm | 23:00 |
Worked Example — Flight Duration
Context
Flight departs 09:55, arrives 13:00. How long is the flight?
Count up
09:55 → 10:00 = 5 min. 10:00 → 13:00 = 3 hours. Total: 3 hours 5 minutes.
Section I — Time Rounding
Rule
If minutes ≥ 30 → round up to next hour. If minutes < 30 → round down (keep the hour).
Worked Example
Context
A journey takes 5 hours 49 minutes. Round to the nearest hour.Check minutes
49 ≥ 30 → round up. Answer: 6 hours.
Section J — Timetable Pattern Extension
Strategy
Find the repeating interval, then add it to the last known time. For tidal tables: the interval is usually given or can be calculated from two successive times.
Worked Example — Tides
Context
Low tides occur every 12 hours 21 minutes. The last low tide shown is 6:14 pm. When is the next low tide?
Add the interval
6:14 pm + 12 h 21 min = 6:35 am (next day). ✓ Accept ±20 minutes on this type.
Section K — Reasonableness Checking
The single most common examiner complaint — every year
NZQA markers repeatedly report students accepting obviously wrong answers. After every calculation, ask: "Is this a sensible real-world number?" This habit alone can save you from factor-of-1000 calculator errors.
The Reasonableness Habit — 4 Questions
1. Is the unit right?
You're asked for minutes but your answer is 0.036 — did you forget to multiply by 60?
2. Is the magnitude sensible?
You calculated a bag of popcorn weighs 4,500 kg — a small car weighs that much. Something went wrong.
3. Are you off by ×10 or ×1000?
The most common calculator error. Check: did you accidentally divide instead of multiply? Is there a missing zero?
4. Does the context make sense?
"A bottle of sunscreen lasts 0.002 hours" is impossible. "Hiring an e-scooter costs $4,000 per hour" is impossible. If it's absurd, recalculate.
Length & distance
- A door ≈ 2 m tall
- A car ≈ 4.5 m long
- A typical room ≈ 4–5 m wide
- A city block ≈ 100–200 m
- A ruler = 30 cm
Mass & volume
- 1 L water = 1 kg ← exam fact
- A school bag ≈ 5 kg
- A can of drink ≈ 330 mL
- A bath ≈ 150–200 L
- A standard brick ≈ 2 kg
Temperature
- Body temp ≈ 37 °C
- Room temp ≈ 20 °C
- Warm shower ≈ 40 °C
- Boiling water = 100 °C
- Freezing = 0 °C
Time
- 1 hour = 60 minutes
- 1 day = 24 hours = 1,440 min
- 1 week = 7 days = 10,080 min
- 1 year ≈ 365 days ≈ 525,600 min
- A walk across town ≈ 20–40 min
Exam example — catching a ×10 error
A question says: "Sunscreen covers 200 cm² per mL. A bottle holds 240 mL. How many cm² can be covered?"
Correct: 200 × 240 = 48,000 cm² ← about 4.8 m² (a small room's floor). Reasonable for sunscreen.
Wrong (common): 200 ÷ 240 = 0.83 cm² ← less than a fingernail. Impossible. The student divided instead of multiplying — the unit check would have caught this.
🎯 Warm-up: Outcome 1 — Identify the Approach click to expand
Match the problem to the correct method before calculating.
🎲
Module 5
Probability
Probability scale, fractions, independent events, probability from data. Appears in every CAA — often as the final Outcome 3 question in a context.
Section A — The Probability Scale
Scale: 0 to 1
0
Impossible
Impossible
~0.1
Unlikely
Unlikely
0.5
Even chance
Even chance
~0.9
Likely
Likely
1
Certain
Certain
Exam Format — Arrow on a Scale
The exam shows a number line from 0 to 1 with 5 arrows labelled A–E. You circle the arrow that best matches the probability. Convert your probability to a decimal first, then place it on the scale.
Worked Example — Place on Scale
Context
5 schools from the South Auckland area out of 11 total schools. What is the probability of a South Auckland school winning?
Convert to decimal
5 ÷ 11 ≈ 0.45
Place on scale
0.45 is just below 0.5, so select the arrow just to the left of centre.
Section B — Probability Forms
Three equivalent forms
- Fraction: 5/11
- Decimal: 5 ÷ 11 ≈ 0.45
- Percentage: 0.45 × 100 = 45%
Exam trap — "1 in 100"
1 in 100 = 0.01 (not 0.1). Divide 1 by the second number. 1 in 10 = 0.1. 1 in 100 = 0.01. 1 in 1,000 = 0.001.
Section C — Probability from Counting
Formula
P(event) = (number of favourable outcomes) ÷ (total number of outcomes)
Worked Example
Context
A bag has 3 red, 5 blue, and 2 green counters. What is the probability of picking a blue counter?
Count outcomes
Favourable = 5 (blue). Total = 3 + 5 + 2 = 10.
Calculate
P(blue) = 5/10 = 1/2 = 0.5 — an even chance.
Section D — Independent Events (Coin Toss)
Key Concept
Each coin toss is independent — past results have absolutely no effect on future results. The probability is always ½, regardless of what happened before.
✅ Strong Answer
"Either heads or tails. Each coin toss is an independent event — the probability of heads or tails is always ½ regardless of previous results."
❌ Wrong Thinking
"Heads is more likely now because we've had three tails." This is the gambler's fallacy — coins have no memory.
NZQA Note
On this question type, either heads or tails is accepted as the position. What matters is explaining the independence principle. You cannot fail by choosing the "wrong" side — only by failing to explain why it doesn't matter.
Section E — Probability from a Data Display
Method
Count the relevant dots/tally marks. Divide by the total. Express as a fraction, decimal, or percentage.
Worked Example — Snapper Length
Context
A dot plot shows 100 snapper lengths. The median is at 30.5 cm. The legal minimum is 30 cm.
Count keepable snapper
Approximately 50 dots fall at or above 30 cm (to the right of the threshold line).
Express as probability
P(keepable) = 50/100 = ½ = 0.5. "About half the snapper are keepable."
Section F — Compound Probability (at least one success)
Worked Example — Free Throws
Context
Lisa has a 50% chance per free throw. She gets 2 throws. What is the probability of scoring at least once?
Wrong approach
50% + 50% = 100% ✗ — this is impossible and double-counts.
Method 1 — Complement
P(miss both) = ½ × ½ = ¼. P(at least one) = 1 − ¼ = ¾.
Method 2 — List all outcomes
HH, HM, MH, MM — 4 outcomes. 3 have at least one hit. P = 3/4.
Section G — Probability as Outcome 3
Format
A table or tally gives you data. A claim is made about a percentage or probability. You take a position, calculate, and link back to the claim.
Worked Example — Rugby 7s Finals
Context
NZ appeared in the Rugby 7s final 5 times out of 8 World Cups. Claim: "NZ has been in the final for over 60% of World Cups."
Calculate
5 ÷ 8 = 0.625 = 62.5%
Compare and conclude
62.5% > 60%. Agree — the claim is correct.
Strong answer
"I agree. 5 ÷ 8 = 62.5%, which is over 60%, so the claim is correct."
Weak Answer
"They've been in most finals so the claim is probably true." No numbers — not accepted.
🎯 Warm-up: Outcome 1 — Identify the Approach click to expand
Match the problem to the correct method before calculating.
🔗
Module 6
Patterns, Sequences & Counting
Timelines, visual patterns, arithmetic sequences, combinations, coalitions, linear tables. Every single real CAA paper has opened with a timeline question.
Section A — Timelines (Number Lines with Negatives)
Exam Fact
Both 2024 CAA papers opened with a timeline question (Q1a each). Expect one every sitting.
Reading the scale
Left = further back (more negative = further past or deeper below sea level). Right = present / positive. The scale is linear — equal spacing between marks.
Worked Example — Geological Timeline
Context
A timeline runs from −500 million years to 0 (today). Where does "225 million years ago" go?
Convert to the scale
−225 million years sits between the −500M mark and 0, roughly at the 45% point from the left. It is closer to 0 than to −500M.
On the exam
Circle the arrow that is closest to this position on the scale. The arrows are labelled A–E from left to right.
Section B — Visual Growth Patterns
Strategy — Don't look for a formula
Look at what changes between each step. What is added each time? Is it a constant amount, or does it grow?
Worked Example — Growing Pattern
Pattern
Step 1: 1 tile. Step 2: 4 tiles. Step 3: 9 tiles. Step 4: 16 tiles.
Find what changes
Differences: +3, +5, +7 — each step adds 2 more than the previous addition.
Step 5
Add 9 more: 16 + 9 = 25 tiles. (These are square numbers: 1², 2², 3², 4², 5².)
Real Exam Note
The exam showed a visual pattern — students count squares in a picture, including squares of all sizes. Be systematic: count each size separately, then add.
Section C — Arithmetic Number Sequences
Definition
An arithmetic sequence adds the same amount each time (constant difference).
Worked Example — Election Years
Context
NZ elections are held every 3 years. Starting from 2023, was 1987 an election year?
Find the gap
2023 − 1987 = 36 years.
Divide by interval
36 ÷ 3 = 12 exactly (whole number) → Yes, 1987 was an election year.
Rule
(target − known year) ÷ interval = whole number → it fits the pattern.
Section D — Counting Combinations
Multiplication Principle
When you choose ONE from group A AND ONE from group B:Total combinations = |A| × |B|
Worked Example — Meal Combos
Context
4 main courses and 6 desserts. How many different meal combinations?
Multiply
4 × 6 = 24 combinations.
Common Mistake
Adding instead of multiplying: 4 + 6 = 10. Wrong. When you pick one AND one, multiply.
Section E — Finding All Valid Coalitions
Strategy — Be Systematic
List all possible 2-party pairs. Check each total against the majority threshold. Then list 3-party combinations if needed. Missing even one = wrong answer.
Worked Example — Parliament
Context
4 parties with 35, 30, 22, 13 seats (total 100). Majority = 51+. Which 2-party coalitions work?
List all pairs systematically
35+30=65 ✓ | 35+22=57 ✓ | 35+13=48 ✗
30+22=52 ✓ | 30+13=43 ✗ | 22+13=35 ✗
30+22=52 ✓ | 30+13=43 ✗ | 22+13=35 ✗
Valid 2-party coalitions
3 valid pairs: (35,30), (35,22), (30,22).
Section F — Linear Relationships in Tables
Strategy
- Find the difference in y for each step of x → that is the multiplier m
- Find c: substitute one known (x, y) pair into y = mx + c
- Use the rule to find any missing value
Worked Example
Table
x: 1, 2, 3, 4 → y: 5, 8, 11, 14
Find m
Difference = 3 each time → m = 3.
Find c
When x=1, y=5: 5 = 3×1 + c → c = 2. Rule: y = 3x + 2.
Use the rule
When x = 10: y = 3(10) + 2 = 32.
Section G — Formation / Array Counting
Method
Formation A total = rows × cols. Formation B total = rows × cols (must be equal). Minimum movers = total − (people who can stay in a correctly-sized row).
Worked Example
Context
40 performers. Formation A: 4 rows of 10. Formation B: 5 rows of 8. Minimum movers?
People who can stay
Each row in B needs 8. Each row in A has 10. Matching rows = min(4,5) = 4. Each matching row can keep 8. Total staying = 4 × 8 = 32.
Minimum movers
40 − 32 = 8 performers must move.
🎯 Warm-up: Outcome 1 — Identify the Approach click to expand
Match the problem to the correct method before calculating.
🎯
Full CAA Simulator
5 themed contexts · 25–30 questions · AI checks written responses
This simulator mirrors the real CAA paper as closely as possible. Work through five NZ-based scenarios, each with multiple questions covering all 6 domains and all 3 outcomes. Values are randomised each attempt.
Outcome 3 (written justification) questions are AI-checked at the end — feedback on position, calculation, and linking.
Tips Before You Start
- Read the full context paragraph before answering any sub-questions
- Attempt every question — blank is always wrong, a guess might be right
- For Outcome 3: position → calculation with real numbers → link back
- Use a real calculator alongside this screen
- Real CAA is 60 minutes — use the optional timer to practise under pressure
Calculator Hacks
Smart calculator strategies that save time and reduce errors on the CAA.