Free LNAAT Numeracy Practice Questions (With Worked Solutions)

The numeracy requirement for New Zealand teacher registration is assessed through the LNAAT, an adaptive test — the questions get easier or harder depending on how you’re going. That makes a steady, methodical approach more valuable than raw speed. Below are 8 practice questions at the right level, each with a full worked solution that shows the method.

Try them, then sit the complete, full-length numeracy mock exam — free for instant marking and a worked explanation on every question.

Attempt each question before reading the solution — understanding why a method works is what makes it stick.

The questions

1. A discount

A tablet costs NZ$250. It’s reduced by 20% in a sale. What’s the sale price?

Worked solution. 10% of 250 = 25, so 20% = 50. Sale price = 250 − 50 = NZ$200.

2. Percentage of a quantity

A school has 480 students, and 35% travel by bus. How many is that?

Worked solution. 10% of 480 = 48, so 30% = 144. 5% = half of 48 = 24. 35% = 144 + 24 = 168 students.

3. Mixing in a ratio

Paint is mixed blue : white = 3 : 2, making 20 litres in total. How much white paint is used?

Worked solution. 3 + 2 = 5 parts; 20 ÷ 5 = 4 litres per part. White = 2 parts = 2 × 4 = 8 litres.

4. A fraction of an amount

A student has read three-quarters of a 200-page book. How many pages is that?

Worked solution. One-quarter = 200 ÷ 4 = 50. Three-quarters = 3 × 50 = 150 pages.

5. A rate

A tap fills a tank at 15 litres per minute. How long to fill 240 litres?

Worked solution. 240 ÷ 15 = 16 minutes.

6. Reading data — range

Daily temperatures were 12, 15, 9, 18, 14 °C. What is the range?

Worked solution. Range = highest − lowest = 18 − 9 = 9 °C.

7. Reverse percentage — the trap

A jacket costs NZ$96 after a 20% discount. What was the original price?

Worked solution. $96 is 80% of the original (100% − 20%). So 1% = 96 ÷ 80 = 1.20, and 100% = 1.20 × 100 = NZ$120. (Check: 20% of 120 = 24, and 120 − 24 = 96 ✓.)

8. Measurement — perimeter

A rectangular field is 25 m by 15 m. What is its perimeter?

Worked solution. Perimeter = 2 × (length + width) = 2 × (25 + 15) = 2 × 40 = 80 m.

How to turn practice into progress

Because the LNAAT adapts, a calm, accurate run matters more than rushing. Lock in a few reliable methods — percentages from 10%, sharing by parts, “of means multiply”, and always checking your answer. For each question you miss, note the single step that tripped you and redo a similar one a day later.

Not sure where to start? See the maths topics to prioritise and how the adaptive LNAAT works.

Ready for the real thing?

Sit the full-length numeracy mock exam — free, no card — real length and timing, instant marking, and a worked solution for every question, so you know exactly which topics to prioritise.

FAQ

Are these real LNAAT questions? No — real questions are confidential. These are original questions at the same level, testing the same skills, so the methods transfer directly.

Is the LNAAT adaptive? Yes — it adjusts difficulty based on your answers. That’s why steady accuracy beats rushing.

What’s the pass standard? See the New Zealand teacher maths requirement, explained.

When do I need to pass it? See when you have to pass the NZ maths requirement.