21 free questions · worked solutions

LANTITE numeracy practice questions

Free LANTITE numeracy practice questions, grouped by the skill each one tests and written to match the style and difficulty of the real paper. Every question carries a worked solution that shows the step, not just the answer. People search for a LANTITE maths test as often as a numeracy one, and they are the same thing: the numeracy component covers number, measurement, statistics and probability, applied to situations a teacher would actually meet.

These are not a full LANTITE numeracy practice test, and they are not ACER's questions. They are a way to find out which skills need your time before you sit.

NC1

Number sense and operations

3 questions, each with a worked solution.

Directed number in context

Q1. A canteen account starts the term $85 overdrawn. It takes $240 over the first week and then pays a $130 invoice. What is the balance at the end of the week?

  1. A −$25
  2. B $25
  3. C $110
  4. D $155
Show answer

Answer: B · $25

Start at −$85. Adding $240 gives $155. Paying the $130 invoice leaves $155 − $130 = $25 in credit. Answering $110 comes from ignoring the overdraft, and $155 from forgetting the invoice.

Fractions of a remainder

Q2. Of the 180 students in a year group, two fifths chose Japanese. One third of the remaining students chose German. How many chose German?

  1. A 36
  2. B 44
  3. C 60
  4. D 72
Show answer

Answer: A · 36

Two fifths of 180 is 72, so 108 students remain. One third of 108 is 36. Answering 60 comes from taking a third of the whole 180 rather than the remainder, and 72 is the number who chose Japanese.

Ordering decimals

Q3. Which list is ordered from smallest to largest?

  1. A 0.07, 0.077, 0.7, 0.71
  2. B 0.07, 0.7, 0.077, 0.71
  3. C 0.077, 0.07, 0.71, 0.7
  4. D 0.7, 0.71, 0.07, 0.077
Show answer

Answer: A · 0.07, 0.077, 0.7, 0.71

Compare place by place, padding to the same length: 0.070, 0.077, 0.700, 0.710. The common error is reading 0.077 as smaller than 0.07 because it has more digits.

NC2

Proportional and algebraic reasoning

3 questions, each with a worked solution.

Percentages

Q4. A class of 28 students sat a test and 21 of them passed. What percentage of the class passed?

  1. A 68%
  2. B 72%
  3. C 75%
  4. D 78%
Show answer

Answer: C · 75%

21 out of 28 is 21 ÷ 28 = 0.75, which is 75%.

Proportional reasoning

Q5. A recipe for 24 biscuits uses 300 g of flour. Keeping the same proportions, how much flour is needed to make 36 biscuits?

  1. A 400 g
  2. B 420 g
  3. C 450 g
  4. D 480 g
Show answer

Answer: C · 450 g

Flour per biscuit is 300 ÷ 24 = 12.5 g. For 36 biscuits: 12.5 × 36 = 450 g.

Ratio

Q6. In a school the ratio of students to teachers is 15 to 1. If there are 420 students, how many teachers are there?

  1. A 24
  2. B 28
  3. C 30
  4. D 32
Show answer

Answer: B · 28

Divide the students by 15: 420 ÷ 15 = 28 teachers.

NC3

Time and money

3 questions, each with a worked solution.

Rates and time

Q7. A teacher marks 5 essays in 40 minutes at a steady rate. At the same rate, how long will it take to mark 18 essays?

  1. A 2 h 10 min
  2. B 2 h 24 min
  3. C 2 h 40 min
  4. D 3 h
Show answer

Answer: B · 2 h 24 min

Each essay takes 40 ÷ 5 = 8 minutes. For 18 essays: 8 × 18 = 144 minutes, which is 2 hours 24 minutes.

Elapsed time

Q8. A parent-teacher evening runs from 3:45 pm to 7:20 pm, including a single 25-minute break. How long is spent in meetings?

  1. A 3 h 10 min
  2. B 3 h 35 min
  3. C 3 h 55 min
  4. D 4 h
Show answer

Answer: A · 3 h 10 min

From 3:45 pm to 7:20 pm is 3 hours 35 minutes, or 215 minutes. Removing the 25-minute break leaves 190 minutes, which is 3 hours 10 minutes. Answering 3 h 35 min is the elapsed time with the break left in.

Budgeting in stages

Q9. A faculty has a budget of $1,450. It spends $890 on texts, then spends 20% of what is left on printing. How much of the budget remains?

  1. A $268
  2. B $448
  3. C $470
  4. D $560
Show answer

Answer: B · $448

After the texts, $1,450 − $890 = $560 remains. Printing takes 20% of $560, which is $112, leaving $560 − $112 = $448. Answering $560 forgets the printing, and $470 comes from taking 20% of the original $1,450.

NC4

Measurement and units

3 questions, each with a worked solution.

Area and fractions

Q10. A rectangular classroom is 8 m long and 6 m wide. A rug covers exactly one quarter of the floor. What area does the rug cover?

  1. A 6 m²
  2. B 12 m²
  3. C 18 m²
  4. D 24 m²
Show answer

Answer: B · 12 m²

The floor area is 8 × 6 = 48 m². One quarter of 48 is 48 ÷ 4 = 12 m².

Converting area units

Q11. A sports field measures 90 m by 45 m. What is its area in hectares? (1 hectare = 10,000 m²)

  1. A 0.0405 ha
  2. B 0.405 ha
  3. C 4.05 ha
  4. D 40.5 ha
Show answer

Answer: B · 0.405 ha

The area is 90 × 45 = 4,050 m². Dividing by 10,000 gives 0.405 ha. The wrong answers are the same digits with the decimal point moved, which is the usual slip when converting area units.

Scale drawings

Q12. On a site plan drawn at a scale of 1:200, a hall measures 7.5 cm long. What is the hall's real length?

  1. A 1.5 m
  2. B 15 m
  3. C 150 m
  4. D 27.5 m
Show answer

Answer: B · 15 m

7.5 cm on the plan is 7.5 × 200 = 1,500 cm in reality, and 1,500 cm is 15 m. Answering 150 m keeps the answer in centimetres by mistake, and 1.5 m divides by the scale instead of multiplying.

NC5

Space, shape and direction

3 questions, each with a worked solution.

Distance and direction

Q13. A student walks 300 m north, then turns and walks 400 m east. In a straight line, how far is the student from the starting point?

  1. A 350 m
  2. B 500 m
  3. C 700 m
  4. D 1,200 m
Show answer

Answer: B · 500 m

The two legs meet at a right angle, so the straight-line distance is the hypotenuse: √(300² + 400²) = √250,000 = 500 m. Answering 700 m adds the two legs, which is the distance walked rather than the distance from the start.

Surface area of a solid

Q14. A storage cube has an edge length of 5 cm. What is its total surface area?

  1. A 30 cm²
  2. B 100 cm²
  3. C 125 cm²
  4. D 150 cm²
Show answer

Answer: D · 150 cm²

Each face is 5 × 5 = 25 cm², and a cube has six faces, so 6 × 25 = 150 cm². Answering 125 cm² gives the volume (5³) instead, and 100 cm² counts only four faces.

Coordinates and reflection

Q15. A point at (3, −2) is reflected in the x-axis. What are the coordinates of the reflected point?

  1. A (−3, −2)
  2. B (−3, 2)
  3. C (3, 2)
  4. D (−2, 3)
Show answer

Answer: C · (3, 2)

Reflecting in the x-axis leaves the x-coordinate alone and changes the sign of the y-coordinate, giving (3, 2). Answering (−3, −2) reflects in the y-axis instead, and (−2, 3) swaps the coordinates.

NC6

Data and statistics

3 questions, each with a worked solution.

Working backwards from a mean

Q16. Four classes sat the same test. Across all four the mean was 68%. Three of the classes averaged 65%, 71% and 64%. What was the fourth class's average?

  1. A 66%
  2. B 68%
  3. C 72%
  4. D 74%
Show answer

Answer: C · 72%

The four class averages must total 4 × 68 = 272. The three known averages total 65 + 71 + 64 = 200, so the fourth is 272 − 200 = 72%. Answering 68% assumes every class matched the overall mean.

Percentage of a total

Q17. In a survey of 240 students, 90 walk to school, 78 catch a bus and 54 are driven. The rest cycle. What percentage of the students cycle?

  1. A 6%
  2. B 7.5%
  3. C 9%
  4. D 12.5%
Show answer

Answer: B · 7.5%

The three listed groups total 90 + 78 + 54 = 222, so 240 − 222 = 18 students cycle. As a percentage, 18 ÷ 240 = 0.075, which is 7.5%.

Interpreting spread

Q18. Class A's test scores range from 42 to 88. Class B's range from 61 to 75. Which statement is best supported by that information alone?

  1. A Class A has the higher mean.
  2. B Class B's scores are more consistent.
  3. C Class B has more students than Class A.
  4. D Class A has the higher median.
Show answer

Answer: B · Class B's scores are more consistent.

The range describes spread and nothing else. Class B's scores sit in a 14-mark band against Class A's 46, so Class B is more consistent. Nothing here fixes either group's mean, median or size.

NC7

Evaluating and probability

3 questions, each with a worked solution.

Probability of a complement

Q19. A bag holds 5 red counters, 3 blue and 4 green. One counter is drawn at random. What is the probability that it is not blue?

  1. A 1/4
  2. B 1/3
  3. C 2/3
  4. D 3/4
Show answer

Answer: D · 3/4

There are 12 counters and 3 are blue, so 9 are not. The probability is 9/12 = 3/4. Answering 1/4 gives the probability that it is blue.

Choosing a measure of centre

Q20. Seven students scored 4, 5, 6, 7, 8, 9 and 22. Which measure best represents a typical score for this group, and why?

  1. A The mean, because it uses every score.
  2. B The median, because the score of 22 pulls the mean above most of the group.
  3. C The mean, because it is higher than the median.
  4. D The range, because it shows the full spread.
Show answer

Answer: B · The median, because the score of 22 pulls the mean above most of the group.

The mean is 61 ÷ 7 ≈ 8.7, which is higher than five of the seven scores. The median of 7 sits in the middle of the group, so it describes a typical student better when one score is far from the rest.

Evaluating a claim

Q21. A school finds that students who attend voluntary tutoring score higher on average than those who do not, and concludes that the tutoring caused the improvement. What is the strongest objection to that conclusion?

  1. A Averages should never be compared between two groups.
  2. B Students who choose to attend tutoring may already differ from those who do not.
  3. C The sample of students was too large to draw a conclusion from.
  4. D The result should have been reported as a percentage rather than an average.
Show answer

Answer: B · Students who choose to attend tutoring may already differ from those who do not.

Attendance was voluntary, so the two groups were not formed at random. Students who opt in may already be more motivated or better supported, and that difference, not the tutoring, could explain the gap. A larger sample is a strength, not a weakness.

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These are original, Teacher Passport-authored practice questions written to resemble the style and difficulty of LANTITE. They are not real LANTITE questions and are not an official practice test. Teacher Passport is not affiliated with ACER. The only official practice materials are free from ACER at teacheredtest.acer.edu.au.