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Free NAPLAN Numeracy Practice: Linear & non-linear relationships — Year 9 (10 Questions, Instant Results)

10 questions on linear and non-linear relationships, pitched at Year 9, marked instantly with an explanation for every item. The set is chosen from 14 curriculum-aligned questions on this topic, one slice of the 3,261 free practice questions on this site, and you can get a fresh set with one click.

Start the quiz ↓   Or take the free 15-minute Skills Check →

✅ Victorian Curriculum aligned⚡ Instant marking + explanations📚 3,261 free practice questions

Free practice quizzesNAPLAN Numeracy Year 9 quiz › Linear & non-linear relationships

How NAPLAN tests linear and non-linear relationships in Year 9

NAPLAN reports a Year 9 result in four proficiency levels, and the difference between Developing and Strong is usually a handful of specific skills. Linear & non-linear relationships is one of the areas where our tutors see that gap most often. Use this single-topic quiz to test it directly, then the mixed NAPLAN quiz to see how it holds up alongside everything else.

What Year 9 students need to know about linear and non-linear relationships

A short orientation first. Year 9 graphing covers gradient and intercept, sketching straight lines, midpoint and distance between points, parallel and perpendicular lines, and a first look at parabolas, circles and exponential curves.

Our tutors wrote and checked these questions against the Victorian Curriculum, which is why the wording and the difficulty match what a Year 9 student meets at school.

The usual linear and non-linear relationships errors at Year 9

If your child gets a question wrong here, it is worth checking whether one of these is behind it. They are the linear and non-linear relationships misconceptions RHZ tutors correct most often with Year 9 students:

Each of these is fixable in a session or two once it has been named, which is why the results panel below shows the correct answer and an explanation rather than just a score.

How to practise linear and non-linear relationships at home

Practice works when it is short, regular and specific. For linear and non-linear relationships, our tutors suggest:

  1. Draw the basic parabola and circle by hand until their shapes are familiar.
  2. Sketch every line from its intercept and gradient rather than a table.
  3. Use graphing software to see how changing m and c moves a line.

For Years 7 to 10, practise the way a test is sat: mixed questions, time limits, full working. Then mark it honestly and re-do the errors.

How the 10 questions are chosen

Every set on this page is a seeded selection of 10 from the 14 linear and non-linear relationships questions that pass our quality gate. A different seed gives a different set, and there are many more combinations than any one student will need. The correct answers never appear in the page source; the browser asks our server for them after you press Mark my answers.

Because every question here is on linear and non-linear relationships, a low score is a clear signal and a high score is genuinely reassuring for this topic. What it cannot tell you is whether the other Year 9 NAPLAN Numeracy topics are equally secure, or how far above the year level the student can go; the free Skills Check covers both.

The quiz: 10 questions

Choose one answer for each question, then press Mark my answers. Set 14853 · New set of questions →

Question 1
Linear & non-linear relationships

A taxi charges a $3.50 flag fall plus $2.20 per kilometre. A ride-share charges $1.00 flag fall plus $2.60 per kilometre. For what distance (in km) is the total cost the same for both services? Give your answer to one decimal place.

Question 2
Linear & non-linear relationships

Find the midpoint of (2, 3) and (8, 7).

Question 3
Linear & non-linear relationships

Find the gradient of the line through (1, 2) and (4, 11).

Question 4
Linear & non-linear relationships

Solve simultaneously: y = 2x and y = x + 4.

Question 5
Linear & non-linear relationships

The graph of y = x² − 4 cuts the x-axis at:

Question 6
Linear & non-linear relationships

What is the gradient of y = −4x + 1?

Question 7
Linear & non-linear relationships

A linear function passes through (0, −3) and has gradient 2. A second linear function passes through (0, 5) and has gradient −2. At what point do these two lines intersect?

Question 8
Linear & non-linear relationships

What is the y-intercept of y = 3x + 7?

Question 9
Linear & non-linear relationships

A line is y = 2x − 3. Find y when x = 4.

Question 10
Linear & non-linear relationships

A line passes through the points (−2, 1) and (4, 13). Another line has equation y = 2x − 5. Are these two lines parallel, perpendicular, or neither?

How to read a score out of 10

9 or 10 out of 10
The easy and at-level content is secure. The useful question now is how far above the year level the student can go, which a ten-item quiz cannot show. The free Skills Check adds stretch and challenge questions on every topic so you can see the ceiling as well as the floor.
7 or 8 out of 10
Solid, with one or two specific gaps. Look at which topic the incorrect answers came from (the results panel names the weakest topic) and spend a week on that topic before re-testing with a different seed.
5 or 6 out of 10
Some core ideas are shaky. The pattern matters more than the score: two misses in the same topic is a gap; misses scattered across topics usually means reading the question too fast. Either way, the Skills Check will tell you which.
4 or fewer out of 10
Foundations from an earlier year are probably missing, which is common and fixable. Try the quiz one year level down to confirm, then talk to a tutor about a short catch-up plan rather than more of the same practice.

What to do with the result

1. Want the full picture?

The free Skills Check takes about 15 minutes, covers every Year 9 topic including stretch and challenge questions, and sends a same-day topic-by-topic report. A tutor calls to walk you through it, no obligation.

Start the free Skills Check →

2. Printable practice with answers

Our Year 9 practice papers are full-length, curriculum-aligned and come with worked answers, so a student can practise on paper the way the real test is sat.

Browse practice papers →

3. Tutoring in Melbourne's west or online

Small groups from $25 an hour and 1:1 from $35 an hour at our Truganina centre, or online anywhere in Australia. Same tutors, same Skills Check, same progress notes either way.

See NAPLAN tutoring → All tutoring →

Questions? Call 03 9509 3293 or book a free consultation. RHZ Tutoring, 17/47 Apex Drive, Truganina VIC 3029.

Frequently asked questions

Is this Year 9 linear and non-linear relationships quiz free?

Yes, completely: no sign-up, no email, no payment, and you can take it as many times as you like. It is one of 3,261 free practice questions RHZ Tutoring publishes across Prep to Year 12. Press New set of questions, or add ?seed= to the address, for a different selection from the same topic.

Why only 10 questions on one topic?

Because a single-topic set is the most precise free check available: if the score is low, the gap is in linear and non-linear relationships and nowhere else. There are 14 eligible questions on this topic in our Year 9 NAPLAN Numeracy bank, so several different sets are available before any repeat.

Where do the linear and non-linear relationships questions come from?

From RHZ Tutoring's own Year 9 NAPLAN Numeracy question bank, written to the Victorian Curriculum, checked by a tutor and passed through an automated quality gate. The same bank feeds our tutoring sessions and the free Skills Check. The questions on this page sit at the easy and at-level tiers.

What should I do if the score is low?

Read the explanation for each incorrect answer first; most gaps in linear and non-linear relationships are one of the misconceptions listed on this page. Then try a second set a few days later. If it is still low, the free Skills Check will show whether the gap is confined to this topic, and a tutor can build a short catch-up plan.

Is there a mixed Year 9 NAPLAN Numeracy quiz?

Yes. The Year 9 NAPLAN Numeracy quiz spreads ten questions across every topic for the year, and the hub lists topic quizzes for every year level from Prep to Year 12.

Other NAPLAN Numeracy topics for Year 9

Mixed NAPLAN Numeracy Year 9 quiz (all topics) →

All 3,261 free practice questions, Prep to Year 12 →