Free · No sign-up · Year 9 · Maths · Trigonometry

Free Year 9 Trigonometry Quiz — 10 Questions, Instant Results

A single-topic check for Year 9 maths: 10 multiple-choice questions on trigonometry, selected from 20 items our tutors have checked, marked on the page with explanations. It is one of the 3,261 free practice questions across our whole bank, and there is nothing to sign up for.

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

Free practice quizzesYear 9 Maths quiz › Trigonometry

What trigonometry covers in Year 9 maths

Before the quiz, here is what the topic means at this level. Year 9 trigonometry introduces the sine, cosine and tangent ratios in right-angled triangles, finding unknown sides and angles, and applying them to angles of elevation and depression.

Every question on this page was written to a specific Victorian Curriculum reference for Year 9 and checked by an RHZ tutor before it could be served.

Where Year 9 students go wrong with trigonometry

Most errors in trigonometry are not random. When Year 9 students sit our Skills Check, the same handful of misunderstandings account for the majority of lost marks:

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.

What to do if trigonometry needs work

Three things a parent or student can do this week:

  1. Check the calculator mode at the start of every session.
  2. Draw bearing diagrams with north marked before calculating.
  3. Learn the exact values for 30, 45 and 60 degrees.

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 this trigonometry quiz works

Every set on this page is a seeded selection of 10 from the 20 trigonometry 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 trigonometry, 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 maths 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 11873 · New set of questions →

Question 1
Trigonometry

Which equation is Pythagoras' theorem?

Question 2
Trigonometry

The ratio opposite ÷ hypotenuse is:

Question 3
Trigonometry

A right-angled triangle has a hypotenuse of 15 cm. One angle is 50°. A student calculates the side opposite the 50° angle as 15 ÷ sin(50°). What error did the student make, and what is the correct length to 1 decimal place?

Question 4
Trigonometry

In a right triangle, the angle is 30° and the hypotenuse is 10 cm. The opposite side is:

Question 5
Trigonometry

What is the exact value of sin 30°?

Question 6
Trigonometry

A surveyor stands 80 m from the base of a building. The angle of elevation to the top is 32°. Which expression gives the height of the building?

Question 7
Trigonometry

A right triangle has legs 3 cm and 4 cm. Find the hypotenuse.

Question 8
Trigonometry

A 5 m ladder rests with its base 3 m from a wall. How high up the wall does it reach?

Question 9
Trigonometry

In a right-angled triangle, the side opposite the right angle is the:

Question 10
Trigonometry

You know the opposite and adjacent sides and want the angle. Use:

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 Maths 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 trigonometry 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 trigonometry and nowhere else. There are 20 eligible questions on this topic in our Year 9 Maths bank, so several different sets are available before any repeat.

Where do the trigonometry questions come from?

From RHZ Tutoring's own Year 9 Maths 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 trigonometry 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 Maths quiz?

Yes. The Year 9 Maths 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 Maths topics for Year 9

Mixed Year 9 Maths quiz (all topics) →

Trigonometry in other year levels

Year 10 Trigonometry · Year 11 Trigonometry

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