9th Class Maths Chapter 6 Online Test: 25 MCQs with Answers

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This 9th class maths chapter 6 online test covers Chapter 6 of the Class 9 Mathematics course, Trigonometry. It has 25 multiple-choice questions, shown one at a time, and it marks itself the moment you finish. There is no timer and no sign-up. When you press finish you get your score, and every question is shown again with your answer, the correct option and a short explanation of why that option is right. An Urdu medium version of the same test is given further down this page.

What Chapter 6 Covers

The 25 questions are spread across the whole unit rather than one exercise, so the test is a fair check of whether you are ready for a class test or the annual paper:

  • Degree and radian measure — the definition of a radian, converting 292.5° to radians and 5π/24 rad to degrees.
  • Degrees, minutes and seconds — expressing a value such as 123.456° in that form.
  • Arc length and sector area — ℓ = rθ and A = ½r2θ, with θ in radians.
  • Trigonometric ratios of standard angles — sin 60°, cot 30° and the rest of the standard table.
  • Fundamental identities — sin2θ + cos2θ = 1, sec2θ − tan2θ = 1 and 1 + cot2θ = cosec2θ.
  • Quadrants and coterminal angles — where 135° lies, and why 45°, 405° and −315° are coterminal.
  • Right-triangle problems — angles of elevation, and finding a side when the hypotenuse and an angle are given.

Revise These Before You Start

Most marks in this unit are lost on the same few points. Read through these once before attempting the test:

  • A radian is the angle subtended at the centre by an arc equal in length to the radius, and 1 radian is about 57.3°.
  • The formulas ℓ = rθ and A = ½r2θ only work when θ is in radians. Convert first, every time.
  • sec2θ − tan2θ = 1 and 1 + cot2θ = cosec2θ follow directly from sin2θ + cos2θ = 1.
  • cos2x + sin2x = 1 whatever x is, so cos2 100π + sin2 100π = 1 without any calculation.
  • Coterminal angles differ by a whole number of complete turns, so they share the same terminal arm and the same ratios.
  • One degree is 1/360 of a full turn, and one-eighth of a turn is 45°.

How the Test Works

  • 25 questions, one at a time, with Next and Previous buttons.
  • No timer, so you can work a calculation out on paper before answering.
  • Automatic marking the moment you finish.
  • Answer review with the correct option and an explanation for every question.
  • Retake as many times as you like, and your score is not stored anywhere.

Start the Chapter 6 Online Test

Before you answer anything with a sector in it, check whether the angle is in degrees or radians — that one habit protects several marks. Keep a pen and rough paper beside you: the numerical questions are quick, but they are much easier to get right written down than in your head. Aim for 20 out of 25 or better before you move on to the next unit.

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Class 9 Mathematics Chapter 6 Online Test — Trigonometry (English Medium)

1 / 25

In a right triangle, the hypotenuse is 13 units and one of the angles is θ = 30°. The length of the opposite side is:

2 / 25

A person standing 50 m away from a building sees the top of the building at an angle of elevation of 45°. Height of the building is:

3 / 25

sec²θ − tan²θ = ______.

4 / 25

If sin θ = 3/5 and θ is an acute angle, cos² θ = ______.

5 / 25

5π/24 rad = ______ degrees.

6 / 25

292.5° = ______ rad.

7 / 25

Which of the following is a valid identity?

8 / 25

sin 60° = ______.

9 / 25

cos² 100π + sin² 100π = ______.

10 / 25

A degree (°) represents which part of a full rotation around a point?

11 / 25

1° is equal to:

12 / 25

The angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle is:

13 / 25

1 radian is approximately equal to:

14 / 25

If r is the radius and θ (in radians) is the central angle, then the area of the sector is:

15 / 25

1 + cot²θ = ______.

16 / 25

cot 30° = ______.

17 / 25

The angles 45°, 405° and −315° are:

18 / 25

The arc length of a sector with radius r = 10 cm and central angle θ = 60° is approximately:

19 / 25

The area of a sector with radius r = 8 cm and central angle θ = 45° is approximately:

20 / 25

One-eighth (1/8) of a turn is equal to:

21 / 25

The angle 135° lies in the:

22 / 25

123.456° in degrees, minutes and seconds is:

23 / 25

sin 60° cos 30° + cos 60° sin 30° = ______.

24 / 25

If the arc length of a sector of radius 5 cm is 11 cm, then the central angle is:

25 / 25

If tan θ = 3/4 and θ lies in the first quadrant, then sin θ = ______.

Your score is

0%

Chapter 6 Online Test — Urdu Medium

Urdu medium students can attempt the same Chapter 6 test with every question, option and explanation written in Urdu. It behaves exactly like the English test above: 25 questions one at a time, no timer, and a full answer review at the end.

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Class 9 Mathematics Chapter 6 Online Test — Trigonometry (Urdu Medium)

1 / 25

قائمۃ الزاویہ مثلث میں، وتر 13 اکائیاں اور ایک زاویہ θ = 30° ہے۔ مخالف ضلع کی لمبائی ہے:

2 / 25

عمارت سے 50 m دور کھڑا شخص عمارت کی چوٹی کو 45° کی بلندی کے زاویے پر دیکھتا ہے۔ عمارت کی اونچائی ہے:

3 / 25

sec²θ − tan²θ = ______۔

4 / 25

اگر sin θ = 3/5 اور θ ایک حادہ زاویہ ہو تو cos²θ = ______۔

5 / 25

5π/24 rad = ______ ڈگریاں۔

6 / 25

292.5° = ______ rad۔

7 / 25

درج ذیل میں سے کون سی ایک درست تکونیاتی اکائی ہے؟

8 / 25

sin 60° = ______۔

9 / 25

cos² 100π + sin² 100π = ______۔

10 / 25

ایک ڈگری (°) کسی نقطے کے گرد مکمل چکر کا کون سا حصہ ظاہر کرتی ہے؟

11 / 25

1° برابر ہے:

12 / 25

کسی دائرے کے مرکز پر اُس قوس کے ذریعے بنایا گیا زاویہ جس کی لمبائی دائرے کے رداس کے برابر ہو، کہلاتا ہے:

13 / 25

1 ریڈین تقریباً برابر ہے:

14 / 25

اگر r رداس اور θ (ریڈین میں) مرکزی زاویہ ہو تو علاقہ کا رقبہ ہے:

15 / 25

1 + cot²θ = ______۔

16 / 25

cot 30° = ______۔

17 / 25

زاویے 45°، 405° اور −315° ہیں:

18 / 25

اُس علاقہ کی قوس کی لمبائی جس کا رداس r = 10 cm اور مرکزی زاویہ θ = 60° ہو، تقریباً ہے:

19 / 25

اُس علاقہ کا رقبہ جس کا رداس r = 8 cm اور مرکزی زاویہ θ = 45° ہو، تقریباً ہے:

20 / 25

ایک چکر کا آٹھواں حصہ (1/8) برابر ہے:

21 / 25

زاویہ 135° واقع ہے:

22 / 25

123.456° ڈگری، منٹ اور سیکنڈ میں ہے:

23 / 25

sin 60° cos 30° + cos 60° sin 30° = ______۔

24 / 25

اگر کسی علاقہ میں قوس کی لمبائی 11 cm اور رداس 5 cm ہو تو مرکزی زاویہ ہے:

25 / 25

اگر tan θ = 3/4 ہو اور θ پہلے ربع میں واقع ہو تو sin θ = ______۔

Your score is

0%

Mistakes Students Make in This Unit

When you look through your answer review, check whether any of your wrong answers came from these:

  • Using degrees in ℓ = rθ or A = ½r2θ, which is the most commonly lost mark in this chapter.
  • Mixing up 1 + tan2θ = sec2θ with 1 + cot2θ = cosec2θ.
  • Converting degrees to radians by multiplying by 180/π instead of π/180.
  • Reading the angle of elevation from the wrong side of the triangle.
  • Rounding part-way through a multi-step calculation.

What to Do After the Test

A score on its own teaches you very little. Go through the answer review properly and write down the number of every question you got wrong, along with the topic it came from. If two or three of them come from the same section of the unit, that section is what you revise next — not the whole chapter again. Then retake the test a day or two later rather than immediately, because answering correctly from memory is not the same as understanding it. Once you are consistently scoring above 20, move on and come back to this test in your final week of revision.

Frequently Asked Questions

What exactly is a radian?

It is the angle at the centre of a circle subtended by an arc whose length equals the radius. Because it is defined by a ratio of lengths it has no units, and a full turn is 2π radians, roughly 6.28.

Why must θ be in radians for arc length and sector area?

Both formulas are derived from the fraction of the circle the sector covers, and that derivation uses the radian definition. Put degrees in and the answer is wrong by a factor of π/180.

How do I convert degrees to radians?

Multiply by π/180. So 292.5° × π/180 gives 13π/8 radians. To go the other way, multiply by 180/π.

Is this test free?

Yes. There is no sign-up, no limit on retakes and nothing is locked. Your score is not saved or shared.

Related Class 9 Maths Resources

Carry on with the Chapter 6 test paper for written practice, the Chapter 5 online test (Linear Equations and Inequalities), the Chapter 7 online test (Coordinate Geometry). For full-length practice, download the 25 Class 9 Maths guess papers, each a complete 75-mark bilingual paper. You can also browse all Class 9 Maths test papers and every Class 9 Maths online test, or open the Class 9 Mathematics section for everything in one place.

Studying the other subjects too? There are self-marking chapter tests for Class 9 Physics and Class 9 Biology, and you can browse the whole Class 9 section by subject.

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