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Bearing - Math Revision for Year 11 Maths Adv; Topic Specific

Math Revision for Year 11 Maths Adv; Topic Specific

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math advanced

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• 11

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Cherrybrook Technology High School

Academic year: 2023/2024

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ADV: Trigonometry (Adv), T1 Trigonometry and Measure of Angles

(Adv)

Bearings (Y11)

Teacher: Helen Tolhurst

Exam Equivalent Time: 72 minutes (based on HSC allocation of 1 minutes approx. per

mark)

HISTORICAL CONTRIBUTION

T1 Trigonometry and Measure of Angles contains content that has been taken from

both the old Mathematics and Ext1 courses. Our analysis has it accounting for an

estimated 5% of past papers.

This topic has been split into four sub-topics for analysis purposes: 1-Trig Ratios, Sine

and Cosine Rules (2%), and 2- 3D Trigonometry (0%), Bearings (1%) and Circular

Measure (1%).

This analysis looks at the sub-topic Bearings.

HSC ANALYSIS - What to expect and common pitfalls

Bearings is a prime topic area to test Advanced and Standard 2 students with

common content. The 2020 exam confirmed this with a common question worth a

substantial 5 marks.

Before 2020, bearings was most recently tested in the Advanced exam in 2018 and

2014. We expect this topic to be examined more regularly going forward, and with

good mark allocations on offer when it is asked, a revision focus is warranted.

A number of Std2 past HSC questions have been included in this database (identified

by 2ADV* in the title).

1. Measurement, STD2 M6 SM-Bank 2 MC

2. Measurement, STD2 M6 SM-Bank 3 MC

3. Trigonometry, 2ADV* T1 2010 HSC 10 MC

Questions

Which of the following expresses S60°W as a true bearing?

A.

B.

C.

D. Which of the following expresses S65°W as a true bearing?

A. 065°

B. 155°

C. 245°

D. 295°

A plane flies on a bearing of 150° from to.

What is the bearing of from?

(A)

(B)

(C)

(D)

4. Trigonometry, 2ADV* T1 2012 HSC 20 MC

Town is 80 km due north of Town and 59 km from Town.

Town is 31 km from Town.

What is the bearing of Town from Town?

(A)

(B)

(C)

(D)

5. Trigonometry, 2ADV* T1 2014 HSC 23 MC

The following information is given about the locations of three towns , and :

is due east of
is on a bearing of from
is on a bearing of from.

Which diagram best represents this information?

9. Trigonometry, 2ADV T1 2018 HSC 12a

10. Trigonometry, 2ADV T1 2020 HSC 15

A ship travels from Port A on a bearing of 050° for 320 km to Port B. It then travels on a bearing of

120° for 190 km to Port C.

i. What is the size of? (1 mark)

ii. What is the distance from Port A to Port C? Answer to the nearest 10 kilometres. (2 marks)

 Part a: RAP Data - Bottom 10%: School result (94%) was -1% below state average (95%)

 Part b: RAP Data - Bottom 16%: School result (85%) was 1% above state average (84%)

 Part c: RAP Data - Bottom 7%: School result (57%) was -2% below state average (59%)

Mr Ali, Ms Brown and a group of students were camping at the site located at. Mr Ali walked with

some of the students on a bearing of 035° for 7 km to location. Ms Brown, with the rest of the

students, walked on a bearing of 100° for 9 km to location.

N

P

9 km

7 km

A

B

NOT TO

SCALE

a. Show that the angle is 65°. (1 mark)

b. Find the distance. (2 marks)

c. Find the bearing of Ms Brown's group from Mr Ali's group. Give your answer correct to the nearest

degree. (2 marks)

11. Trigonometry, 2ADV T1 2004 HSC 3c

12. Trigonometry, 2ADV T1 2014 HSC 13d

The diagram shows a point which is 30 km due west of the point.

The point is 12 km from and has a bearing from of 070°.

i. Find the distance of from. (2 marks)

ii. Find the bearing of from. (2 marks)

 Part ii: RAP Data - Bottom 23%: School result (61%) was 3% above state average (58%)

Chris leaves island in a boat and sails 142 km on a bearing of 078° to island. Chris then sails

on a bearing of 191° for 220 km to island , as shown in the diagram.

i. Show that the distance from island to island is approximately 210 km. (2 marks)

ii. Chris wants to sail from island directly to island. On what bearing should Chris sail? Give

your answer correct to the nearest degree. (3 marks)

13. Trigonometry, 2ADV* T1 2005 HSC 27c

14. Trigonometry, 2ADV* T1 2009 HSC 27b

The bearing of from is 250° and the distance of from is 36 km.

i. Explain why is. (1 mark)

ii. If is 15 km due north of , calculate the distance of from , correct to the nearest

kilometre. (3 marks)

A yacht race follows the triangular course shown in the diagram. The course from to is 1.

km on a true bearing of 058°.

At the course changes direction. The course from to is 2 km and.

i. What is the bearing of from? (1 mark)

ii. What is the distance from to? (2 marks)

iii. The area inside this triangular course is set as a ‘no-go’ zone for other boats while the race is on.

What is the area of this ‘no-go’ zone? (1 mark)

15. Trigonometry, 2ADV* T1 2007 26a

The diagram shows information about the locations of towns , and.

i. It takes Elina 2 hours and 48 minutes to walk directly from Town to Town.

Calculate her walking speed correct to the nearest km/h. (1 mark)

ii. Elina decides, instead, to walk to Town from Town and then to Town.

Find the distance from Town to Town. Give your answer to the nearest km. (2 marks)

iii. Calculate the bearing of Town from Town. (1 mark)

3. Trigonometry, 2ADV* T1 2010 HSC 10 MC

4. Trigonometry, 2ADV* T1 2012 HSC 20 MC

COMMENT: Drawing a parallel

North/South line through

makes this question much simpler

to solve.

5. Trigonometry, 2ADV* T1 2014 HSC 23 MC

6. Trigonometry, 2ADV* T1 2016 HSC 25 MC

7. Trigonometry, 2ADV* T1 2008 HSC 17 MC

♦ Mean mark 47%.

8. Measurement, STD2 M6 2019 HSC 4 MC

9. Trigonometry, 2ADV T1 2018 HSC 12a

i.

ii.

12. Trigonometry, 2ADV T1 2014 HSC 13d

i.

ii.

13. Trigonometry, 2ADV* T1 2005 HSC 27c

i.

ii.

TIP: Draw North-South parallel

lines through relevant points to

help calculate angles as shown in

the Worked Solutions.

14. Trigonometry, 2ADV* T1 2009 HSC 27b

i.

(ii)

+

(iii)

²

♦♦ Mean mark part (ii) 31%.

16. Trigonometry, 2ADV* T1 2017 HSC 30c

(i)

(ii)

STRATEGY: This deserves

repeating again: Draw North-South

parallel lines through major points

to make the angle calculations

easier!

MARKER'S COMMENT: The best

responses showed clear working

on the diagram.

17. Trigonometry, 2ADV* T1 2011 HSC 24c

i.

ii.

iii.

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Bearing - Math Revision for Year 11 Maths Adv; Topic Specific

Subject: math advanced

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ADV: Trigonometry (Adv), T1 Trigonometry and Measure of Angles

(Adv)

Bearings (Y11)

Teacher: Helen Tolhurst

Exam Equivalent Time: 72 minutes (based on HSC allocation of 1.5 minutes approx. per

mark)

HISTORICAL CONTRIBUTION

T1 Trigonometry and Measure of Angles contains content that has been taken from

both the old Mathematics and Ext1 courses. Our analysis has it accounting for an

estimated 5.8% of past papers.

This topic has been split into four sub-topics for analysis purposes: 1-Trig Ratios, Sine

and Cosine Rules (2.2%), and 2- 3D Trigonometry (0.7%), Bearings (1.3%) and Circular

Measure (1.6%).

This analysis looks at the sub-topic Bearings.

HSC ANALYSIS - What toexpect and commonpitfalls

Bearings is a prime topic area to test Advanced and Standard 2 students with

common content. The 2020 exam conﬁrmed this with a common question worth a

substantial 5 marks.

Before 2020, bearings was most recently tested in the Advanced exam in 2018 and

2014. We expect this topic to be examined more regularly going forward, and with

good mark allocations on offer when it is asked, a revision focus is warranted.

A number of Std2 past HSC questions have been included in this database (identiﬁed

by 2ADV* in the title).

1.Measurement, STD2 M6 SM-Bank 2 MC

2.Measurement, STD2 M6 SM-Bank 3 MC

3.Trigonometry, 2ADV* T1 2010 HSC 10 MC

Questions

Which of the following expresses S60°W as a true bearing?

A. 

B. 

C. 

D. 

Which of the following expresses S65°W as a true bearing?

A. 065°

B. 155°

C. 245°

D. 295°

A plane ﬂies on a bearing of 150° from  to  .



What is the bearing of  from ?

(A) 

(B) 

(C) 

(D) 

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Bearing - Math Revision for Year 11 Maths Adv; Topic Specific

math advanced

HSC

Cherrybrook Technology High School

Recommended for you

Comments

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Preview text

ADV: Trigonometry (Adv), T1 Trigonometry and Measure of Angles

(Adv)

Bearings (Y11)

Teacher: Helen Tolhurst

Exam Equivalent Time: 72 minutes (based on HSC allocation of 1 minutes approx. per

mark)

HISTORICAL CONTRIBUTION

T1 Trigonometry and Measure of Angles contains content that has been taken from

both the old Mathematics and Ext1 courses. Our analysis has it accounting for an

estimated 5% of past papers.

This topic has been split into four sub-topics for analysis purposes: 1-Trig Ratios, Sine

and Cosine Rules (2%), and 2- 3D Trigonometry (0%), Bearings (1%) and Circular

Measure (1%).

This analysis looks at the sub-topic Bearings.

HSC ANALYSIS - What to expect and common pitfalls

Bearings is a prime topic area to test Advanced and Standard 2 students with

common content. The 2020 exam confirmed this with a common question worth a

substantial 5 marks.

Before 2020, bearings was most recently tested in the Advanced exam in 2018 and

2014. We expect this topic to be examined more regularly going forward, and with

good mark allocations on offer when it is asked, a revision focus is warranted.

A number of Std2 past HSC questions have been included in this database (identified

by 2ADV* in the title).

1. Measurement, STD2 M6 SM-Bank 2 MC

2. Measurement, STD2 M6 SM-Bank 3 MC

3. Trigonometry, 2ADV* T1 2010 HSC 10 MC

Questions

Which of the following expresses S60°W as a true bearing?

A.

B.

C.

D.

Which of the following expresses S65°W as a true bearing?

A. 065°

B. 155°

C. 245°

D. 295°

A plane flies on a bearing of 150° from to.

What is the bearing of from?

(A)

(B)

(C)

(D)

4. Trigonometry, 2ADV* T1 2012 HSC 20 MC

Town is 80 km due north of Town and 59 km from Town.

Town is 31 km from Town.

What is the bearing of Town from Town?

(A)

(B)

(C)

(D)

5. Trigonometry, 2ADV* T1 2014 HSC 23 MC

The following information is given about the locations of three towns , and :

Which diagram best represents this information?

9. Trigonometry, 2ADV T1 2018 HSC 12a

10. Trigonometry, 2ADV T1 2020 HSC 15

A ship travels from Port A on a bearing of 050° for 320 km to Port B. It then travels on a bearing of

120° for 190 km to Port C.

i. What is the size of? (1 mark)

ii. What is the distance from Port A to Port C? Answer to the nearest 10 kilometres. (2 marks)

 Part a: RAP Data - Bottom 10%: School result (94%) was -1% below state average (95%)

 Part b: RAP Data - Bottom 16%: School result (85%) was 1% above state average (84%)

 Part c: RAP Data - Bottom 7%: School result (57%) was -2% below state average (59%)

Mr Ali, Ms Brown and a group of students were camping at the site located at. Mr Ali walked with

some of the students on a bearing of 035° for 7 km to location. Ms Brown, with the rest of the

students, walked on a bearing of 100° for 9 km to location.

N

P

9 km

7 km

c. Find the bearing of Ms Brown's group from Mr Ali's group. Give your answer correct to the nearest