Maths Standards 1 HSC Questions by Topics PDF

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Nesa's collection of HSC questions by topic, great for revision of Year 11 content, which could be helpful for practice. Best of luck!!...

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Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

MATHEMATICS STANDARD 1 HSC Exam* Questions by Topic 2021 - 2017

v2022

Licensed from NESA

Year 11 Course

Year 12 Course

Complete Papers

Algebra

Algebra

2021 HSC

A1: Formulae and equations

A3.1: Simultaneous Linear Equations

2020 HSC

A2: Linear relationships

A3.2: Graphs of practical situations

Measurement

Measurement

M1.1: Practicalities of measuring

M3: Right-angled triangles

M1.2: Perimeter, area and volume

M4: Rates

M1.3: Units of energy and mass

M5: Scale drawings

M2: Working with time

Financial Mathematics

Financial Mathematics

F2: Investments

F1.1: Interest and depreciation

F3: Depreciation and loans

F1.2: Earning & managing money

Statistical Analysis

F1.3: Budgeting & household expenses

Statistics Analysis S1.1: Classifying & representing data S1.2: Summary Statistics S2: Relative frequency & probability

2019 HSC

Question Difficulty Easy Mid-range Difficult

S3.1: Statistical investigation process S3.2: Exploring data from 2 variables

Networks and Paths N2.1: Networks N2.2: Shortest paths

Mathematics Standard 1 Reference Sheet (2021 HSC)

Questions by Topic from … • 2021 – 2019 Mathematics Standard 1 HSC • NESA Mathematics Standard 1 Sample exam questions [SQ] (2019) • Selected NESA Topic Guidance questions [TG] (2018) • 2017 – 2018 Mathematics General 2 HSCs (eg 17 MG)

HSC Examination Papers Mathematics Standard 2 (2021 - 2019); Mathematics General 2 (20182017); Mathematics Advanced (2021, 2020); Mathematics (2019 – 2017); Mathematics Extension 1 (2021 – 2017) and Mathematics Standard 1 (2021 - 2019) © NSW Education Standards Authority for and on behalf of the Crown in right of the state of New South Wales.

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

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Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

Year 11: Measurement M2: Working with time

Back

Syllabus: updated November 2019. Latest version @ https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-standard-2017

Reference Sheet

21

15

MS1

City A is in Sweden and is located at (58°N, 16°E). Sydney, in Australia, is located at (33°S, 151°E). Robert lives in Sydney and needs to give an online presentation to his colleagues in City A starting at 5:00 pm Thursday, local time in Sweden.

3

Solution

What time and day, in Sydney, should Robert start his presentation? It is given that 15o = 1 hour time difference. Ignore daylight saving.* COMMON QUESTION: NESA 2021 Mathematics Standard 1* and Standard 2 HSC Examinations

20

15

MS1

The time in Melbourne is 11 hours ahead of Coordinated Universal Time (UTC). The time in Honolulu is 10 hours behind UTC. A plane departs Melbourne at 7 pm on Tuesday and lands in Honolulu 9 hours later.

2

Solution

What is the time and day in Honolulu when the plane lands? NESA 2020 Mathematics Standard 1 HSC Examination

19 MS 1

2

What is the time difference between 8:35 am and 2:10 pm? A. 5 hours and 25 minutes B. 5 hours and 35 minutes C. 6 hours and 25 minutes D. 6 hours and 35 minutes

1

Solution

NESA 2019 Mathematics Standard 1 HSC Examination

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

Page 3

Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

SQ MS

ME 5 Band

3-5

Part of a train timetable is shown. Kris arrives at Amesham station at 1.45 pm and needs to get to Frampton as quickly as possible. Assuming all trains run to schedule, what is the EARLIEST timFe that Kris can arrive at Frampton station? A. 2.29 pm B. 2.38 pm C. 2.47 pm D. 2.55 pm

1

Solution

NESA Mathematics Standard 1 Sample examination materials

SQ MS

ME 18 Band

3-5

13

27e

MG

Karin is in Athens, which is two hours ahead of Coordinated Universal Time (UTC). Marco is in New York, which is five hours behind UTC. (a) Karin is going to ring Marco at 10 pm on Tuesday, Athens time. What day and time will it be in New York when she rings? (b) Marco is going to fly from New York to Athens. His flight will leave on Wednesday at 9 am, New York time, and will take 11 hours. What day and time will it be in Athens when he arrives?

Solution

1 2

NESA Mathematics Standard 1 Sample examination materials NESA 2013 General Mathematics HSC Examination

18

29a

1 hours ahead of the time in New Delhi. John flew 2 from New Delhi to Brisbane via Singapore. His plane left New Delhi at 11:30 am (New Delhi time), stopped for 3 hours in Singapore, and arrived in Brisbane at 9:00 am the following day (Brisbane time). What was the plane’s total flying time?

27d

Island A and island B are both on the equator. Island B is west of island A. The longitude of island A is 5oE and the angle at the centre of the earth (O), between A and B, is 30o. (i) What is the longitude of island B? (ii) What time is it on island B when it is 10 am on island A? (iii) Projectmaths: not in Maths Stand 1

MG

The time in Brisbane is 4

3

Solution

NESA 2018 Mathematics General 2 HSC Examination

17 MG

Solution

1 1

Not to scale NESA 2017 Mathematics General 2 HSC Examination

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

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Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

Year 12: MS – M: Measurement Back

M6: Right-angled triangles Syllabus: updated November 2019. Latest version @ https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/stage-6-learning-areas/stage-6-mathematics/mathematics-standard-2017

Reference Sheet

21

10

MS 1

The compass bearing of B from A is N38oE.

1

Solution

What is the true bearing of A from B? A. 128o B. 218o C. 232o D. 322o

NESA 2021 Mathematics Standard 1 HSC Examination

21

28

MS 1

Solution

A right-angled triangle XYZ is shown. The length of XZ is 16 cm and  YXZ = 30°.

(a) Find the side length, XY, of the triangle in centimetres, correct to two decimal places.

2

(b) Hence, find the area of triangle

3

XYZ in square centimetres, correct to one decimal place. NESA 2021 Mathematics Standard 1 HSC Examination

20 MS 1

11

Solution

Consider the triangle shown. (a)

Find the value of degree.

, correct to the nearest

2

(b)

Find the value of x, correct to one decimal place.

2

COMMON QUESTION: NESA 2020 Mathematics Standard 1 and Standard 2 HSC Examinations

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

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Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

19

4

Which compass bearing is the same as a true bearing of 110°? A. S20°E B. S20°W C. S70°E D. S70°W

12

A surfer is 150 metres out to sea. From that point, the angle of elevation to the top of a cliff is 12°.

MS 1

1

Solution

COMMON QUESTION: NESA 2019 Mathematics Standard 1 and Standard 2 HSC Examinations

19 MS 1

2

Solution

How high is the cliff, to the nearest metre?

NESA 2019 Mathematics Standard 1 HSC Examination

19

31

MS 1

Two right-angled triangles, ABC and ADC, are shown.

Solution

3

Calculate the size of angle , correct to the nearest minute.

COMMON QUESTION: NESA 2019 Mathematics Standard 1 and Standard 2 HSC Examinations

SQ MS x

ME 1

In which triangle is sin  =

Band

4 7

1

?

Solution

2-3

A.

B.

C.

D.

NESA Mathematics Standard 1 Sample examination materials

SQ MS

ME 4

Which of the following expresses S20oW as a true bearing? A. 020o B. 070o C. 160o

1

Solution

1

Solution

1

Solution

o

D. 200

Band

2-3 NESA Mathematics Standard 1 Sample examination materials

SQ MS

ME 7 Band

5-6

Abbey walks 2 km due west from home to a coffee shop. She then walks on a bearing of 148o to school, which is due south of her home. How far south, to the nearest 0.1 km, is Abbey from home? A. 1.1 km B. 1.2 km C. 3.2 km D. 3.8 km NESA Mathematics Standard 1 Sample examination materials

SQ MS

ME 8 Band

4-5

Paul travels from A to B on a bearing of 150o. He then turns and walks to C on a bearing of 055o. What is the size of  ABC? A. 85o B. 90o o C. 95 D. 115o NOT TO SCALE NESA Mathematics Standard 1 Sample examination materials

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

SQ MS

ME 9 Band

4-5

The angle of depression from a window to a car on the ground is 40o. The car is 50 metres from the base of the building. How high above the ground is the window, correct to the nearest metre? A. 32 m B. 38 m C. 42 m D. 48 m

Page 6

1

Solution

NESA Mathematics Standard 1 Sample examination materials

SQ MS

ME 17 Band

4-6

A school badge is made up of an isosceles right triangle and arcs of two circles, as shown. In triangle ABC, AB = AC = 2 cm. The point D is the midpoint of BC, that is BD = CD. The arc BEC is part of a circle with centre A. The arc BFC is part of a circle with centre D. (a) The hatched area (BDCE) is to be silver plated. Show that this area, correct to 2 decimal places, is 1.14 cm2. (b) The shaded area which is not hatched (BECF) is to be gold plated. Calculate this area, correct to 2 decimal places.

Solution

2

2

NESA Mathematics Standard 1 Sample examination materials

TG

1

Solution

What is the length of the side MN in the following triangle, correct to two decimal places?

NESA Mathematics Standard 2 Year 11 Topic Guide: Measurement

17

8

MG

The diagram shows a right-angled triangle. What is the value of , to the nearest minute? (A) 70o 16’ (B) 70o 17’ (C) 70o 27’ (D) 70o 28’

1

Solution

2

Solution

NESA 2017 Mathematics General 2 HSC Examination

17 MG

26d

A sewer pipe needs to be placed into the ground so that it has a 2o angle of depression. The length of the pipe is 15 000 mm. How much deeper should one end of the pipe be compared to the other end? Answer to the nearest mm.

Not to scale

NESA 2017 Mathematics General 2 HSC Examination

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

Page 7

Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

2021 Standard 1 HSC Paper 21

1

MS 1

Back twentyone

1

A network diagram is shown. How many vertices are in this network?

Solution

A. 5 B. 6 C. 7 D. 8 NESA 2021 Mathematics Standard 1 HSC Examination

21

2

MS1

A survey of which of the following would provide data that are both categorical and nominal?

1

Solution

A. Hair colour B. Height in centimetres C. Number of people present at a concert D. Size of coffee cup classified as small, medium or large NESA 2021 Mathematics Standard 1 HSC Examination

21

3

MS 1

1

Consider the network diagram.

Solution

What is the sum of the degrees of all the vertices in this network? A. 5 B. 8 C. 14 D. 16 COMMON QUESTION: NESA 2021 Mathematics Standard 1 and Standard 2 HSC Examinations

21

4

MS 1

1

Three years ago an appliance was valued at $2467.

Solution

Its value has depreciated by 15% each year, based on the declining-balance method. What is its salvage value today, to the nearest dollar? A. $952

B. $1110

C. $1357

D. $1515

NESA 2021 Mathematics Standard 1 HSC Examination

21

5

Which of the following best represents the graph of y = –3x + 4?

1

Solution

MS1

NESA 2021 Mathematics Standard 1 HSC Examination

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

Page 8

Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

21

6

MS1

Blood pressure is recorded as systolic pressure/diastolic pressure and measured in mmHg.

1

Solution

When standing upright, Mary’s blood pressure was 139/85. Three minutes after sitting down, her blood pressure was 118/74. What was the change in Mary’s diastolic blood pressure? A. There was an increase of 11 mmHg. mmHg.

B. There was an increase of 21

C. There was a decrease of 11 mmHg.

D. There was a decrease of 21 mmHg. NESA 2021 Mathematics Standard 1 HSC Examination

21

7

MS1

Suppose a =

Solution

1

b , where b = 22. 7

What is the value of a, correct to three significant figures? A. 3.14

B. 3.15

C. 3.142

D. 3.143

COMMON QUESTION: NESA 2021 Mathematics Standard 1 and Standard 2 HSC Examinations

21

8

MS1

A student is thinking of a number. Let the number be x. When the student subtracts 8 from this number and multiplies the result by 3, the answer is 2 more than x.

1

Solution

Which equation can be used to find x? A. 3(x – 8) = 2x

B. 3x – 8 = 2x

C. 3(x – 8) = x + 2

D. 3x – 8 = x + 2

COMMON QUESTION: NESA 2021 Mathematics Standard 1 and Standard 2 HSC Examinations

21

9

MS1

James invests $5000 at 3% per annum simple interest for 2 years, while Sally invests $5000 at 3% per annum compounded annually for 2 years.

1

Solution

For the given investments, which of the following statements is TRUE? A. James earns more interest than Sally. B. Sally earns more interest than James. C. James and Sally earn the same amount of interest. D. There is not enough information to compare the interest earned by James and Sally. NESA 2021 Mathematics Standard 1 HSC Examination

21 MS1

10

The compass bearing of B from A is N38oE.

1

Solution

What is the true bearing of A from B? A. 128o B. 218o C. 232o D. 322o

NESA 2021 Mathematics Standard 1 HSC Examination

HSC Maths Standard 1, Maths Gen 2, General Maths © NSW Education Standards Authority for & on behalf of the Crown in right of State of NSW

Page 9

Mathematics Standard 1 HSC Examinations by Topics compiled by projectmaths.com.au

21

11

MS1

Chocolate of a particular brand can be bought in three different sizes.

Solution

2

Option 1: 100 grams for $1.50 Option 2: 300 grams for $4.20 Option 3: 500 grams for $7.25 Which option gives the lowest price per 100 grams? Justify your answer with calculations NESA 2021 Mathematics Standard 1 HSC Examination

21

12

MS1

A dance school runs a holiday program and charges $150 per student.

3

Solution

The costs of running the program are: Dance teacher: $110 per hour Room hire: $52 per hour plus 10% GST. The program goes for two hours a day for five days. What profit does the dance school make if 20 students pay for the program? NESA 2021 Mathematics Standard 1 HSC Examination

21

13

MS1

The fuel consumption for a car is 6.7 litres /100 km. On a road trip, the car travels a distance of 1560 km and the fuel cost is $1.45 per litre.

2

Solution

What is the total fuel cost for this trip? COMMON QUESTION: NESA 2021 Mathematics Standard 1 and Standard 2 HSC Examinations

21

14

MS1

It costs $2.45 for a car to travel on a toll road.

2

Solution

Due to inflation, the cost is to increase by 3% each year. How much will it cost for a car to travel on the toll road in 5 years time? NESA 2021 Mathematics Standard 1 HSC Examination

21

15

MS1

City A is in Sweden and is located at (58°N, 16°E). Sydney, in Australia, is located at (33°S, 151°E). Robert lives in Sydney and needs to give an online presentation to his colleagues in City A starting at 5:00 pm Thursday, local time in Sweden.

3

Solution

What time and day, in Sydney, should Robert start his presentation? It is given that 15o = 1 hour time difference. Ignore daylight saving.* COMMON QUESTION: NESA 2021 Mathematics Standard 1* and Standard 2 HSC Examinations

21

16

Make r the subject of the formula P = 2r + 10

2

Solution

MS1 NESA 2021 Mathematics Standard 1 HSC Examination

21 MS1

17

Solution

The network diagram shows the travel times in minutes along roads con...