# 2016 HSC Maths General 2 Marking Guidelines

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2016 HSC Mathematics General 2 Marking Guidelines

Section I

Multiple-choice Answer Key

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Answer B D B B C D A B D A C D A A D A B C A C D C C B D

– 1 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Section II

Question 26 (a)

Criteria • Provides correct answer or correct numerical expression Sample answer: Surface area = 4πr2

= 4 × π × 52 = 314.1592 = 314 cm2

Question 26 (b)

Criteria • Provides correctly simplified algebraic expression • Provides one correctly simplified variable

Sample answer: 8x4y = x 24x3y5 3y4

Question 26 (c)

Criteria • Provides correct solution • Makes progress towards the solution

Sample answer:

Country driving: 170 × 5.9 = 10.03 L 100

City driving:

25 × 7.3 = 1.825 L 100

Total fuel used

= 10.03 + 1.825 = 11.855 L

– 2 –

Marks 1

Marks 2 1

Marks 2 1

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 26 (d)

Criteria • Provides correct answer • Attempts to use Pythagoras’ Theorem

Sample answer:

AB = 322 + 332 = 45.9673… = 46 m

Question 26 (e)

Criteria • Provides correct answer • Makes significant progress towards the answer • Provides correct weekly pay, or equivalent merit

Sample answer: Holiday loading = 0.175 × ($63 752 ÷ 52) × 4

= $858.20 Holiday pay = ($63 752 ÷ 52) × 4 + 858.20

= $4904 + $858.20 = $5762.20

Marks 2 1

Marks 3 2 1

– 3 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 26 (f) (i)

Criteria • Provides correct answer or correct numerical expression Sample answer: Taxable income = $82 521 + $10 920 – $13 420

= $80 021

Marks 1

Question 26 (f) (ii)

Criteria • Provides correct answer • Attempts to use correct tax bracket, or equivalent merit

Sample answer:

Tax payable = $17 547 + 0.37(80 021 – 80 000) = $17 547 + 0.37 × 21 = $17 547 + $7.77 = $17 554.77

Marks 2 1

Question 26 (f) (iii)

Criteria • Provides correct solution with conclusion • Calculates the tax payable including Medicare levy, or equivalent merit

Sample answer:

Total tax payable = $1600.42 + $17 554.77

= $19 155.19

Tax refund

= $20 525 – $19 155.19

= $1369.81

∴ Theo will receive a tax refund of $1369.81

Marks 2 1

– 4 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 27 (a)

Criteria • Provides correct solution • Provides one correct description, or equivalent merit

Marks 2 1

Sample answer:

If Alice is responsible for a car accident, then Compulsory Third Party Insurance covers injury to people, while Third Party Property Insurance covers damage to other people’s property.

Question 27 (b)

Criteria • Provides correct answer with justification • Identifies that there are 7 samples, or equivalent merit

Sample answer: Mean of mean heights = 153 + 168 + 174

3 = 165 cm The mean of all possible sample means is equal to the population mean.

Marks 2 1

Question 27 (c)

Criteria • Provides correct answer • Provides one correct quartile, or equivalent merit

Sample answer:

Q3 = 172 cm Q1 = 136 cm IQR = 172 – 136

= 36 cm

Marks 2 1

– 5 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 27 (d) (i)

Criteria • Provides correct values for A and B • Provides one correct value Sample answer: A = $19 000 B = 17 915.67 + 71.66 – 436

= $17 551.33

Question 27 (d) (ii)

Criteria • Provides correct answer • Makes progress towards correct answer Sample answer: X = Prn

= 18 640 × 0.004 × 1 = $74.56 OR X = 18 278.56 + 436 – 18 640 = $74.56

Question 27 (d) (iii)

Criteria • Provides correct answer or correct numerical expression Sample answer: Total amount = $436 × 48

= $20 928

Marks 2 1

Marks 2 1

Marks 1

– 6 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 27 (e) (i)

Criteria • Provides correct answer or correct numerical expression Sample answer: Difference = 145° – 55°

= 90°

Question 27 (e) (ii)

• Provides correct solution Sample answer: Time difference = 90

15 = 6 hours

Criteria

Question 27 (e) (iii)

Criteria • Provides correct answer • Makes progress towards the solution

Sample answer:

Time of departure in Melbourne = 11:30 pm Friday

= 23:30

Time of arrival (Melbourne time) = 23:30 + 15 h

= 14:30 Saturday

Time of arrival in Dubai

= 14:30 – 6 h

= 8 h 30 min

= 8:30 am on Saturday

Marks 1

Marks 1

Marks 2 1

– 7 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 28 (a) (i)

• Provides correct answer Sample answer: P(gold coin) = 4

37

Criteria

Question 28 (a) (ii)

Criteria • Provides correct answer • Makes progress towards the solution

Sample answer:

4 × Total = 20 37

Total = 20 × 37 4

= 185 OR x = 20 33 4

x = 33 × 5 = 165 silver coins

165 silver coins and 20 gold coins = 185 ∴ Total number of coins is 185.

Question 28 (b) Criteria

• Provides correct answer • Makes progress towards the answer Sample answer: Total cost: $990 + 505 × $0.35 × 5

$990 + $883.75 $1873.75

– 8 –

Marks 1

Marks 2 1

Marks 2 1

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 28 (c) (i)

Criteria • Provides correct answer • Provides a correct probability

Sample answer: P(Win and Draw in any order) = P(WD) + P(DW)

= 0.7 × 0.2 + 0.2 × 0.7 = 0.28

Marks 2 1

Question 28 (c) (ii)

Criteria • Provides a correct explanation

Marks 1

Sample answer: Paul is not correct because the probability of an event occurring cannot be greater than 1.

Question 28 (d)

Criteria • Provides correct answer or correct numerical expression • Provides correct value from the table or multiplies $75 000 with a value

from the correct row or column in the table

Sample answer:

r = 3% pa = 0.75% pq n = 6 years = 24 quarters ∴ payment = 0.0382 × $75 000

= $2865

Marks 2

1

– 9 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 28 (e) (i)

Criteria • Provides correct volume • Makes progress towards the volume

Sample answer: Volume = πr2h

= π(2.5)2 × 3 = 58.904… = 58.9 cm3

Question 28 (e) (ii)

Criteria • Correct solution • Makes significant progress towards the solution • Makes some progress towards the solution

Sample answer: Volume of chocolate = (15 × 10 × 6) – (6 × 2 × 58.904…)

= 193.1416… = 193 cm3 (nearest cm3)

Marks 2 1

Marks 3 2 1

– 10 –

Section I

Multiple-choice Answer Key

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Answer B D B B C D A B D A C D A A D A B C A C D C C B D

– 1 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Section II

Question 26 (a)

Criteria • Provides correct answer or correct numerical expression Sample answer: Surface area = 4πr2

= 4 × π × 52 = 314.1592 = 314 cm2

Question 26 (b)

Criteria • Provides correctly simplified algebraic expression • Provides one correctly simplified variable

Sample answer: 8x4y = x 24x3y5 3y4

Question 26 (c)

Criteria • Provides correct solution • Makes progress towards the solution

Sample answer:

Country driving: 170 × 5.9 = 10.03 L 100

City driving:

25 × 7.3 = 1.825 L 100

Total fuel used

= 10.03 + 1.825 = 11.855 L

– 2 –

Marks 1

Marks 2 1

Marks 2 1

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 26 (d)

Criteria • Provides correct answer • Attempts to use Pythagoras’ Theorem

Sample answer:

AB = 322 + 332 = 45.9673… = 46 m

Question 26 (e)

Criteria • Provides correct answer • Makes significant progress towards the answer • Provides correct weekly pay, or equivalent merit

Sample answer: Holiday loading = 0.175 × ($63 752 ÷ 52) × 4

= $858.20 Holiday pay = ($63 752 ÷ 52) × 4 + 858.20

= $4904 + $858.20 = $5762.20

Marks 2 1

Marks 3 2 1

– 3 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 26 (f) (i)

Criteria • Provides correct answer or correct numerical expression Sample answer: Taxable income = $82 521 + $10 920 – $13 420

= $80 021

Marks 1

Question 26 (f) (ii)

Criteria • Provides correct answer • Attempts to use correct tax bracket, or equivalent merit

Sample answer:

Tax payable = $17 547 + 0.37(80 021 – 80 000) = $17 547 + 0.37 × 21 = $17 547 + $7.77 = $17 554.77

Marks 2 1

Question 26 (f) (iii)

Criteria • Provides correct solution with conclusion • Calculates the tax payable including Medicare levy, or equivalent merit

Sample answer:

Total tax payable = $1600.42 + $17 554.77

= $19 155.19

Tax refund

= $20 525 – $19 155.19

= $1369.81

∴ Theo will receive a tax refund of $1369.81

Marks 2 1

– 4 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 27 (a)

Criteria • Provides correct solution • Provides one correct description, or equivalent merit

Marks 2 1

Sample answer:

If Alice is responsible for a car accident, then Compulsory Third Party Insurance covers injury to people, while Third Party Property Insurance covers damage to other people’s property.

Question 27 (b)

Criteria • Provides correct answer with justification • Identifies that there are 7 samples, or equivalent merit

Sample answer: Mean of mean heights = 153 + 168 + 174

3 = 165 cm The mean of all possible sample means is equal to the population mean.

Marks 2 1

Question 27 (c)

Criteria • Provides correct answer • Provides one correct quartile, or equivalent merit

Sample answer:

Q3 = 172 cm Q1 = 136 cm IQR = 172 – 136

= 36 cm

Marks 2 1

– 5 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 27 (d) (i)

Criteria • Provides correct values for A and B • Provides one correct value Sample answer: A = $19 000 B = 17 915.67 + 71.66 – 436

= $17 551.33

Question 27 (d) (ii)

Criteria • Provides correct answer • Makes progress towards correct answer Sample answer: X = Prn

= 18 640 × 0.004 × 1 = $74.56 OR X = 18 278.56 + 436 – 18 640 = $74.56

Question 27 (d) (iii)

Criteria • Provides correct answer or correct numerical expression Sample answer: Total amount = $436 × 48

= $20 928

Marks 2 1

Marks 2 1

Marks 1

– 6 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 27 (e) (i)

Criteria • Provides correct answer or correct numerical expression Sample answer: Difference = 145° – 55°

= 90°

Question 27 (e) (ii)

• Provides correct solution Sample answer: Time difference = 90

15 = 6 hours

Criteria

Question 27 (e) (iii)

Criteria • Provides correct answer • Makes progress towards the solution

Sample answer:

Time of departure in Melbourne = 11:30 pm Friday

= 23:30

Time of arrival (Melbourne time) = 23:30 + 15 h

= 14:30 Saturday

Time of arrival in Dubai

= 14:30 – 6 h

= 8 h 30 min

= 8:30 am on Saturday

Marks 1

Marks 1

Marks 2 1

– 7 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 28 (a) (i)

• Provides correct answer Sample answer: P(gold coin) = 4

37

Criteria

Question 28 (a) (ii)

Criteria • Provides correct answer • Makes progress towards the solution

Sample answer:

4 × Total = 20 37

Total = 20 × 37 4

= 185 OR x = 20 33 4

x = 33 × 5 = 165 silver coins

165 silver coins and 20 gold coins = 185 ∴ Total number of coins is 185.

Question 28 (b) Criteria

• Provides correct answer • Makes progress towards the answer Sample answer: Total cost: $990 + 505 × $0.35 × 5

$990 + $883.75 $1873.75

– 8 –

Marks 1

Marks 2 1

Marks 2 1

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 28 (c) (i)

Criteria • Provides correct answer • Provides a correct probability

Sample answer: P(Win and Draw in any order) = P(WD) + P(DW)

= 0.7 × 0.2 + 0.2 × 0.7 = 0.28

Marks 2 1

Question 28 (c) (ii)

Criteria • Provides a correct explanation

Marks 1

Sample answer: Paul is not correct because the probability of an event occurring cannot be greater than 1.

Question 28 (d)

Criteria • Provides correct answer or correct numerical expression • Provides correct value from the table or multiplies $75 000 with a value

from the correct row or column in the table

Sample answer:

r = 3% pa = 0.75% pq n = 6 years = 24 quarters ∴ payment = 0.0382 × $75 000

= $2865

Marks 2

1

– 9 –

BOSTES 2016 HSC Mathematics General 2 Marking Guidelines

Question 28 (e) (i)

Criteria • Provides correct volume • Makes progress towards the volume

Sample answer: Volume = πr2h

= π(2.5)2 × 3 = 58.904… = 58.9 cm3

Question 28 (e) (ii)

Criteria • Correct solution • Makes significant progress towards the solution • Makes some progress towards the solution

Sample answer: Volume of chocolate = (15 × 10 × 6) – (6 × 2 × 58.904…)

= 193.1416… = 193 cm3 (nearest cm3)

Marks 2 1

Marks 3 2 1

– 10 –

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