This document provides the solutions to questions from the 2010 General Mathematics Higher School Certificate (HSC) exam in New South Wales, Australia. It includes answers to multiple choice questions, open response questions involving word problems on topics like profit/loss, financial planning, and statistics. Diagrams are provided for some geometry questions. The solutions show step-by-step working and explanations for full and partial marks on the exam.

1. http://www.maths.net.au/ 2010 General Mathematics HSC Solutions
2010 General Mathematics HSC Solutions
Section I – Multiple Choice Question 24
1. C 2. D 3. B 4. A 5. A (a) (i)
6. D 7. C 8. C 9. C 10. D
11. D 12. C 13. B 14. A 15. A (ii)
16. B 17. B 18. B 19. C 20. D
21. B 22. D
(b) is the break-even point. Ashley must
Section II – Open Response produce and sell more than 4 frames to
make a profit.
Question 23
(c) (i)
(a)
(ii) Same as the mean = 100
(iii) 80 has a z-score of –2
110 has a z-score of 1
(b) (i) Shower
(ii) 5000 mm
(iii)
80 100 110
34%
50%
(c) (i) 34 2.5% 47.5%
(ii)
(d) (i) (d) (iv)
(ii)
(v) In ,
(iii) In two weeks, he will have $240
(already saved) + $160 (from
telephone and internet and savings).
He will need a further
. This is $110
per week. He could reallocate money
from variable expenses of
entertainment and clothes and gifts, to
a total of $100 (i.e. he could keep $5
for each in his budget).
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2. http://www.maths.net.au/ 2010 General Mathematics HSC Solutions
Question 25 Question 26
(a) (i) (a) (i) Number of plates is
(ii)
(b) (i) X is 15
(ii)
Diagram from 2010 General Mathematics HSC Examination. NSW Board of Studies
(ii) Prediction for 120 days = 1170 mm
(b)
(c) (i)
Diagram from 2010 General Mathematics HSC Examination. NSW Board of Studies
(ii) (iii) From the diagram, median = 155
(iv) With the number of cars passing the
school increasing by about triple, their
could be a safety concern. Recommend
40 km/h school zone, speed bumps and
crossing for children.
(c)
(d) $600 will grow to:
i.e. a loss of 90c
(d) By cosine rule,
Annuity:
gcalc
This is not enough.
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3. http://www.maths.net.au/ 2010 General Mathematics HSC Solutions
Question 27 Question 28
(a) (a) (i)
(ii)
Therefore, the bank would not approve
the loan.
(b) (i) (iii) Jack’s loan balance goes down faster,
per month, in the first 12 years than
(ii) after 12 years, due to higher loan
repayments Xiang’s balance goes down
(iii)  In 2000 the ages were negatively more steadily. Jack may have a lower
skewed, but in 2010 the ages were interest rate than Xiang in the first 12
positively skewed. years and then a higher interest rate
 In 2000 the median age was 12, which after 12 years.
has decreased to 6 in 2010.
 The interquartile range in 2000 was 8 (b) (i)
and it has increased to 10 in 2010.
(iv) There are more children who are (ii)
younger, which might mean that more
preschool and primary school places are
required. (iii)
(c) (i) tax
(ii)
It will have a volume 4 times as big.
(iv) The minimum surface area (from the
(iii) tax for every earnt first graph) is when the radius is 6 cm.
From the second graph, when the radius
(iv)
is 6 cm, the height needs to be 14 cm, to
have the required volume.
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