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Mathematics A 2008
Sample assessment instrument and student responses
Supervised assessment: Managing money and
Linking 2 and 3 dimensions
This sample is intended to inform the design of assessment instruments in the senior phase of
learning. It highlights the qualities of student work and the match to the syllabus standards.
Criteria assessed
• Knowledge and procedures
• Modelling and problem solving
• Communication and justification
Assessment instrument
The student work presented in this sample is in response to assessment items.
Term One — Supervised Exam
Topics — Managing Money 1 and Linking 2 and 3 Dimensions
Remember, throughout your response: organise and present your information; use mathematical
terminology and conventions; and show mathematical reasoning to develop your logical sequences.
Knowledge and procedures
Q1.
-1
Using the formula: θ = tan �
𝑜𝑝𝑝
𝑎𝑑𝑗
�
Find the angle (to one decimal place) of pitch in the following roof structure.
2850 mm
12 000 mm
Q2.
Using the simple interest formula: I = PRT and A = P + I,
calculate the total amount Cathy would have if she invested $8200 at the rate of
4.5% per annum, simple interest, for 6 months.
Q3.
Which of the following graphs best represents the interest due on a loan if
15% per annum simple interest is charged?
Q4.
A building site plan uses a scale of 1:150. What real life length would be represented
by a plan length of 5 cm?
Q5.
Given that the amount of interest earned from an investment is $420 and the
investment was paying 7% simple interest for 4 years, calculate the principal that was
initially invested.
Q6.
An amount of $6500 is to be invested at 6% per annum with interest compounded
annually. Draw a graph (use graph paper attached) to illustrate an investment over 4
years. Use this graph to estimate the future value of the investment at the end of 18
months.
Q7.
A symmetrical roof has a pitch of 15 . Find the height of the king post in the roof truss
if the building is 14 m wide.
Q8.
A mechanic purchases tools with a total value of $3300. The value of the tools
depreciates by $600 per year. When the value of the tools falls below $900 they
should be replaced. When should the mechanic replace his tools?
Q9.
A bank advertises its credit card interest rate as 16.95% per annum. On investigation,
the customer found that the interest compounds daily. Calculate the actual Effective
Rate of Interest (ERI) charged on the credit card.
Q10.
A wall 6 m in length is to be built using 200 bricks. The dimensions of the bricks are
230 mm x 110 mm x 76 mm. Assume the mortar thickness is 10mm. What would the
height of the wall be?
°
2 | Mathematics A: Sample student assessment and responses Supervised assessment
Q11.
The hip roof in the diagram below has a king post height of 2.1 m.
Use this information and the diagram below to calculate the total area of the roof.
Q12.
James has just inherited $10 000 and can save $2400 per year from other income. He
wants to buy a new car costing $19 000, so he invested his inheritance in an account
that pays simple interest at a rate of 12%. Determine when (time) James will have
enough money to buy the car.
Modelling and problem solving
Q1.
ABC transport purchases a new truck for $450 000. The value of the truck depreciates
by 15% per annum. By calculating the value of the truck at the end of each year, find
the number of years it will take for the salvage value of the truck to fall below half its
original value.
Q2.
Max wants to build a rectangular pergola on his house. He needs to order cement and
mesh for the footings. Max has a budget of $2000 to purchase the cement and the
mesh. Based on your calculations and considering the following information, does
Max have sufficient funds?
•
The pergola is 9.5 m long x 8.5 m wide.
•
The footings are 400 mm wide and 500 mm deep.
•
Trench mesh comes in 6 m lengths.
•
A 50 cm overlap is needed at the corners when 2 sheets of mesh meet.
•
Building standards require 2 layers of trench mesh to be laid.
3
•
Cement costs $210 per m .
•
Trench mesh costs $70 per length.
Q3.
Ben wants to build a new carport with the dimensions of 4m wide, 7m long and 3m
high. The 3 walls of the carport need to be cladded and Ben has the choice of using
either Colorbond® steel or bricks. Ben wants to choose the option that saves him the
most money on materials. By calculating the cost for both options, which materials
should Ben choose? In your answer, reflect on the strength and/or limitations of the
mathematical model.
Colorbond®:
• is supplied in sheets that can be cut to any length
• has an effective width of 750 mm for each sheet
• costs $49.50 per linear metre.
Bricks:
•
•
•
are of a standard dimension (230 mm x 110 mm x 76 mm)
will have a mortar thickness of 10 mm
2
cost $72.30 per m .
Queensland Studies Authority May 2013 | 3
Q4.
Emma’s grandfather gave her $10 000 on the condition that she invested the whole
amount. Emma needs to decide which of the following options would make her the
most money after at least 5 years:
• Option 1: 7% per annum simple interest
• Option 2: 6.17% per annum compounded annually.
Provide advice to Emma. In your advice consider:
• the future value of both investments over the minimum time period and
beyond
• an alternative option
• reflect on the strengths and/or limitations of the mathematical model.
4 | Mathematics A: Sample student assessment and responses Supervised assessment
Instrument-specific criteria and standards
Student responses have been matched to instrument-specific criteria and standards; those that
best describe the student work in this sample are shown below. For more information about the
syllabus dimensions and standards descriptors, see
<www.qsa.qld.edu.au/1888.html#assessment>.
Standard A
Knowledge and
procedures
Modelling and
problem
solving
Communication
and
justification
The student work has the following characteristics:
•
accurate use of rules and formulas in simple through to complex situations
•
application of simple through to complex sequences of mathematical procedures in
routine and non-routine situations.
The student work has the following characteristics:
•
use of strategies to model and solve problems in complex routine through to simple
non-routine situations
•
investigation of alternative solutions and/or procedures to complex routine through to
simple non-routine problems
•
informed decisions based on mathematical reasoning in complex routine
through to simple non-routine situations
•
reflection on the effectiveness of mathematical models including recognition of the
strengths and limitations of the model.
The student work has the following characteristics:
•
accurate and appropriate use of mathematical terminology and conventions in simple
non-routine through to complex routine situations
•
organisation and presentation of information in a variety of representations in simple
non-routine through to complex routine situations
•
analysis and translation of information displayed from one representation to another
in complex routine situations
•
use of mathematical reasoning to develop logical sequences in simple non-routine
through to complex routine situations using everyday and/or mathematical language
•
justification of the reasonableness of results obtained through technology or other
means.
Note: Colour highlights have been used in the table to emphasise the qualities that discriminate
between the standards.
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Student response — Standard A
The annotations show the match to the instrument-specific standards.
Comments
Use of given
rules and
formulas in
simple
rehearsed
situations
(Q1, Q2)
Application
of simple
mathematical
procedures
in simple
rehearsed
situations
(Q1–Q4)
6 | Mathematics A: Sample student assessment and responses Supervised assessment
Comments
Use of rules
and formulas
in simple
routine
situations
(Q5, Q6)
Application
of simple
sequences of
mathematical
procedures
in routine
situations
(Q5, Q6)
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Comments
Organisation
and presentation
of information in
variety of
representations
in simple routine
situations
8 | Mathematics A: Sample student assessment and responses Supervised assessment
Comments
Use of rules
and formulas
in simple
routine
situations
(Q7, Q8)
Application of
simple
sequence of
mathematical
procedures in
routine
situations
(Q7, Q8)
Accurate use
of rules and
formulas in
simple
situations or
use of rules
and formulas
in complex
situations
(Q9)
Application of
simple
sequences of
mathematical
procedures in
non-routine
situations or
complex
sequences in
routine
situations
(Q9)
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Comments
Accurate use
of rules and
formulas in
simple
situations or
use of rules
and formulas
in complex
situations
(Q10)
Application of
simple
sequences of
mathematical
procedures in
non-routine
situations or
complex
sequences in
routine
situations
(Q10)
Accurate use
of rules and
formulas in
simple through
to complex
situations
(Q11)
Application of
simple through
to complex
sequences of
mathematical
procedures in
routine and
non-routine
situations
(Q11)
Response continues
over page
10 | Mathematics A: Sample student assessment and responses Supervised assessment
Comments
Accurate use
of rules and
formulas in
simple
through to
complex
situations
(Q12)
Application
of simple
through to
complex
sequences of
mathematical
procedures
in routine
and nonroutine
situations
(Q12)
Queensland Studies Authority May 2013 | 11
Comments
Use of given
strategies for
problem
solving in
simple
rehearsed
situations
(Q1)
12 | Mathematics A: Sample student assessment and responses Supervised assessment
Comments
Use of familiar
strategies for
problem solving
in complex
routine
situations
(Q2)
Response continues
over page
Queensland Studies Authority May 2013 | 13
Comments
Informed
decisions based
on
mathematical
reasoning in
simple routine
situations
(Q2)
Use of
strategies to
model and
solve problems
in complex
routine through
to simple nonroutine
situations (Q4)
Informed
decisions based
on
mathematical
reasoning in
complex routine
through to
simple nonroutine
situations (Q4)
Response continues
over page
14 | Mathematics A: Sample student assessment and responses Supervised assessment
Comments
Investigation
of alternative
solutions to
complex
routine
through to
simple nonroutine
problems (Q4)
Reflection on
the
effectiveness
of
mathematical
models
including
recognition of
strengths and
weaknesses
(Q4)
Judgments about communication and justification are made across the
range of tasks. The response demonstrates:
•
accurate and appropriate use of mathematical terminology and
conventions in simple non-routine through to complex routine
situations
•
organisation and presentation of information in a variety of
representations in simple non-routine through to complex
routine situations
•
use of mathematical reasoning to develop logical sequences in
simple non-routine through to complex routine situations using
everyday and/or mathematical language.
Queensland Studies Authority May 2013 | 15