Mathematics A 2008 · investment was paying 7% simple interest for 4 years, calculate the principal...

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. Using the formula: θ = tan-1 �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.

2 | Mathematics A: Sample student assessment and responses Supervised assessment

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?

Queensland Studies Authority May 2013 | 3

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. • Cement costs $210 per m3. • 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 • cost $72.30 per m2.


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.


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

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.

Modelling and problem solving


• 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.

Communication and justification


• 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.

http://www.qsa.qld.edu.au/1888.html#assessment


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)


Comments

Use of rules and formulas in simple routine situations (Q5, Q6) Application of simple sequences of mathematical procedures in routine situations (Q5, Q6)


Comments

Organisation and presentation of information in variety of representations in simple routine situations


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)


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


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 non-routine situations

(Q12)


Comments

Use of given strategies for problem solving in simple rehearsed situations (Q1)


Comments

Use of familiar strategies for problem solving in complex routine situations (Q2)



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 non-routine situations (Q4) Informed decisions based on mathematical reasoning in complex routine through to simple non-routine situations (Q4)



Comments

Investigation of alternative solutions to complex routine through to simple non-routine 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.

Mathematics A 2008 · investment was paying 7% simple interest for 4 years, calculate the principal...

Documents

Transcript of Mathematics A 2008 · investment was paying 7% simple interest for 4 years, calculate the principal...