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SAMPLE ASSESSMENT TASK
KS
MATHEMAATICS: APPLICATIONS
ATTAR YEAR 11
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© School Curriculum and Standards Authority, 2014
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resources relevant to the course.
2014/11910v2
1
Sample assessment task
Mathematics: Applications
Task 5 (Test 2) – Unit 1
Assessment type: Response
Conditions
Time for the task: Up to 50 minutes, in-class, under test conditions
Materials required
Section 1: Calculator-free
Section 2: Calculator-assumed
Standard writing equipment
Calculator (to be provided by the student)
Other materials allowed
Drawing templates, one page of notes in Section Two
Marks available
Section 1: Calculator-free
Section 2: Calculator-assumed
50 marks
(22 marks)
(28 marks)
Task weighting
4.5%
_____________________________________________________________________________________
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
2
Section One: Calculator-free
Suggested time: 20 minutes
Marks available: 22
Question 1
 2 3
A =  5 7 
 −1 8 
(7 marks)
1 2 8 
B=

7 0 11
 −4 
C =  −1
 3 
D = [ 2 5 10]
 7 9
E = 11 3
10 5
0 0 
F =

0 0 
Using the matrices given above, calculate the following.
Where the operation is not possible, provide an explanation.
(1)
b) DC
(2)
c) A 2
(1)
d) 3B
(1)
e) FB
(1)
f) F 3
(1)
a)
E+A
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
3
Question 2
(5 marks)
A section of a spreadsheet, provided below, shows the number of hours worked by three students
during the course of a week. The students are paid time and a half on Saturdays and double time on
Sundays.
1
A
B
C
D
E
F
Name
Rate
($/hour)
Weekday
hours
Saturday
hours
Sunday
hours
Total pay
2
Gen
20
5
6
3.5
3
Bri
22.5
10
3
3
4
Ala
23.68
8
4
6
a)
How much will Gen earn in a week?
(3 marks)
b)
Using cell references (e.g. A1 for row 1 column A), state the formula to calculate Ala’s total pay
for one week.
(2 marks)
Question 3
(6 marks)
Give matrices to fit the following descriptions.
a)
A row matrix with 3 columns
(1 mark)
b)
A square matrix A in which there are 2 rows and aij = i + j
(2 marks)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
4
c)
8 10
Matrix B where 5B + 3I = 

0 18
Question 4
(Note I is the identity matrix)
(3)
(4 marks)
Members of one family, Gino, Cara, Nick and Tina live in four different places and they communicate
regularly. They all use the same internet texting app as well as email to send messages to each other.
Skype is used by Cara, Nick and Tina but only to talk with Gino who is overseas. Both landline and
mobile text are used by Cara, Tina and Nick. Facebook is used by Gino, Cara and Nick to communicate.
With each row representing a different person, create a labelled matrix to represent the number of
ways each person communicates with each of the others.
Assume no-one communicates with themselves.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
5
Section Two: Calculator-assumed
Suggested time: 30 minutes
Marks available: 28
Question 5
(3 marks)
One formula for calculating the surface area (SA) of a person’s skin is given below.
SA = 0.007184 × W 0.425 × H 0.725
W = weight (kg), H = height (cm), SA=surface area (m2)
Sol is 80 kg in weight and 159 cm tall.
a)
Write an expression for calculating the SA of Sol’s skin.
b)
Calculate the SA of Sol’s skin.
c)
Express the SA of Sol’s skin in cm2, given that there are 10 000 cm2 in 1 m2.
Question 6
(3 marks)
John wants to see which of the two banks in his portfolio of shares is the better performer, and he uses
the P/E ratio to compare the two banks.
⁄
=
ℎ
ℎ
The AAA bank’s shares are currently $33.65 while ZZZ bank’s shares are currently $32.055.
Dividends from both banks are paid twice a year and in the last year the AAA bank gave dividends at 82c
and 84c per share while the two dividends from the ZZZ bank were 66c and 79c per share.
Use John’s method to determine which bank is the better performer.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
6
Question 7
(6 marks)
Mary keeps records of her blood tests and some of the data are reproduced in the table below.
Ideal range
Year
2009
2011
2012
2013
2014
Blood test type
HDL
Chol.
LDL
1.1 to 3.5 <5.5
<3.5
1.4
1.6
1.3
1.5
1.7
5.7
7.2
5.2
5.4
4.9
3.8
5
3.4
3.4
2.8
PTRI
<1.5
1.1
1.3
1.1
1
0.8
Risk
<3.5
4.1
a)
Circle all the entries for which Mary’s test results are outside the ideal range of values.
(2 marks)
b)
Mary knows that the “Risk” value is found by dividing one variable by another but cannot
remember the rule and she used a “guess-and-check” method to work it out.
c)
State a general expression to calculate the “Risk” value.
(2 marks)
Calculate the “Risk” value for 2014.
(2 marks)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
7
Question 8
(3 marks)
Chocolate Easter eggs are on special at a local supermarket.
The larger eggs (110 g each) are advertised at “Two for $4” and the smaller ones (39 g) cost $1 each. By
calculating the cost per gram of chocolate, determine which size represents better value for money.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
8
Question 9
(7 marks)
Lucy has invented a new method for scoring points in the game of Tins. Each participant can score in any
of four ways (M, S, T & G) and their scores are added to form a grand total.
There are as follows:
•
•
•
•
10 points for a match (M)
7 points for a set (S)
3 points for a touch (T)
1 point for each game (G)
The number of matches, sets, touches and games for 5 different players (P1, P2, P3, P4, P5) are
provided in the matrix below.
P1
P2
P3
P4
P5
M
S
T
G
2
1

2

3
 0
10
5
6
10
3
4
15
3
2
1
20 
10 
20 

30 
15 
a)
Write the column matrix, with rows representing in order M, S, T and G that represents the points
for each way of scoring.
(1 mark)
b)
Show the matrix calculation needed to multiply the column matrix (from part a) by the matrix
provided above. Calculate this product.
(2 marks)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
9
c)
What is the total score for P1? Where in the matrix from part b) is this score located?
(2 marks)
d)
Describe the data stored in the matrix generated in part b).
(2 marks)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
10
Question 10
(6 marks)
Three friends are planning a trip overseas and want to take some foreign currency with them.
They have made a table showing the number of Australian dollars they will take to each city.
Kate
Guy
Alex
Bali (Indonesia)
$1000
$2000
$500
Singapore
$2000
$4000
$800
Hong Kong
$1500
$2500
$1200
The exchange rates when they convert their money are as follows:
1 AUD= 10 328.61 IDR (Indonesian rupiah)
1AUD = 1.15389 SGD
(Singapore dollars)
1 AUD = 7.09056 HKD
(Hong Kong dollars)
a)
How many Indonesian rupiah will Kate get (assuming she pays no commission fees)?
(1 mark)
b)
How many Hong Kong dollars will Guy get (assuming he pays no commission fees)?
(1 mark)
c)
Using the same exchange rates are given above, what is each Singapore dollar worth in Australian
dollars?
(1 mark)
d)
Show how matrix operations could be used to calculate the amount of foreign currency for each
country that each person will receive (assuming no commission fees are payed) when their
Australian dollars are converted.
Matrix calculations are not required.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
(3 marks)
11
Summary table of syllabus content assessed
Question
Syllabus reference
1.2.6
perform matrix addition, subtraction, multiplication by a scalar, and matrix
multiplication, including determining the power of a matrix using technology
with matrix arithmetic capabilities when appropriate
1.1.8
use a spreadsheet to display examples … consumer arithmetic
1.2.3
use a spreadsheet or an equivalent technology to construct a table of values
from a formula, including tables for formulas with two variable quantities …
1.2.5
recognise different types of matrices (row, column, square, zero, identity)
and determine their size
1.2.4
use matrices for storing and displaying information that can be presented in
rows and columns; for example, databases, links in social or road networks
1.2.2
substitute numerical values into algebraic expressions, and evaluate (with
the aid of technology where complicated numerical manipulation is required)
1.1.7
… compare share values by calculating a price-to-earnings ratio
1.2.1
substitute numerical values into algebraic expressions, and evaluate …
1.2.3
use a spreadsheet or an equivalent technology to construct …
1.1.4
compare prices and values using the unit cost method
1.2.7
use matrices, including matrix products … to model and solve problems
1.1.6
use currency exchange rates to determine … the value of a given amount of
foreign currency when converted to Australian dollars
1.2.7
use matrices, including matrix products… to model and solve problems
1
2
3
4
5
6
7
8
9
10
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
12
Solutions and marking key for sample assessment task 5 (Test 2)
*Note: Each item has been classified as Simple(S) or Complex(C) to provide teachers with some
indication of the anticipated difficulty which may be helpful with grading. However, it must be
recognised that the classifications have been provided a-priori and will need refining once the
tasks have been administered (that is after evidence as to the effect has been gathered).
Section One: Calculator-free
Question 1
a)
Solution
Behaviours
 9 12 
16 10 


 9 13
Add two matrices correctly
1
Item*
(S/C)
S
Correct multiplication of two matrices (1)
Use brackets to denote matrix type (1)
Applies conditions for matrix
multiplication to a 3x2 matrix.
2
C
1
C
Multiplies matrix by scalar
1
S
Multiplies two matrices, one being the
zero matrix
1
S
S
[17]
b)
Marks
c)
Not possible because the number of
columns in A does not equal the
number of rows in A
d)
 3 6 24 
 21 0 33 


e)
0 0 0 
0 0 0 


0 0 
0 0 


Recognises unique property of zero matrix
1
f)
Solution
Behaviours
Marks
Gen :
= 20 x 5 + 6 x 20 x 1.5 + 3.5 x 2 x 20 =
100 + 180 + 140
= 420
Selects correct and all data to be included
Multiplies by 1.5 and 2 appropriately
Adds all three correctly
1
Item
(S/C)
S
B4(C4 + D4 x 1.5 + E4 x 2)
Uses correct cell references throughout
Correctly orders operations
1
1
1
C
S
C
1
C
Question 2
a)
b)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
13
Question 3
Solution
a)
[2
5 10 ]
b)
2 3
3 4


a b 
Let B = 

c d 
3 0
3I = 

0 3
Behaviours
Marks
Writes a matrix with 1 row and 3 columns
1
Item
(S/C)
S
Creates a square matrix with 2 rows and 2
columns
Calculates each element correctly
Correctly uses 3I in the addition
Establishes equations which link elements
in matrix B to elements in matrix 5B + 3I
Solves equations to determine elements
in B.
1
S
1
1
1
C
C
C
1
C
5b 
 5a + 3
B + 3I = 
5d + 3
 5c
c)
5a + 3 = 8 so a = 1
5b = 10 so b = 2
5c = 0 so c = 0
5d + 3 = 18 so d = 3
1 2 
B=

0 3 
Question 4
Solution
G C N T
G
C
N
T
0
4

4

3
4 4 3
0 5 4 
5 0 4

4 4 0
Behaviours
Labels rows and columns
Has 0s on the leading diagonal
Creates a symmetrical matrix
Enters correct data
Marks
1
1
1
1
Item
(S/C)
S
S
C
C
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
14
Section 2: Calculator assumed section
Question 5
Solution
a)
b)
c)
Behaviours
0.007184 x 800.425 x 1590.725
Correctly substitutes given values for
pronumerals
Uses calculator correctly
Multiplies accurately by 10 000
1.8247 m2
18247 cm2
1
Item
(S/C)
S
1
1
S
S
Marks
Question 6
Solution
Behaviours
For AAA P/E ratio = 3365/(82+84) = 20.271
For ZZZ P/E ratio = 3205.5/(66 + 79) =
22.107
ZZZ bank is the better performer
Marks
Adds dividends for the year
Uses operations in correct order
Calculates P/E and selects bank with the
highest ratio
1
1
1
Item
(S/C)
S
S
S
Question 7
Solution
HDL
Chol.
LDL
PTRI
Risk
1.1 to 3.5
<5.5
<3.5
<1.5
<3.5
2009
1.4
5.7
3.8
1.1
4.1
2011
1.6
7.2
5
1.3
2012
1.3
5.2
3.4
1.1
2013
1.5
5.4
3.4
1
2014
1.7
4.9
2.8
0.8
Ideal
range
Year
a)
Chol. ÷ HDL
b)
2.9
c)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
Behaviours
Marks
Identifies all
values outside
the ranges given
as ideal.
(1 if at least 3)
2
Item
(S/C)
S
Selects both
variables
correctly
Selects correct
year
Uses formula
created to
determine Risk
2
C
1
S
1
S
15
Question 8
Solution
Behaviours
Marks
Large eggs cost 400÷220 = 1.81 c/g
Small eggs cost 100÷39 = 2.56 c/g
The larger eggs are the better value because
they cost less per gram.
Accurately (1) divides number of cents by
number of grams (1) for both sizes.
Correctly concludes on the basis of less
cost per gram
1
1
Item
(S/C)
S
S
1
S
Question 9
Solution
10
7
 
3
 
1
a)
b)
c)
125
Row 1 column 1
Each row represents the total score for the players who
are in row order of P1 to P5.
d)
Determines correct
column matrix
1
Item
(S/C)
S
Writes down the
correct matrix
product
Performs
multiplication of
matrices using
technology
1
S
1
C
Has the correct total
for P1
Locates position of
data in the matrix
Identifies each row
as belonging to a
different player.
Nominates data as
being the total
number of points
1
S
1
S
1
S
1
C
Behaviours
Marks
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
16
Question 10
Behaviours
Marks
Selects correct rate and
multiplies by 1000
Selects correct rate and
multiplies by 2500
Chooses division of correct
numbers
Establishes correct matrices
Matrices are written in
correct order
Uses matrix multiplication
1
Item
(S/C)
S
1
S
1
C
1
1
S
S
1
S
Solution
a)
b)
c)
10 328.61 x 1000 = 10 328 610 IDR
7.09056 x 2500 = 17726 HKD
1 ÷ 1.15389 = 0.8666 AUD
1000 2000 1500  10328.61
 2000 4000 2500  ×  1.15389 

 

 500 800 1200   7.09056 
d)
Each column of the first matrix represents one
person’s money.
Each column of the first matrix represents the
money for that country.
In the second matrix the rows represent the
exchange rate.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
17
Sample assessment task
Mathematics: Applications
Task 4 (Investigation 2) – Unit 1
Assessment type: Investigation
This investigation introduces the students to the topic of Matrices and matrix arithmetic. It provides an
opportunity for students who have previously seen and used data in labelled tables to use and operate
with similar data in a more abstract form.
Notes for teachers
 No prior preparation is expected for this investigation.
 Students will not be expected to use matrix operations on their calculators during this
investigation.
 Ideally, this investigation is conducted before the Matrices and matrix arithmetic topic (1.2.4 to
1.2.7) is introduced in class.
 Students should have had experience in the use of tables and spreadsheets containing data and
pronumerals.
 Students should be able to identify the rows and columns in a table.
Conditions
Time for the task: Up to 50 minutes, in-class, under test conditions
Materials required
Other materials allowed
Standard writing equipment
Calculator (to be provided by the student)
Drawing templates
Marks available
45 marks
Task weighting
3.5%
_____________________________________________________________________________________
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
18
INTRODUCTION
Related data which are set out in tables may also be presented in matrix form.
Example 1: Table of data for hours worked by three students on weekdays last week
Monday
Tuesday
Wednesday
2
1
2
0
1
0
1
1
3
Wing
Jason
Jake
Thursday
3
1
0
Friday
3
1
2
This data can be represented by the following matrix. Wing’s data are in Row 1.
2
1

 2
0
1
3
1
0
1
3
1
0
3
1 
2 
In this matrix, the different rows represent the different students and each column represents a
different day.
Example 2: Amount of protein and carbohydrate per 100 g in four different cereals.
Cereal 1
Cereal 2
Cereal 3
Cereal 4
Protein
(g /100 g)
12.8
8.8
10.6
7.8
Carbohydrate
(g /100 g)
56.7
71.8
71.3
64.8
This data can be represented by the
following matrix.
12.8
 8.8

10.6

 7.8
56.7 
71.8 
71.3 

64.8 
In this matrix, each row represents a different cereal. The first column represents the grams of protein
per 100 g of cereal for each of the four cereals while the second column stores the number of grams of
carbohydrate per 100 g of the respective cereal.
Note:
1. A matrix consists of related data which are set out in rows and columns.
2. Rows are numbered 1, 2, … from top to bottom: columns are numbered 1, 2, … from left to right
3. The data must be inside a bracket: here a square bracket is used.
4. The arrangement of the values in a matrix is rectangular in shape.
5. Sometimes a matrix may contain labels to indicate the nature of the data.
M T W Th F
Wing  2 0 1 3 3 
This labelled matrix shows the data for Example 1.
Jason 1 1 1 1 1 
Jake  2 0 3 0 2 
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
19
Question 1
(4 marks)
In a Perth metropolitan school there are many students with different cultural backgrounds.
Ms Murphy had classes in each of the years 8–10 and asked her students where they were born.
Her results are presented in the table below.
Year
Perth
Rural WA
Asia
Africa
Elsewhere
8
16
4
4
3
5
9
16
4
5
1
6
10
8
6
3
5
6
11
2
2
5
0
1
12
4
5
4
2
8
a)
Create a matrix (unlabelled) to represent these data with each column representing a different
year group.
(2 marks)
b)
How many students in Ms Murphy’s Year 11 class?
c)
Describe the position of the numbers that must be added in order to determine the number of
Ms Murphy’s students who were born in Africa?
(1 mark)
Question 2
(1 mark)
(4 marks)
The Year 8 mathematics class was studying time allocation on television. They collected data for three
different TV channels (Channels 2, 4 and 6) over a 5 hour period. TV time was classified as either
educational or entertaining. There were 3 hours of educational programs on Channel 2, 2 hours on
Channel 4 and 1 hour on Channel 6. The rest of the time on each channel was classified as entertaining.
Create a matrix (unlabelled) to represent these data: place each channel in separate rows in order of
channel number from smallest to largest and let the first column represent the time allocated to
educational.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
20
Question 3
(11 marks)
The data provided in this matrix give the approximate percentage of household income spent on
different living costs by different age groups. The columns store the % of household income spent, with
the first column containing data for food, the second column represents housing, the third column
clothing and transport is in the last column. The rows are in age order and represent the age groups
21–30, 31–40, 41–50 and 51–60 with the ages in years.
36
26

20

22
25
22
18
11
16
14
12
10
15 
20
18 

18 
Based on the data provided in the above matrix:
a)
What % of household income was spent on food by people in the 21–30 age group?
(1 mark)
b)
What % of household income was spent on housing by people in the 31–40 age group?
(1 mark)
c)
What does 12 represent?
d)
What % of household income do people in the 51–60 age group have left for other costs?
(2 marks)
e)
Does it make sense to add the numbers in the first column? Explain your answer?
(2 marks)
(1 mark)
f)
In one report of this data, the matrix was transposed: the rows were written as columns and the
columns written as rows i.e. row 1 became column 1.
(4 marks)
(i)
Write the transposed version of the given matrix.
(ii) What do the numbers given in the second row now represent?
(iii) In which row and column of the transposed matrix is the % of household income spent on
clothing by people in the 51–60 age group represented?
Note: Sometimes it is possible and sensible to add matrices (more than 1 matrix)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
21
Question 4
a)
(12 marks)
Examine the following additions of matrices and answer the questions provided. (3 marks)
Situation 1: Number of drivers caught breaking the law for three different infringements
Female
Male
Describe the data contained in the sum of the
Texting
two matrices.
 45 
33
 78






Speeding
+
12 
18  = 30 
15 
 6 
 9 
No lights
Situation 2: Scored kicks (G=goals, P=points) by 4 players during a football match
First half
Second half
Describe the data contained in the sum of the
G P
G P
two matrices.
Gary
Gary
2
3
1
5
3
8






0 4
0 3
0 7 
Mike
Mike

 +

 = 

1 1 
4 2
Matt
Matt  3 1 






Al
Al
4 0
2 0
6 0 
Situation 3: Test results (N=number, M=measurement, S=statistics) for two students. There were three
different tests and each test had two sections, no calculator and calculator.
No calculator
Calculator
N M S
N M S
Ruby
15 18 13
19 20 16   34 38 29 
+ Ruby


11 15 14  =  22 29 26 
Lisa

11 14 12 

 
Lisa
Describe the data contained in the sum of the two matrices.
b)
Determine
(i)
[3
12 7 ] + [ 4 5 11]
(iii)
 4  0   3 
 2  2   8 
 + + 
 6   3   11 
     
 7   −1  −8
(3 marks)
(ii)
 −2 3 11 8 
 1 0  +  7 −4 

 

Sample assessment tasks | Mathematics: Applications | ATAR Year 11
22
c)
Examples of matrices which cannot or should not be added are given below.
Example 1
Example 2
Example 3
(6 marks)
 −9 0 4 
 2 4 −7  and [1 2 7 ] cannot be added



Wing  2
Jason 1

Jake  2
Su  2
0
1
0
0
1
1
3
1
3
1
0
2

3 and
1

2
3 
Wing  2 0 1 3 3 
cannot be added
Jason 1 1 1 1 1 
Jake  2 0 3 0 2 
Results for tests and investigations (%) for two students
Tests
 67 
 75  and
 
Investigations
These two matrices should not be added
 73
69 
 
For the addition of matrices
(i)
Explain why the matrices should not be added in Example 3.
(ii)
Provide two matrices (other than the ones above) which cannot be added.
(iii)
Describe how addition of matrices is performed.
(iv)
Describe TWO conditions that are necessary for addition to be possible or justified.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
23
Information about matrices.
 The data items in a matrix are called elements.
 Matrices are represented by capital (uppercase) letters.
 Elements are represented by lowercase letters.
 The order of a matrix refers to the number of rows and columns e.g. 2 x 2
 In a square matrix, the number of rows is equal to the number of columns.
3
M=
4
−5 
− 7 
N = [2
−1 6
M is a 2 x 2 (square) matrix because there are 2 rows and 2 columns.
The element m21 is 4 (row 2, column 1).
3]
8
P= 
12 
N is a 1 x 4 matrix because there is 1 row and 4 columns. The element
n13 is 6 (row 1, column 3)
P is a 2 x 1 matrix because there are 2 rows and 1 column. The
element p21 is 12 (row 2, column 1)
Question 5
(7 marks)
Consider two matrices, A and B both with 5 rows and 4 columns.
a)
What is their order?
(1 mark)
b)
How is the element in the 3rd row and the 4th column of matrix A written?
(1 mark)
c)
Write an expression to add the corresponding elements in the first row and third column of these
two matrices.
(2 marks)
d)
Write an expression to add the corresponding elements in any row and column of these two
matrices.
(2 marks)
e)
When adding two or more matrices, what is a necessary condition of their order? (1 mark)
Note: Two matrices A and B can only be multiplied to form AB if the number of columns in A is equal
to the number of rows in B i.e. if A has order m × n and B has order p × q then AB only exists if n = p.
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
24
Question 6
(7 marks)
For each of the following statements, write TRUE or FALSE. Justify your answer by providing an example
or an explanation.
a)
1 2 
When A =  3 4  and B =
 2 −1
2 1 
 2 1  then AB exists


 3 −9 
b)
 −2 
When A = [ 2 5 1] and B =  4  then AB exists
 1 
(1 mark)
c)
Any square matrix can be multiplied by itself.
(2 marks)
d)
Any square matrix can be added to any other square matrix.
(2 marks)
e)
If a matrix is transposed and then that matrix is transposed, the final matrix is the same as the
original matrix.
(1 mark)
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
(1 mark)
25
Solutions and marking key for sample assessment task 4 (Investigation 2)
*Note: Each item has been classified as Simple(S) or Complex(C) to provide teachers with some
indication of the anticipated difficulty which may be helpful with grading. However, it must be
recognised that the classifications have been provided a-priori and will need refining once the
tasks have been administered (that is after evidence as to the effect has been gathered).
Question 1
Uses a bracket to contain data
Enters correct values into correct positions
1
1
Item
(S/C)
S
S
Correctly adds numbers in column 4
Read matrix location.
1
1
S
S
Solution
a)
b)
c)
16 16 8 2 4 
 4 4 6 2 5


 4 5 3 5 4


 3 1 5 0 2
 5 6 6 1 8 
10
Row 5
Behaviours
Marks
Question 2
Solution
Behaviours
3 2
2 3


 1 4 
Given matrix has 3 rows
Given matrix has 2 columns
Places row and column data accurately in correct
order
Provides unlabelled matrix with brackets
Marks
1
1
1
1
Item
(S/C)
C
C
S
S
Question 3
Solution
a)
b)
c)
d)
e)
f)
36%
22%
% of household income spent on
clothing (1) by people in the 41–50 age
group (1)
22+11+10+18 = 61
100 – 61 = 39 so 39%
No. The numbers represent % and the
total has no meaning because the
percentages are for different groups
and different items.
36
 25

16

15
26
22
14
20
20
18
12
18
22 
11 
10 

18 
Reads data in matrix
Reads data from correct location in
matrix
Interpret correct location of data in
matrix, relating both items to the
context of the question
Read matrix and add numbers in row 4
Subtracts sum from 100
Recognise the lack of value held by the
total of these numbers.
1
1
Item
(S/C)
S
C
1
C
1
1
1
1
C
C
C
C
Writes matrix in transposed form
1
S
Recognise relationship to original matrix
1
S
Locate correct row number (1) and
column number (1) for data item
2
S
Behaviours
Marks
Percentage spent on housing
Row 3, column 4
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
26
Question 4
1
Item
(S/C)
S
Recognise that the two halves
make up the whole game
1
S
Recognise that the two matrices
represent the two sections of the
test.
1
S
Correctly add two 1x3 matrices
1
S
Correctly add two 2x2 matrices
1
S
Correctly add three 4x1 matrices
1
C
Recognise the sum does not make
sense.
1
C
1
S
2
S
2
C
Solution
a)
Behaviours
•
Total number of drivers (both male and
female) caught breaking the law for the
three different infringements
•
Scored kicks for the four players for the
whole game
•
Total test marks for each of the three
topics for each girl
(i)
[7
17 18]
9 11 


8 −4 
7
12 
(iii)  
 20 
 
 −2 
(ii)
b)
(i) Values in the matrix are proportions of
different values, not counts of objects
1 
 
(ii) 2 and [3 2 1]
 
 3 
c)
Recognises that male and female
make up the total amount
Provides matrices with different
sizes.
(iii) Values in corresponding positions
i.e. same row and same column from
two matrices are added
(iv) Matrices must have the same number of
rows. Matrices must have the same
number of columns. The sum of the two
numbers must have value / make sense
Accurately describes the addition
process
States the need to have the same
dimensions &/or the
appropriateness of adding the
data.
Marks
Question 5
Solution
a)
b)
c)
d)
e)
5x4
a34
a13 + b13
axy + bxy
Order of matrices being
added must be the same
Behaviours
Marks
Identifies and presents order in correct format
Writes the element using correct notation
Writes the sum of the correct elements using correct
notation
Writes the sum of the correct elements using notation
including variables. Defines variables used.
Correctly states relationship between addition and
order of matrices being added.
1
1
Item
(S/C)
S
S
2
C
2
C
1
S
Sample assessment tasks | Mathematics: Applications | ATAR Year 11
27
Question 6
Solution
a)
b)
c)
d)
False: There are 2 columns in A but 3
columns in B.
True: The number of columns in A is 3
and there are 3 rows in B.
True: A square matrix has the same
number of rows and columns so the
rule will be followed.
False: A and B are both square but the
number of columns in A may not equal
the number of rows in B.
 2 3
A= 

0 1
1 1 1 


B= 1 0 1


 2 2 2 
True:
 2 3
 then transposed is
0 1
2 0
3 1


 2 3
and this transposed is 

0 1
If A = 
e)
1
Item
(S/C)
S
1
S
2
C
Recognise that all square matrices do
not have the same size so that the
number of columns of the first matrix
will not necessarily equal the number of
rows of the second.
2
C
Transposes a matrix twice in succession
to accurately create the original matrix.
1
C
Behaviours
Recognise that the rule for
multiplication is not followed.
Identifies number of rows and columns
in column and row matrices. Recognise
that the rule for multiplication is not
followed.
Apply the given definition of a square
matrix to the rule for multiplication.
Marks
Sample assessment tasks | Mathematics: Applications | ATAR Year 11