Australian International Academy, Kellyville

Year 9 Unit: X Attack

Key Concept: Related Concepts: Global Context:​ Scientific MYP Criteria​:

Statement of inquiry:
We can find unknown values and make predictions based on logic and patterns.
ATL Skills
● Reflection and Transfer Skills

NSW NESA outcomes:

● MA5.2-3WM - constructs arguments to prove and justify results

● MA5.3-1WM - uses and interprets formal definitions and generalisations when explaining solutions and/or
conjectures

● MA5.3-2WM - generalises mathematical ideas and techniques to analyse and solve problems efficiently

● MA5.3-3WM - uses deductive reasoning in presenting arguments and formal proofs

● MA5.2-9NA - uses the gradient-intercept form to interpret and graph linear relationships

● MA5.3-8NA - uses formulas to find midpoint, gradient and distance on the Cartesian plane, and applies
standard forms of the equation of a straight line

Marking Scheme
19-20 8
17-18 7
15-16 6
13-14 5
10-12 4
7-9 3
4-6 2
1-3 1
0 0

Criteria C  TOTAL 
MARKS: 
   / 8 

Criterion C: Communicating
Achievement Level Descriptor Task Descriptors
level

0 The student does not reach a standard described by any of the descriptors
below.

1–2 The student is able to: The student is able to: Identify
i. use limited mathematical language some patterns and graph on
ii. use limited forms of mathematical representation to present information. Online software. There is some
iii. communicate through lines of reasoning that are difficult to interpret. explanation on their findings.

3–4 The student is able to: The student is able to: Identify
i. use some appropriate mathematical language. some patterns and graph
ii. use appropriate forms of mathematical representation to present information correctly on Online software.
adequately. There is some use of
iii. communicate through lines of reasoning that are able to be understood, mathematical language to
although these are not always clear. explain their findings.
iv. adequately organize information using a logical structure.

5–6 The student is able to: The student is able to: Identify
i. usually use appropriate mathematical language patterns and graph correctly on
ii. usually use appropriate forms of mathematical representation to present the Online software. They also
information correctly discuss their findings correctly
iii. move between different forms of mathematical representation with some using all the appropriate
success mathematical language.
iv. communicate through lines of reasoning that are clear although not always
coherent or complete
v. present work that is usually organized using a logical structure.

7–8 The student is able to: The student is able to: Explore
i. consistently use appropriate mathematical language. various functions, identify
ii. use appropriate forms of mathematical representation to consistently present patterns and graph correctly on
the information correctly. Online software. They also
iii. move effectively between different forms of mathematical representation. discuss their findings correctly
iv. communicate through lines of reasoning that are complete and coherent using all the appropriate
v. present work that is consistently organized using a logical structure. mathematical language. (Q 11 –
15 must be completed
accurately)

 
ATL Descriptor
Self-management- Reflection and Transfer Skills
1 - Needs Attention 2- Acceptable 3 - Good 4 - Very Good 5 - Online excellent

Description of Activity​: ​For this investigation, you will be exploring various functions and will be identifying 
patterns in order to better understand how we create functions. You will be using Online software to assist in 
graphing and will also be using Word to summarise your findings.​ ​https://www.desmos.com/calculator 

Your final assessment task must be submitted as a word document and it should include all the tables and 
graphs that have been drawn on Excel or any other Online software. 

You can view this video for your reference.​ ​https://www.youtube.com/watch?v=ITgT3YPDeLs  

Functions Investigation
1. Graph the following functions in Online software (on the same set of axes): (1mark) 
o y = 2x  
o y = 2x + 4  
o y = 2x + 6

 
2. Copy your graph into Word and then discuss your findings by comparing and contrasting the 
graphs, i.e. comment on what features of each graph are similar and what are different. 
(1mark) 
The things that are the same is that all the graphs have the same slope/gradient, the slope/gradient is 
positive, they are all linear functions and they are all parallel to each other . The only difference is that 
they have different x-intercepts and y-intercepts.  
 
3. Graph the following functions in Online software (on the same set of axes): (1mark) 
o y = 2x  
o y = 2x − 3  
o y = 2x − 5

 
 4. Copy your graph into Word and then discuss your findings by comparing and contrasting the 
graphs, i.e. comment on what features of each graph are similar and what are different. 
(1mark) 
The things that are the same is the slope/gradient is similar, all three of the graphs are linear functions, 
they are all parallel to each other and the only difference is the x-intercepts and the y-intercepts. 
Comparing y=2x-3 is 3 units below y=2x and y=2x-5 is 5 units below y=2x.  
 
 
5. Graph the following functions in Online software (on the same set of axes): (1mark) 
o y = x − 2 
o y = 3x − 2  
o y = 5x − 2

 
6. Copy your graph into Word and then discuss your findings by comparing and contrasting the 
graphs, i.e. comment on what features of each graph are similar and what are different. 
(1mark) 
The similarities between the graphs are that they are all linear functions, they all have the same 
y-intercepts and the slope/gradient is all positive. The difference is the slope/gradient and the 
x-intercepts.  
y=5x-2 has a higher gradient out of the three graphs and y=x-2 has the lowest gradient out of the three.  
 
7. Calculate the gradient of each of your functions from question 6. (2marks) 
 
To calculate the gradient, y=mx+b, m is the gradient.  
● y=x-2: The gradient is 1. 
● y=3x-2: The gradient is 3.  
● y=5x-2: The gradient is 5.  
 
8. Graph the following functions in Online software (on the same set of axes): (1mark) 
o y =− x + 4  
o y = − 2x + 4  
o y = − 4x + 4

 
 
 
 
 
  
9. Copy your graph into Word and then discuss your findings by comparing and contrasting the 
graphs, i.e. comment on what features of each graph are similar and what are different. 
(1mark) 
The similarities between the three graphs are that they are all linear functions, they have the same 
y-intercepts and they all have a negative slope/gradient. The differences are slope/gradient and the 
x-intercepts.  
 
10. Calculate the gradient of each of your functions. (2marks) 
To calculate the gradient, y=mx+b, m is the gradient.  
● y=-x+4: The gradient is -1.  
● y=-2x+4: The gradient is -2.  
● y=-4x+4: The gradient is -4.  
 
 
  
11. Graph the following functions in Online software (on the same set of axes): (2marks) 
o y = x + 5 
o y = − 2x − 3  
o y = x2 + 5  
o y = − 2x 2 − 3

 
12. Copy your graph into Word and then discuss your findings by comparing and contrasting the 
graphs, i.e. comment on what features of each graph are similar and what are different. 
(2marks) 
● The 1st two graphs (y=x+5 & y=-2x-3) are straight lines which are considered as linear functions.  
● The last 2 graphs (y=x^2+5 & y=-2x^2-3) are curved lines which are considered as non-linear 
functions.  
● The 3rd and 4th (y=x^2+5 & y=-2x^2-3) are the same shape but one is looking up and the other 
is looking down.  
● Both non-linear graphs don’t have an x-intercept.  
● y=x+5 & y=x^2+5 have the same y-intercept. 
● y=-2x-3 & y=2x^2-3 gave the same y-intercept.  
 
 
 
 
 
 
 
 
 
 13. Linear functions take the form: y = mx + b . Using your findings from questions 1-12 summarise 
what the coefficients m and b represent in a linear function. Ensure that you are specific about 
what occurs. Provide some examples for full justification. (2marks) 
All graphs in Question 1 & Question 3 have the same slope/gradient. By looking at the functions, the 
coefficient of x is the same for all the graphs. Therefore, linear function in the form y=mx+b, m 
represents the slope/gradient, If m is a positive number, it goes up from left to right, and if m is a 
negative number, it goes down from left to right.  
From Question 1 & Question 3 is an example of a positive slope/gradient and Question 8 is an example 
of a negative slope/gradient. All the graphs in Question 8, pass the y-intercept at the same time. By 
looking at the function, the constant is the same for all of them. Therefore, b represents the y-intercept 
of the function.  
 
14. Using your knowledge from this investigation, predict what the following linear functions would 
look like when it is graphed. Ensure you are using correct mathematical terminology during your 
discussion. (1mark) 
o y = 2x + 5  
o y = − 4x + 7
y=2x+5 has the slope/gradient of positive 2. Therefore the graph will be going up from left to right and it 
has a y-intercept of 5.  
y=-4x+7 has the slope/gradient of negative 4. Therefore the graph will be going down from left to right 
and it has a y-intercept of 7.   
 
15. Look back at your graphs from question 11. When you reflect on these graphs some of them 
were linear functions however the others were non-linear functions. Investigate what type of 
nonlinear functions they are. How can you easily identify the type of function in the future? 
(1mark) 

The two nonlinear functions we have graphed are the same shape. The only difference is one is looking 
up and the other is looking down. Both the power of the graph of x is 2. The power of x helps in 
understanding what type of non-linear function it is. If the maximum power of variables is 2, it’s called a 
‘quadratic function’. 

y=x^2+5 = Looking up 

y=-2x^2+3=Looking down 
Reflection
I think I will achieve a level __6___ because…

I have understood most of the questions and I have explained it to the best of my abilities.
I achieved a level _____ because…
_______________________________________________________________________________________
_______________________________________________________________________________________
__________________
To better my level, I need to….
_______________________________________________________________________________________
_______________________________________________________________________________________
_________________

All the best ☺