Final Exam_Extended Mathematics - Marking Scheme
Subject
Grade
Points
Extended Mathematics
MYP4
A 25
B 25
C 25
Duration
Start time
125 mins
May 22, 12:00 pm
D 25
May 22, 12:00 pm(School
TZ)
Instructions
Final Term Examination May 2023 MYP®
Extended Mathematics
2
hours
READ THESE INSTRUCTIONS FIRST
1. Onscreen calculators are allowed
2. Do not shift between tabs
3. Do not ask any teacher any question unless there is an error in the question.
4. Formula sheet can be accessed from the Resource Sheet button.
5. There are separate tasks in this examination. Each task may have more than one question.
Answer all the questions in the response boxes provided. No uploads are allowed.
6. The maximum marks for this examination is 100 marks. Marks for each question and
criteria are mentioned next to it.
Task
1,2,3,4,5,
6
9
7,8
Mark
Main criteria
Criterion
s
assessed
Marks
A
25
C
8
B
25
C
9
D
25
C
8
Knowing & Understanding
33
Investigating Patterns
34
Applying mathematics in real-life
contexts
33
Page 1 of 37
Task 1 (Criteria A)
In this task you will interact with different aspects of form in terms of representation.
The task will assess Criteria A (Knowing and Understanding)
The suggested time for this task is 5 minutes
Page 2 of 37
Q 2.1
A6
Select the correct option to complete the table
For f(x)
a is
Positive
b is
Negative
c is
Positive
b is
Negative
c is
Negative
For g (x)
a is
Negative
Page 3 of 37
Task 2(Criteria A)
In this task you will interact with different aspects of form in terms of representation.
The task will assess Criteria A (Knowing and Understanding) and Criteria C (Communication)
The suggested time for this task is 5 minutes
Q 3.1Identify the three expressions that simplify to 6x-5. Drag and drop the three
expressions to the allocated space below. Show your working
A2
C1
Teacher's explanation
Page 4 of 37
Task 3(Criteria A)
In this task you will interact with different aspects of form in terms of representation.
The task will assess Criteria A (Knowing and Understanding)
The suggested time for this task is 5 minutes
Select the term from the drop-down menu which correctly describes the distribution of each graph.
Q 4.1
Large
A 0.5
Standard Deviation
Page 5 of 37
Q 4.2
Zero
A 0.5
Standard Deviation
Q 4.3
A 0.5
different
mean
same
standard deviation
Page 6 of 37
Q 4.4
A1
different
mean
different
standard deviation
Q 4.5
A 0.5
same
mean
different
standard deviation
Page 7 of 37
Task 4(Criteria A & C)
In this task you will interact with different aspects of form in terms representation.
The task will assess Criteria A (Knowing and Understanding) and Criteria C (Communication)
The suggested time for this task is 10 minutes
One of four main blood types can be found in a human body. They are known as A, B, AB and O.
Each blood type can be further classi ed as either a Rhesus positive (+) or Rhesus negative (-). For
example, a possible combination is blood type O and Rhesus negative which is written as O- The pie
charts below shows the distribution of the blood types and Rhesus types for a blood donor centre
recorded in 2019.
Q 5.1People with blood type O- are known as universal donors. They can donate their
A1
blood to patients with any blood type. Show that the probability that a randomly
C1
selected person has blood type O- is 0.1.
Teacher's explanation
Page 8 of 37
Q 5.2Thirty people donate blood one morning. Determine the expected number of people
A1
that have blood type O-.
Teacher's explanation
Page 9 of 37
Q 5.3Two of the thirty donors are selected at random. Write down the missing values in
A3
the tree diagram below.
Teacher's explanation
Page 10 of 37
Q 5.4Given that the second donor has blood type O-, nd the probability that the rst
donor does not have blood type O-.
A2
C2
Teacher's explanation
Page 11 of 37
Task 5(Criteria A & C)
In this task you will interact with different aspects of form in terms models.
The task will assess Criteria A (Knowing and Understanding) and Criteria C (Communication)
The suggested time for this task is 5 minutes
Page 12 of 37
Q 6.1Using the information provided in the diagram below, nd the height of a carton.
A3
C2
Teacher's explanation
Page 13 of 37
Task 6(Criteria A & C)
In this task you will interact with different aspects of form in terms of system.
The task will assess Criteria A (Knowing and Understanding) and Criteria C (Communication)
The suggested time for this task is 10 minutes
Page 14 of 37
Q 7.1Find the value of x.
A2
C2
Teacher's explanation
Q 7.2Hence, determine the area of the triangle
A2
Teacher's explanation
Page 15 of 37
Task 7(Criteria D & C)
In this task you will use Relationships within the global context of Scienti c and Technical
Innovation. This task focuses on Criterion D (Applying Mathematics in real-life contexts) and
Criterion C (Communication)
The suggested time for this task is 25 minutes
Different fuels are used to power motor vehicles. The most common types of vehicle fuel are petrol
and diesel. Petrol and diesel powered vehicles contribute to polluting vehicle emissions and
increased carbon footprints. To reduce carbon footprint there is an intention to replace them with
electric powered vehicles.
A government promotion will be presented to you to encourages potential buyers to purchase
electric powered vehicles. In this question, you will make calculations to choose between electric
powered vehicles and a petrol powered vehicle.
Page 16 of 37
Q 8.1Vehicle A is advertised to buy for £31 250. As part of a government incentive the
vehicle cost is reduced by 20%.
C1
D2
Calculate the vehicle cost after the government incentive for vehicle A.
Teacher's explanation
Award last mark on C
Q 8.2A person drives 14 000 miles on average per year.
D2
Determine the annual fuel cost of vehicle A
Teacher's explanation
Page 17 of 37
Q 8.3The annual fuel cost of Vehicle B is £11 90. Find the percentage savings of the
annual fuel cost when purchasing vehicle A instead of vehicle B.
C1
D2
Teacher's explanation
Award second mark on C
The total cost (T) of owning a vehicle is the sum of the vehicle price and the annual fuel cost. The
following graph shows the linear relationship for the total cost, T, of owning Vehicle A for n years,
driving 14 000 miles per year.
Q 8.4Write down a linear equation for the total cost, T, of owning vehicle A for n years.
D2
Teacher's explanation
Page 18 of 37
Q 8.5Discuss whether vehicle A or vehicle B is a better buy.
C5
D5
Use the information provided in the table and your answers from parts (a) to (d). In
your answer, you should:
• identify three relevant factors to consider when deciding whether to buy vehicle A
or vehicle B
• draw a graph that describes the linear relationship for the total cost (T) of owning
vehicle A for n years
• determine after how many years the total cost of owning vehicle A is equal to
vehicle B
• justify whether vehicle A or vehicle B is a better buy and how this may impact
communities and the environment
• comment on the accuracy of the total cost of owning the different vehicles.
Note: Use algebra in the graph for writing the equation to draw the line, OR use
tool--->line segment and then select two points to draw the line
Teacher's explanation
Page 19 of 37
Award F2, G1,2, J2, A2 on C
Page 20 of 37
Task 8 (Criteria D & C)
In this question, you will make calculations for changes that individuals can make to save water on a
daily basis.
The task will assess Criteria D (Knowing and Understanding) and Criteria C (Communication)
The suggested time for this task is 20 minutes
Q 9.1Write down the missing percentage for drinking and cooking on the pie chart.
D1
Teacher's explanation
Page 21 of 37
Q 9.2It is estimated that the daily water usage per person is 120 litres. Determine the
D2
amount of water used for showering.
Teacher's explanation
Q 9.3A regular shower has a
ow rate of 8 Litres (L) per minute. Using your answer from
D2
Q2, determine the duration of a regular shower.
Teacher's explanation
Page 22 of 37
Q 9.4In a water-saving condition the
ow rate of a shower can be reduced to be 5 L per
D2
minute. Given that the duration of the shower does not change: Determine the
amount of water used for showering in a water-saving condition.
Teacher's explanation
Q 9.5The amount of water used by the washing machine is 14.4 L. The eco-setting for
C1
washing machines reduces water by 5%. Calculate the amount of water used by
D2
the washing machine in the eco-setting.
Teacher's explanation
Page 23 of 37
Q 9.6
D1
Suggest the order of activities in which it is most important to save water. Drag and
drop the activities in the appropriate order.
Teacher's explanation
Page 24 of 37
Q 9.7
C1
D2
Justify your chosen order in Q6. You should refer to your answers from previous
parts.
Teacher's explanation
Page 25 of 37
Task 9(Criteria B & C)
In this task, you will use logic in space and patterns . The task focuses on Criterion B(Investigating
Patterns) and Criterion C (Communication).
The suggested time for this task is 35 minutes
The line y = 2x + 1 is shown on the coordinate axes below. Vertical line segments can be added
between the line and the x axis, one unit apart horizontally. In this question, you will investigate
areas of different trapeziums formed.
Page 26 of 37
Q
For stage 3, show that the area of the trapezium is 6 units squared.
10.1
B1
C1
Teacher's explanation
Page 27 of 37
Page 28 of 37
Q
Write down the missing values in the table up to stage 6
B1
10.2
Stage (n)
Area of Trapezium (A)
1
2
2
4
3
6
4
8
Teacher's explanation
Q
Write down a general rule for A in terms of n
10.3
B1
C1
Teacher's explanation
Page 29 of 37
Q
Describe in words two patterns you see in table A.
B2
10.4
Teacher's explanation
Marking Scheme pasted here:
Examples of accepted terminology:
Even numbers, multiples of 2
Increasing by 2, adds 2 every time, goes up by 2, moving up by 2
Difference is 2
Second difference is zero
Arithmetic progression, Arithmetic sequence
DO NOT ACCEPT
the rule in words e.g. 2 times n, n multiplied by 2, double of n, twice stage
number, the product of n and 2
dividing area by 2 gets n
the area is half the stage number
follows the 2 times table
Increasing
Arithmetic series
Note:
More than two different patterns, all correct award (2 marks)
More than two different patterns, at least one correct award (1 mark)
Q
Verify your general rule for A
B3
10.5
Teacher's explanation
Page 30 of 37
Using the same line, you will now look at how different trapeziums are formed.
Page 31 of 37
Page 32 of 37
Page 33 of 37
Q
Investigate to nd a relationship for T in terms of n. In your answer, you should
10.6
B 17
C6
• predict more values and record these in the table.
describe in words two patterns for column T
nd a general rule for T in terms of n
test your general rule for T
prove or verify and justify your general rule for T
ensure that you communicate all your working appropriately.
Stage (n)
Area of Trapezium (T )
1
2
2
6
3
12
4
20
5
6
7
Teacher's explanation
Page 34 of 37
Page 35 of 37
Page 36 of 37
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