MYP 4&5 Standard Mathematics - 9 - copy
Subject
Grade
Points
Standard Mathematics
MYP 5
A 25
B 25
C 25
D 25
Question 1
Knowing and understanding
In this task (questions 1 to 4), you will interact with different aspects of form using a variety of
related concepts. This task focuses on criterion A (Knowing and understanding) and criterion
C (Communication).
Find if the given events are independent or not.
There are four red boxes and four blue boxes, and four $20 bills that are to be placed in the given
eight boxes. Each bill is to be placed in a separate box. A box is called a "lucky box" if it contains the
$20 bill in it. Let A and B be two events as follows.
A: You pick a lucky box.
B: You pick a blue box.
Q 1.1
Write down the value of P (A ) .
A1
Words: 0
Page 1 of 22
Suppose one $20 bill is placed in a blue box and other three $20 bills are placed in three red boxes.
Q 1.2
If you picked a blue box, then write down the probability of not picking a lucky box.
A2
Words: 0
Q 1.3
State if the event A (picking up a lucky box) and event B (picking up a blue box)
A1
are independent or not.
Words: 0
Suppose that in a new con guration two $20 bills are places in two separate blue boxes and two
$20 bills are placed in two separate red boxes.
Q 1.4
State if the events A and B are independent or not according to the new
A2
con guration.
Words: 0
Page 2 of 22
Question 2
Use linear equations to compare the taxi fare on weekdays and weekends.
An organization called Transport for London(TFL) is responsible for reviewing and setting taxi fares
and tariffs in London city. The picture displays the tariff charges for availing taxi services within a
given time period.
Image 1
Q 2.1
Write down the mathematical equations for fare calculation if a taxi is hired on the
A2
weekend. Assume the total fare of the taxi be "y" and the miles traveled by the taxi
C1
be "x".
Words: 0
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Q 2.2
Show that taxi fare for the same number of miles is higher on weekends than on
A2
weekdays between 05:00 - 20:00.
C2
Words: 0
Page 4 of 22
Question 3
Compare the areas required to open Classic car door and Scissor car door.
Page 5 of 22
Doors are one of the attractive features in driving cars. Two of the famous types of car doors are
classic door and scissor door.
Image 1
Image 2
Page 6 of 22
Physics behind the opening of scissor car door.
Video 1
Scissor car door
00:00/00:14
Page 7 of 22
Physics behind the opening of classic car door.
Video 1
car door animation
00:00/00:02
Q 3.1
Select the shape of the path of opening these car doors.
A1
A Square
B Rectangular
C Circular
D Pentagonal
Page 8 of 22
Q 3.2
If the width of a car door is 14 feet and height is 7 feet, determine the radii/sides of
A2
the path of opening for each car door ?
Words: 0
On an average classic door opening angle is 70° whereas for scissor doors the angle made varies
from 90° to 130°.
Q 3.3
The width of the car door is 14 feet and the height is 7 feet for both the cars.
A3
Compare the horizontal area required for opening a classic car door with the
C2
maximum vertical area required for opening a scissor car door.
Words: 0
Page 9 of 22
Question 4
Calculate the dissolved oxygen levels in water using given data.
Video 1
How to Measure Dissolved Oxygen in Water
00:00/01:10
Table below displays one-time Dissolved Oxygen[DO] levels observed at different points in La Torre,
Guadarrama watershed, Spain.
Sampling Point 1
Dissolved oxygen
Level (mg/l)
2.6
0.2
Sampling Point 2
4.6
0.2
Sampling Point 3
2.3
0.2
Sampling Point 4
5.3
0.2
Page 10 of 22
Q 4.1
Determine the maximum and minimum DO levels at Sampling Point 1.
A2
Words: 0
The box and whisker plot for the above data is shown below.
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Q 4.2
Write down the 5-point summary for the above box and whisker plot.
A5
Words: 0
Q 4.3
Using the plot, estimate what percentage up to one decimal place of the values are
A1
lower than the minimum DO values in Utah city.
C1
Words: 0
Q 4.4
Determine if mean DO level in La Torre will be considered a healthy DO value in
A1
Utah city.
C1
Words: 0
Page 12 of 22
Question 5
Applying mathematics in real-life contexts
In this task (questions 5 and 6), you will use relationships to apply mathematics within the global
context of orientation in space and time. This task focuses on criterion D (Applying mathematics in
real-life contexts) and criterion C(Communication).
Explore the relationship between the zoom level and meters per pixel.
In digital maps like google maps the scale is hard to determine due to different sizes and resolutions
of screens like mobile and computer. A similar concept called zoom levels that does not vary as per
the user’s screen is used. For google maps the zoom levels and information it stores is given by the
equation
P=
102993
2z
Here, P is the meters per pixel and z is zoom in level 0 ≤ x ≤ 20.
Q 5.1
Write down the values in the table predicting values of P at different zoom levels.
D3
Give your answer rounded off to one-decimal place.
Zoom in Level (z)
Meters Per Pixel (P)
0
10
20
Page 13 of 22
Q 5.2
Show that with increase in the value of z, P will zoom into the image.
C1
D2
Words: 0
Q 5.3
A user searched for Niagara waterfalls in google maps. Comment at which zoom
C1
level the user will see the below map. Consider that the spread of the continent
D4
North America is 24,709,000,000,000 m2 and 2329 pixel2 are displaying the
information of North America.
Hint: If there are 23 m in 1 pixel then there will be 23 × 23 m2 in 1 × 1 square pixels.
Words: 0
Page 14 of 22
Question 6
Design ice cream cones from the given sheet of paper.
A local ice cream company is planning to launch a new product of ice cream cones in its line of
products. You are given the task to design the ice cream cone. The ice cream cone is decided to be
conical in shape and is to be cut from a circular piece of paper as shown in the following gure. In
addition to this a circular lid is kept at the top of the cone to prevent spillage of ice cream. A
waterproofed material is used for the product.
Page 15 of 22
Q 6.1
Let SA denote the total surface area of paper used in the construction of an ice
C2
cream cone. Let s be the radius of circle A and r be the radius of circle B. Write
D1
down the equation for SA in terms of s and r.
Words: 0
The total surface area of paper used in the construction of ice cream cone is 63π square
centimetres. The radius of circle A is 18 cm.
Q 6.2
Calculate the area of paper used for the construction of lid of ice cream cone. Give
D5
your answer correct to two decimal places.
Words: 0
The company uses two separate rectangular sheets of paper for the construction of ice cream cones.
The conical ice cream shape is cut from a rectangular piece of paper of dimensions 110 cm × 72 cm.
The ice cream lid is cut from a rectangular sheet piece of paper of dimensions 60 cm × 18 cm.
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Q 6.3
Discuss the number of ice cream cones that can be completed if one rectangular
C4
sheet of paper is used for cones and one rectangular sheet of paper is used for ice
D 10
cream lids. In your answer, you should:
nd the maximum number of ice cream cones that can be constructed from
one circle A.
calculate the number of ice cream cones that can be completed from the
rectangular sheet of dimension 110 cm × 72 cm.
calculate the maximum number of ice cream lids that can be completed from
the rectangular sheet of dimension 60 cm × 18 cm.
mention the sum of unused area of both the rectangular sheets.
write down the maximum number of complete ice cream cones (ice cream
cone with lid) that can be completed using both the rectangular sheets.
ensure you communicate all the information properly.
Words: 0
Page 17 of 22
Question 7
Investigating patterns
In this task (question 7), you will use logic to investigate the creation of shapes from circles. You will
be assessed using criterion B (Investigating patterns) and criterion C (Communication).
Describe patterns and nd general rules in shapes created from different coloured maps.
Page 18 of 22
In mathematics, the Four-colour map problem posed in the early 1850s and not solved until 1976 is
about nding the minimum number of different colours required to colour a map such that no two
adjacent regions are of the same colour. When Four color map problem is applied on a plane of
equidistant parallel lines (parallel lines that have same distance between them) we get following
results.
Image 1
Image 2
Image 3
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Image 4
Q 7.1
Write down the missing values in the table for the number of strips of red color at
B3
each stage.
Stage (n)
Number of strips of red color (R)
1
2
3
4
5
Q 7.2
Describe in words one pattern of R.
B2
C1
Words: 0
Page 20 of 22
Q 7.3
Predict values in table for odd n.
B2
n
R
1
1
3
5
7
9
Q 7.4
Write down a general formula for R in terms of n whenever n is odd.
B2
C1
Words: 0
Q 7.5
Write down the complete general formula for R in terms of n.
B2
C1
Words: 0
Q 7.6
Verify your rule for R.
B2
C1
Words: 0
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Q 7.7
Investigate the relationship between percentage of area (P) covered by color red in
B 12
terms of stage (n) rolled. In your answer you should:
C6
complete the table.
describe in words two patterns for P when n is even and when n is odd.
nd the general rule for P.
test your general rule for P.
verify your rule for P.
ensure that you communicate your working properly.
Stage (n)
Percentage of area covered by color red (P)
1
100%
2
3
4
50%
5
6
Page 22 of 22