GRADE: 9
SUBJECT: MATHEMATICS
TERM FOUR 2015
FORMAL ASSESSMENT TASK - ASSIGNMENT
Name: _______________________________________________________
Class: ___________________________ Date: ______________________
School: __________________________ Teacher: ___________________
FAT
Activity
4.1
ASSIGNMENT
TOTAL
Marks
80
%
1
MATHEMATICS GRADE 9 FORMAL ASSESSMENT TASK (FAT) 4.1:
ASSIGNMENT: Transformation Geometry; Geometry of 3D objects;
Data handling & Probability
Total: 80 Marks
Time: 90 minutes
Name: _____________________________________
Date: _____________
Instructions:
1)
2)
3)
4)
5)
6)
Write your name and date in the spaces provided.
Show calculations as requested on question paper.
You may use a calculator.
It must be your own work.
Round answers to 2 decimal numbers unless stated otherwise. Check your answers.
On page 14 is a list of formulae that you can use to answer questions.
Question 1: Transformation Geometry
Use the diagram below and answer the following questions:
Mathematics Grade 9
2
1.1 Determine the coordinates of A, B, C and D.
(4)
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1.2
Determine the coordinates of 𝐴′ , 𝐵′ , 𝐶 ′ 𝑎𝑛𝑑 𝐷 ′, the images of A, B, C and D, if the figure is shifted
one unit vertically down and 2 units horizontally to the right.
(4)
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1.3
Determine the coordinates of 𝐶 ′′ , the image of C, if the image is reflected in the x-axis.
(2)
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1.4
Determine the coordinates of 𝐵′′ , the image of B, if the figure is reflected in the y-axis.
(2)
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Mathematics Grade 9
3
1.5
1.5.1
The length of 1 side of square ABCD is 6,7 units.
Calculate the perimeter of the figure if the length of the sides is halved.
(3)
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1.5.2
Determine the ratio of the area of square ABCD to the area of the reduced figure.
(3)
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1.6 Describe the transformation and write down the rule used in the form (𝑥; 𝑦) → ⋯
(2)
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[20]
Mathematics Grade 9
4
Question 2: Geometry of 3D-objects ; Volume and total surface area of 3D-objects
2.1
Complete the following statements:
2.1.1
Platonic solids are a group of polyhedra that have faces that are
________________________________ polygons .
2.1.2
(1)
A cetain 3D object have the following properties:



no flat faces
no straight edges
one curved face.
This 3D-object’s name is ................................................?
(1)
2.2
Facts: There are only five geometric solids that can be made using a regular polygon and having the same
number of these polygons meet at each corner.
2.1 Complete the table by writing the correct answer to the letters ( A - E).
Platonic
Solid
Picture
Number
of Faces
(F)
Tetrahedron
4
Cube
B
A
8
Mathematics Grade 9
Shape of
Faces
Triangle
Number
Number
of
of Edges
Vertices
(E)
(V)
4
D
Square
8
12
Triangles
6
12
Unfolded
Polyhedron
(Net)
E
5
Number Number
of
of
Vertices Edges
(V)
(E)
Number
of Faces
(F)
Shape of
Faces
Dodecahedron
12
Pentagons
C
30
Icosahedron
20
Triangles
12
30
Platonic Solid
Picture
Unfolded
Polyhedron
(Net)
(5)
2.2
A rectangular prism have dimensions of 6 cm, 9 cm and 12 cm.
2.1.1
Calculate the volume of this rectangular prism.
(2)
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2.1.2 Calculate the total external surface area of this rectangular prism.
(2)
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Mathematics Grade 9
6
2.2
Determine the volume of a cylinder if 𝑟 = 7𝑐𝑚 and ℎ = 20 𝑐𝑚 .
N.B: Use 𝜋 = 3,14 . Round your answer to one decimal place.
(3)
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2.3
The volume of the cylinder is 324 cm3 and the
diameter 6cm, calculate the height,
H, of the cylinder, correct to two decimal places.
Use 𝜋 = 3,14 in your calculations.
H
(4)
66x
cm
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[18]
Mathematics Grade 9
7
Question 3: Data Handling
3.1
An organisation called Auto Rescue recorded the following numbers of calls from
motorists each day for roadside service during March 2014.
28
122
217
130
120
86
80
90
120
140
70
40
145
187
113
90
68
174
194
170
l00
75
104
97
75
123
100
82
109
120
81
3.1.1 Complete the following table:
Number of calls
0 - 40
41 - 80
Tally marks
//
////
Frquency
2
5
121 - 160
////
5
201 - 240
Total
/
1
31
(4)
3.2
A fruit farmer wants to know which of his trees are producing good plums, and which
tree need to be replaced. He collects 100 plums each from two trees and measures their
masses. The data below gives the mass of plums from the first tree (Tree 1).
Mass of plums (g)
Frequency
3.2.1
20 - 29
6
30 - 39
18
40 - 49
34
50 - 59
30
60 - 69
12
Use the following graph paper (on next page) and draw a histogram to represent the
data:
Mathematics Grade 9
Frequency
8
(5)
Mass of plums
3.2.2
The following data gives the mass of plums of a second tree (Tree 2).
Mass of plums (g)
Frequency
20 - 29
3
30 - 39
14
40 - 49
26
50 - 59
36
60 - 69
21
The farmer draws a histogram to represent the mass of the same type of plums on a second
tree (Tree 2).
Mathematics Grade 9
9
Study the two histograms and then comment on the number of plums produced
by the two trees.
(2)
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3.3
Vincent is a salesperson at a men’s shoe store. His employer asks him to record information
about the sizes of the shoes she sells in the space of one week, so that he can make business
decisions about future purchases. He records 20 sales in a week, and records the sizes as follows:
8
9
5
10
9
7
6
8
7
5
14
6
11
8
7
6
8
7
8
10
3.3.1
Give the range of the data recorded.
(1)
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3.3.2
Give the size of an outlier, if there is any.
(1)
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3.3.3
Calculate the mean of the shoe sizes sold.
(2)
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3.3.4 Draw a stem and leaf plot of the given data.
(2)
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Mathematics Grade 9
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3.3.5
Determine the median of the shoe sizes sold.
(2)
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3.3.6
Give the mode of the shoe sizes sold.
(1)
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3.3.7 Which of these three measures of central tendency (mean, median, mode) would be
the most valuable to Vincent’s employer? Briefly explain your answer.
(2)
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3.4
The table below shows the shoe sizes and mass of 10 men.
Shoe
sizes
5
12
7
10
10
9
8
11
6
8
Mass in
kg
65
97
68
92
78
78
76
88
74
80
3.4.1
Draw a scatter plot diagram of the given data. Use the graph paper below.
Mathematics Grade 9
(3)
11
3.4.2 Describe the trend, in the correlation, shown by the scatter plot.
(1)
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[26]
Question 4: Probability
4.1
A letter from the word MATHEMATICS is chosen at random. What is the probability that the
following letters are chosen?
4.1.1
S
(1)
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4.1.2
A vowel
(2)
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4.2
Describe in words the probability of each event below occurring?
4.2.1
The captain of the BAFANA BAFANA winning the toss at a soccer game.
(1)
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Mathematics Grade 9
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4.2.2
That the sun will set in the west.
(1)
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4.3
A deck of cards contains 52 cards which are divided into 4 suits:
Clubs (black), Spades (black)
Hearts (red) and Diomands (red)
There are thirteen cards of each suit.
Each suit contains numbers 2 to 10 as well as 3 picture cards (Jack, Queen, King) and an Ace.
2 is the lowest and Ace is the highest card in a suit.
What is the probability of randomly drawing:
4.3.1
A Jack (write your answer as a fraction in its simplest form)
(1)
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4.3.2
Any card smaller than 5 (write your answer as a decimal fraction)
(2)
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Mathematics Grade 9
13
4.3.3
Any picture card (write your answer as a percentage)
(2)
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4.4
80 people were asked which one of three TV Channels they preferred to watch.
4.4.1 Complete the partially filled, two-way contingency table below.
(3)
SABC 1
8
12
Male
Female
Total
SABC 2
SABC 3
7
Total
20
28
80
What is the probability that a person selected at random:
4.4.2 preferred SABC 1?
(1)
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4.4.3 was female?
(1)
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4.4.4
was male and preferred SABC 2?
(1)
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[16]
Mathematics Grade 9
14
TOTAL: 80
LIST OF FORMULAE:
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒: 𝑃 = 4 × 𝑠𝑖𝑑𝑒
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒: 𝐴 = 𝑠𝑖𝑑𝑒 × 𝑠𝑖𝑑𝑒
𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒: 𝑃 = 2𝑙 + 2𝑏
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒: 𝐴 = 𝑙 × 𝑏
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒: 𝑃 = 2𝜋𝑟
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒: 𝐴 = 𝜋𝑟 2
𝑉𝑜𝑙𝑢𝑚𝑒 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟: 𝑉 = 𝜋𝑟 2 ℎ
𝑉𝑜𝑙𝑢𝑚𝑒 𝑐𝑢𝑏𝑒: 𝑉 = 𝑠 3
𝑉𝑜𝑙𝑢𝑚𝑒 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚: 𝑉 = 𝑙𝑏ℎ
𝑇𝑜𝑡𝑎𝑙𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑢𝑏𝑒: 𝑇𝑆𝐴 = 6𝑠 2
𝑇𝑜𝑡𝑎𝑙𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟: 𝑇𝑆𝐴 = 2𝜋𝑟 2 + 2𝜋𝑟
𝑇𝑜𝑡𝑎𝑙𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚: 𝑇𝑆𝐴 = 2𝑙ℎ + 2ℎ𝑏 + 2𝑙𝑏
NOTATION
A′ - means the image of A after a transformation (translation, reflection, rotation,
enlargement, reduction). HINT: Refer to the original point A.
𝐶 ′′ - means the image of C after a second transformation (translation, reflection, rotation,
enlargement, reduction). HINT: read the question to understand which point to refer to.
Mathematics Grade 9