GRADE: 9
SUBJECT: MATHEMATICS
TERM FOUR 2015
FORMAL ASSESSMENT TASK - ASSIGNMENT
Name: _______________________________________________________
Class: ___________________________ Date: ______________________
School: __________________________ Teacher:___________________
FAT
Activity
4.1
ASSIGNMENT (MEMORANDUM)
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: __________MEMORANDUM_____________
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.
 one mark per
correct answer
A (-2;2)
B(-5; -4)
C (1;-7)
D (4;-1)
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)
A (-2;2)  𝑨′ (𝟎; 𝟏)
B(-5; -4)  𝑩′ (−𝟑; −𝟓)
C (1;-7)  𝑪′ (𝟑; −𝟖)
D (4;-1)  𝑫′ (𝟔; −𝟐)
1.3
(4)
 one mark per
correct answer
CA from 1.1
Determine the coordinates of 𝐶 ′′ , the image of C, if the image is reflected in the x-axis.
(2)
′′
C (1;-7)  𝑪 (𝟏; 𝟕)
1.4
  𝑪 (𝟏; 𝟕)
′′
Determine the coordinates of 𝐵′′ , the image of B, if the figure is reflected in the y-axis.
(2)
′′
B (-5;- 4)  𝑩 (𝟓; − 𝟒)
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.
Perimeter of ABCD = 3,35 × 4 = 13,4 units
1.5.2
  𝑩 (𝟓; −𝟒)
′′
 3,35
 substitution in correct
formula
 answer
(answer only: full marks)
Determine the ratio of the area of square ABCD to the area of the reduced figure.
Area ABCD : Area reduced figure
(𝟔, 𝟕)𝟐 : (𝟑, 𝟑𝟓)𝟐
44,89 : 11,2225
4
: 1
Mathematics Grade 9
(3)
 method
 44,89 : 11,2225
 answer
(3)
3
1.6
Describe the transformation and write down the rule used in the form (𝑥; 𝑦) → ⋯
(2)
 answer
(𝒙; 𝒚) → (𝒙 + 𝟖; 𝒚 − 𝟏)
[20]
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 polyhedral that have faces that are
________________________________ polygons .
congruent regular
2.1.2
(1)
congruent
 regular
A cetain 3D object have the following properties:



no flat faces
no straight edges
one curved face.
This 3D-object’s name is ................................................?
sphere
Mathematics Grade 9
(1)
sphere
4
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
Tetrahedron
Picture
Number
of
Faces
(F)
4
Shape of
Faces
Triangle
Number Number
of
of
Vertices Edges
(V)
(E)
4
Unfolded
Polyhedron
(Net)
D-6
E
Cube
B - 6
Square
8
12
AOctahedron
8
Triangles
6
12
Dodecahedron
12
Pentagons
C-20
30
Icosahedron
20
Triangles
12
30
(5)
Mathematics Grade 9
5
2.2
A rectangular prism have dimensions of 6 cm, 9 cm and 12 cm.
2.1.1
Calculate the volume of this prism.
.
𝑽 =𝒍×𝒃×𝒉
= 𝟏𝟐 × 𝟗 × 𝟔
= 𝟔𝟒𝟖 𝒄𝒎𝟑
(2)
substitution in correct
formula
 answer (penalize for
SI-unit once in task)
2.1.2 Calculate the total external surface area of the prism.
𝑻𝑺𝑨 = 𝟐𝒍𝒃 + 𝟐𝒃𝒉 + 𝟐𝒍𝒉
= 𝟐(𝟏𝟐 × 𝟗) + 𝟐(𝟗 × 𝟔) + 𝟐(𝟏𝟐 × 𝟔)
= 𝟒𝟖𝟔 𝒄𝒎𝟐
(2)
substitution in correct
formula
 answer (penalize for
SI-unit once in task)
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.
𝑽𝒐𝒍𝒖𝒎𝒆 = 𝝅𝒓𝟐 𝒉
= 𝟑, 𝟏𝟒 × 𝟕𝟐 × 𝟐𝟎
= 𝟑𝟎𝟕𝟕, 𝟐 𝒄𝒎𝟑
substitution in correct
formula
 answer
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
Mathematics Grade 9
(3)
6
substitution in correct
formula
r=3
 answer
𝑽𝒐𝒍𝒖𝒎𝒆 = 𝝅𝒓𝟐 𝒉
𝟑𝟐𝟒 = 𝟑, 𝟏𝟒 × 𝟑𝟐 × 𝑯
𝟑𝟐𝟒
𝑯 = 𝟑,𝟏𝟒 ×𝟑𝟐 𝒄𝒎𝟑
𝑯 = 𝟏𝟏, 𝟒𝟔 𝒄𝒎
[18]
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
81 - 120
121 - 160
161 - 200
201 - 240
Total
Tally marks
//
////
///// ///// ////
/////
////
/
Frquency
2
5
14
5
4
1
31
(4)
3.2
A fruit farmer wants to know which of his trees are producing good plums, and which
trees 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).
Mathematics Grade 9
7
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 and draw a histogram to represent the data:
 one mark per
bar plotted correct
(5)
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
8
Study the two histograms and then comment on the number of plums produced
by the two trees.
The second tree produces fewer small plums (less than 40
g) and more plums that are bigger than 50 g. So the second
tree should be kept and the first one should be replaced.
observation
 conclusion
(2)
3.3
Vincent is a salesperson at a men’s shoe store. His employer asks him to record information
about the sizez 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.
Range = 14 -5 =9
Mathematics Grade 9
(1)
answer
9
3.3.2
Give the size of an outlier, if there is any.
14
(1)
answer
3.3.3
𝒎𝒆𝒂𝒏 =
Calculate the mean of the shoe sizes sold.
𝟐×𝟓+𝟑×𝟔+𝟒×𝟕+𝟓×𝟖+𝟐𝟗+𝟐∪𝟏𝟎+𝟏𝟏=𝟏𝟒
𝟐𝟎
= 𝟕, 𝟗𝟓
3.3.4
0
1
method
answer
Draw a stem and leaf plot of the given data.
5566677778888899
0014
3.3.5
(2)
(2)
method
answer
Determine the median of the shoe sizes sold.
8
(2)
answer
3.3.6
Give the mode of the shoe sizes sold.
8
(1)
answer
3.3.7 Which of these three measures of central tendancy (mean, median, mode) would be
the most valuable to Vincent’s employer? Briefly explain your answer.
(2)
For the shoe sizes, the mode is the most useful because it
indicates the most popular size
Mathematics Grade 9
mode
reason
10
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.
(3)
 all 10 points plotted correct
 5-9 points plotted correct
 0-4 points plotted correct
3.4.2 Describe the trend in the associations shown by the scatter plot.
Positive correlation
(1)
 answer
[26]
Mathematics Grade 9
11
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
𝟏
𝟏𝟏
or 0,09 or 9,09%
4.1.2
𝟒
𝟏𝟏
4.2
S
 answer
A vowel
or 0,36 or 36,36%
(2)
 number of vowels - 4
 answer
Describe in words the probabilility of each event belown occuring?
4.2.1
The captain of the BAFANA BAFANA winning the toss at a soccer game.
half a chance
4.2.2
(1)
 answer
A deck of cards contains 52 cards which are divided into 4 suits:
Mathematics Grade 9
(1)
 answer
That the sun will set in the west.
certain/definite
4.3
(1)
12
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
𝟓
𝟓𝟐
= 𝟏𝟑
4.3.2
𝟏𝟐
𝟓𝟐
A Jack (write your answer as a fraction in its simplest form)
𝟏
(1)
𝟏
 answer 𝟏𝟑
Any card smaller than 5 (write your answer as a decimal fraction)
= 𝟎, 𝟐𝟑
(2)
𝟏𝟐
 𝟓𝟐
answer 𝟎, 𝟐𝟑
4.3.3
Any picture card (write your answer as a percentage)
𝟏𝟐
= 𝟐𝟑, 𝟎𝟖%
𝟓𝟐
(2)
𝟏𝟐
 𝟓𝟐
answer 𝟎, 𝟐𝟑
Mathematics Grade 9
13
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
20
Male
Female
Total
SABC 2
5
28
33
SABC 3
7
20
27
Total
20
60
80
5
 both answers - 20 & 60
 all 3 answers – 20, 33 & 27
What is the probability that a person selected at random:
4.4.2 preferred SABC 1?
𝟐𝟎
𝟖𝟎
(1)
1
answer
or 4 or 0,25 or 25%
4.4.3 was female?
𝟔𝟎
𝟖𝟎
4.4.4
(1)
3
answer
or 4 or 0,75 or 75%
was male and preferred SABC 2?
𝟓
1
(1)
answer
or 16 or 0,0625 or 6,25%
𝟖𝟎
[16]
TOTAL: 80
Mathematics Grade 9
14
Mathematics Grade 9