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8/4/2019 17 LO4 Revision of Grade 10 and 11
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Grade 12 Mathematical Literacy
LO4 Revision of Grade 10 and 11
1. The table below shows the marks out of 250 of the Grade 12Mathematical Literacy class for their two September examination
papers added together:
189 236 125 59 89 178 122
223 221 69 45 190 183 210
223 221 69 45 190 183 210
200 45 221 211 89 153 132
189 236 125 59 89 178 122
167 245 185 187 99 103 208
98 106 211 89 97 93 10397 93 103 200 45 221 211
167 245 185 187 99 103 208
1.1 Draw up a frequency and tally tableof the above information, using intervalsof 50, starting with a class interval of 1 50.
1.2 What is the average percentage of the class?
1.3 What percentage of the class achievedless than 45%?
1.4 What advice would you give the learners who achieved lessthan 45%?
2. A group of Grade 1s were measured for their first pair of schoolshoes. The data for the boys and the girls is shown in thefrequency table below:
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Shoe Size 12 1 2 3
Number of girls 8 3 1 2
Number of boys 1 3 12 9
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Grade 12 Mathematical Literacy
2.1 Show the information in the frequency tableabove in a multiple bar graph (Multiple bargraph: two or more bars each category).
2.2 Show the information in the frequency tableabove in a compound bar graph (Compoundbar graph: only one bar per category, but eachbar is divided in the ratio of the parts that makeup the total frequency for the category).
3. The table below is a frequency table of the heights of the learnersin the Grade 12 Mathematical Literacy class.
Height Interval (cm) Frequency
150 159 4160 169 16
170 179 8
180 - 189 2
3.1 Determine the midpoints of each height interval.
3.2 Draw a frequency polygon of the aboveinformation with the number of learners
on the y-axis and the height intervals on thex-axis.
3.3 Determine the cumulative frequency of eachheight interval.
3.4 Draw an ogive to graphically represent the cumulativefrequency as determined in 3.3 above.
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Grade 12 Mathematical Literacy
4. Conserving water in South Africa is a major issue. Below is asummary of the Matese familys water consumption over a twoyear period. Use the information in the table to answer thequestions that follow.
Matese Family water consumption over two years in kilolitres
Year Month J F M A M J J A S O N D
2006 f 54 54 46 54 28 28 25 28 28 46 58 58
2007 f 59 59 51 51 26 26 26 20 34 26 26 34
4.1 What is the definition of a mean?4.2 What is the definition of the median?
4.3 What is the definition of the mode?
4.4 How do you determine the range?
4.5 Calculate the mean for 2007.
4.6 Calculate the median for 2007.
4.7 Calculate the mode for 2007.
4.8 Determine the range for 2007.
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Grade 12 Mathematical Literacy
4.9 Compare the tabulated data in the incomplete frequency tablesbelow with the raw data in the table above and complete thefrequency tables.
Water consumption in 2006 Water consumption in 2007
Kilolitres(x) Xx
Kilolitres(x) Xx
25 20 28 26
46 34
54 51
58 59
=.
( Xx) =.
=.
( Xx) =.
4.10 Assume that the mean for 2006 is 42 and complete the tablebelow:
2006s WaterConsumption(x)
Mean ( x ) Difference (xx )
( xx )
54 42
54 42
46 4254 42
28 42
28 42
25 42
28 42
28 42
46 42
58 42
58 42
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Grade 12 Mathematical Literacy
4.11 Use the formula
n
xxSumof2
2 )( =
to determine the variance in the above table.
4.12 The standard deviation = = square root of the variance.Determine the standard deviation.
5. The percentage pass rate over the past four years at Livingston
High School is given in the table below:
Year 2003 2004 2005 2006
Percentage
Pass Rate
74 74,6 75,2 75,8
5.1 Draw a histogram graph to show the differences as very largedifferences.
5.2 Draw a bar graph to show the differences as very smalldifferences.
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Grade 12 Mathematical Literacy
6. The tree diagram below shows possible descriptions of a personworking for Christina Storm Modelling Agency.
Find the probability that the agency will get:
6.1 a tall blond female model?
6.2 a tall male model?
6.3 A short model who is not blond?
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Grade 12 Mathematical Literacy
ANSWERS
1.1
1.2 21660
1
100
250
54150,
,
=
= 60,22%
1.3 51121
250
100
45,=
All those who achieved less than 112,5 out of 250 have apercentage less than 45%.
There are 24 learners who achieved less than 45%.
1.4 The learners should practice more Mathematical Literacyquestions and ask more questions in class in order to improvetheir marks.
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Class Intervals Tally Frequency1 50 1111 4
51 100 1111 1111 1111 15
101 150 1111 1111 10
151 200 1111 1111 1111 11 17
201 - 250 1111 1111 1111 11 17
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Grade 12 Mathematical Literacy
2.1
Shoe sizes of children starting school
0
2
4
6
8
10
12
14
12 1 2 3
Shoe size
Numberofgirlsandboys
Number of Girls
Number of Boys
2.2
Shoe sizes for Grade 1's
0
2
4
6
8
10
12
14
12 1 2 3
Shoe size
Numberofgirlsandboys
Number of boys
Number of Girls
3.1
Height Interval (cm) Midpoints Frequency
150 159 154,5 4
160 169 164,5 16
170 179 174,5 8180 - 189 184,5 2
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http://www.csus.edu/atcs/images/childchart.gif8/4/2019 17 LO4 Revision of Grade 10 and 11
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Grade 12 Mathematical Literacy
3.2
Frequency line graph of heights
0
2
4
6
8
10
1214
16
18
150 159 160 169 170 179 180 - 189
Height intervals
Numberoflearne
rs
Frequency
3.3
Height Interval (cm) Midpoints Frequency CumulativeFrequency
150 159 154,5 4 4
160 169 164,5 16 20
170 179 174,5 8 28
180 - 189 184,5 2 30
3.4
Ogive of heights
0
5
10
15
20
25
30
35
150 159 160 169 170 179 180 - 189
Height intervals
Numberoflearners
Ogive
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8/4/2019 17 LO4 Revision of Grade 10 and 11
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Grade 12 Mathematical Literacy
4.1 Mean: The sum of all the data values divided by the number ofdata values (average).
4.2 Median: The value in the middle when all the data values havebeen arranged from smallest to biggest. (If there are two in themiddle, add them together and divide by 2.)
4.3 Mode: The data value that appears most frequently (can bemore than one).
4.4 Range: The difference between the largest and the smallestdata values in a set (largest minus/subtract smallest).
4.5 Mean: 53612
438,=
4.6 Median:20; 26; 26; 26; 26; 26; 34; 34; 51; 51; 59; 59
Therefore: 302
3426=
+ )(
4.7 26 = appears 5 times.
4.8 Range: 59 20 = 39
4.9Water consumption in 2006 Water consumption in 2007
Kilolitres(x) Xx
Kilolitres(x) Xx
25 1 25 20 1 20
28 4 112 26 5 130
46 2 92 34 2 6854 3 162 51 2 102
58 2 116 59 2 118
= 12( Xx) =507 = 12
( Xx) =438
4.10
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Grade 12 Mathematical Literacy
2006s WaterConsumption(x)
Mean ( x ) Difference (xx )
( xx )
54 42 12 144
54 42 12 14446 42 4 16
54 42 12 144
28 42 -14 196
28 42 -14 196
25 42 -17 289
28 42 -14 196
28 42 -14 196
46 42 12 144
58 42 16 256
58 42 16 256
4.1112
21772=
421812
,=
4.12 42181 ,=
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Grade 12 Mathematical Literacy
5.1
5.2
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Grade 12 Mathematical Literacy
6.18
1
6.2 8
1
6.34
1
8
2=
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