17 lo4 revision of grade 10 and 11

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:

Maths & Science Marketing

Shoe Size 12 1 2 3

Number of girls 8 3 1 2

Number of boys 1 3 12 9
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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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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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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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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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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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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.


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
http://images.google.co.za/imgres?imgurl=http://www.freespirit.com/files/IMAGE/COVER/LARGE/614.jpg&imgrefurl=http://www.freespirit.com/catalog/item_detail.cfm%3FITEM_ID%3D54&h=600&w=440&sz=80&hl=en&start=4&tbnid=nBYiOr0ccyBxEM:&tbnh=135&tbnw=99&prev=/images%3Fq%3DTESTS%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DGhttp://images.google.co.za/imgres?imgurl=http://sbfmedia.relationalhost.com/prodimg/ESSAY_TEST_COVER2_400PX.jpg&imgrefurl=http://sbfmedia.relationalhost.com/index.php%3Fcateg%3D8%26start%3D0%26num%3D10&h=517&w=400&sz=162&hl=en&start=53&tbnid=4U9LbJC_3ffmaM:&tbnh=131&tbnw=101&prev=/images%3Fq%3DTESTS%26start%3D36%26gbv%3D2%26ndsp%3D18%26svnum%3D10%26hl%3Den%26sa%3DN


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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

http://www.csus.edu/atcs/images/childchart.gif


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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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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

http://images.google.co.za/imgres?imgurl=http://www.mathleague.com/help/data/median.gif&imgrefurl=http://www.mathleague.com/help/data/data.htm&h=380&w=419&sz=7&hl=en&start=1&tbnid=5JoA9YXytFjWxM:&tbnh=113&tbnw=125&prev=/images%3Fq%3DMEDIAN%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG


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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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5.1

5.2



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6.18

1

6.2 8

1

6.34

1

8

2=

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17 lo4 revision of grade 10 and 11

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