math slit

Maths Literacy

Paper 1 and 2

Spring School 2011

3rd – 7th October

Learner’s Guide

Maths Literacy Paper 1 & 2 Exam Revision Learner’s Guide

Spring School October 2011

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Contents

Introduction ............................................................................................. 3

Programme Outline ................................................................................. 4

Broadcast Schedules .............................................................................. 5

Topic Tips for Financial Maths ................................................................ 6

Topic 1: Financial Maths ......................................................................... 6

Topic Tips for Space, Shape and Measurement ................................... 16

Topic 2: Space, Shape and Measurement ............................................ 18

Topic Tips for Data Representation ...................................................... 24

Topic 3: Data Representation ............................................................... 26

Solutions to Topic 1: Financial Maths ................................................... 31

Solutions to Topic 2: Space, Shape and Measurement ......................... 37

Solutions to Topic 3: Data Representation ............................................ 39



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Introduction

Have you heard about Mindset? Mindset Network, a South African non-profit organisation, was founded in 2002. We develop and distribute quality and contextually relevant educational resources for use in the schooling, health and vocational sectors. We distribute our materials through various technology platforms like TV broadcasts, the Internet (www.mindset.co.za/learn) and on DVDs. The materials are made available in video, print and in computer-based multimedia formats. At Mindset we are committed to innovation. In the last two years, we successfully ran a series of broadcast events leading up to and in support of the NSC examinations Now we are proud to announce our 2011 edition of Matric Exam Revision, which began with our Winter School in July. We’ve expanded the broadcast to support you in seven subjects - Mathematics, Physical Sciences, Life Sciences, Mathematical Literacy, English 1st Additional Language, Accounting and Geography. During our Spring School, you will get exam overviews, study tips on each of the topics we cover, detailed solutions to selected questions from previous examination papers, short question and answer sessions so you can check you are on track and live phone in programmes so you can work through more exam questions with an experienced teacher. Getting the most from Spring School Before you watch the broadcast of a topic, read through the questions for the topic and try to answer them without looking up the solutions. If you get stuck and can’t complete the answer don’t panic. Make a note of any questions you have. When watching the Topic session, compare the approach you took to what the teacher does. Don’t just copy the answers down but take note of the method used. Make sure you keep this booklet for after Spring School. You can re-do the exam questions you did not get totally correct and mark your own work by looking up the solutions at the back of the booklet. Remember that exam preparation also requires motivation and discipline, so try to stay positive, even when the work appears to be difficult. Every little bit of studying, revision and exam practice will pay off. You may benefit from working with a friend or a small study group, as long as everyone is as committed as you are. Mindset believes that the 2011 Spring School programme will help you achieve the results you want. If you find Spring School a useful way to revise and prepare for your exams, remember that we will be running Exam School from 15th October to 22nd November as well where we will be repeating material from Spring School with additional live shows. See the full schedule below.

http://www.mindset.co.za/learn



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Programme Outline

The Mindset Winter School is designed to focus on two subjects each day. For each subject you will find the following sessions:

Examination Overview This is a 15 minute session that gives details of what you can expect in each examination paper. Practical guidelines are also given on how to prepare for the day of the exam.

Topics Tips In this session you will be given a 15 minutes summary of the key ideas you need to know, common errors and study hints to help you prepare for your exams.

Topic Session An expert teacher will work through specially selected questions from previous exam papers.

Live Phone-in This is your chance to ask your own questions. So submit your question to the Help Desk and we might call you back to help you live on TV. All questions you submit will be answered within 48 hours as normal. The Help Desk is available through the following channels.

Web: www.learnxtra.co.za

MXit: learnxtrahelpdesk

Facebook: www.facebook.com/learnxtra

Email: [email protected]

Phone: 086 105 8262

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mailto:[email protected]



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Broadcast Schedules

Spring School

Monday 3

rd

October Tuesday 4

th

October Wednesday 5

th

October Thursday 6

th

October Friday 7

th

October

09h30 Maths Paper 1: Calculus

English FAL: Paper 2

Physical Sciences Paper 1: Waves, Sound and Light

Maths Paper 2: Trigonometry – Graphs and Solving 3D Problems

Physical Sciences Paper 2: Electrochemistry

13h00 Lunch

13h30 Maths Literacy: Shape and Space

Accounting: Manufacturing Accounts

Life Sciences Paper 1: Evolution

Geography: Climatology

Life Sciences Paper 2: Environmental Studies

17h00 Maths Paper 1: Linear Programming


Physical Sciences Paper 1: Mechanics

Maths Paper 2: Trigonometry – Equations and Identities

Physical Sciences Paper 2: Organic Chemistry

19h00 Maths Literacy: Data Handling

Accounting: Cash Flow and Interpreting Statements

Life Sciences Paper 1: DNA & RNA

Geography: Geomorphology

Life Sciences Paper 2: Life Processes

21h00 Maths Paper 1: Functions


Physical Sciences Paper 1: Electricity and Magnetism

Maths Paper 2: Co-ordinate Geometry and Transformations

Physical Sciences Paper 2: Rates and Chemical Equilibrium

23h00 Maths Literacy: Financial Maths

Accounting: Financial Statements

Life Sciences Paper 1: Genetics

Geography: Mapwork Life Sciences Paper 2: Reproduction

01h00 Broadcast Ends

Exam School

Saturday 15th October: Prelim Review – Mathematics, Physical Sciences, Life Sciences, Maths Literacy

Wednesday 19th October: Maths Literacy Paper 2

Thursday 20th October: Mathematics Paper 2

Friday 21st October: English FAL

Saturday 22nd October: Prelim Review - Mathematics, Physical Sciences, Life Sciences, Maths Literacy

Sunday 23rd October: Accounting

Monday 24th October: Accounting

Tuesday 25th October: Mathematics Paper 1

Wednesday 26th October: Maths Literacy Paper 1

Thursday 27th October: Mathematics Paper 1

Saturday 29th October: Mathematics Paper 2

Tuesday 8th November: Physical Sciences Paper 1

Wednesday 9th November: English FAL

Thursday 10th November: Physical Sciences Paper 1

Saturday 12th November: Physical Sciences Paper 2

Sunday 13th November: Physical Sciences Paper 2

Monday 14th November: English FAL

Wednesday 16th November: Life Sciences Paper 1

Thursday 17th November: Life Sciences Paper 1

Saturday 19th November: Life Sciences Paper 2

Sunday 19th November: Life Sciences Paper 2

Monday 21st November: Geography

Tuesday 22nd November: Geography



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Topic Tips for Financial Maths

Overview

Personal and business finance Key Concepts

Income Expenses Profit / Loss / Breakeven Tax Inflation Interest Currency fluctuations

Key Skills

Using your calculator Using tables to complete calculations Percentage calculations for inflation, tax and interest Reading values off graphs Drawing graphs Converting between currencies

Topic 1: Financial Maths

Question 1

1.1. Calculate the price of one 500g brick of margarine if a box containing thirty

500g bricks of margarine costs R399,00. (2)

1.2 Naledi intends selling oranges at her school market day. She buys one dozen

oranges for R9,00. She decides to sell the oranges in packets of six at R6,00

per packet.

Calculate:

1.2.1 The cost price of ONE orange. (2)

1.2.2 The profit she will make per dozen oranges sold. (2)

1.2.3 How much it would cost Naledi to buy 108 oranges. (2) 1.3 Convert $1 215,00 to rand. Use the exchange rate $1 = R10,52 (2) 1.4 Andrew earns a taxable salary of R 8 525,00 per month after deductions for

pension and medical aid. His tax rate is 28%. How much money will be deposited into his account? (2)



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Question 2

Adapted from2008 DoE Preparatory Examination Paper 1

The pie charts below show the yearly expenditure of the Pythons Soccer Club and the Mamba Soccer Club for 2010. 2.1. What was the total expenditure of Pythons Soccer Club for 2010? (1)

2.2. What percentage was spent by the Mamba Club on transport? (1)

2.3. What percentage was spent by the Mamba Club on equipment? (2)

2.4. Calculate the actual amount spent by the Pythons Club on maintenance. (2)

2.5. The Pythons Club receives its income from membership fees. The club had 100 members in 2010, each paying R450 membership fee for the year. All the members paid in full for 2010. What was the club’s income from membership fees in 2010? (2)

2.6. The Pythons Club increased its membership fees by 6% for 2011. Calculate the new membership fee for ONE member. (3)

2.7. The total income of the Mamba Club for 2010 was R42 000. Calculate the club’s surplus (profit) for 2010.

Profit = Income – Expenditure (2) [13]



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Question 3

Adapted from November 2008 Paper 1

The Lighthouse Foundation provides food parcels, uniforms and clothing to needy children in Limpopo. Each year the Lighthouse Foundation presents a financial report to all its stakeholders (see Table below).

TABLE: Lighthouse Foundation Financial Report for 1 Mar 2010 to 28 Feb 2011

INCOME EXPENSES

Item Amount (in rand)

Item Amount (in rand)

Private donations Administration costs Local

78 240 Salaries for part-time employees

128 833

Overseas 57 120 Telephone 15 571

Subsidy Stationery/Postage 2 379 Local municipality 308 160 Bank charges 2 899

Services rendered to children

Food parcels 178 200

Vegetable gardens (seedlings, fertiliser, etc.) 5 812

School uniforms 10 047

Clothing 30 456

Transport costs

22 822

TOTAL INCOME 443 520 TOTAL EXPENSES 397 019

Use the information in the table above to answer the following questions: 3.1. Write down the period of time covered by the financial report. (1)

3.2. Name the Lighthouse Foundation's main source of income. (1)

3.3. Express the subsidy from the local municipality as a percentage of the total income. (Round off the answer to ONE decimal place.) (4)

3.4. Calculate the average cost of ONE school uniform if 48 children received school uniforms. (3)

3.5. The overseas donations are from Japanese businessmen. Determine the

amount in yen that the Foundation received from overseas donations.

1 Japanese yen (¥) = 0,08 South African rand (R). (3)

[12]



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Question 4

Mrs Phumzile is starting a transport business. She owns one taxi, and she employs Pieter as a taxi driver. The table below shows a list of the income and expenses of Mrs Phumzile’s business for the month of February 2007.

Income Expenses

Maintenance costs:

a) Fuel R1065.40

b) Service and repairs R546.09

c) Cleaning R60.00

Insurance for taxi R305.45

Taxi licence fee R400.00

Taxi driver’s salary R3 500.00

Taxi association fee R200.00

Fares collected R7 842.00

TOTAL R7 842.00 R6 076.94

4.1. Determine the following:

4.1.1. The total cost of maintenance. (2)

4.1.2. How many litres of fuel were used if fuel costs R7,00 a litre. (2)

4.1.3. What percentage of the total expenses is allocated to salary. (3)

4.2. On Monday 18 February, Pieter worked from 06:00 to 15:30. How many hours did he work on that day? (2)

4.3. Pieter’s basic salary is R17,50 per hour. If Pieter wants to earn R200,00 per day, how many hours does he have to work? Give your answer to the nearest hour. (3)

4.4. Mrs Phumzile asks Pieter to go on a trip of 120 km. Pieter drives the taxi at an average speed of 90 km/h. How long will the trip take? Write your answer correct to one decimal place. Given the formulae:

Distance = Speed x Time

Time

Distance Speed

Speed

Distance Time (3)

[15]



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Question 5 Adapted from November 2009 Paper 1

5.1. What percentage of the grants allocated during 2007 were for old-age

pensioners? (1)

5.2. Calculate the difference between the number of beneficiaries receiving child support grants during 2005 and 2007. (3)

5.3. Calculate the following missing values from the table:

5.3.1. A (2)

5.3.2. B (2)



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5.4. The percentage of the total number of beneficiaries for each type of grant during 2005 is represented as a bar graph on the next page. Complete the graph by adding in bars to represent the percentage of allocations for the different types of grants during 2007.

(4) [12]



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Question 6

Adapted from DoE/Feb-Mar Exam 2009 Paper 2)

If one loaf of brown bread requires 450g of flour, determine the maximum number of loaves of brown bread that can be baked from a 12,5kg bag of flour. (4)

6.1. The table below shows the weekly cost of making the bread.

TABLE: Weekly cost of making brown bread

Number of loaves 0 40 80 120 160 B 300

Total income (in rand)

400 540 680 A 960 1 240 1 450

The formula used to calculate the total cost per week is:

Total cost per week = Fixed weekly cost + (number of loaves of bread × cost per loaf) Use the given formula to determine the values of A and B in the table. (4)

6.2. The table below shows the weekly income from selling the bread.

TABLE: Weekly income received from selling bread.

Number of loaves 0 40 120 150 D 250 300

Total income (in rand) 0 240 C 900 960 1 500 1 800

Determine the values of C and D in the table. (4)

6.3. Use the values from the Tables in question 2.1 and 2.2 to draw TWO straight-line graphs on the same grid, showing the total COST per week of making bread and the INCOME per week from selling bread. Clearly label the graphs ‘COSTS’ and ‘INCOME’. (8) [20]

The Hospitality Studies department of Ses’fikile High School bakes brown bread in order to raise funds for the shortfall incurred in their day-to-day expenses. The school charges the Hospitality Studies department a fixed weekly cost of R400,00 for water and electricity. The cost of producing one loaf of brown bread, including labour and ingredients, is R3,50. The brow bread is sold at R6,00 a loaf.



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Question 7:

Adapted from DoE Preparatory Exam 2008 Paper 2

7.1. Express the cost of the most expensive stage of the work as a percentage of the total labour cost. (3)

7.2. The length of the top floor is 11 m; the width, including the balcony, is 7,60 m and the thickness is 17 cm. Calculate the volume of the concrete used for the top floor.

Volume of a rectangular prism = length × width × height (4)

7.3. A cubic metre of concrete costs R850,00. How much did Mukala pay for the concrete for the top floor? (3)

[10]

Mukala is busy building his new house. The length of the house is 11 m and the

width is 6,10 m. The building is a double storey. The details below are found in his

notebook

TABLE 3

STAGE OF WORK LABOUR COST

1. Foundations R5 500,00

2. Building of walls below the top floor R7 000,00

3. Plastering of walls inside and outside below the

top floor

R6 000,00

4. Preparing for throwing the concrete on the top

floor

R4 500,00

5. Throwing the concrete on the top floor R18 000,00

6. Building of support columns R4 500,00

7. Roofing R14 000,00

8. Electrical installation R3 600,00

9. Building of walls on the top floor up to the roof R9 000,00

10. Plastering of walls inside and outside on the top

floor

R11 000,00



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Question 8

Adapted from November Exam 2008 Paper 2

Mrs Maharaj makes duvet sets, which she sells at the local street market at R150,00 per set

(including VAT).

If she makes 50 or less duvet sets per month, her production costs are R100,00 per set.

If she makes more than 50 duvet sets per month, her production costs are reduced by 15% per set.

Mrs Maharaj has to pay R8 400 annually for the rental of her stall and she has weekly

transport costs of R75.

8.1. Mrs Maharaj prepares a monthly budget.

8.1.1. Show that her fixed cost for the month of February is R1 000,00. (2)

8.1.2. How does her fixed cost for February compare to her average

monthly fixed costs? Show ALL calculations. (5)

8.2. Calculate the production cost per duvet set if 90 sets are made per month. (2)

8.3. The table below shows Mrs Maharaj's production cost for different quantities

of duvet sets made in February.

TABLE 1: Cost of duvet sets made in February

Number of duvet sets 0 30 50 51 56 60 70 D

Total cost per month (in rand)

1 000 4 000 6 000 5 335 5 760 6 100 C 7 800

The formula used to calculate the total cost is:

Total cost = fixed monthly cost + (number of duvet sets cost per set)

Use the formula and the given information to determine the missing values C

and D. (5)

8.4. Mrs Maharaj draws two graphs to represent her income and expenses for

different quantities of duvet sets. The graph showing her INCOME for

different quantities of duvet sets has already been drawn on the next page.



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Use the values from TABLE 1 to draw a second graph on this grid showing

the total EXPENSES for February for making different quantities of duvet

sets. Label the graph as 'EXPENSES'. (7)

8.5. Use the two graphs to answer the following questions:

8.5.1. How many duvet sets must Mrs Maharaj sell to break even? (2)

8.5.2. What profit will she make if all 80 duvet sets are sold? (3)

8.5.3. Suppose Mrs Maharaj makes 80 duvet sets, but only sells 70 of

them. Calculate her profit for February. (3)

[29]

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

0 10 20 30 40 50 60 70 80

Am

ou

nt

in r

an

d

Number of duvet sets

INCOME AND EXPENSES



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Topic Tips for Space, Shape and Measurement

Overview Perimeter Area Volume

Perimeter Key Concepts

Length of the outside of a shape The perimeter of a circle is also known as the circumference Always change all measurements to the same units before starting any

calculation Unit can be mm, cm, m or km

Common Errors

Careless errors Not changing units to the same unit before starting any calculation Forgetting units in the answer

Study Hints

Practice, practice and practice (Use old papers)

Area Key Concepts

Always use the formulae given in the question Two dimensional shape, normally with a length and breadth or a length and

height Always change all measurements to the same units before starting any

calculation

Units 2 Common Errors

Not using the given formula Careless errors Not changing units to the same unit before starting any calculation Forgetting units in the answer

Not using units2

Study Hints




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Volume Key Concepts

Always use the formulae given in the question Three dimensional shape, normally with a length, breadth and a height. Always change all measurements to the same units before starting any

calculation

Units 3

Common Errors

Not using the given formula Careless errors Not changing units to the same unit before starting any calculation Forgetting units in the answer

Not using units3

Study Hints


In Summary:



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Topic 2: Space, Shape and Measurement

Question 1 Adapted from November, 2010, Paper 1, Question 1.3 During an experiment, an amount of liquid was poured into a calibrated rectangular container, as shown in the diagram below. A calibrated container has accurate measurements marked on it. It is used to measure volume. The dimensions of the container are: Length = 50cm, breadth = 40cm and height = 45cm

1.1 Calculate the volume, in 3cm , of the container.

Use the following formula: heightbreadth length Volume (2)

1.2 3 000 3cm of the liquid was poured into the calibrated container. Calculate the height of the liquid in the container by using the following ` formula:

breadth length

liquid of volume liquid ofHeight

(2)



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Question 2 Adapted from November, 2010, Paper 1 Question 2.1 Thandiwe wants to make a new pencil holder. She has a choice of an open cylindrical holder or an open rectangular holder. She wants to cover the outside of the holder to match the table cloth on her desk. A cylindrical holder with : radius = 5cm and height = 15cm A rectangular holder with: length = 10cm, breadth = 8cm and height = 15cm Determine the surface area of : 2.1 the cylindrical holder

3,14 using and height, radius 2 cylinder a of area Surface

2.2 the rectangular holder

height breadth length 2 prismr rectangula a of area Surface



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Question 3 Adapted from November, 2010, Paper 1, Question 4.2 Mrs. Smith and her touring parting decide to visit an indoor swimming pool. 3.1 The kiddies pool at the indoor pool has a diameter of 5m. There is a protective fence 3m around the outside of the perimeter of the pool as shown in the diagram below: . 3.1.1 Determine the perimeter of the fence. Use the formula: 3,14 using and diameter, Perimeter (3)

3.1.2 The area between the pool and the fence needs to be grassed. Grass

is bought in trays which can cover 4 2m and each tray costs R89,95. Determine how much it will cost to grass the required area.ℓ

Use the formula: 3,14 using , r circle a of Area 2 (11)

3.2 The kiddies pool is filled with 6 000 litres of water. Mrs. Smith wanted to know what this volume of water would be in gallons. Convert the volume of water in the pool into gallons if 1 gallon = 4,546 l (2)

Pool Fence

5m

3m



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Question 4 Adapted from November, 2010, Paper 1, Question 5.1 Mr J Khoso owns a plot, as shown in the diagram below (not drawn to scale). His house (D) is on the eastern side of the plot. Also on the plot is a cattle kraal (A), a circular water tank (B), and a vegetable garden (C). 4.1 Give the general direction for the water tank from the house? (1) 4.2 Determine the perimeter of Mr. Khoso's plot. (3) 4.3 Calculate the volume of water in the circular water tank, if the height of the water in the tank is 2m.

Use the formula: 3,14 using and height, radius Volume2

(3)

4.4 Determine the area of the cattle kraal.

Use the formula: height base 2

1 triangleof Area (3)

4.5 Calculate the total area of Mr Khoso's plot

Use the formula: height sides parallel of sum 2

1 trapeziuma of Area (4)



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Question 5 Adapted from November, 2010, Paper 2, Question 4 5.1 Triggers Enterprises was awarded the tender for making rectangular cardboard boxes to package bottles of cough syrup. Each bottle is packed in a cardboard box with a square base, as shown below: * The diameter of the base of the bottle is 58mm and the height of the box is 143mm. * The length of the side of the box must be approximately 105% of the diameter of the base of the bottle. * The height of the box is approximately 102% of the height of the bottle.

The following formulae may be used:

3,14 using and ,radius circle a of Area2

2length side square a of Area

breadth length rectangle of Area

The following conversions may be useful:

22 100mm cm 1 22 cm 000 10 m 1

5.1.1 Calculate the height of the bottle to the nearest mm. (3) 5.1.2 In order to minimise the cost of cardboard required for the box, the following guideline is used:

The difference between the areas of the base of the cardboard box and the base of the bottle should not be more than 11cm2

Determine whether the dimensions of this cardboard box satisfy the above guideline. Show ALL appropriate working. (11)



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5.2 To ensure that the box is strong enough, the cardboard used for the box has a

mass of 240 grams per 2m . 2/ mg

The layout of the opened cardboard box is shown below. * Section C is a semicircle

* The area of each section D = 1 832 mm 2

* The area of section E = 2 855mm2

5.2.1 Calculate the total mass of the cardboard needed for one box, to the nearest gram. (11) 5.2.2 The total cost of the cough syrup includes the cost of the cardboard box. Use the following frmula to calculate the cost of a boxed bottle of cough syrup: kgper R20,00 box) cardboard of (mass R16,00 cost Total (3)



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Topic Tips for Data Representation

Overview Bar Charts Histograms Pie Charts

Bar Charts Key Concepts

Data is represented in a vertical or horizontal bar. Bars are separated by spaces indicating discrete data. Useful for representing data where different categories of data are being

compared in size. The size of the individual bars is in proportion to the value of the data and needs

a suitable scale. Common Errors

No spaces left between bars. Incorrect scales.

Study Hints

Pay particular attention to compound bar charts.

Histograms Key Concepts

Used to represent a continuous range of data. No spaces between bars. Used when one category of data has a range of possible values e.g. Birth

weights. Common Errors

Not realising that a bar represents a range of values (use half way value in calculations)

Not keeping data continuous. (i.e. leaving spaces on chart) Study Hints

Learn how to calculate the mean from histogram data

Pie Charts Key Concepts

Calculate percentages and convert data to percentages. Used to represent portions of a whole set of data.

Common Errors

Trying to make data that is not part of a whole fit the pie chart diagram



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Mis-representation of Data Key Concepts

Use of Scales Starting points of data

Common Errors

Assuming data is equally spaced Assuming data starts at zero



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Topic 3: Data Representation

Question 1: Bar Charts Adapted from Feb/March, 2010, P1, Question 2 Mr Le Roux publishes children's books. Initially he published the children's books only in English. He now intends to translate the books into other official South African languages. The bar graph below shows the percentage distribution of the South African population according to official language groups. The population of South Africa was approximately 47 900 000 in 2009.

1.1 Which official language is spoken by the largest percentage of South Africa's population?(1) 1.2 Use the graph to list the official languages that are used by less than 5% of the population.(2) 1.3 What percentage of the population uses Siswati as an official language? (2) 1.4 Calculate the number of South Africans that uses English as an official language. (3)



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Question 2: Histograms The histogram represents the weights of 60 babies and 6 babies weigh from 4 to 4.5kg.

2.1 Which category of birth weight had the most recorded births? (2) 2.2 Calculate the number of babies weighing less than 3kg. (4) 2.3 Create a frequency table for the information in this histogram. (8) 2.4 Create a frequency polygon from the information in the table in 2.3 (6) Question 3: Pie Charts Adapted from November, 2010, P2, Question 3 Mr Riet wanted to show his colleagues that the South African government was spending more on education than on most other departments. The two graphs below show the budgeted government expenditure for the financial years 2009/2010 and 2010/2011.



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The total expenditure budgeted for 2009/2010 was R834,3 billion and for 2010/2011 wasR900,9 billion.

3.1 Show that the difference between the amounts budgeted for education for the financial years 2009/2010 and 2010/2011 is more thanR20 000 000 000. (8) 3.2 Give TWO possible reasons why you think the South African government should increase its budgeted expenditure for education. (4)



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Question 4: Mis-Representation of Data Examine the Bar Graph below and answer the questions that follow.

4.1 What is the difference between the number of national passengers and international passengers carried in 2003? (3) 4.2 What is the ratio of national passengers to international passengers carried in 2003? (3) 4.3 Does the airline carry more national or more international passengers? (2) 4.4 Explain what message this chart wants people to believe about the statistics and how it has achieved this. (4)



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Question 5: Compound Bar Graphs Examine the Bar Graph below and answer the questions that follow.

5.1 What percentage(%) of people took out medical insurance with a financial adviser? (2) 5.2 What percentage of people had life cover without having used a financial planner? (2) 5.3 What is the difference in % between the people who use a financial adviser

and those that do not when providing for retirement? (3) 5.4 Explain what message this chart wants people to believe about the statistics and whether it succeeded or not. (4) 5.5 Explain why a pie chart was not used to represent the information in this

chart. (2)



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Solutions to Topic 1: Financial Maths

1.1. 30

R399

= R13,30 OR Total number of grams in a box = 500g x 30 = 15 000g

Cost of 500g = 00015

R399 × 500

= R13,30

1.2

1.2.1 Cost of 1 orange = 12

9,00 R

= R0,75 (2)

1.2.2 dozen oranges sell for R12,00 Profit = E12,00 – R9,00 = R3,00 (2)

1.2.3. Cost = 108 × R0,75 = R81,00

(2)

1.3. $1 = R10,52 $1 215,00 = R10,52 x 1215,00

= R12 781,80 (2) 1.4 Tax: R 8 525,00 x 0,28 =R 2 387,00 Income: R 8 525,00 – R 2 387,00 =R 6 138,00 (2)

Question 2

2.1. Pythons: R54 000 (1) 2.2. 45% (1) 2.3. 100% - (45% + 11% + 14%)

= 30% (2) 2.4. 33% of R54 000

= 0,33 × 54000 = R17 820 (2)

2.5. 100 × R450 = R45 000 (2)



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2.6. R450 + (6% of R450)

= R450 + (100

6 × R450)

= R450 + R27 = R477 (3)

2.7. R42 000 – R35 000 = R7 000 (2)

[13] Question 3

3.1. 1 March 2010 – 28 February 2011 or 12 months

(1)

3.2. Local municipality or Subsidy (1)

3.3. 520R443

160R308 × 100%

= 69, 48051948 % 69,5% (4)

3.4. Average cost of one school uniform = R10 047 ÷ 48

= R209,3125

= R209,31 (3)

3.5. R0,08 : 1 yen = R57 120 : x

1

08,0 =

x

12057

0,08 x = 57 120

08,0

08,0 x =

08,0

12057

x = 714 000 yen (3) [12]

Question 4 4.1.1. Maintenance costs:

= R1065,40 + R546,09 + R60 = R1 671,49 (2)

4.1.2. No. of litres of fuel = R1065,40 ÷ 7 = 152,2l (2)

4.1.3. 076,94 R6

500 R3 × 100%

= 57,59% (3)

4.2. Hours worked = 15:30 – 6:00 = 9h30 min (2)

4.3. No. of hours = R200 ÷ R17,50 = 11,4287 ≈ 12 hrs (3)



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4.4. Speed

Distance Time

km/h 90

km 120 Time

Time = 1h 20 min (3) [15]

Question 5 5.1. 18,2% (1)

5.2. Difference = 7 908 138 – 5 662 911 = 2 245 227 (3)

5.3. Missing values

5.3.1. A = 100% - 22,3% - 60,2% - 3,6% A = 13,9% (2)

5.3.2. B = 2 194 066 + 7 908 138 + 1 420 335 + 517 580

B = 12 036 739 (2) 5.4. The graph Old-age 2007 (accept 18%) Child support in 2007 (accept 66%) Disability in 2007 (accept 12%) Other in 2007 (accept 4%) (4)

[12]



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Question 6

6.1. Number of loaves = g 450

kg 12,5

= g 450

g 500 12

= 27,78 27 loaves (4)

6.2. Total cost = fixed cost + (number of loaves × cost per loaf) A = 400 + (120 x R3,50) A = R820 AND 1 240 = 400 + (B × R3,50) 840 = (B × R3,50)

3,50

840 =

3,50

B 3,50

240 loaves = B (4)

6.3. Income = number of loaves × price of loaf C = 120 x R6,00 C = R720,00 AND 960 = D x R6,00 960 = 6D

6

960 =

6

6D

D = 160 loaves (4)

Question 7

7.1. R5 5000 + R7 000 + R6 000 + R4 500 + 18 000 + R4 500 + R14 000 + R3 6000 + R9 000 + R11 000 = R83 100,00

Percentage = 100 R83

000 R18 × 100%

= 21,6606…% = 21,7% (3)

7.2. Length = 11 m Wide = 7,60m Thickness = 17cm = 0,17m Volume of the slab = l × w × h = 11 x 7,60 x 0,17 = 14,212m3 (4)

7.3. A cubic meter cost R850 including the delivery. Volume of the slab = 14,212 m3 Mukala will pay: 14,212 m3 × R850 = R12 089,20 (3)



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Question 8

8.1.1. Fixed monthly cost = 12

400 R8 + 4 × R 75

= R700 + R300

= R 1 000 (2)

8.1.2. Annual transport costs = R75 × 52

= R3 900,00

Total annual costs = R8 400,00 + R3 900,00

= R12 300

Average monthly costs = 12

30012R

= R1 025,00

The fixed costs for February is R25,00 less than the average monthly

fixed costs.. (5)

8.2. 15% reduction means the cost = 85% of R100

New production cost = 0,85 × R100 = R85,00

(2)

8.3. 80 is more than 50, so the cost is R85 per duvet set.

Total cost = fixed cost + (no. of duvet sets cost per set)

So C = R1 000 + 70 × R85 = R1 000 + R5 950 = R 6 950

R 1 000 + D R 85 = R 7 800

D R 85 = R 6 800

D = 85R

8006R

D = 80 (5)



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8.4.

Plotting given points from table Plotting calculated points (C; D)

Joining points up to (50; 6000) with straight lines

Plotting (51 ; 5335) Joining points up to (80 ; 7800) (7)

Using the graphs:

8.4.1. 20 Duvet sets (2)

8.4.2. Profit = Income – expenses

= R12 000 – R7 800

= R4 200 (3)

8.4.3. Profit = Income from 70 sets – Expenses from 80 sets

= R10 500 – R7 800

= R2 700 (3)

[8]

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

0 10 20 30 40 50 60 70 80

Am

ou

nt

in r

an

d

Number of duvet sets

INCOME AND EXPENSES



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Solutions to Topic 2: Space, Shape and Measurement

Question 1 1.1 Volume = length × breadth × height = 50cm × 40cm × 45 cm

= 90 000 cm 3 1.2

1,5cm

000cm 2

000cm 3

40cm 50cm

000cm 3

breadth length

liquid of volume liquid ofHeight

2

3

3

Question 2 2.1

2cm 471

15cm 5cm 3,14 2

height radius 2 cylinder a of area Surface

2.2

2cm 540

15cm 18cm 2

15cm 8cm) 10cm ( 2

height breadth length 2 prismr rectangula a of area Surface

Question 3 3.1.1

34,54m

11m 3,14

3m) 3m (5m 3,14

diameter Perimeter

3.1.2

2

22

22

22

m 75,36

19,625m - 94,985m

6,25) 3,14 ( - )25,30 (3,14

)2,5 (3,14 - )5,5 3,14 (

)r ( - )r (

Area Pool - Area Total Area Grassed



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trays19

trays18,84

m 4 m 75,36 required traysofNumber 22

05 709, R1

R89,95 trays19 grass ofCost

3.2 gallons = 6 000 l ÷ 4,546 l = 1 319,84 gallons Question 4 4.1 South Westerly direction. 4.2 Perimeter = 250m + 200m + 150m + 200m + 224m = 1024m 4.3

3

2

2

2

m 628

2m m 100 3,14

2m m) (10 3,14

height radius Volume

4.4

2m 000 20

200m 200m 2

1

height base 2

1 triangleof Area

4.5

2m 000 60

200m 600m 2

1

200m 150m)) (200m (250m 2

1

height sides parallel of sum 2

1 trapeziuma of Area

Question 5 5.1.1

mm 140

m140,19...m

102

100 143mm bottle ofHeight



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5.1.2

2

22

22

22

22

22

10,6807cm

cm 100 mm 07 1068,

- mm 2640,74- 3708,81mm

- )841mm (3,14- 3708,81mm

)(29mm) (3,14 - (60,9mm)

)r ( - ) (

bottle of base of area -box of base of area areasin Difference

l

Therefore the dimensions of the cardboard box satisfy the guideline. 5.2.1

2

222

22222

22

2

m0,05534684

000m 10100cm 55346,84mm

2855mm 7328mm 2911,42mm 7417,62mm 834,8mm 34

1) 855mm (2 4) 832mm (1

2) 2

1 30,45mm)( (3,14 2) 60,9mm (60,9mm 4) 60,9mm(143mm

1) (E 4) (D 2) (C 2) (B 4)(A Area

13g

240g m0,05534684 box 1 of Mass 2

5.2.2

R16,26

R0,26 R16,00

R20,00 0,013kg R16,00

R20,00 1000g) (13g R16,00

kgper R20,00 box) cardboard of (mass R16,00 cost Total

Solutions to Topic 3: Data Representation

Question 1 1.1 Isizulu 1.2 IsiNdebele, Tshivenda, Xitsonga, Siswati 1.3 100%-(14,3+8,6+1,5+17,6+23,8+9,4+7,9+8,2+1,7+4,4)= 2,6%

1.4 8,6% of 47 900 000 = 47 900 000 X

=4 119 400 people.



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Question 2 2.1 3-3.5kg 2.2 21 babies 2.3

Category/kg Frequency Cum. Freq.

1-1.5 2.5 2.5

1.5-2 2.5 5

2-2.5 6 11

2.5-3 11 22

3-3.5 13 35

3.5-4 10 45

4-4.5 6 51

4.5-5 5 56

5-5.5 2 58

5.5-6 2 60

2.4

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7

Series1



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Question 3 3.1 17% of 834,3 billion in 2009 and 18% of 900,9 billion in 2010 Difference is 20.331 billion 3.2 An increase in school going population means there are more children

needing education and teachers deserve better salaries. Question 4 4.1 6.2 million- 4.8 million = 1.4 million passengers 4.2 1,4:4,8 or 7:24 4.3 More international passengers. 4.4 There has been a large increase in passengers especially international passengers. By starting the scale at 3.8 million rather than zero the change in passenger volumes looks larger than it really is. Question 5 5.1 96% 5.2 80% 5.3 58-42= 16% 5.4 People who had various insurances used a financial adviser to get the products. Financial advisers are a key component to getting proper insurance cover and investment products. 5.5 No- Each category is a unit on its own and does not form part of a whole.

math slit

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