Grade 12 Study Guide Mathematical Literacy

FET Phase Grade 12 • Study Guide

Mathematical Literacy CAPS IEB

Mathematical Literacy Study guide

1812-E-MAL-SG01

Í2,È-E-MAL-SG01NÎ

Grade 12

CAPS aligned

E Brönn A Kies

Study Guide G12 ~ Mathematical Literacy

CONTENTS Lesson elements ................................................................................................................ 5 Preface ................................................................................................................................ 6 Assessment requirements ................................................................................................ 6 The assessment programme ............................................................................................ 7 Year planning ..................................................................................................................... 8 UNIT 1: REVIEW OF BASIC SKILLS ............................................................................... 10 Part 1: Rounding ................................................................................................... 10 Activity 1 ....................................................................................................... 10 Part 2: Rounding to the nearest 10, 100, 1 000..................................................... 11 Activity 2 ....................................................................................................... 11 Part 3: Scientific notation ...................................................................................... 12 Important ...................................................................................................... 12 Activity 3 ....................................................................................................... 12 Part 4: Percentages .............................................................................................. 13 Important ...................................................................................................... 14 Activity 4 ....................................................................................................... 16 Part 5: Ratios ........................................................................................................ 17 Activity 5 ....................................................................................................... 18 Part 6: Rates ......................................................................................................... 18 Activity 6 ....................................................................................................... 19 Part 7: Proportions ................................................................................................ 19 Activity 7 ....................................................................................................... 20 UNIT 2: MEASUREMENT ................................................................................................. 21 Lesson 1: Revision – Measurement ...................................................................... 21 Activity 8 ....................................................................................................... 21 Lesson 2: Time...................................................................................................... 22 Activity 9a ..................................................................................................... 22 REMEMBER ................................................................................................. 23 Activity 9b ..................................................................................................... 24 Lesson 3: Temperature ......................................................................................... 24 Activity 10 ..................................................................................................... 24 Lesson 4: Travel and timetables ........................................................................... 25 Activity 11a ................................................................................................... 26 Activity 11b ................................................................................................... 27 Lesson 5: Tide timetables ..................................................................................... 28 Activity 12 ..................................................................................................... 29

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Study Guide G12 ~ Mathematical Literacy

UNIT 3: FINANCE ............................................................................................................. 30 Important terminology ................................................................................... 30 Revision activity ............................................................................................ 31 Learning objectives ....................................................................................... 34 Lesson 6: Break-even analysis ............................................................................. 35 Activity 13 ..................................................................................................... 38 Lesson 7: The budget and revenue and expenditure of the government .............. 39 Important to remember ................................................................................. 40 Activity 14a ................................................................................................... 40 Activity 14b ................................................................................................... 40 Activity 15 ..................................................................................................... 43 Lesson 8: Running a business .............................................................................. 44 Activity 16 ..................................................................................................... 45 Activity 17 ..................................................................................................... 46 Activity 18 ..................................................................................................... 47 Activity 19 ..................................................................................................... 48 Activity 20 ..................................................................................................... 48 UNIT 4: DATA-HANDLING ............................................................................................... 49 Lesson 9: Interpreting statistics ............................................................................. 49 Activity 21 ..................................................................................................... 51 Activity 22 ..................................................................................................... 52 Activity 23 ..................................................................................................... 52 Activity 24 ..................................................................................................... 60 Activity 25 ..................................................................................................... 60 Lesson 10: Summarise data with quartiles and percentiles .................................. 71 Activity 26 ..................................................................................................... 78 UNIT 5: MORE FINANCES ............................................................................................... 83 Lesson 11: Hire purchase ..................................................................................... 83 Activity 27 ..................................................................................................... 83 Activity 28 ..................................................................................................... 85 Lesson 12: Interest................................................................................................ 85 Activity 29 ..................................................................................................... 89 Lesson 13: Loans .................................................................................................. 89 Activity 30 ..................................................................................................... 92 Activity 31 ..................................................................................................... 93 Lesson 14: Annuities and investments .................................................................. 95 Activity 32 ..................................................................................................... 98 Lesson 15: Inflation ............................................................................................... 98 Activity 33 ................................................................................................... 100 UNIT 6: MAP WORK ....................................................................................................... 102 Revision activity .......................................................................................... 103

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Study Guide G12 ~ Mathematical Literacy

Lesson 16: Travel costs ...................................................................................... 108 Activity 34 ................................................................................................... 111 Activity 35 ................................................................................................... 112 Lesson 17: Compass directions .......................................................................... 113 Lesson 18: Longitudes and latitudes ................................................................... 114 Activity 36 ................................................................................................... 118 Activity 37 ................................................................................................... 119 Activity 38 ................................................................................................... 120 Lesson 19: Scales ............................................................................................... 120 Activity 39 ................................................................................................... 121 Application activity ...................................................................................... 123 UNIT 7: MEASUREMENT – PERIMETER, AREA, VOLUME ......................................... 125 Lesson 20: Calculating the perimeter .................................................................. 127 Activity 40 ................................................................................................... 129 Lesson 21: Calculate area .................................................................................. 131 Activity 41 ................................................................................................... 132 Lesson 22: Calculate volume .............................................................................. 133 Activity 42 ................................................................................................... 138 Activity 43 ................................................................................................... 141 Lesson 23: Body mass index .............................................................................. 144 Activity 44 ................................................................................................... 146 Lesson 24: Medicine dosages ............................................................................. 146 Activity 45 ................................................................................................... 148 Activity 46 ................................................................................................... 148 UNIT 8: FINANCES – TAX, EXCHANGE RATES .......................................................... 149 Learning objectives ..................................................................................... 149 Lesson 25: Unemployment Insurance Fund (UIF)............................................... 149 Activity 47 ................................................................................................... 149 Lesson 26: Income Tax ....................................................................................... 150 Important terminology ................................................................................. 150 Activity 48 ................................................................................................... 153 Activity 49 ................................................................................................... 155 Lesson 27: Calculate the net salary .................................................................... 156 Activity 50 ................................................................................................... 157 Lesson 28: Exchange rates ................................................................................. 159 Activity 51 ................................................................................................... 160 Activity 52 ................................................................................................... 161 UNIT 9: MAPS AND PLANS ........................................................................................... 162 Lesson 29: Floor plans ........................................................................................ 166 Activity 53 ................................................................................................... 167 Activity 54 ................................................................................................... 168

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Study Guide G12 ~ Mathematical Literacy

Lesson 30: Profile maps ...................................................................................... 169 Lesson 31: Elevations ......................................................................................... 169 Activity 55 ................................................................................................... 171 Lesson 32: Models and instructions .................................................................... 172 Activity 56 ................................................................................................... 172 UNIT 10: PROBABILITY ................................................................................................. 174 Lesson 33: Probability ......................................................................................... 174 Activity 57 ................................................................................................... 177 Activity 58 ................................................................................................... 179 Lesson 34: Probability to win the Lotto ................................................................ 181 Lesson 35: Prediction .......................................................................................... 183 Activity 59 ................................................................................................... 185 Lesson 36: Expression of probability in the media .............................................. 186 BIBLIOGRAPHY ............................................................................................................. 189

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Study Guide G12 ~ Mathematical Literacy

LESSON ELEMENTS LEARNING AIMS What candidates should know at the end of the lesson. Taken from CAPS.

IMPORTANT TERMINOLOGY New terminology to extend understanding of the subject as part of the lesson.

DEFINE Definitions of concepts to help candidates understand the content.

IMPORTANT A summary or explanation of key concepts explained in the lesson.

TIPS Information in addition to the content to guide candidates through the learning process.

FOR THE CURIOUS Encouragement for candidates to do in-depth research about the content on his/her own.

ACTIVITY Formative assessment to test candidates’ progress and knowledge of the lesson completed.

EXERCISE Formative assessment to test candidates’ progress and knowledge of the unit completed.

CORE CONTENT Reinforcement of core of content; in-depth explanation of a specific section of the lesson.

STUDY/REVISION Demarcation or summary of work to be revised in preparation for tests and examinations.

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Study Guide G12 ~ Mathematical Literacy

Preface Recommended book Any additional book can be used in conjunction with this study guide. It is always a good idea to refer to other textbooks, in addition to the study guide, to gain a broader perspective on the subject.

• The Answer Series 3 in 1 Mathematical Literacy • Mathematical Literacy for the Classroom

Assessment requirements In this facilitator’s guide, you will note that there are constant references to TL1, TL2, TL3 and TL4. This is the thinking level that is required to answer the specific question that is being asked. The thinking levels represent the following skills: Thinking level 1: Knowing Thinking level 2: Applying routine procedures in familiar contexts Thinking level 3: Applying multi-step procedures in a variety of contexts Thinking level 4: Reasoning and reflecting When tasks, investigations and especially tests and examinations are set, the guidelines below are used to allocate a number of marks to a specific thinking level.

Distribution of marks according to the thinking levels: Percentage of marks allocated

Thinking levels Thinking level 1: Knowing

30% (±5%)

Thinking level 2: Applying routine procedures in familiar contexts

30% (±5%)

Thinking level 3: Applying multi-step procedures in a variety of contexts

20% (±5%)

Thinking level 4: Reasoning and reflecting

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20% (±5%)

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Study Guide G12 ~ Mathematical Literacy

The assessment programme All formal assessments can be found in the portfolio book and the portfolio book memorandum. The examinations will be made available separately to the approved invigilator.

The assessment programme below indicates the number of assessment tasks and their weighting: Final Examination (75%)

Continuous assessment (25%) 25%

Grade 12

Term 1 Assignment (10%) + Investigation (10%) Term 1 test (10%)

Term 2

Term 3

Assignment/ Investigation (10%)

Term 3 test (10%)

June Examination (25%)

Preliminary Examination (25%)

Term 4

Additional information regarding the examination papers In each examination, you are required to complete two papers. The two papers consist of the same content but differ in intensity, cognitive demand and the nature of context.

Paper 1: • 60% (±5%) of the marks at level 1 (knowing).

• 35% (±5%) of the marks at level 2 (applying routine procedures in familiar contexts).

• 5% (minimum) of the marks at level 3 (applying multi-step procedures in a variety of contexts).

Paper 2: • 25% of the marks at level 2 (applying routine procedures in familiar contexts).

• 35% of the marks at level 3 (applying multi-step procedures in a variety of contexts).

• 40% of the marks at level 4 (reasoning and reflecting).

Marks and time for examinations: • June Examination: 2 papers of 100 marks, 2 hours each • Preliminary Examination: 2 papers of 150 marks, 3 hours each • Final Examination: 2 papers of 150 marks, 3 hours each

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Study Guide G12 ~ Mathematical Literacy

Weighting of topics that will be assessed

Basic skills topics

Application topics

Topic Interpreting and communicating answers and calculations Numbers and calculations with numbers Patterns, relationships and representations Finance Measurement Maps, plans and other representations of the physical world Data-handling Probability

Weighting (%) No weighting is provided for these topics. They are integrated with the application topics.

35% (±5%) 20% (±5%) 15% (±5%) 25% (±5%) Minimum of 5% (±5%)

Year planning UNIT 1 2 3 4 5 6 7 8 9 10

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THEME REVIEW OF BASIC SKILLS MEASUREMENT FINANCE DATA-HANDLING MORE FINANCES MAP WORK MEASUREMENT (PERIMETER, AREA, VOLUME) FINANCES – TAX & EXCHANGE RATES MAPS AND PLANS PROBABILITY REVISION

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TERM 1: JANUARY – MARCH

TERM 2: APRIL – JUNE

TERM 3: JULY – AUGUST SEPTEMBER: PRELIMINARY EXAMINATION NOVEMBER: FINAL EXAMINATION

Study Guide G12 ~ Mathematical Literacy

Suggested time to be spent on each unit: Term 1

2

3

Unit 1 2 3 4 5 6 7 8 9 10

Theme Review of basic skills Measurement Finance Data-handling More finances Map work Measurement (perimeter, area, volume) Finances – tax and exchange rates Maps and plans Probability

Number of weeks Own time/worked in 1 3 5 2 1 4 1 3 2

The time allocation per topic is only a guideline and can be adapted to the pace of candidates. It is nevertheless important to know that the lessons in question have to be completed before tests or examinations can be written.

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Study Guide G12 ~ Mathematical Literacy

Unit

1

UNIT 1: REVIEW OF BASIC SKILLS Learning objectives After completing this unit, you should be able to do the following: • Apply basic mathematical skills.

• Understand rounding down, scientific notation, percentages, ratio, proportion and complete calculations.

Part 1: Rounding EXAMPLES Round the following numbers to the number of decimal places indicated in brackets: 1.1

3,14823 (2 decimal places) Answer: ≈ 3,15

Note: Look at the third decimal. A number less than 4 makes no difference to the second decimal. If the third decimal is 5 and higher, the second decimal should be rounded up to the next number.

1.2

1.3

23,89432 (3 decimal places) Answer: ≈ 23,894 215,899 (2 decimal places) Answer: ≈ 215,90 Activity 1

Round the following numbers to TWO decimal places: 1.

2,3568 2.

0,356789 3.

1,9999 4.

13,4386 5.

234,8765

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Study Guide G12 ~ Mathematical Literacy

Unit

Part 2: Rounding to the nearest 10, 100, 1 000 EXAMPLES 2.1

2.2

2.3

Round the following numbers to the nearest 10: 2.1.1 65 ≈ 70 2.1.2 16 ≈ 20 2.1.3 173 ≈ 170 2.1.4 589 ≈ 590

Round the following numbers to the nearest 100: 2.2.1 65 ≈ 100 2.2.2 1 082 ≈ 1 100

Round the following numbers to the nearest 1 000: 2.3.1 5 999 ≈ 1 000 2.3.2 4 956 ≈ 5 000 Activity 2

Round the following numbers to the nearest 10, 100 of 1 000: 1.

2.

3.

4.

5.

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58 (nearest 10) 345 (nearest 100) 1 367 (nearest 1 000) 1 356 (nearest 10, 100 and 1 000, respectively) 2 835 (nearest 10, 100 and 1 000, respectively)

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Study Guide G12 ~ Mathematical Literacy

Unit

Part 3: Scientific notation Important One million: 1 000 000 (6 zeroes) One billion: 1 000 000 000 (9 zeroes) One trillion: 1 000 000 000 000 (12 zeroes) Scientific notation is used for very large or very small numbers. It is written differently to make it easier to read.

EXAMPLES •

Convert 0,0043 to scientific notation.

•

Convert 81 500 to scientific notation.

• • • •

14 000 000 → can be written as 1,4 x 107 582 000 000 000 → can be written as 5,82 x 1011 0,0000018 → can be written as 1,8 x 10–6 0,00000000005 → can be written as 5,0 x 10–11 Activity 3

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1.

Write the following numbers in scientific notation: 1.1.

4 800 000 1.2.

2 500 1.3.

0,00000012 1.4.

0,00023

2.

Write the following as an ordinary number: 2.1.

3,4 x 105 2.2.

6,28 x 109 2.3.

2,3 x 10–6 2.4.

4,5 x 10–9

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Study Guide G12 ~ Mathematical Literacy

Unit

1

Part 4: Percentages Percentages are expressed as a common fraction or as a decimal number, e.g. 25% = 4.1

25

100

= 0,25

Calculation of percentage

EXAMPLES 4.1.1 Calculate 15% of R1 200.

Note: remember the word “of” means multiplication.

15

100

× R1 200 = R180,00

Sequence on calculator: 15 ÷ 100 x 1 200 = 4.1.2 Janet gets

26 40

for a Mathematical Literacy test. What is her percentage for the test?

26 × 100 = 65% 40

Sequence on calculator: 26 ÷ 40 x 100 = 4.2

Determining new values for given percentages

EXAMPLES 4.2.1

A packet of chips costs R3,20 without VAT (value-added tax).

How much will you pay if VAT is added? (VAT is 14%) 14

100

× R3,20 = R0,448

or

R3,20 + R0,448 = R3,65 You will pay R3,65.

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R3,20 × 114% = R3,65

Study Guide G12 ~ Mathematical Literacy

4.2.2

Unit

1

A vendor increases his prices by 6%. If the original price is R21,99, what will the price be after the increase?

6

100

× R21,99 = R1,32

R21,99 × 106% = R23,31

or

R1,32 + R21,99 = R23,31

The new price will be R23,31.

4.2.3

A shop has a sale with 25% off all jeans. What will you pay for a pair of jeans if the original price was R395,00?

25

100

× R395 = R98,75

or

100 – 25 = 75%

R395 − R98,75 = R296,25

75% x R395 = R296,25

The pair of jeans will now cost R296,25.

4.2.4

The petrol price decreases with 4,5%. How much will we pay now if we previously paid R12,30 per litre?

4,5

100

× R12,30 = R0,5535

or

100 – 4,5 = 95,5%

R12,30 – R0,5535 = R11,75

95,5% x R12,30 = R11,75

We will now pay R11,75.

4.3

Determining the original value when a percentage is given Important Remember that the original value must be determined – the previous amount, before it was increased or decreased.

4.3.1

A slab of chocolate costs R15,10 with VAT included. VAT is 14%. What is the price of the chocolate without VAT? P: price without VAT P x 114% = R15,10

P=

15,10

114%

[114% = 100% + 14%]

or

R15,10 ÷ 1,14

P = R13,25 The original price was R13,25.

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Study Guide G12 ~ Mathematical Literacy

4.3.2

Unit

1

A butcher increases his meat prices by 6%. Boerewors now costs R25,75/kg. What was the original price before the increase?

P: original price P x 106% = R25,75 P = 25,75 ÷ 106% = R24,29 The original price was R24,29.

4.3.3

A shoe shop has a sale at 25% discount. If the selling price of a pair of sneakers is now R348, 25, what was the original price before the discount?

(100% – 25% = 75%) P: original price P x 75% = R348,25 P = R348,25 ÷ 75% = R464,33 The original price of the sneakers was R464,33.

4.4

Percentage increase and percentage reduction The following formula is useful to calculate the increase and decrease in percentages. current value − previous value

4.4.1

previous value

× 100

In 2014, a school had 1 252 learners and by 2015, there were 1 385 learners in the school. By which percentage did the enrolment increase? current value − previous value previous value

1 385−1 252 1 252

= 10,62%

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(Do not enter %)

× 100

15

× 100

Study Guide G12 ~ Mathematical Literacy

Unit

1

Activity 4 1.

Calculate: 1.1.

35% of R1 500 1.2.

33⅓% of R4 500

2.

Megan gets

46 75

for a Geography test. What is her percentage? (Round off

your answer to the nearest whole number.)

3.

A shop assistant forgot to add VAT when she calculated the price of several items. The following items must be recalculated: Chocolate bars at R6,25 Sweets at R3,45 Chips at R4,20 Soft drink cans at R5,85 Calculate the correct new price of each item. VAT is 14%.

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4.

JC buys a second-hand motorcycle at R25 000, which includes 14% VAT. What would the cost have been before VAT was added?

5.

The price of petrol decreases with 1,3%. We now pay R12,34 per litre.

How much did we previously pay per litre?

6.

A handbag that was sold at R235,00 is now selling for R135,00. Calculate the percentage discount to the nearest whole number.

7.

What percentage is 36 minutes of an hour?

8.

A bag of groceries costs R456,00 after an inflation increase. If the inflation increase was 6,5%, what would the cost of the bag of groceries have been before the increase?

9.

A certain company has 312 employees, of which 176 are female. What percentage of the employees are male? Round off to the nearest whole number.

10.

Thabiseng now earns R15 457,00 per month. Previously, she earned R14 450. The average annual salary increase for the company was 5%.

Show by calculation that Thabiseng’s new salary is in line with the company average.

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Study Guide G12 ~ Mathematical Literacy

Unit

1

Part 5: Ratios A ratio describes the relationship between two quantities that are measured in the same unit.

3

•

Notation: 3 to 7 or 3 : 7 or

•

Always write ratios in their simplest form.

E.g. 8 : 12 → 2 : 3 (divide each number by 4)

•

Increase R5,80 in the ratio 3 : 5.

5

•

3

7

× R5,80 = R9,67

(Nominator highest value)

× R5,80 = R3,48

(Nominator lowest value)

Decrease R5,80 in the ratio 3 : 5.

3 5

Distribution of ratios a)

R5 000 is divided between Ben, Melissa and Thabo in the ratio 2 : 3 : 5.

How much will each get?

Determine the total by adding up 2 + 3 + 5 = 10.

Ben:

2

10

× R5 000 = R1 000 3

Melissa: Thabo: b)

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5

10

× R5 000 = R1 500

× R5 000 = R2 500

A piece of string of 18 m is divided in the ratio 1 : 2 : 3. How long is each piece?

Part 1:

1

Part 2:

2

Part 3:

3

6 6

6

× 18 = 3 m × 18 = 6 m

× 18 m = 9 m

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Study Guide G12 ~ Mathematical Literacy

Unit

1

Activity 5 1.

Write the following ratios in their simplest form: 1.1.

27 : 33 1.2.

3 days : 3 weeks 1.3.

1,3 litres : 250 mℓ

2.

The following ratio is given on a cold drink concentrate bottle: “mix 1 : 4 with water”.

2.1.

What does it mean?

2.2.

How many millilitres of concentrate should be added if you have one litre of water?

3.

4.

5.

Divide R2 310 between Mari, Lebo and Gloria in the ratio 12 : 7 : 23.

Increase R133,45 in the ratio 2 : 3.

Decrease 135 kg in the ratio 11 : 7. (Round off your answer to two decimal places.)

Part 6: Rates A rate is a relationship between two quantities of different units.

E.g. R/kg; rand/dollar; km/ℓ; m/s; km/h.

EXAMPLES 6.1

The exchange rate is R16,64 for a British pound (£).

If you have £2 500, how much is it in rand?

2 500 x R16,64 = R41 600

6.2

If you have R50 000, how many British pounds is it?

R50 000 ÷ 16,64 = £3 004,81

6.3

A water tank with a capacity of 100 ℓ leaks at a rate of 1,4 ℓ/min.

How long will it be before there is only 74 ℓ left in the tank? Provide your answer in terms of minutes and seconds.

100 – 74 = 26 ℓ 26 ℓ ÷ 1,4 = 18,57 minutes 18 minutes and (57 x 60) 18 minutes 34 seconds

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Study Guide G12 ~ Mathematical Literacy

Unit

Activity 6 If €1 (euro) → R12,18: 1.

2.

How many rands are equivalent to €20 000?

If you have R63 400, how many euros (€) will it be?

Part 7: Proportions Two ratios that are equal are proportional.

1:2=2:4 Direct proportion As one quantity increases, the other quantity increases at the same rate.

Reverse or indirect proportion As one quantity increases, the other quantity decreases.

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Study Guide G12 ~ Mathematical Literacy

Unit

1

Activity 7 1.

Weight in kg Cost in rand 2.

3.

4.

Tomatoes cost R10,99/kg. Complete the following table by entering the missing values: 1

5

10

c

20

e

30

R10,99

a

b

R164,85

d

R274,75

f

Draw a line graph on a labelled axis to represent the above graphically.

What type of proportion is this? Motivate your answer.

A group of friends wants to hire a bus to take them to a rugby match. It costs R3 000 to rent the bus. The amount that each person should contribute depends on how many people will be using the bus.

4.1.

Complete the following table to determine the amount per person.

Number of people 1 2 3 4 5 10 50 60 on the bus Amount per person 4.2.

4.3.

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R3 000 R1 500

a

b

c

R300

d

R50

Draw a line graph to represent the above graphically.

What type of proportion is represented here? Motivate your answer.

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Study Guide G12 ~ Mathematical Literacy

Unit

UNIT 2: MEASUREMENT Learning objectives After completing this unit, you should be able to do the following: • Conversions.

• Write time in hours, minutes and seconds.

• Convert temperatures.

• Analyse travel and timetables.

• Interpret tide tables.

Lesson 1: Revision – Measurement Important conversions to remember 1 m = 1 000 mm

1 cm = 10 mm

1 km = 1 000 m

1 m = 100 cm

1 ton = 1 000 kg

1 kg = 1 000 g

𝟏𝟏 𝓵𝓵 = 𝟏𝟏 𝟎𝟎𝟎𝟎𝟎𝟎 𝒎𝒎𝓵𝓵 1 g = 1 000 mg

1 cup = 250 mℓ

1 tablespoon = 15 mℓ

1 teaspoon = 5 mℓ

1 ℓ = 1 000 cm3

1 m3 = 1 000 000 cm3 Activity 8

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1.

Convert the following units to the units in brackets: 1.1.

35 mm (cm) 1.2.

1,58 km (m) 1.3.

2 085 g (kg) 1.4.

2 450 kg (ton) 1.5.

1,5 ℓ (mℓ) 1.6.

750 mℓ (ℓ)

2.

Convert the following units to the units in brackets: 2.1.

3 cups (mℓ) 2.2.

3 tablespoons (mℓ) 2.3.

280 mℓ (cups and tablespoons)

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Study Guide G12 ~ Mathematical Literacy

3.

Unit

Study the following table: Baking powder Flour 5 mℓ → 4 g 5 mℓ → 3 g

2

Salt Sugar 5 mℓ → 5,5 g 5 mℓ → 4 g

Convert to the units in brackets. Round off to ONE decimal place.

3.1.

3.2.

4.

275 g flour (mℓ) 12,5 mℓ salt (g)

Study the following imperial and metric units and then convert to the units in brackets:

Length Weight Volume 4.1.

4.2.

4.3.

Imperial → metric 1 mile → 1,609 km 1 ounce → 28,35 g 1 pound (16 ounce) → 453,59 g 1 US gallon (8 pints) → 3,785 ℓ 285 miles (km) 12 pounds 3 ounces (kg) 40,5 US gallons (ℓ)

Metric → imperial 1 km → 0,621 mile 1 g → 0,035 ounce 1 kg → 2,205 pounds 1 ℓ = 0,264 US gallons Use this conversion

Lesson 2: Time

1 hour = 60 minutes

1 minutes = 60 seconds

1 day = 24 hours

1 week = 7 days

1 year = 52 weeks

1 year = 365 days

Activity 9a 1.

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Look at the watch and write the time in words and digital time:

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Study Guide G12 ~ Mathematical Literacy

2.

Unit

What is the time on the stopwatch?

Time conversion REMEMBER 2h30 ≠ 2,3 hours, but is 2 hours and 30 minutes, which means 2,5 hours. a) To convert from hours and minutes to hours: • Divide the minutes by 60.

• Add the hours.

• Round as requested.

EXAMPLE Convert 3h17 to hours.

• Minutes to hours → 17 ÷ 60 = 0,28333…

• Add the hours to the answer → 3 + 0,28333…

• Answer: 3,28 hours b)

To convert hours and minutes to minutes: • Multiply hours with 60.

• Add the minutes.

• Round as requested.

EXAMPLE Convert 3h17 to minutes.

• Hours to minutes → 3 x 60 = 180 minute • Add the minutes to the answer = 17 + 180 = 197 • Answer: 197 minutes Calculations with time Use the DMS or º ‘ “ button on the calculator.

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Study Guide G12 ~ Mathematical Literacy

Unit

2

EXAMPLE A train departs from Cape Town Station at 06:15 and arrives at Stellenbosch Station at 07:03. How long did it take the train to reach its destination?

07:03 – 06:15 Calculator 07 º ‘ “ 03 º ‘ “ – 06 º ‘ “ 15 º ‘ “ = Calculator answer 0º48’0” The answer is 48 minutes (0 hours 48 minutes 0 seconds).

Activity 9b 1.

Convert the following time: 4h28 1.1 To hours.

1.2 To minutes.

1.3 To seconds.

2.

A bus leaves Johannesburg at 08:45. The bus arrives in Beaufort-West at 17:25. How long did it take the bus to reach its destination?

(USE A CALCULATOR.)

3.

4.

5.

How many hours are there in 456 days?

How many weeks are there in 4 years?

How many seconds are there in 2 years?

Lesson 3: Temperature The following formulas are important to know when you are working with temperature. You should be able to convert from Fahrenheit to Celsius and vice versa.

Activity 10 1.

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℉ = (𝟏𝟏, 𝟖𝟖 × ℃) + 𝟑𝟑𝟑𝟑° ℃ = (℉ − 𝟑𝟑𝟑𝟑°) ÷ 𝟏𝟏, 𝟖𝟖

Convert the following to the units in brackets: 1.1.

65 ℉ (℃) 1.2.

28 ℃ (℉) 1.3.

–3 ℃ (℉)

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Study Guide G12 ~ Mathematical Literacy

2.

Unit

2

The following recipe is provided: Italian pudding 2 eggs 0,5 oz castor sugar 0,75 pints of milk 2 oz cake crumbs 0,5 pound pitted dates

0,5 pounds pitted raisins 2 oz mixed peel 0,2 teaspoons nutmeg 1 pound cooking apples

Method: • Make a custard by whisking the eggs and sugar together and adding it to the warm milk.

• Add the cake crumbs.

• Mix the dates, rasins, peel and nutmeg. Peel and remove the seeds from the apples. Cut the apples into thin slices.

• Arrange the apple slices at the bottom of a pie dish.

• Add the mixed fruit and cover with the custard.

• Bake at 335 ºF for one hour in a preheated oven.

• Serve hot or cold.

2.1.

Measure length weight volume

Rewrite the whole recipe and make use of metric units.

Imperial → metric 1 mile → 1,609 km 1 ounce → 28,35 g 1 pound (16 ounces) → 453,59 g 1 US gallon (8 pints) → 3,785 ℓ

2.2.

Convert 335 ºF to ºC.

Metric → imperial 1 km → 0,621 miles 1 g → 0,035 ounces 1 kg → 2,205 pounds 1 ℓ = 0,264 US gallons

Lesson 4: Travel and timetables • • •

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Travel tables, maps and timetables provide information to help people plan their trips.

It provides useful information about the departure times, arrival times and routes of airplanes, buses or trains.

A travel fee table provides useful information on the costs of routes and destinations.

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Study Guide G12 ~ Mathematical Literacy

Unit

2

Activity 11a Source: Adapted from National Senior Certificate Paper 1, March 2009 A train timetable to travel from Durban to Bloemfontein and then to Kimberley is shown: The train travels from Durban to Kimberley via Bloemfontein.

Shosholoza Meyl Durban-Bloemfontein-Kimberley Frequency: From Durban on Wednesdays Town Arrives Departs Stop at station in minutes 18:30 Durban 20:53 21:10 17 Pietermaritzburg 00:33 27 Ladysmith 03:23 03:53 30 Harrismith 05:20 05:40 20 Bethlehem 07:49 08:19 30 Kroonstad 08:57 08:59 2 Hennenman 09:17 09:19 2 Virginia 09:50 09:52 2 Theunissen 10:25 10:27 2 Brandfort 11:15 11:45 30 Bloemfontein 14:50 Kimberley

1.

2.

3.

4.

5.

On which day of the week does the train arrive in Kimberley?

What is the duration of the whole trip? Give your answer in hours.

At what time does the train leave Ladysmith?

Calculate the total time that the train stops between Durban and Kimberley. Give your answer in minutes.

Without adding the time that passes while the train stops, the actual travel time is 17,6 hours and the distance between Durban and Kimberley is 842 km. Calculate the average speed at which the train travels.

Use the formula: Speed =

6.

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distance time

Sipho travels from Durban to Brandfort on the same train. He must get onto a bus that leaves the bus station at 11:00. It takes 5 minutes to walk from the train station to the bus terminal. Determine whether Sipho will be on time to catch the bus. Show all calculations.

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Study Guide G12 ~ Mathematical Literacy

Unit

2

Activity 11b Use the travel fee table to answer the questions.

Travel expenses MyCiti is a cashless system except for the airport route, where paper tickets are accepted. To travel on all other routes you have to load money on your Myconnect card.

Source: Via Afrika: 2013

1.

2.

3.

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Who can travel free?

The first sentence states that MyCiti is a cashless system. This means you have to buy a card for you to be able to travel. What is the cost of a card?

Determine the cost of: 3.1.

One trip from the Civic Centre to Table View.

3.2.

Five trips from the Civic Centre to Table View.

3.3.

Ten trips from the Civic Centre to Table View.

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