Mathematical Literacy Grade 12 - Woza Matrics

[Pages:238]12 Mathematical

Literacy

Study Guide

Grade

? Department of Basic Education 2015

This content may not be sold or used for commercial purposes. Curriculum and Assessment Policy Statement (CAPS) Grade 12 Mind the Gap study guide for Mathematical Literacy ISBN 978-1-4315-1936-1 This publication has a Creative Commons Attribution NonCommercial Sharealike license. You can use, modify, upload, download, and share content, but you must acknowledge the Department of Basic Education, the authors and contributors. If you make any changes to the content you must send the changes to the Department of Basic Education. This content may not be sold or used for commercial purposes. For more information about the terms of the license please see: . Copyright ? Department of Basic Education 2015 222 Struben Street, Pretoria, South Africa Contact person: Dr Patricia Watson Email: watson.p@.za Tel: (012) 357 4502 Call Centre: 0800202933 The first edition, published in 2012, for the Revised National Curriculum Statement (RNCS) Grade 12 Mind the Gap study guides for Accounting, Economics, Geography and Life Sciences; the second edition, published in 2014 , aligned these titles to the Curriculum and Assessment Policy Statement (CAPS) and added more titles to the series in 2015, including the CAPS Grade 12 Mind the Gap study guide for Mathematical Literacy. ISBN 78-1-4315-1936-1 Mind the Gap team Series managing editor: Dr Patricia Watson Production co-ordinators: Lisa Treffry-Goatley and Radha Pillay Production assistants: Nomathamsanqa Hlatshwayo and Motshabi Mondlane Authors: Michael William Fortuin, Denise Antoinette Grootboom, Madikhungwane Naughty Mbanyane, Zandile Mdiniso, Simangele Linda Cynthia Mnisi, Motshidisi Martha Moatlhodi, Raesetja Gladys Mogoroga, Setwadi Stewart William Mokgako, Nomsa Motshoane, Khonziphi Dolly Happy Ngema and Karen van Niekerk Expert readers: Julie Hannah, Sue Jobson, Thomas Masango and John Ostrowick Proofreaders: John Ostrowick and Angela Thomas Designers: Sonja McGonigle and Erika van Rooyen Illustrators: Michele Dean, Vusi Malindi, Khosi Pholosa, John Ostrowick, Kenneth Tekane Cover illustration: Alastair Findlay Afrikaans Translation: Johan Steenkamp Onsite writers' workshop IT support: Wayne Cussons Special thanks to Winning Teams, CEO Denzil Hollis, for the organisation's subject expertise and workshop support. Winning Teams board game facilitators: Mantse Khoza and Sue Jobson

? Department of Basic Education 2015

Ministerial foreword

The Department of Basic Education (DBE) has pleasure in releasing the second edition of the Mind the Gap study guides for Grade 12 learners. These study guides continue the innovative and committed attempt by the DBE to improve the academic performance of Grade 12 candidates in the National Senior Certificate (NSC) examination.

The study guides have been written by teams of exerts comprising teachers, examiners, moderators, subject advisors and coordinators. Research, which began in 2012, has shown that the Mind the Gap series has, without doubt, had a positive impact on grades. It is my fervent wish that the Mind the Gap study guides take us all closer to ensuring that no learner is left behind, especially as we celebrate 20 years of democracy.

The second edition of Mind the Gap is aligned to the 2014 Curriculum and Assessment Policy Statement (CAPS). This means that the writers have considered the National Policy pertaining to the programme, promotion requirements and protocols for assessment of the National Curriculum Statement for Grade 12 in 2014.

The CAPS aligned Mind the Gap study guides take their brief in part from the 2013 National Diagnostic report on learner performance and draw on the Grade 12 Examination Guidelines. Each of the Mind the Gap study guides defines key terminology and offers simple explanations and examples of the types of questions learners can expect to be asked in an exam. Marking memoranda are included to assist learners to build their understanding. Learners are also referred to specific questions from past national exam papers and examination memos that are available on the Department's website ? .za.

The CAPS editions include Accounting, Economics, Geography, Life Sciences, Mathematics, Mathematical Literacy and Physical Sciences Part 1: Physics and Part 2: Chemistry. The series is produced in both English and Afrikaans. There are also nine English First Additional Language (EFAL) study guides. These include EFAL Paper 1 (Language in Context); EFAL Paper 3 (Writing) and a guide for each of the Grade 12 prescribed literature set works included in Paper 2. These are Short Stories, Poetry, To Kill a Mockingbird, A Grain of Wheat, Lord of the Flies, Nothing but the Truth and Romeo and Juliet. (Please remember when preparing for EFAL Paper 2 that you need only study the set works you did in your EFAL class at school.)

The study guides have been designed to assist those learners who have been underperforming due to a lack of exposure to the content requirements of the curriculum and aim to mind-the-gap between failing and passing, by bridging the gap in learners' understanding of commonly tested concepts, thus helping candidates to pass.

All that is now required is for our Grade 12 learners to put in the hours required to prepare for the examinations. Learners, make us proud ? study hard. We wish each and every one of you good luck for your Grade 12 examinations.

Matsie Angelina Motshekga, MP Minister of Basic Education

__________________________________

Matsie Angelina Motshekga, MP Minister of Basic Education 2015

? Department of Basic Education 2015

iv INTRODUCTION

Mind the Gap Life Sciences

? Department of Basic Education 2015

Table of contents

Dear Grade 12 learner ...............................................................vii

How to use this study guide ........................................................ix

Top 10 study tips ...........................................................................x

Mnemonics .................................................................................... xi

Mind maps....................................................................................xii

On the day of the exam .............................................................xiii

Question words to help you answer questions....................... xiv

Vocabulary .................................................................................... xv

General terms .............................................................................. xv

Technical terms.......................................................................... xvii

The maths you need................................................................. xxvi

Unit 1: Numbers and calculations with numbers .................... 1

1.1 Using a calculator ........................................................................ 1 1.2 Common fractions ....................................................................... 4 1.3 Decimals ...................................................................................... 4 1.4 Percentages ................................................................................. 6 1.5 Ratio, proportion and rate......................................................... 10 1.6 Rounding off according to the context ..................................... 16 1.7 Squares and cubes of numbers ............................................... 18 1.8 Time............................................................................................ 20

Unit 2: Patterns and graphs ......................................................23

2.1 Making sense of graphs that tell a story.................................. 23 2.2 Plotting points on a graph grid ................................................. 24 2.3 Reading information from a graph ........................................... 25 2.4 Touching the axes...................................................................... 26 2.5 Graphs going up (increasing) and down (decreasing) ............ 27 2.6 Continuous and discrete graphs .............................................. 28 2.7 More than one line on the same graph ................................... 31 2.8 Direct and indirect proportion .................................................. 34 2.9 Exponential number patterns and graphs ............................... 36 2.10 How to identify the kind of relationship in a graph ................. 38 2.11 Reading the scale of a graph.................................................... 39

Unit 3: Finance ............................................................................ 41

3.1 Financial documents................................................................. 41 3.2 Budgets, income and expenditure statements ....................... 57 3.3 Banking, interest and tax .......................................................... 63 3.4 Inflation ...................................................................................... 73 3.5 Payslips, deductions and tax .................................................... 75

? Department of Basic Education 2015

Mind the Gap Mathematical Literacy

CONTENTS v

? Department of Basic Education 2015

Unit 4: Measurement .................................................................79

4.1 Converting between different units of measurement ............. 79 4.2 Measuring length....................................................................... 83 4.3 Measuring mass or weight........................................................ 85 4.4 Measuring volume and capacity............................................... 88 4.5 Perimeter, area and volume...................................................... 92 4.6 Calculating elapsed time ........................................................103

Unit 5: Maps, plans and other representations of the physical world.............................................................. 110

5.1 Scale......................................................................................... 110 5.2 Maps.........................................................................................119 5.3 Plans.........................................................................................126 5.4 Models......................................................................................136

Unit 6: Data handling ...............................................................139

6.1 Developing research questions ..............................................139 6.2 Collecting data.........................................................................140 6.3 Classifying and organising data.............................................. 141 6.4 Summarising data ................................................................... 144 6.5 Representing, interpreting and analysing data .....................159 6.6 Misleading data ....................................................................... 171

Unit 7: Probability .....................................................................179

7.1 The probability scale ............................................................... 179 7.2 Games of chance.....................................................................180 7.3 Using tree diagrams ................................................................183 7.4 Using a two-way table to show combined outcomes............. 187 7.5 Using predictions in various situations ..................................190 7.6 False positives and false negatives........................................ 191

vi CONTENTS

? Department of Basic Education 2015

Mind the Gap Mathematical Literacy

? Department of Basic Education 2015

Dear Grade 12 learner

This Mind the Gap study guide helps you to prepare for the end-of-year CAPS Grade Maths Literacy 12 exams.

The study guide does NOT cover the entire curriculum, but it does focus on core content of each knowledge area and points out where you can earn easy marks.

You must work your way through this study guide to improve your understanding, identify your areas of weakness and correct your own mistakes.

To ensure a good pass, you should also cover the remaining sections of the curriculum using other textbooks and your class notes.

Overview of the Grade 12 exam

The following topics make up each of the TWO exam papers that you write at the end of the year:

TERM 1 2 3

4

GRADE 12

Control Test

Paper 1 2 hours (100 marks)

Paper 2 2 hours (100 marks)

Control Test

Control Test

Paper 1 3 hours (150 marks)

Paper 2 3 hours (150 marks)

External Examinations

Paper 1 3 hours (150 marks)

Paper 2 3 hours (150 marks)

We are confident that this Mind the Gap study guide can help you to prepare well so that you pass the end-of-year

exams.

? Department of Basic Education 2015

Mind the Gap Mathematical Literacy

INTRODUCTION vii

? Department of Basic Education 2015

Intention

Structure and scope of content and/or skills

Level 1 Level 2 Level 3 Level 4 Contexts

PAPER 1

Basic skills' paper assesses proficiency of content and/or skills

PAPER 2

Applications' paper assesses ability to use both mathematical and nonmathematical techniques/considerations to explore familiar and unfamiliar contexts.

5 questions

Four questions deal with contexts relating to each of the topics: ? Finance ? Measurement ? Maps, plans and other

representations of the physical world ? Data handling

Fifth question integrates content from across all of these topics.

Likelihood will be examined in the

context or one or more of the other questions.

Each question can contain more than one context.

4 or 5 questions

Each question deals with contexts drawing integrated content from across all of the topics: ? Finance ? Measurement ? Maps, plans and other representations

of the physical world ? Data handling

Likelihood will be examined in the

context or one or more of the other questions.

Each question can contain more than one context.

60% 35% 5%

Familiar', i.e. limited to the contexts listed in the CAPS document.

25% 35% 40% Both `familiar' and `unfamiliar', i.e. not limited to the contexts listed in the CAPS document.

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 Likelihood

Weighting (%) No weighting is provided for these topics. Rather, they will be assessed in an integrated way throughout the Application Topics.

35% (?5%) 20% (?5%) 15% (?5%)

25% (?5%) Minimum 5%

The four levels of the Mathematical Literacy assessment taxonomy

PAPER 1

Level 1: Knowing Level 2: Applying routine procedures in familiar contexts Level 3: Applying multi-step procedures in a variety of contexts Level 4: Reasoning and reflecting

60% ? 5% 35% ? 5%

5% 0

GRADE 12 PAPER 2

25% ? 5% 35% ? 5% 40% ? 5%

OVERALL ALLOCATION

30% ? 5% 30% ? 5% 20% ? 5% 20% ? 5%

viii INTRODUCTION

? Department of Basic Education 2015

Mind the Gap Mathematical Literacy

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download