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mathematics and statistics

MX2000CA course and assessment guide ncea level 2

2015

mathematics and statistics (mx2000) teacher contact details When you first make contact with your teacher, please fill out their details below, for future reference. TEACHER’S name:

telephone: 0800 65 99 88

ext:

alternative telephone number: email address: Private Bag 39992, Wellington Mail Centre, Lower Hutt 5045 Please keep your Mathematics and Statistics Level 2 (MX2000) Course and assessment guide in a safe place so that you can use it to plan your study and to record your assessment results. For future information about courses at this level, please refer to Student Guide to Years 11–13 and the Student Guide to National Certificates, both available on the school website (www.tekura.school.nz).

Cover photo: iStock 15798783 Copyright © 2012 Board of Trustees of Te Aho o Te Kura Pounamu, Private Bag 39992, Wellington Mail Centre, Lower Hutt 5045, New Zealand. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means without the written permission of Te Aho o Te Kura Pounamu. © te ah o o te k u ra p ou n am u

contents 1

Welcome to MX2000

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Getting started information

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MX2000 course outline

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Assessment information

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My Mathematics and Statistics assessment record (MX2000)

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MX2000 suggested course planner

7 Formulae

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welcome to mx2000 Welcome to the Level 2 Mathematics and Statistics (MX2000) course offered by Te Aho o Te Kura Pounamu.

overview of mx2000

Mathematics is more than just numbers; it is the exploration and use of patterns and relationships in quantities, space and time. Statistics is the exploration and use of patterns and relationships in data. Both disciplines equip you with effective means for investigating, interpreting and making sense of the world. Mathematics provides powerful communication and problem solving tools by using symbols, graphs and diagrams to investigate these patterns and relationships, and creating models to represent real life and hypothetical situations, as well as reflecting a range of social, cultural, scientific, technological, health, environmental and economic contexts. Mathematics develops an ability to think creatively, critically, strategically and logically. You learn to structure, to organise and to process and communicate information. By studying mathematics and statistics, you will learn to create models and to predict outcomes, to conjecture, to justify and to verify. What this course involves This NCEA Level 2 course covers all major areas of mathematics and statistics at curriculum level 7. You will learn skills, and use and apply mathematical and/or statistical concepts that are needed in solving problems involving number, algebra, geometry, measurement, probability and statistics. This course can be endorsed with Merit or Excellence if, in a single year, you gain 14 or more credits at Merit and/or Excellence within Level 2 Mathematics and Statistics. At least three of these credits must be from externally assessed standards and three from internally assessed standards. What equipment do I need? Course materials are mailed to you. The MX2000 course also has online support for students with internet access. Check this Course and assessment guide carefully to be sure that you can access the appropriate equipment needed to study effectively. If you are not sure, contact your Mathematics and Statistics teacher.

assessment (internal and external)

Internal Internal assessments are assessed by your teacher. You can be assessed any time you and your supervisor are ready, though each assessment task has conditions that you must follow. Both you and your supervisor must make sure that you keep to these conditions and you are both required to sign an authentication statement to say that you have done so. External External assessment means that your grade is decided by an examination. The NCEA examinations take place at the end of each year and have a strict timetable. If you enter for an examination, you must attend these at the specified location and time. After you have sat the examination at an examination centre, it is sent off to be assessed by NZQA. 2

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welcome to mx2000

Te Aho o Te Kura Pounamu provides practice examinations late in term three to help you prepare for the NZQA external assessments.

achievement standards and national certificates

Throughout your programme you will have many opportunities to be assessed and to gain credits towards National Certificates and/or build up your NZQA Record of Learning. Without sitting examinations you can gain credits towards NCEA Level 2 achievement standards with the grades of Achieved, Merit or Excellence for up to 11 internally assessed achievement standards. Are there any particular internally assessed achievement standards you want or need? Write them here.

Do you want to gain credit towards: • the National Certificate in Educational Achievement (NCEA), Level 1 or 2? Yes No • any other National Certificate?

external achievement standards by examination

Your programme could be designed to prepare you for up to three achievement standards that can be gained only through the NZQA examinations held at the end of each year. If you are aiming to do this, you should be confident in a range of mathematics and statistics skills at curriculum level 7. nzqa examination-assessed achievement standards

interested ✓ or ✗

Apply algebraic methods in solving problems AS91261 2.6 Apply calculus methods in solving problems AS91262 2.7

Apply probability methods in solving problems AS91267 2.12

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welcome to mx2000

You will not need to make a final decision about this until July. You will be contacted by the Qualifications team here at Te Kura. If you do decide to attempt the external achievement standards you will be sent trial examination activities prepared by Te Kura in term 3 to assist your preparation for the NZQA examinations. There are many reasons why you have enrolled in this MX2000 course. There are a large number of resources in this course to support your learning. If your circumstances or goals change, you can negotiate alterations to your programme with your teacher. Please let your teacher know about your wishes when you send in your work. Your teacher may also make further recommendations based on your progress. You will be provided with revision notes you may need to help you with your learning. Best wishes for your future Mathematics and Statistics learning and achievements.

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getting started information how this course is delivered

Plan a regular time to study. Some people learn best from frequent short sessions while others do better with fewer, longer sessions. It is important to have a plan or a timetable and to keep to it. There is a suggested planner in the back of this guide for you to plan your programme of study. You may wish to consult with your subject teacher to help you decide on your plan. Getting your study underway is very important. Your first return of work should be two to three weeks after you first enrol. If you have any issues returning your work within this time please contact your subject teacher. For more information on how to study successfully, refer to the Student Guide to Years 11–13 (www.tekura.school.nz).

te kura codes

Your course code is: MX2000. MX is the code for Mathematics and Statistics and 2000 refers to Level 2. ‘MX2011’ refers to a booklet that covers a particular learning topic in the MX2000 course. ‘MX2012Y1’ refers to the first assessment for an Achievement Standard (AS91256) for MX2000. ‘AS’ is the code for Achievement Standard.

resources you need • • • •

A computer to access the OTLE website for MX2000. A protractor, ruler and compass. Scientific or graphic calculator. A graphic calculator is recommended. Quad paper and refill paper.

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getting started information

what will your mathematics and statistics programme be? It will start with MX2000CA and MX2031 (Sequences and Series 1).

Other mathematics and statistics work will depend on what you have already learnt in mathematics and what you would like to study in this NCEA Level 2 course. Your learning journey is personal and at times specific. We encourage you to address your mathematical and statistical strengths and weaknesses, so that you receive a balanced learning programme.

teacher support

You will be assigned a Mathematics and Statistics teacher. Please make contact with them on a regular basis so that they can assist you in monitoring and tailoring your programme as you progress.

self-marking

Many activities are self-marked. You’ll find an Answer guide in each resource. Use these answers to mark your own work and make corrections where necessary. Self-marking is very important as it gives you instant feedback on how well you understand the ideas, concepts or information that have been covered.

assessment

There are self-assessments contained within the booklets. Please check your work as you progress through each resource and make contact with your Mathematics and Statistics teacher if you require help along your learning journey. You are required to send in your self-marked activities and the teacher-assessed review answers. Your teacher will return your work with feedback in each resource that you complete. The internal achievement standard tasks will be sent to you when you have submitted the work from the last booklet in the series that relates to the particular standard you are working towards. The detailed criteria for achievement standards, including conditions of assessment, are given in the relevant booklets and tasks. They can also be found by searching the subject and level in the NCEA part of the NZQA website (www.nzqa.govt.nz) and then finding the relevant standard(s). If there are two assessment opportunities, one is called ‘Y1’ for an Achievement Standard and the other is called ‘Y2’. For example, MX2012Y1 is the first assessment for AS91256 and MX2013Y2 is the second assessment opportunity. The standards offered in the MX2000 course, along with the learning material associated with them, are found on page 8 of this guide.

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getting started information

time commitment

A normal pace of learning is similar to what a student does at school. As a guide, expect to do at least five hours work per week. There is a lot of flexibility for you to design a course that will suit your needs at NCEA Level 2. Each resource indicates how many study hours it is likely to require to complete it. Before deciding on the pace of learning, read through this Course and assessment guide and ask yourself the following: • How much time can I set aside for study each week? • Will I be able to keep a steady pace of five hours of study each week? • What do I want to do next year? How many credits will I need to do this? • Will I be doing externally and internally assessed standards? • Do I intend to sit the external examination at the end of the year? • Do I need specific external or internal credits as a prerequisite for next year’s study or for work?

flexible pace of learning

If you have less than a year because you start later or need to finish earlier, you can decide the pace at which you work. You could still complete the whole course by devoting more time and effort to it.

choosing topics and standards

You may only wish to do some topics. For example, you may want to do only internal standards for this course. You should look carefully at the course outline and make your choices. It is important to consider how well this will meet your learning goals (such as gaining enough credits to achieve your NCEA Level 2, or meeting the entry requirements for your tertiary course or any future study). You should discuss your options with your learning advisor and/or your Mathematics and Statistics teacher.

cover sheets

The back cover of the booklet is called the cover sheet. You must fill it in and sign it before sending your work back to Te Kura. Your supervisor, if applicable, must also sign this sheet as part of our authenticity requirements. All students are encouraged to submit as much as possible of their work on line via the OTLE Dropbox. When work requires authentication, students will follow the instructions provided in OTLE.

It is important to contact your Mathematics and Statistics teacher if you have any queries about your work. It helps to have your ID number, booklet code (for example, MX2011) and the activity or question number when you contact your teacher, but it is not essential. © te aho o t e k ur a p o un a m u

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mx2000 course and assessment outline This table shows standards offered in the MX2000 course along with associated learning resources.

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standard

title

study material (code)

suggested time

AS91256 2 credits Internal

Apply co-ordinate geometry methods in solving problems

MX2011, MX2012

3–5 weeks

AS91257 4 credits Internal

Apply graphical methods in solving problems

MX2021, MX2022, MX2023

6–7 weeks

AS91258 2 credits Internal

Apply sequences and series in solving problems

MX2031, MX2032

3–5 weeks

AS91259 3 credits Internal

Apply trigonometric relationships in solving problems

MX2041, MX2042

3–5 weeks

AS91260 2 credits Internal

Apply network methods in solving problems

MX2051

3 weeks

AS91261 4 credits External

Apply algebraic methods in solving problems

MX2061, MX2062, MX2053

6–7 weeks

AS91262 5 credits External

Apply calculus methods in solving problems

MX2071, MX2072, MX2073

6–7 weeks

AS91263 3 credits Internal

Design a questionnaire

MX2081, MX2082

3–5 weeks

AS91264 4 credits Internal

Use statistical methods to make an inference

MX2091, MX2092

3–5 weeks

AS91265 3 credits Internal

Conduct an experiment to investigate a situation using statistical methods

MX2101

3 weeks

AS91266 2 credits Internal

Evaluate a statistically based report

MX2111

3 weeks

AS91267 4 credits External

Apply probability methods in solving problems

MX2121, MX2122

3–5 weeks

AS91268 2 credits Internal

Investigate a situation involving elements of chance using a simulation

MX2131, MX2132

3–5 weeks

AS91269 2 credits Internal

Apply systems of equations in solving problems

MX2022, MX2062

3–5 weeks

MX2000CA

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mx2000 course and assessment outline

conditions of assessment for some achievement standards

Assessment of the standards could include, but is not restricted to, a written test, an extended task or an investigation. In all cases authenticity needs to be assured. Internal assessment provides considerable flexibility in collection of evidence. Care is taken to give you opportunities to present your best evidence against the standard. Tasks will allow for the awarding of all levels of achievement. Holistic decisions may be used in awarding a grade by reference to the achievement criteria. Partial solutions can provide evidence.

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assessment information The National Qualifications Framework has two types of national standards: Achievement and Unit Standards. Credits from both Achievement Standards and Unit Standards count towards NCEA. Please refer to our Student Guide to National Certificates or Te Kura (www.tekura.school.nz) and NZQA websites (www.nzqa.govt.nz) for more information about National Certificates of Educational Achievement and assessment.

internal assessment

Some Achievement Standards are internally assessed. This means that your teacher sets and marks all assessments that count towards a standard.

external assessment

External assessment means that an external examiner marks your assessment. This may be through NZQA examinations at the end of the year or (for subjects such as Graphics, Technology and Art) by submitting a portfolio or project. You will be able to complete practice assessments and Te Kura examinations for external standards.

te kura practice examinations

You should complete the Te Kura practice examinations for any external standards with an end of year examination you have entered. It is important that you complete all practice external assessments and examinations. If for some reason, such as illness, you are unable to sit the examinations at the end of the year you will only be eligible for consideration for a derived grade (compassionate consideration) if you have completed the practice examinations.

resubmissions

If you have made mistakes in your standard assessment, your teacher may offer you one resubmission opportunity. This means you have made errors that you are capable of discovering and correcting by yourself. A resubmission allows you to improve your result.

further assessment opportunities for internal assessments

You will be able to complete a second assessment called a ‘further assessment opportunity’ to improve your results.

authenticity

Authenticity means students complete and submit work that is their own. When you submit work to Te Kura you sign an authentication declaration that the work you are submitting is your own and was done under the required assessment conditions. Where applicable, your supervisor signs this declaration to confirm this. When submitting work online via the OTLE Dropbox, if it requires authentication, students must follow the instructions provided in OTLE.

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assessment information

If for any unexpected reason you are not able to sit your end of year examination or to submit final work towards an external standard (portfolios or projects), you may be eligible for a derived grade. Please refer to the Student Guide to National Certificates and contact your learning advisor as soon as possible to find out more should you feel this is necessary.

appeals

You have the right to query an assessment result if you want further clarification or disagree with the result. If you are still not satisfied, you may appeal. Refer to the Student Guide to National Certificates for more information. You can also appeal any other decisions, procedures or policies about assessments. Contact your teacher or learning advisor if you wish to appeal. More information and a form that students can use to appeal is available on the Te Kura website in the Student toolkit area (www.tekura.school.nz and go to Student toolkit).

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my mathematics and statistics assessment record (mx2000) Use this sheet to keep track of your assessment results and progress through the course. Standard number

Assessment details

Credits

Examination Assessment

AS91256

Internal – Closed book assessment on coordinate geometry

AS91257

Internal – Closed book assessment on graphical methods

AS91258

Internal – Closed book assessment on sequences and series

AS91259

Internal – Open book assessment on trigonometry

AS91260

Internal – Closed book assessment on networking

AS91261

External – Apply algebraic methods in solving problems

November exam*

AS91262

External – Apply calculus methods in solving problems

November exam*

AS91263

Internal – Open book assessment on designing a questionnaire

AS91264

Internal – Open book assessment on using statistical methods to make an inference

AS91265

Internal – Open book assessment on conducting an experiment to investigate a situation using statistical methods

AS91266

Internal – Open book assessment on evaluating a statistically based report

AS91267

External – Apply probability methods in solving problems

AS91268

Internal – Open book assessment on investigating a situation involving elements of chance using a simulation

AS91269

Internal – Closed book assessment on applying systems of equations

November exam*

*NZQA examination results available in January.

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mx2000 suggested programme planner The following table outlines some suggested programmes of learning. Construction and infrastructure and Manufacturing and technology and The primary industries and Mathematics only

The service industries and Statistics only

General Mathematics and Statistics course

Working on sequences and series MX2031, MX2032

Working on sequences and series MX2031, MX2032

Working on sequences and series MX2031, MX2032

Working on coordinate geometry MX2011, MX2012

Working on graphing MX2021, MX2022, MX2023

Working on coordinate geometry MX2011, MX2012

Term 1

Working on networks MX2051

Working on networks MX2051

Term 2 Working on algebra and graphing MX2021, MX2022, MX2023, MX2061, MX2062, MX2063

Working on algebra and graphing MX2021, MX2022, MX2023, MS2061, MX2062, MX2063

Working on statistics MX2081, MX2082

Working on calculus MX2071, MX2072, MX2073

Working on statistics MX2101, MX2111

Working on calculus MX2071, MX2072, MX2073

Working on trigonometry MX2041, MX2042

Working on probability MX2121, MX2122

Working on statistics MX2091, MX2092

Working on probability MX2131, MX2132

Working on statistics MX2101, MX2111

Optional interest topics

Working on probability MX2131, MX2132

Working on statistics MX2091, MX2092

Term 3

Term 4

Optional interest topics

Note: These scenarios are only a guide to give you examples of how a course could be put together to address your requirements/needs for learning Mathematics and Statistics at NCEA Level 2. It is based on a return of at least one booklet every two weeks. ÂŠ te aho o t e k ur a p o un a m u

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formulae You may refer to this list of mathematical formulae while doing this booklet.

algebra Quadratics If ax2 + bx + c = 0 then x =

-b ±

b2 – 4ac 2a

Exponents am x an = am+n (am)n = amn a0 = 1 (a ≠ 0) am ÷ an = am–n (ab)m = ambm Logarithms If y = bx then logby = x logbxn = n logbx logax logbx + logby = logbxy logbx = logab x logbx – logby = logb y Series Arithmetic Geometric a + (a + d) + (a + 2d) + (a + 3d) + ...

a + ar + ar2 + ar3 + ...

tn = a + (n – 1)d tn = arn–1

a(1 – rn) n [ 2a + (n – 1)d ] Sn = r≠1 1–r 2 a n (t + t ) S∞ = 1 – r , -1 < r < 1 Sn = 2 1 n r n A = P(1 + ) 100

Sn =

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formulae

coordinate geometry Distance Midpoint d =

x1 + x2 y1 + y2 , (x2 – x1)2 + (y2 – y1)2 2 2

Gradient y –y m = x2 – x1 2 1 Lines Perpendicular y = mx + c Two lines with gradients m1 and m2 y – y1 = m(x – x1) are perpendicular if m1 × m2 = –1

trigonometry Triangle a b c 1 = = Area = bcsin A sin B sin C sin A 2 a2 = b2 + c2 – 2bccos A

calculus Differentiation y = f(x)

dy limit f(x + h) – f(x) or f '(x) f  '(x) = h → 0 h dx

axn anx n-1

Integration f '(x) f(x)

axn (n ≠ -1)

a n+1 n + 1 x  + c

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cover sheet â&#x20AC;&#x201C; mx2000ca students â&#x20AC;&#x201C; place student address label below or write in your details. Full Name ID No. Address (If changed)

authentication statement I certify that the assessment work is the original work of the student named above.

Signed

Signed

(Student)

(Supervisor)

for school use only assessment

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MX2000CA 2015

Maths Course and assessment guide