tuanaki calculus - tekura.school.nz · 2 getting started 3 mx3000 course outline 4 ncea level 3...

tuanaki

calculus

2015/2

MX3000CAcourse and assessment guide

ncea level 3

© te aho o te kura pounamu

calculus (mx3000) teacher contact details

Cover image: Pencil and graph, © iStock 11542652

Copyright © 2013 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.

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 Calculus (MX3000) 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 futher information about courses at this level, please refer to Student Guide to Years 11–13 and the Student Guide to National Certificates, both are available on the school website (www.tekura.school.nz).

MX3000CA© te aho o te kura pounamu 1

contents

1 Welcome to MX3000

2 Getting started

3 MX3000 course outline

4 NCEA level 3 Mathematics conditions of assessment

5 Assessment summary

6 Assessment information

7 Diagnostic information

8 Year planner: NCEA level 3 Mathematics

9 My Calculus assessment record (MX3000)

MX3000CA © te aho o te kura pounamu2

welcome to mx30001

Welcome to the Level 3 Calculus (MX3000) course offered by Te Aho o Te Kura Pounamu.

overview of mx3000Mathematics 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. These two disciplines are related but different ways of thinking and of solving problems. Both equip students with effective means for investigating, interpreting, explaining and making sense of the world in which they live.

Mathematicians and statisticians use symbols, graphs and diagrams to help them find and communicate patterns and relationships, and they create models to represent both real-life and hypothetical situations. These situations are drawn from a wide range of social, cultural, scientific, technological, health, environmental and economic contexts.

This course is designed to prepare the student for the study of mathematics, pure and applied sciences, or engineering at a tertiary level. The focus of this NCEA Level 3 Mathematics course is on calculus, with students encountering algebra and trigonometry topics, as well as the manipulation of real and complex numbers, geometry and conic sections. Students can select from the following Achievement Standards to a maximum total of 24 credits.

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 3 Calculus. At least three of these credits must be from externally assessed standards and three from internally assessed standards.


getting started2

how this course is deliveredMX3000 is a blended course with some print-based material, that can be downloaded from the online teaching and learning environment (OTLE), and an interactive online component in OTLE.

You will receive an email explaining how to log in to OTLE. This email includes a link to set your password if you have not logged into the OTLE before.

You can access OTLE by clicking on www.tekura.school.nz/login. It is recommended that you bookmark this site in your browser. This will take you to a page with links to your courses.

Your username and initial password is your Te Kura student ID number. You will be asked to set a new password when you first log in. After that, if you need to reset your password you can click on the ‘Forgot password’ link on the login page.

If you have difficulties logging in, please email: [email protected]

organising your studyPlan 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 course 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 received your initial work. 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).

resources you need • pens and pencils • eraser • your own paper to work on – squared or quad paper is recommended • a scientific, graphics or CAS calculator • a computer with mathematics software is recommended but not essential.

choosing topics and standardsNZQA advises that a one-year course should lead to 18–20 credits. You may only wish to study 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 3, or whether you are working towards course endorsement, or meeting the entry requirements for your tertiary course or any future study).

4 © te aho o te kura pounamuMX3000CA

getting started

To be awarded University Entrance you must have: • NCEA Level 3 • Three subjects – at Level 3 or above, made up of:

– 14 credits each, in three approved subjects • Literacy – 10 credits at Level 2 or above, made up of:

– 5 credits in reading – 5 credits in writing

• Numeracy – 10 credits at Level 1 or above made up of: – achievement standards – specified achievement standards available through a range of

subjects, or – unit standards – package of three numeracy unit standards (26623, 26626, 26627 – all

three required).

To see the list of approved subjects refer to: www.nzqa.govt.nz/qualifications-standards/awards/university-entrance/approved-subjects/

To see the list of standards which count towards University Entrance literacy refer to: www.nzqa.govt.nz/qualifications-standards/awards/university-entrance/literacy-requirements-for-university-entrance-from-2014/

To see the list of standards which count towards University Entrance numeracy refer to: www.nzqa.govt.nz/qualifications-standards/qualifications/ncea/subjects/literacy-and-numeracy/level-1-requirements/lit-num-subjects/

You should discuss your options with your learning advisor and/or your teacher.

self-assessmentMany 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 important as it gives you instant feedback on how well you understand the ideas, concepts or information that have been covered.

assessmentYou are required to send in your self-marked and teacher-assessed work. Your teacher will return your work with feedback and advice in preparation for NCEA internal and/or external assessments.

The detailed criteria for Achievement Standards will be given in the relevant resources. 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).

External assessment preparation includes:

• teacher-assessed activities • Te Kura practice examinations.

5© te aho o te kura pounamu MX3000CA

getting started

time commitmentThere are eight topics and 17 booklets in this course. Each booklet indicates how many study hours it is likely to require. For example, booklet MX3011 may take approximately 10 hours of work to complete at the normal pace, representing about two weeks of work at 5 hours per week. If you are to achieve at Excellence level, it is likely that you will have to study substantially more than the suggested guideline.

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 attempting both externally and internally assessed standards? • Will I be able to keep a steady pace of five hours of study each week? • Do I intend to sit the external examination at the end of the year? • Do I need specific external or internal credits for next year’s study or work?

normal pace of learningAs a guide, expect to do at least 5 hours work per week in this subject. This means completing five to six booklets or two topics each term so that you complete the course before the external examination at the end of the school year.

flexible pace of learningIf 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. Your teacher can ensure that you receive the resources you need in time to do this.

cover sheetsThe back cover of the booklet becomes the cover sheet for your work. Fill it in, sign it and attach it to the front of your work before sending back to Te Kura. If applicable, your supervisor also signs the cover sheet as part of our authenticity requirements.

All students are encouraged to submit as much of their work as possible online via the OTLE Dropbox. When work requires authentication, students will follow the instructions provided in OTLE.

te kura codesYour course code is: MX3000. MX is the code for Calculus and 3 refers to Level 3.

‘MX’ refers to a resource that covers a particular learning topic in the MX3000 course. ‘MX3012Y1’ refers to the first assessment for an Achievement Standard (91573) for MX3000. ‘AS’ is the code for Achievement Standard.

queries about your workIt is important to contact your teacher if you have any queries about your work. It helps to have your ID number, booklet code (for example, MX3000) and the activity or question number when you contact your teacher, but it is not essential.


getting started

about youCircle any of the following that you think are appropriate. Feel free to add your own comments.

I have enrolled in this programme because:

I intend to go on with maths study. I enjoy doing maths.

I am studying this because I have been told to. I am doing maths for interest.

It will be useful for future training/exams/jobs. I like solving problems.

I think mathematics is a valuable life skill. I like meeting the challenge of new topics.

Other:

Your possible career choice?

what maths have you studied before? • Write down the number of years you have studied maths at secondary-school level

before now.

• What topics in mathematics at senior level do you remember doing before?

• Write down any past achievements or results you have gained in maths.

If your answers to the questions later in this booklet show that you might benefit from working at a lower level for a short while, would you like to:

first try the work at this level and see how it goes?

or

have a chance to revise, gain confidence and build up your skills at the lower level first?


getting started

personal situation informationIs there anything you would like your teacher to know about your personal situation that could help us plan your programme?

How can we be in contact with you?

Telephone (H) (W)

Mobile Fax

Email

computer informationDo you have access to a computer? yes no

Do you have internet access on a computer? yes no

Where is this computer? At school in the computer room

At school in the classroom

At home

Other

Are you interested in accessing online maths resources? yes no

graphics calculatorDo you have a graphics calculator? yes no

If yes, is it a Casio model? yes no

Your teacher will send you some relevant help appropriate to Mathematics with calculus if you have the calculator named above. Otherwise, your graphics calculator handbook will help you.


getting started

your situationHighlight or tick the situation that seems closest to yours. You may want to adjust the description to meet your situation more closely.

I have a lot of Level 2 credits and I’m doing calculus and stats this year. I want to gain all the Level 3 internally assessed and externally assessed standards. Entry into the course I want to do at uni is very competitive, so I’m aiming for Merit or Excellence in as many achievement standards as possible.

I need a good calculus background to do sciences or engineering. I’ll be doing all the topics in the calculus course and will probably sit some externals at the end of the year.

I’m aiming for primary teaching – maths at this level will be very useful but there are no specific topics needed. I’m going to start with differentiation then do the algebra applied from the stats course. By then, hopefully I’ll have the 14 credits for university entrance without having to sit an exam. I might need to revise some of the Level 2 work and I might even have some time to do some stats or geometry later in the year.


getting started

I’ve always been pretty good at maths and I decided to do calculus rather than statistics. I’m going to do the internal achievement standard in trigonometry and then decide what topics I’ll do the externals for. I’ll contact the university when I’ve made up my mind on what I want to do at uni. There are probably a few standards I could aim for merit or excellence in. That would look good on my record.

Maths hasn’t really been my strong point so I’m going to wait for my teacher’s recommendation when he or she has seen my algebra results in this booklet. I really need to get the 14 credits for university entrance.

I’m doing maths for interest and certainly don’t want to sit an exam. I want to study a mixture of levels and include the topics I’m interested in. I’ll take whatever credits come my way – they could be useful later.


getting started

Level 3

AS91573 3.1Apply the geometry of conic sections in solving problems

3 credits Internal

AS91577 3.5Apply the algebra of complex numbers in solving problems

5 credits External

AS91574 3.2Apply linear programming methods in solving problems

3 credits Internal

AS91578 3.6Apply differentiation methods in solving problems

6 credits External

AS91575 3.3Apply trigonometric methods in solving problems

4 credits Internal

AS91579 3.7Apply integration methods in solving problems

6 credits External

AS91576 3.4Use critical path analysis in solving problems

2 credits Internal

AS91587 3.15Apply systems of simultaneous equations in solving problems

3 credits Internal

Conic sections Linear Prog Trigonometry Critical path Algebra Calculus Linear Systems 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.15 INT INT INT INT EXT EXT EXT INT

MX3021MX3011

MX3012

MX3031

MX3032

MX3041

MX3042

course resources


getting started

Level 3

AS91573 3.1Apply the geometry of conic sections in solving problems

3 credits Internal

AS91577 3.5Apply the algebra of complex numbers in solving problems

5 credits External

AS91574 3.2Apply linear programming methods in solving problems

3 credits Internal

AS91578 3.6Apply differentiation methods in solving problems

6 credits External

AS91575 3.3Apply trigonometric methods in solving problems

4 credits Internal

AS91579 3.7Apply integration methods in solving problems

6 credits External

AS91576 3.4Use critical path analysis in solving problems

2 credits Internal

AS91587 3.15Apply systems of simultaneous equations in solving problems

3 credits Internal

Conic sections Linear Prog Trigonometry Critical path Algebra Calculus Linear Systems 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.15 INT INT INT INT EXT EXT EXT INT

MX3061

MX3062

MX3063

MX3051

MX3052

MX3053

MX3071

MX3072

MX3073

MX3151


mx3000 course outline3

course item/ booklet

title learning outcomes standard

MX3011 Conic sections Apply the geometry of conic sections in solving problems

Working towards AS91573

MX3012 Solving problems using conic sections

Apply the geometry of conic sections in solving problems


MX3021 Applying linear programme methods in solving problems 1

Apply linear programming methods in solving problems


MX3031 Developing trigonometric skills in solving problems

Apply trigonometric methods in solving problems


MX3032 Applications of trigonometry in solving problems



MX3041 Critical path analysis 1 Use critical path analysis in solving problems


MX3042 Critical path analysis 2 Use critical path analysis in solving problems


MX3051 Developing algebraic skills Apply the algebra of complex numbers in solving problems



mx3000 course outline

MX3052 Solving equations Apply the algebra of complex numbers in solving problems


MX3053 Complex numbers Apply the algebra of complex numbers in solving problems


MX3061 Learning about differentiation Apply differentiation methods in solving problems


MX3062 Developing skills in differentiation Apply differentiation methods in solving problems


MX3063 Applying differentiation methods in solving problems

Apply differentiation methods in solving problems


MX3071 Integration – the process Apply integration methods in solving problems


MX3072 Applying integration methods in solving problems

Apply integration methods in solving problems


MX3073 Modelling using differential equations



MX3151 Linear systems 1 Apply systems of simultaneous equations in solving problems



4 ncea level 3 mathematics conditions of assessment

general information

Subject Reference Mathematics and Statistics

Domain Algebra, Trigonometry, Geometry, Statistics, Probability

Level 3

for all standardsAssessment tasks are designed so that each task gives students an opportunity to provide evidence for all grades. There are not separate tasks for each grade. Holistic decisions will be used in the awarding of a grade by reference to the achievement criteria in the standard.

Many of the standard titles use the wording ‘… in solving problems’. It is important to note that acceptable evidence could come from a partially successful solution to a problem. Communication of the process of solving a problem may yield the required evidence of thinking, even though a correct final solution to the problem is not obtained.

Internal assessment provides considerable flexibility in the collection of evidence. Care must be taken to allow students opportunities to present their best evidence against the standard that is free from unnecessary constraints. Collection of evidence for this standard could include, but is not restricted to, an extended task, an investigation, or a more formal activity. Access to appropriate technology is expected.

Authenticity will be assured. For example, for an investigation carried out over several sessions, this could include teacher observations or the use of milestones such as meetings with students, or journal entries of progress.Source: www.nzqa.govt.nz

specific information for individual internal achievement standards

In the teaching and learning of tangents and normals, note should be taken that implicit differentiation has been removed from the assessment of AS 3.6. This does not preclude teaching this in a programme of teaching and learning.

Achievement Standard Number 91573 Mathematics and Statistics 3.1

Title Apply the geometry of conic sections in solving problems

Number of Credits 3


assessment summary5

credits offered: 32 ncea level 3 calculus (mx3000)

standard number standard title study material/ resources

further assessment opportunity

AS915733.13 credits

Apply the geometry of conic sections in solving problems

MX3011MX3012

MX3012Y1MX3012Y2

Yes

AS915743.23 credits

Apply linear programming methods in solving problems

MX3021

MX3021Y1MX3021Y2

Yes

AS915753.34 credits


MX3031MX3032

MX3032Y1MX3032Y2

Yes

AS915763.42 credits

Use critical path analysis in solving problems

MX3041MX3042

MX3042Y1MX3042Y2

Yes

AS915773.55 credits

Apply the algebra of complex numbers in solving problems

MX3051MX3052MX3053

No

AS915783.66 credits

Apply differentiation methods in solving problems

MX3061MX3062MX3063

No

AS915793.76 credits


MX3071MX3072MX3073

No

AS915873.153 credits

Apply systems of simultaneous equations in solving problems

MX3151

MX3151Y1MX3151Y2

Yes


assessment information6

standardsMX3000 offers credits from Achievement Standards which count towards NCEA Level 3.

Please refer to our Student Guide to National Certificates or Te Kura and New Zealand Qualifications Authority (NZQA) websites for more information about National Certificates of Educational Achievement and assessment:• www.nzqa.govt.nz• www.tekura.school.nz

internal assessmentMX3000 offers six Achievement Standards that are internally assessed. This means that your teacher sets and marks all assessments that count towards credits gained for these standards.

The assessment opportunity for an Achievement Standard is coded ‘Y1’ and if there is a second assessment opportunity offered, this is coded ‘Y2’. For example, MX3012Y1 is the first assessment for AS91573 and MX3012Y2 is the second assessment opportunity.

external assessmentExternal assessment means that an external examiner marks your assessment work. This may be through the NZQA examinations at the end of the year. You will be able to complete Te Kura practice examinations for external standards.

te kura practice examinationsYou 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 NZQA 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 Te Kura practice examinations.

resubmissions for internal assessmentsIf you have made mistakes in your standard assessment activity, 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 correct your errors and improve your result.

further assessment opportunities for internal assessmentsFor some standards, you may be able to complete a second assessment called a ‘further assessment opportunity’ to improve your results. These standards are indicated in the assessment summary. You should take this opportunity where it is available.


assessment information

authenticityAuthenticity means that 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 work and was done under the required assessment conditions. Where applicable, your supervisor signs to confirm this declaration.

When submitting work online via the OTLE Dropbox, if it requires authentication, students must follow the instructions provided in OTLE.

derived grades (compassionate consideration)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 teacher or learning advisor as soon as possible to find out more should you feel this is necessary.

appealsYou 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. Further 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).

new zealand scholarshipNew Zealand Scholarship examinations are designed to extend very high achieving Level 3 NCEA students. Students who wish to enter for the NZ Scholarship examinations must discuss this option with their Te Kura subject teacher. The list of subjects available for NZ Scholarship can be found at: www.nzqa.govt.nz/qualifications-standards/awards/scholarship/scholarship-subjects/


diagnostic information7

Fill in your name and ID number.

Student Name: ________________________________

Student ID: ___________________________________

some calculus questionsNow it’s time to get into some calculus! To assist the teachers we need to find out about where you are with your knowledge.

this is what you doWork on your own to answer the following questions.

Answer all the questions you can. It doesn’t matter how little or how much you can do.

If you get someone else to help you, it will mislead your teacher, who chooses the learning materials especially for you.

Allow yourself plenty of time.

Show your working in the spaces provided. You may use a calculator – scientific, graphics or CAS enabled.

When you have done all you can, complete the cover sheet and send this diagnostic booklet to your Mathematics and Statistics teacher, then continue with the resources your teacher has dispatched to you.

1. Expand the brackets and simplify where possible:

a. (x − 7)(x + 3)

b. (2x – 5)2

c. (a − b)(a + b)

2. Factorise:

a. x2 + 9x + 20

b. 2x2 + 9x – 5

c. 4y2 – 1


diagnostic information

3. Simplify:

a. 5x2

15x2y

b. m2 + 4mm

c. y2 – 4y2 + 3y – 10

d. (x4)3 + (x2)–5

e. (9m4)– 1

2

f. 4x –

3x

g. 4x + 4

+

2x + 3

4. Rearrange C = 59 (F – 32) to make F the subject of the formula.

5. Find the point of intersection of the lines y = –x + 4 and y = 2x − 5.

6. Write down the equation of the parabola shown in the diagram:

3

2

1

0

–1

–2

–3

–4

–5(2, –4)

0 1 2 3 4 5 6x

y


diagnostic information

7. Solve the following equations: a. x2 – 6x = 0

b. x2 + x = 6

c. 3x = 50

d. log10 x = 3.2

e. sin x = 0.866, 0 ≤ x ≤ 360°

f. 3cos (2x) = 1, 0 ≤ x ≤ 180°

8. Differentiate the functions given below, that is, find dydx :

a. y = x2 – 5x + 3

b. y = 7x4

what to do nowFill in the cover sheet on the back of this booklet and send this booklet to your Mathematics teacher.


8 year planner: ncea level 3 mathematics

Here is a suggested one-year planner. The suggestions are based on the assumption that you are going to be enrolled for a full-year course at the beginning of the school year, study all the content and attempt all the standards offered.

term suggested plan Time (approximate)

1

Read MX3000CA, complete your course planner and consult your teacher.

MX3051

MX3061 MX3062MX3063

MX3031MX3032MX3032Y1

And/or:MX3021MX3021Y1

And/or:MX3151MX3151Y1

1 day

1 week

6 weeks

4 weeks

2–3 weeks

2–3 weeks

2

MX3052MX3053

And/or:MX3041MX3042MX3042Y1

4 weeks

4 weeks

3

MX3071MX3072MX3073

MX3011MX3012MX3012Y1

Revision and practice exam

6–8 weeks

4 weeks

4

Complete all unfinished booklets and send in any resubmissions.

Revision for externals.


my calculus assessment record (mx3000)

9

standard number assessment details exam/assessment due date

grade awarded

credits achieved

AS91573

Calculus 3.1

3 credits

Internal

MX3012Y1MX3012Y2

AS91574

Calculus 3.2

3 credits

Internal

MX3021Y1MX3021Y2

AS91575

Calculus 3.3

4 credits

Internal

MX3032Y1MX3032Y2

AS91576

Calculus 3.4

2 credits

Internal

MX3042Y1MX3042Y2

AS91577

Calculus 3.5

5 credits

External – NZQA exam

Te Kura practice exam

November exam*

AS91578

Calculus 3.6

6 credits



November exam*


my mathematics assessment record (mx3000)

AS91579

Calculus 3.7

6 credits



November exam*

AS91587

Calculus 3.15

3 credits

Internal

MX3151Y1MX3151Y2

* NZQA examination results are available in January.

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

for school use only

assessment

www.tekura.school.nz

cover sheet – mx3000ca

students – place student address label below or write in your details.

Full Name

ID No.

Address (If changed)

Signed(Student)

Signed(Supervisor)

tuanaki calculus - tekura.school.nz · 2 getting started 3 mx3000 course outline 4 ncea level 3...

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