mathematics with calculus

Transcription

1 te pāngarau me te taunaki mathematics with calculus mx301 planning your programme ncea level /1

2 Copyright 2011 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 aho o te kura pounamu

3 kia ora! welcome to mathematics with calculus what s this booklet all about? It contains questions for you to complete about: your aims for studying the topics you might choose to study what mathematics you kw already. what will your programme be? It will start with the first booklet, MX701 Algebra revision, and then the first pack will be MXDFP Differentiation. Other topics will depend on what your answers in this booklet tell us about: what you want to do what you already kw what is the other booklet mx300ca for? You should refer to this whenever you need to. It has: information about the learning and assessment in mathematics with calculus places for you to record your progress throughout your programme. what do i do w? Work your way through this booklet and check the information in MX300CA, if it helps. When you have done everything you can, make sure your name and ID is on the cover sheet and send this booklet to Te Kura. Keep the handbook MX300CA (Programme and assessment guide) at home so that you can refer to it whenever you need to. You might want to take the time to go through it in more detail before you begin the work in the first booklet, MX701. te aho o te kura pounamu MX301 1

4 about you Circle 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 am studying this because I have been told to. It will be useful for future training/exams/jobs. I think mathematics is a valuable life skill. I enjoy doing maths. I am doing maths for interest. I like solving problems. 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 w. What topics in mathematics at senior level do you remember doing before? Write down any past achievements or results you have gained in maths. (There is space to list level 2 or 3 standards later.) 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? 2 MX301 te aho o te kura pounamu

5 about you personal situation information Is there anything you would like your teacher to kw about your personal situation that could help us plan your programme? How can we be in contact with you? Telephone (H) (W) Mobile Fax computer information Do you have access to a computer? Do you have internet access on a computer? 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? graphics calculator Do you have a graphics calculator? If, is it a Casio model? 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. te aho o te kura pounamu MX301 3

6 about you your individual programme your goals qualifications Throughout your programme, you will have many opportunities to be assessed and gain credits towards an NZQA record of learning; perhaps a national certificate like NCEA or university entrance. Even if you do t want to register these credits with NZQA at this stage, they will remain on your Correspondence School record so that you can use them in future years. If you want a report showing them at any stage you just need to ask your teacher. If you want to kw more about this, look in the Programme and assessment guide, MX300CA, that is enclosed with this booklet MX301. Please give us some idea if you have specific goals in mind at the moment. Tick or add as many as you wish. Do you want to gain: 14 or more credits in mathematics with calculus for university entrance? 14 or more credits in a combined mathematics with calculus and statistics and modelling programme for university entrance? National Certificate of Educational Achievement, Level 3 (NCEA Level 3)? This is the level of most of the learning in this programme. Other: unit standards and internally assessed achievement standards Without sitting an external examination, you can gain credits from Te Kura for unit standards at levels 3 and 4. You can also gain credits from the internally assessed achievement standard in trigometry. There are also three internally assessed achievement standards in the statistics and modelling course at level 3, if you are considering a combined programme. The algebra applied topic is particularly appropriate for students studying mathematics with calculus. You can see all the unit and achievement standards listed in the Programme and assessment guide, MX300CA. Are there any particular unit standards or internally assessed achievement standards you want or need? Write them here. 4 MX301 te aho o te kura pounamu

7 about you examination-assessed achievement standards The flexibility of this programme makes it possible to gain up to 24 credits without having to sit an external examination. You will complete assessment tasks on all the work that you do. In most topics, you can gain level 3 or level 4 credits from internally assessed standards. However, if you are considering going on in mathematics at tertiary level, you are advised to sit national examinations for one or more externally assessed achievement standards to gain the award of achieved with merit or achieved with excellence. You might also want to gain a good ʻgrade averageʼ on your NCEA results slip. The grade average is calculated across those internally assessed and externally assessed achievement standards that you choose to enter. If a grade average is important to you, you need to be careful about your choice and choose only those for which you have a good chance of gaining a high grade. You can find out more about the internal and external standards in this programme in the appropriate sections of the Programme and assessment guide. If you think you might be interested in sitting for one or more external achievement standards, indicate here. I am interested in sitting for one or more external achievement standards. Add your reasons here if you wish. You will t need to make a final decision until about July. If you do decide to sit for one or more external achievement standards, you will be sent a Te Kura trial exam (or exams, if you are doing a programme combined with statistics and modelling) in August. This will give you a better idea of the kinds of questions you will be asked in the national examinations for external achievement standards in November. In those national examinations, you will get an exam booklet (or two booklets, if you have entered for statistics and modelling externals as well) that includes only those external achievement standards that you have entered for. te aho o te kura pounamu MX301 5

8 about you previously gained standards Do you think you have gained any unit or achievement standards before? Write down the numbers of any level 2 or 3 unit standards or achievement standards that you think you have already gained (if you kw them). Indicate beside any achievement standard whether you achieved merit (M) or excellence (E). Unit standards Achievement standards Achieved, merit or excellence? your general goals Mathematical learning resources can be put together to form an individual programme designed to meet your needs and goals. If you have any general ideas about what you want to aim for, write them here. For example, further study at school, polytechnic or university; jobs; further training; a specific career path or area of study; keeping up to date... 6 MX301 te aho o te kura pounamu

9 about you your situation Highlight 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 m aiming for primary teaching maths at this level will be very useful but there are 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. 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. 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 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 trigometry 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. te aho o te kura pounamu MX301 7

10 about you your choice of topics You will complete the diagstic MX301, the booklet MX701 Developing algebra skills and the differentiation topic first. Then the choice of further topics is yours. Sections of the Programme and assessment guide (MX300CA) will be useful in making that choice, particularly the page on the internally assessed standards. It lists the number of credits you could gain for each topic in this programme and in the statistics programme. Ather page of MX300CA tells you about the external standards for calculus. Some of the pathways suggested on the previous page of this booklet might also give you further ideas. You might want to seek advice from your teacher just write any tes clearly on this page with any other ideas about choices you might have. You may be interested in one or more of the topics from the statistics programme list them in the chart below. When you have looked up any information you need, try filling in the chart below. Beside each topic pack, tick if you want to do it and write the order you want to do it in; for example 1, 2, 3, and so on. It can be adjusted later if you change your mind just let your teacher kw, or do the work in a different order if you have already been sent the topic pack(s) you want. Topic packs Differentiation Trigometry Complex numbers Integration Conic sections Statistics topic (pick any youʼre interested in) Algebra Time series Statistical investigation Probability Probability distribution Sampling and confidence Tick to choose and number for order (All students must do MX701 and this one first) 1 Approx hours 50 hours 30 hours 20 hours 60 hours 30 hours 10 to 40 hours 15 hours up to 20 hours 30 hours 15 hours 15 hours 8 MX301 te aho o te kura pounamu

11 about you the algebra questions purpose of these questions As a learning experience to get you back into thinking and using algebra. As a refresher sometimes it needs just a small reminder to start the ideas coming back. To give you an opportunity to show what you already kw. There is intention to score your results your teacher is only interested in how your background might affect what you ve chosen to do. Maybe you will be able to skip some things or maybe you will need some revision work. what you do Work on your own for all the questions. If you do get someone to help you, it will mislead your teacher about whether you can cope with the programme you have chosen. Answer all the questions you can. It doesn t matter how little or how much you get perfect give it a go! Keep going. Give everything a try. Allow yourself plenty of time. You don t need to do everything in one sitting. Show your working in the spaces provided. when you have done all you can Complete the cover sheet and send this booklet to your teacher. Go on with MX701 to further revise and build on your algebra skills, and then start the differentiation pack. Go for it! Kia kaha. te aho o te kura pounamu MX301 9

12 algebra diagstic questions Do as much as you can by yourself. Show your working to help your teacher see whether you are on the right track, even if your final answer is t correct. Write in simplest form. 1. 4x 2 + 5xy 3x 2 + 7y (m 2) 2(m 1) Remove the brackets and simplify where possible. 3. (2a 3)(4a 5) 4. (2x 5) 2 Simplify. 5. (x 4 ) 3 + (x 2 ) (2x ) 4 3x 2 Rename without negative indices. 7. a 3 2 Factorise. 8. 5a a x 2 10 MX301 te aho o te kura pounamu

13 algebra diagstic questions Simplify. 10. m 2 + 4m m x x x 2 x 6 3x 2 7x 6 5y y x x Make F the subject of the formula C = 5 (F 32) 9 Well done, and thank you for taking the time to answer these questions. When you have finished answering all you can, fill in the cover sheet at the back of this booklet and send it in to your teacher w. Go on with booklet MX701 Developing algebra skills. te aho o te kura pounamu MX301 11

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15 evaluation mx301 your teacher will fill this in Thank you for providing the information to help plan your programme in mathematics with calculus. You asked for the following topics in the order shown. Your teacher may have commented or suggested changes. Let your teacher kw if you want to make any changes at any time in the future. Topic packs Choice Teacher comment on your choice: and order Calculus Differentiation Trigometry Complex numbers Integration Conic sections Statistics Algebra applied Time series Stats investigation Probability Probability distributions Sampling and confidence Your answers to the algebra questions indicate that you: should cope with this plan if you work really hard and revise some earlier work. should cope with this plan reasonably well. should cope with this plan very well. will need some revision at an earlier level. Any other comments: external achievement standards You have stated that you are interested / t interested in sitting for one or more of these. Please let your teacher kw if this changes. Best wishes for your future learning and achievement. what you should do when you get this back Find your Programme and assessment guide (MX300CA) and enter your plan on the Your progress topics and booklets completed page. Keep it available to track your progress and any standards you gain on the way. te aho o te kura pounamu

16 cover sheet mx301 students 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 (Student) Signed (Supervisor) for te kura school use only assessment