BASIC MATHEMATICS SYLLABUS FOR FORM I--IV 2010. BY. MWL. JAPHET MASATU.

BASIC  MATHEMATICS SYLLABUS FOR         
                      FORM  I---IV

                             2010

                       FORM  ONE 

 TOPICS/ SUB--TOPICS.
 {1}.NUMBERS {I}.
---- Base ten  Numeration.
---Natural  and   Whole  Numbers.
---Operations  with  Whole  Numbers.
---Factors   and   Multiples  Of  Numbers.
----Integers.  

{2}.FRACTIONS.
---Proper, Improper  and  Mixed  Numbers.
----Comparison   of   Fractions.
----Operations   on   Fractions.


{3}.DECIMALS   AND   PERCENTAGES.
----Decimals.
----Operations  on   Decimals.
----Percentages.

{4}.UNITS.
----Units  Of  Length.
----Units  Of  Mass.
----Units  Of    Time. 
----Units  of  Capacity.  

{5}.APPROXIMATIONS.
----Rounding  off  Numbers.
----Significant  Figures.
---Approximations  in  Calclations.

{6}.GEOMETRY.
----Points  and  Lines.
---Angles. 
---Constructions. 
---Polygons   and  Regions. 
---Circles.

{7}. ALGEBRA {I}.
----Algebraic  Operations.
----Equations  in  One  Unknown.
----Equations  in  Two  Unknowns.
---Inequalities

{8}.NUMBERS{II}.
---Rational  Numbers.
--- Irrational  Numbers.
---Real  Numbers.

{9}.RATIO, PROFIT  AND  LOSS.
---Ratio.
---Profit and   Loss.
---Simple  Interest. 

{10}. COORDINATE  GEOMETRY.
---Coordinates  of  a   point.
---Gradient{Slope } of  a Line.
---Equation  of  a  Line.
---Graphs of  Linear  Equations.
---Simultaneous  Equations. 

{11}. PERIMETERS  AND   AREAS.
--- Perimeters  of  Triangles  and   Quadrilaterals.
---Circumference  of  a  Circle.
---Areas  of  rectangles  and  triangles.
---Areas   of  trapezium   and  parallelogram.
---Area   Of  a  Circle.

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FORM    TWO.
TOPICS/ SUB--TOPICS.

{I}.EXPONENTS  AND   RADICALS.  
---Exponents.
---Radicals.
---Transposition  of  Formula.

{2}.ALGEBRA {II}.
--- Binary  Operations.
---Brackets in  Computation.
---Quadratic  Expressions.
---Factorization.

{3}.QUADRATIC  EQUTIONS.
---Solving  Equations.
---General  Solution  of  a   Quadratic   Equations.

{4}.LOGARITHMS.
--- Standard  Form.
---Laws   of  Logarithms.
---Tables  of  Logarithms.

{5}.CONGRUENCE.
--- Congruence  of  Triangles.

{6}.SIMILARITY.
--- Similar  Figures.

{7}.GEOMETRIACAL   TRANSAFORMATIONS.
----Reflection.
---Rotation.
---Transalation.
---Enlargement.
---Combined  Transformations. 

{8}.PYTHAGORAS  THEOREM.
--- Proof  Of  Pythagoras  Theorem.
---Application  Of  Pythagoras  Theorem.

{9}.TRIGONOMETRY.
--- Trigonometical  Ratios.
---Trigonometric Ratios  Of  Special  Angles.
---Trigonometrical  Tables.
---Angles  Of  Elevation  and  Depression.

{10}. SETS. 
---Description  Of  a  Set.
---Types  Of   Sets.
---Subsets.
---Operations  with  Sets.
---Venn  Diagrams. 

{11}.STATISTICS.{I}.
---Pictograms.
---Bar  Charts.
---Line  Graphs.
---Pie  Chart.
---Frequency  Distribution  Tables.
---Frequency  Polygons.
---Histograms.
--Cumulative  Frequency  Curve.

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FORM  THREE.
TOPICS/ SUB--TOPICS.
{1}.RELATIONS 
--- Relations.
---Graph  Of    a   Relation.
---Domain  and Range  Of  a  Relation.
---Inverse  Of  a  Relation. 

{2}.FUNCTIONS.
---Representation  Of  a   Function.
---Domain and Range  Of  a   Function.
---Graphing  Functions.
---Inverse  Of   a  Function.

{3}.STATISTICS.
---Mean.
---Median.
---Mode.

{4}.RATES  AND   VARIATIONS.
---Rates.
---Variations.

{5}.SEQUENCES  AND  SERIES.
---Sequences.
---Series.
---Compound  Interest.

{6}. CIRCLES.
---Definiton   Of   Terms.
---Central   Angle.
---Angle   Properties.
---Chord  Properties.
---Tangent Properties.

{7}.THE  EARTH  AS  A   SPHERE.
---Features  and  Location  of  Places.
---Distances  Along  Great  Circles.
---Distances  Along   Small  Circles.

{8}.ACCOUNTS.
---Double  Entry.
---Trial   Balance.
---Trading  Profit  and  Loss.
---Balance  Sheet.  


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FORM  FOUR.
TOPICS/SUB- TOPICS 
{1}.COORDINATE  GEOMETY {II}. 
---Equation  Of   a  Line.
---Midpoint   Of  a  Line   Segment.
---Distance  Between  Two   Points  On  a   Plane.
---Paralel  and  Perpendicular  Lines.

{2}. AREA  AND  PERIMETER. 
---Area  Of  any  Triangle.
---Area  Of   a  Rhombus.
---Perimeter  Of  a  Regular  Polygon.
---Area  Of  a  Regular  Polygon.
---Area  Of  Similar  Polygons.



{3}.THREE  DIMENSIONAL  FIGURES. 
---Three   Dimensional  Figures.
---Construction  Of   Three  Dimensional Figures.
---Sketching  Three  Dimensional  Figures.
---Surface  Area  Of   Three  Dimensional  Objects.
---Volume  Of  Three  Dimensional  Objects.

{4}.PROBALITY. 
---Probability   Of  an  Event.
---Combined  Events.


{5}.TRIGONOMETRY.
---Trigonometrical  Ratios.
---Sine  and  Cosine  Functions.
---Sine  and  Cosine  Rules.
---Compound  Angles.

{6}.VECTORS.
---Displacement  and   Position  Vectors.
---Magnitude  and  Direction  Of  a  Vector.
---Sum  and  Difference  Of  Vectors.
---Multiplication  Of  a  Vector  by  a   Scalar.
---Application  Of   Vectors.

{7}.MATRICES  AND   TRANSFORMATIONS.
---Operations  On  Matrices.
---Inverse  Of  a   Matrix.
---Matrices  and   Transformations.


{8}.LINEAR  PROGRAMMING.
---Simultaneous   Equations.
---Inequalities.
---The  Objective  Function.
---Maximum  and  Minimum  Values.


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 REFERENCE:-  Tanzania  Institute  Of   Education,Basic  Mathematics  Syllbus   For  Secondary  Schools, Form  I--IV,2010. Dar--es--Salaam,Tanzania.
 
        

HOW TO STUDY AND PASS EXAMINATIONS.

                                                         

                      HOW   TO  STUDY  AND  PASS EXAMINATIONS.

INTRODUCTION:

When you sit down to study, how do you transfer that massive amount of information from the books and notes in front of you to a reliable spot in your mind? You need to develop good study habits as outlined below. At first, it'll take a good deal of conscious effort to change your studying ways, but after a while, it'll bcome second nature, and studying will be easier to do.                   

STEPS:-

1. 1
   Make things interesting. Logical arguments will not give you motivation to study. Thinking that if I study hard and get into a good university and get a good job, etc., will not interest you. Love what you do. Try to find the beauty of every subject, and most importantly try to link it with the events of your life and things that interest you. This linking may be conscious (ie. performing chemical reactions, physical experiments or manual mathematics calculations in order to prove a formula) or unconscious (eg. You go to the park and look at the leaves. Then you think to yourself, Hmm, let me review the parts of the leaf we learned in bio class last week). Even though this might not sound the most ideal method for theoretical subjects such as English, use your creativity to make stuff up. For example try to write a story with all subjects starting with S, all objects starting with O, and no verbs containing V.
   
   
2. 2
   Manage your time. Make a weekly schedule and devote a certain amount of time per day to studying. This will also improve your grades. That amount will vary depending on whether you're in high school or college, and also varies by field of study.
3. 3
   Study in 20-50 minute chunks. It takes time for your brain to form new long-term memories, and you can't just keep studying flat out. Take 5-10 minute breaks minimum and do something physically active to get your blood flowing and make you more alert. Do a few jumping jacks, run around your house, play with the dog, whatever it takes. Do just enough to get yourself pumped, but not worn out.
   • Make enough time in your schedule to get enough sleep. Think of it this way: If you sleep only 4-5 hours, you'll probably need to double your study time in order to be as effective as if you'd gotten 7-9 hours of sleep. Study more and sleep less? That doesn't sound like a very good deal. Get a good night's sleep every night and you'll be making the best of your study time. If you end up a little sleep deprived despite your best efforts, take a short nap (20 minutes) before studying. Then do some physical activity (like you would do during a break) right before you start.
4. 
   4
   Find a good study spot. You should feel comfortable, but not so comfortable that you risk falling asleep--a bed isn't a very good study spot when you're tired! The place where you study should be relatively quiet (traffic outside your window and quiet library conversations are fine, but interrupting siblings and music blasting in the next room are not).
   • As far as music is concerned, that's up to you. Some people prefer silence, others prefer music in the background. If you belong to the latter group, stick to instrumental music (music that has no words like classical, soundtrack, trance, baroque ) and that you're already familiar with (not something that's bound to distract you)--otherwise, your brain will "multi-task" and not be able to retain information as well.
   • Having the television on while you study is generally a bad idea. It can distract you a lot and suck all of the things you've studied out by making you focused on the show that is on.
5. 
   5
   Clear your mind. If you’ve got a lot on your mind take a moment to write yourself some notes about what you're thinking about before you start studying. This will help to clear your mind and focus all your thoughts on your work.
6. 
   6
   Snack smart while you study. Have your snacks prepared when you begin a study session--don't wait till you get hungry and go rummaging for food. Avoid any snacks or drinks that will give you a rush of energy, because with every rush comes a crash in which all the information you studied is lost to an intense desire to sleep. Focus on "slow release" carbohydrates, which not only give you a steady stream of energy, but they also boost serotonin, a brain chemical that makes you feel good:
7. 
   7
   Rewrite your notes at home. When you're in class, emphasize recording over understanding or neatness when you take notes. That doesn't mean you shouldn't try to understand or organize your notes at all; just don't waste time doing something in class that you can figure out or neaten up at home. Consider your in-class notes a "rough draft" of sorts. Rewrite your notes as soon after the class as possible, while the material is fresh in your mind so that you can fill in any gaps completely from memory. The process of rewriting your notes is a more active approach to studying--it engages your mind in a way that just reading the notes doesn't.
   • You may find it easier to keep two notebooks--one for your "rough draft" notes, and another for your rewritten notes.
   • Some people type their notes, but others find that handwriting enhances their ability to remember the notes.
   • The more paraphrasing you do, the better. Same goes for drawing. If you're studying anatomy, for example, "re-draw" the system you're studying from memory.
8. 
   8
   Learn the most important facts first. Don't just read the material from beginning to end, stopping to memorize each new fact as you come to it. New information is acquired much more easily when you can relate it to material that you already know.
   • When you are beginning to study a new chapter, it will make the information it contains much more meaningful and easier to learn if you first take a few minutes to read the introduction, the headings, the first sentence of every paragraph, and the chapter summary to get a good idea of what the chapter is about before going on to read the chapter as a whole. (Word for word, these portions also contain more information that is likely to be asked about on a test!)
   • If you can, use a highlighter, or underline the most important points in the body of the text, so that you can spot them more easily when you review the material. It also helps to make notes in pencil in the margin in your own words to summarize or comment on important points. (These practices may make your textbook worth less when you sell it back to the bookstore, but it may make it worth a great deal more to you at test time!)
     If the text book belongs to the school, than you can use those highlighted sticky notes, or a regular sticky note beside the sentence or paragraph.
   • You can also read just these portions in order to quickly review the material you have learned while it is still fresh in your memory, and help the main points to sink in.
   • This is also a great way to review the most important ideas just before a test, when your time is especially limited.
   • It's also a good way to periodically review in this manner to keep the main points of what you have already learned fresh in your mind if you need to remember a large amount of material for a longer period -- for a final examination, for a comprehensive exam in your major, for a graduate oral, or for entry into a profession.
   • If you have enough privacy, it also helps to recite your summaries aloud in order to involve more senses in the activity of learning, like listening to music over several channels at once. Incorporate your summaries into your notes, if there is a connection.
   • If you're having trouble summarizing the material so that it "sticks" in your head, try teaching it to someone else. Pretend you're teaching it to someone who doesn't know anything about the topic, or create a wikiHow page about it! For example, How to Memorize the Canadian Territories & Provinces was made as a study guide for an 8th grade student.
9. 9
   Make flash cards. Traditionally, this is done with index cards, but you can also download computer programs that cut down on space and the cost of index cards. You can also just use a regular piece of paper folded (vertically) in half. Put the questions on the side you can see when the paper is folded; unfold it to see the answers inside. Keep quizzing yourself until you get all the answers right reliably. Remember: "Repetition is the mother of skill."
   • You can also turn your notes into flash cards using the Cornell note-taking system, which involves grouping your notes around keywords that you can quiz yourself on later by covering the notes and trying to remember what you wrote based on seeing only the keyword.^[2]
10. 
    10
    Find out if your textbook has a vocabulary section, a glossary, or a list of terms, make sure that you understand these completely. You don't have to memorize them, but whenever there is an important concept in a particular field, there is usually a special term to refer to it. Learn these terms, and be able to use them easily, and you will have gone a long way towards mastering the subject itself. (Besides, teachers frequently draw from these lists as a quick and easy way to make up test questions!)
11. 
    11
    Make associations. The most effective way to retain information is to "tie" it to existing information that's already lodged in your mind.
    • Take advantage of your learning style. Think about what you already learn and remember easily--song lyrics? choreography? pictures? Work that into your study habits. If you're having trouble memorizing a concept, write a catchy jingle about it (or write lyrics to the tune of your favorite song); choreograph a representative dance; draw a comic. The sillier and more outrageous, the better; most people tend to remember silly things more than they remember boring things!
    • Use mnemonics (memory aids). Rearrange the information is a sequence that's meaningful to you. For example, if one wants to remember the notes of the treble clef lines in music, remember the mnemonic Every Good Boy Deserves Fudge = E, G, B, D, F. It's much easier to remember a sentence than a series of random letters. You can also build a memory palace or Roman room to memorize lists like the thirteen original colonies in America, in chronological order. If the list is short, link the items together using an image in your mind.
    • Organize the information with a mind map. The end result of mapping should be a web-like structure of words and ideas that are somehow related in the writer's mind.
    • Use visualization skills. Construct a movie in your mind that illustrates the concept you're trying to remember, and play it several times over. Imagine every little detail. Use your senses--how does it smell? look? feel? sound? taste?
    • Make a study sheet. Try and condense the information you will need into one sheet, or two if absolutely necessary. Bring it around with you and look at it whenever you have downtime during the days leading up to the test. If you type it up onto the computer, you can get a lot more control over your layout by changing font sizes, margin spaces, etc.
12. 12
    Make it a group effort. Get some friends together--friends who are actually interested in studying, that is--and have everyone bring over their flash cards. Pass them around and quiz each other. If anyone is unclear on a concept, take turns explaining them to each other. Better yet, turn your study session into a game like Trivial Pursuit.
13. 
    13
    If you are easily distracted by social networking sites such as YouTube, Facebook, etc., then download the application LetMeWork at http://img.labnol.org/files/18257/letmework.zip. Tried and tested, this will temporarily block these sites and help you study better. Double-click it to instantly block some of the distracting sites on your computer. When you are done with your work, double-click the same file again to unblock access to all the sites as before.

TIPS:-

• Making a study note or sheet can help you organize your notes and you know what to study for your test.
• Try not to just memorize whatever you have learned. Understand it and say/write the answer in your own words, and try to teach the material to friends or to an imaginary audience. (For example, how would you explain it to your mother, or your boyfriend or girlfriend, or your little sister?)
• Eliminate distractions:
  • Make sure your studying area is tidy.
  • Try to stop being distracted. Resist the urge to go on Tumblr, Twitter, Facebook or email. This way, you can manage your time efficiently and get work done faster which leaves more time for sleep.
  • Keep electronics that are unnecessary in another room, another floor of the house or kept hidden out of sight. Take as much time as you need to work on studying but work in chunks. As a reward, you can spend a little amount of time on the unnecessary hidden electronics. If this does not work, you can take the additional step of turning off your devices.
  • If you have long hair, take steps to keep it out of your face.
  • Have only one subject open at a time. You might get distracted by what you'll need to study next.
• Write your own notes so that it's easier for you to understand.
• Keep hydrated. A 2% decrease in hydration can cause up to 20% loss of focus. (Just make sure that your "hydration" is non-alcoholic!)
• When making summaries, use different colours. The brain remembers information more easily when it is associated with colour.
• You should be alert and your mind should be calm before you begin your studies.
• During a test don't worry about if you are last at handing your work in. Pay attention and work to the best of your abilities!
• Pay attention in class. Sit where you are able to see and hear what is going on.
  • Don't hesitate to ask questions or seek extra help during office hours if something is not clear to you. Many instructors have said, "The only dumb question is the one that isn't asked!"
  • Try not to be absent when an important subject is going to be discussed.
  • If you are absent, try to borrow the notes of somebody who is a good note-taker.
• The more you go over your notes, the easier it would be to remember. Don't try to memorize it; just read it.
• Study the most challenging subjects first. Tackle them when you're most alert.
• On the other hand, make sure you are getting enough sleep. Before a big test or exam you should aim for eight hours of sleep.
• Reading key points aloud in different accents can help you remember them - you really focus on the words as you have to think about how to pronounce them. Strange, but it works!
• If you can, it helps to "treat yourself" by giving yourself a special reward when you finish a meaningful unit of work.
  • Don't make the intervals between rewards too long, or the rewards too weak.
  • If you stop and take time to think about the possibilities, you should automatically be able to sense what will work for you and what won't.
• Study and regularly remind yourself about your ultimate goal in order to maintain motivation levels.
• If you get distracted easily, turn all the lights off and study with lighted candles or lamps. At first it will be hard but you'll get used to it and it's very beneficial in concentrating.
• Read out your notes in the tune of a catchy song.
• Try writing questions on notes and sticking them on to a drawer or a cupboard and you're not allowed to open it until you've worked out the answer.
• Late night studies are usually a waste of time.
• Studying with a partner who is as serious about the subject as you can be a good motivator to work harder. Organize the study session into parts, review notes, outline the chapter, and discuss concepts. (Try to teach it to each other so that you are sure you both get it.)
• Add inspirational quotes to inspire you. Write inspirational quotes in your notebooks and on your paper to inspire you to keep working.
• Try typing. (If your word processor has an automatic outlining feature, this is often a great help in rapidly organizing and making your notes more meaningful!) Word process all your notes into multiple summaries. Print out and highlight the important pieces. Word process these pieces, print out and summarize again. This will take the stress off writing with your hands, and it may speed up the process, as well as allowing you to study longer.
• Incorporate jokes or comic doodles in your notes. This might motivate you to review your notes more often.

WARNINGS:-

• Watch out for inclinations to procrastinate. For example, are you reading this article instead of studying? All your efforts will not lead to success, and if you procrastinate, you'll end up blaming your tools.
• If you cannot study because you are just too tense, or something is worrying you, it may be necessary to gain control of your emotions before you are able to successfully study on a regular basis. If you are not able to do this on your own, you may need to consult a school counselor.
• Make sure you're not too comfortable; you can fall asleep doing so! Sit in a sturdy chair with all your notes on a desk. Pillows are not needed to study. Don't relax too much and think that the test is going to be so easy; if you do, you might end up leaving something out because you think it's not worth studying!       "GOD  BLESS  YOU,  SUCCESS  IS YOURS."