SHS Mathematics //Tricks, Questions & Answers

Above is the detailed Note on Polynomial Functions with examples Please, go through and ask questions if you have any for clarification

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✅✅✅✅✅✅✅✅✅✅✅✅ TOPIC: MODULAR ARITHMETIC SUBJECT: CORE MATHEMATICS Modular Equivalence Definition ; Two integers are said to be modular equivalent if they have the same remainder in Modular arithmetic. Example 1 Show that the following pairs of numbers are equivalent in the moduli given: (i) 67 and 94 (mod9) (ii)108 and 97 (mod11) Solution (i) 67=7x9+4 94=10x9+4 Note that the remainder is 4 in each case Thus 94=67(mod9) The integers 67 and 94 are congruent because they have the same modular equivalent (ii) 108=9x11+9 97=8x11+9 Thus 97=108(mod11) Hint: In general,two integers x and y are said to be congruent modulo z, i.e. x=y(mod z) i.e.If the difference of x-y is an integer multiple of z, where the number z is referred to as the modulus of the congruence.

✅✅✅✅✅✅✅✅✅✅✅✅ TOPIC: MODULAR ARITHMETIC SUBJECT: CORE MATHEMATICS Division As a matter of fact, division is the inverse of multiplication,thus we can 1se multiplication table to solve division problems. For example,3➗4=?(mod 5) Let 3➗4=a Then 4a=3 since (3/4=a,then4a=3) It implies that a number(a) multiplied by 4 in mod 5 equals 3. From the table check for 4 on the residues column and 3 on the residues row Therefore ; a=2 i.e.3➗4=2(mod 5) MULTIPLICATION INVERSE Definition ;The multiplication inverse of a number P is a number q such that pq=1.The symbol for the INVERSE OF p is p^-1 or 1/p Also, the multiplication inverse of 5 is 1/5 because 5× 1/5 = 1 As well as the inverse of 3/4 is 4/3

✅✅✅✅✅✅✅✅✅✅✅✅ TOPIC: MODULAR ARITHMETIC SUBJECT: CORE MATHEMATICS Multiplication in Modular Arithmetic Multiplication can be explained as repeated addition e.g.4✖️3(mod 5)i.e. 3+3+3+3=12=2(mod5) i.e.4✖️3=2(mod5)4✖️3=2(mod5) The table above shows multiplication in modulo 5.

✅✅✅✅✅✅✅✅✅✅✅✅ TOPIC: MODULAR ARITHMETIC SUBJECT: CORE MATHEMATICS Modular arithmetic, also known as remainder arithmetic is a type of arithmetic in which an integer is represented by its remainder when divided by another integer. In other words,the modulo of any integer is found by dividing the integer by the given modulo and the remainder identified as the answer. Modulo is written as “mod” for short. For instance, 23 (mod 7) means the remainder when23 is divided by 7. That is: 1. 23÷7=3x7+2=2 2. 23÷7=3 R 2=2 0R 3. 23-7-7-7=2.

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I studied a lot, but I always forget almost all that I have studied. What should I should? Forgetting what you've studied can be frustrating, but there are several strategies you can try to help improve your memory retention: Practice active learning: Instead of simply reading and highlighting your notes, actively engage with the material by summarizing it in your own words, creating flashcards, or teaching the information to someone else. Use memory aids: Mnemonic devices, visual aids, and acronyms can help you remember important information by creating associations or patterns that are easier to recall. Take breaks: Our brains need rest in order to consolidate memories. Taking breaks, going for a walk, or practicing meditation can help you retain more information in the long run. Test yourself: Regular testing can help reinforce your memory and identify areas where you need to focus your study efforts. Get enough sleep: Lack of sleep can impair memory consolidation, so make sure you're getting enough rest each night. Remember, everyone has different learning styles and strategies that work best for them, so it may take some trial and error to find the techniques that work best for you.

✍✍✍✍✍✍✍✍✍✍✍ How To Study For Maths Exams 1. Do the assigned homework for your class. Your math teacher will likely assign homework on a regular basis that is meant to help prepare you for tests and exams. Make sure that you always do the homework, even if it is optional or not worth many points. Doing this extra work will help prepare you for the tests, which will help you pass the class. Complete extra problems if you are having trouble with a concept. For example, if your teacher assigns all of the even problems at the end of the chapter, do the evens and the odds. Your textbook may have a section in the back where you can check your answers. If it does, use it to see how you are doing. Write out the required formula for each problem as you do the homework. This will make it easier for you to remember it when you take a test. 2. Review your notes and focus on what will be covered on the test. If you take good notes, this will be a valuable resource for helping you pass your exams.[8] Try to read your notes on the same day you took them to reinforce the information that you learned in class that day. For example, you could read through your notes after your class, before you do your homework, or when you study. 3. Read the assigned chapters to understand concepts. Although you may not enjoy reading your math textbook, it is a great way to ensure that you understand the concepts and terms your teacher covers in class. Take time to carefully read the chapters your teacher assigns and ask questions if something is unclear. Highlight or underline important passages while you read so that it will be easy for you to come back to them later on. Mark important pages with sticky notes or pens with different colors so you can quickly refer to them. To be continued.... https://t.me/shs_maths_questions_answers

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