Principles of Mathematics 12 Provincial Exam
Note: this guide was written for the 2004-2005 provincial exams and will not be updated.
Principles of Mathematics 12, or simply known as Math 12, is the principle grade 12 level math course (pun intended) in the BC high school curriculum, and it is probably the second most popular provincial course after English 12. You’ll need Math 12 in order to access many post secondary programs, so successful completion of this course may be very important for your future. Hopefully this guide will give you enough help to get the mark you want from P. of Math 12.
Principles of Mathematics 12 is the last and highest level course in the Principles of Mathematics series of courses that are available from grade 8. You need to have to taken all the other courses in the series to be able to enroll in this course, unless you are very good at math, in which case your school may offer enriched classes and tests that allows you to skip certain math courses. Some of you may also be wondering what’s with the long name of the course. Let me clear this up for you. Principles of Mathematics series of courses is the standard level math course in BC high schools. For those who find these courses to be too hard, there is another easier series of courses called the Applications of Mathematics. I think there is an even easier series of course called the Essentials of Mathematics, but I’m not sure whether or not this series has a provincial exam. Principles of Mathematics 12 is the only recognized math course by many post-secondary institutions, so you basically have to take this course to get into those places after high school.
In order to complete Principles of Mathematics 12, you’ll need to have a graphing calculator. The standard model recommended by the Ministry and School Boards is the Texas Instruments TI-83 Plus at the time of writing. The instructions in the textbook are made according this model. You can use another model if you like, but you can’t go wrong with the TI-83. Anyways, here is what I learned during my stay in Principles of Mathematics 12, listed from in the order of the textbook I used. From this point on, I will simply refer to the course as Math 12, since the official name is a hassle to type.
Chapter 1: Functions
This is a pretty easy chapter that serves as warm up for your people who got too lazy during the summer. In this chapter you’ll learn about functions and the multiple ways to flip, flop, stretch, and squeeze the graphs produced from the functions.
Chapter 2: Exponents and Logarithm
This chapter shouldn’t seem too strange to you, since you should have learned this stuff before. This is another pretty easy chapter in my opinion.
Chapter 3: Conics
This is probably the longest chapter in the course, and also one of the hardest. This chapter talks about the various shapes you can create by slicing a cone in various ways and the functions that represent these shapes. The functions are fairly complicated but shouldn’t be too hard if you get the concepts.
Chapter 4: Trigonometric Functions
In this chapter you’ll study cosine, sine, tangent, their inverse functions, and how to use and graph these functions. You’ll also study about radians, which is another way to express angles other than degrees.
Chapter 5: Trigonometric Equations
This chapter is a continuation of Chapter 4. In here you’ll learn how to prove trigonometric identities and how to solve trigonometric equations.
Chapter 6: Sequences and Series
You’ll learn about arithmetic and geometric sequences in this chapter and how to calculate the sum of a certain number of terms in a series.
Chapter 7: Probability
In this chapter you’ll learn about permutations and combinations and how to use these functions to calculate probability in various situations.
Chapter 8: Statistics
I refer to this chapter as “the calculator” chapter, since you can (and probably have to) use your graphing calculator to do most of the operations in this chapter. This chapter is all about statistics and you’ll learn things such as standard deviation, z-index and normal curve. The mathematical operations involved in this chapter are very complex when you try to do them by hand, but you can do these things with your calculator with a few presses of buttons.
These are the eight chapters you will learn out of the textbook through the course. As you would expect from a math course, there is lots of homework, quizzes, tests, and exams. A typical learning class probably involves your teacher going over a section of a chapter and then giving homework questions. That’s about it for Math 12. There are rarely any projects or field trips ever. You’ll spend probably all your classes inside the classroom.
Course Analysis and Tips
Math is one of the fundamental subjects taught in school, so you usually don’t have a choice regarding whether or not you want to take math. Some of you excel in this area, while some of you think that math is the bane of your existence. I think people would usually put me in the first group of people, since I took Math 12 in grade 11. Math 12 is basically what you expect from any high school math class: you go over a section in the textbook, and then you get homework. On some days you have to hand in your homework and on other days you’ll get a quiz, test, or exam.
When I was in Math 12, my teacher would always post up the homework before class starts. In the first half of the class, I and a friend who sat beside me would look into the textbook and try to finish our homework, paying no attention to whatever the teacher was doing in front of the class. After we finish our homework (and we usually do, since the questions are pretty easy most of the time), my friend and I would start chatting a little bit or playing with our graphing calculators. You would think that our teacher must have something to say, but he would usually ignore us, as long as we don’t make too much noise. This is probably because that the teacher knows us pretty well. He knows that we are good at math and we get good marks, so whether or not we pay attention all the time isn’t really a big problem to him. Don’t get me wrong here. I’m not suggesting that you do what I did during Math 12. In fact you should probably do the opposite in most cases, such as you should pay attention when the teacher is talking and save your homework for home. Beside, you probably won’t get a teacher as lenient as the one I had and one who gives homework before class starts. The point of the example is that the Math 12 course follows the textbook very closely. It’s not too difficult for you to learn everything in the course by reading the textbook, like I did. You probably shouldn’t do what I have done in Math 12, but you should know that the best resource you’ll have for studying and review is your textbook. Your teacher may choose to give some notes, and you should use those as well, but in most cases the notes are just repeating what the textbook says with different wording. If you really don’t get something, ask the teacher or a classmate who knows what he/she is talking about.
There is nothing really hard in the whole course, so even those of you who are not so mathematically inclined should be able to get all the concepts with a bit of help. Of course, you might be one of those people who don’t seem to get math, and so here is an important piece of advice for you. Remember this: you just have to remember how to read and use the formulas and functions you are provided. You don’t have to know why something is the way it is and why does this formula work and that one doesn’t. If you are sufficiently good at math, then you can investigate a little bit into the “why”, but if you are not so good at math, not having to think about those things can save you a lot of trouble, since there usually won’t be any high level theory questions on your quizzes, chapter tests, and provincial exam. As long as you know how to complete the operations (and you have your calculator(s) for help), you’ll be just fine.
The Principles of Mathematics 12 Provincial Exam is made up of two main sections. Section 1 is the multiple choice sections made up of 40-50 M/C questions. This section is further divided into two subsections. The first 16 or so multiple choice questions are known as the “non-calculator” questions. You are given about 20 minutes to complete those questions at the start of the exam. During this time, you cannot use your calculators. After the 20 minutes is up, the answer sheet for these questions will be collected, and you can now use your calculators to complete the rest of the exam. Section 2 is made up of a bunch (6-8) extended response questions that you are required to show work for. The total is around 90 marks. As always, the exam is designed to be completed in two hours, but you have an extra 30 minutes if you need it. Visit the Ministry’s website for official exam specifications.
Exam Analysis and Tips
The Math 12 exam is just a final exam that tests you on everything you’ve learned or will learn in Math 12. For review, the only thing that you really have to read is your textbook. You can read your teacher’s notes as well but there isn’t anything on the exam that isn’t in the textbook. You also have many resources to practice for the Math exam. You can 1: do questions out of your textbook; 2: download old exams off the net and complete those and 3: go to quizmeBC for some free online M/C quizzes with old exam questions. The Math 12 exam is one of the easiest exams to prepare for, and you don’t have to remember a lot of stuff either, since there is a data sheet in the exam booklet that provides you with many common identities, equations, and formulas.
Assuming that you have read my exam overview, you probably have noticed that there is a non-calculator subsection in the M/C section. That is a pretty recent phenomenon which started in the 2005 January exam I believe. I know because I took that exam, even though I took the June 2004 exam as well. I retook the exam because I wanted to ace the math provincial, but I got the same score the second time as the first time, and I was alright with that. The non-calculator section might sound a bit scary, but actually it’s pretty easy, since of course all the questions in that subsection don’t require the use of a calculator to complete. In order to do well in this subsection, you’ll need to remember your trigonometric functions and common values (such as sine of 30 degrees equals 1/2 etc.) plus logarithmic identities (ex. Log A + Log B = Log (A * B)). You might also be asked to look at graphs, but those are really simple and you don’t need any advice for those. After you are done with this section, check your answers over because the answer sheet will be collected and you can’t go back to those questions when your answer sheet is gone. The rest of the M/C section (the part where you can use your calculator) isn’t any harder. Your calculator will help you out a lot here, especially on statistics and probability questions which are hard to do by hand but pathetically easy to do by calculator. A good strategy would be to bring two calculators, one scientific and one graphing, to the exam. For simple operations, it’s faster to use the scientific while some more complex operations and of course graphing questions will require your graphing calculator. Having two calculators also allow you to calculate the individual values of one question on one calculator while getting the overall answer on the other. I probably don’t need to say this, but you should skip a question that is taking too long; read the question carefully and never leave an M/C answer blank at the end of the exam.
The written section can be pretty easy too, if you know what you are doing. If you took the time to look at old math exams, you probably noticed that the written section always have the same type of questions. For example, there always seems to be an easy “graphing a function” question and a trigonometric identity proving question. Since you know what the exam is going to ask you, then you can prepare yourself better before going to the exam. You should always write clearly and legibly for written sections. You should present your calculations in a logical and organized manner and don’t skip any steps, since missing steps may mean missing marks for you. Make sure you put down the correct units (if required) when you put down your final answer.
The Math 12 exam is pretty easy if you studied and practiced beforehand. There is nothing out of the ordinary on the exam, and the questions on the exam are probably easier than the ones you’ll see in your textbook. It’s nowhere near as difficult as the English 12 exam, which can be brutal. Most of you should have no trouble getting at least a passing mark from the Math 12 exam, and some of you, like me, stand a pretty good chance of getting 100% on this exam, so good luck to all of you and hope you get the mark you wanted.