Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. Notes Quick Nav Download. You appear to be on a device with a "narrow" screen width i. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.
Inverse Functions — In this section we will define an inverse function and the notation used for inverse functions. We will also discuss the process for finding an inverse function. Trig Functions — In this section we will give a quick review of trig functions. We will cover the basic notation, relationship between the trig functions, the right triangle definition of the trig functions.
We will also cover evaluation of trig functions as well as the unit circle one of the most important ideas from a trig class! Solving Trig Equations — In this section we will discuss how to solve trig equations.
However, the process used here can be used for any answer regardless of it being one of the standard angles or not. Solving Trig Equations with Calculators, Part I — In this section we will discuss solving trig equations when the answer will generally require the use of a calculator i.
Note however, the process used here is identical to that for when the answer is one of the standard angles. The only difference is that the answers in here can be a little messy due to the need of a calculator. Included is a brief discussion of inverse trig functions. Solving Trig Equations with Calculators, Part II — In this section we will continue our discussion of solving trig equations when a calculator is needed to get the answer. The equations in this section tend to be a little trickier than the "normal" trig equation and are not always covered in a trig class.
Exponential Functions — In this section we will discuss exponential functions. We will cover the basic definition of an exponential function, the natural exponential function, i. Logarithm Functions — In this section we will discuss logarithm functions, evaluation of logarithms and their properties.
We will discuss many of the basic manipulations of logarithms that commonly occur in Calculus and higher classes. Exponential and Logarithm Equations — In this section we will discuss various methods for solving equations that involve exponential functions or logarithm functions. Common Graphs — In this section we will do a very quick review of many of the most common functions and their graphs that typically show up in a Calculus class.
Tangent Lines and Rates of Change — In this section we will introduce two problems that we will see time and again in this course : Rate of Change of a function and Tangent Lines to functions. Both of these problems will be used to introduce the concept of limits, although we won't formally give the definition or notation until the next section.
The Limit — In this section we will introduce the notation of the limit. We will also take a conceptual look at limits and try to get a grasp on just what they are and what they can tell us. We will be estimating the value of limits in this section to help us understand what they tell us.
We will actually start computing limits in a couple of sections. One-Sided Limits — In this section we will introduce the concept of one-sided limits.
We will discuss the differences between one-sided limits and limits as well as how they are related to each other. We will also compute a couple of basic limits in this section. Computing Limits — In this section we will looks at several types of limits that require some work before we can use the limit properties to compute them. We will also look at computing limits of piecewise functions and use of the Squeeze Theorem to compute some limits.
Infinite Limits — In this section we will look at limits that have a value of infinity or negative infinity. We will concentrate on polynomials and rational expressions in this section. Continuity — In this section we will introduce the concept of continuity and how it relates to limits.Sec 1 DnT Syllabus 23rd Jan Sec 1 English Lit Syllabus 28th Jan Humanities Sec 1 Humanities Syllabus.
Mathematics Sec 1 Math Syllabus 28th Jan Sec 1 BML Syllabus. Sec 1 HCL Syllabus. Sec 1 HML Syllabus. Sec 1 Math Syllabus. About Us Principal's Message. Vision, Mission and Values. Desired Xinmin Outcomes. Our Learning Experience Framework.
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Quadratics MS. Functions 1. Functions MS 1. Functions 2. Functions 3. Functions 4. Functions 5. Functions 6.Welcome to my online math tutorials and notes. In other words, they do not assume you've got any prior knowledge other than the standard set of prerequisite material needed for that class. The assumptions about your background that I've made are given with each description below.
I'd like to thank Fred J. I've tried to proof read these pages and catch as many typos as I could, however it just isn't possible to catch all of them when you are also the person who wrote the material.
Fred, Mike and David have caught quite a few typos that I'd missed and been nice enough to send them my way. Thanks again Fred, Mike and David! If you are one of my current students and are here looking for homework assignments I've got a set of links that will get you to the right pages listed here.
I've made most of the pages on this site available for download as well. These downloadable versions are in pdf format. Each subject on this site is available as a complete download and in the case of very large documents I've also split them up into smaller portions that mostly correspond to each of the individual topics.
To get the downloadable version of any topic navigate to that topic and then under the Download menu you will be presented an option to download the topic.19. Secondary 1 Math
Here is a complete listing of all the subjects that are currently available on this site as well as brief descriptions of each. In particular it is assumed that the exponents and factoring sections will be more of a review for you. Also, it is assumed that you've seen the basics of graphing equations.
Graphing particular types of equations is covered extensively in the notes, however, it is assumed that you understand the basic coordinate system and how to plot points. There is some review of a couple of Algebra and Trig topics, but for the most part it is assumed that you do have a decent background in Algebra and Trig. These notes assume no prior knowledge of Calculus. It is also assumed that you have a fairly good knowledge of Trig. Several topics rely heavily on trig and knowledge of trig functions.
It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space. These notes assume no prior knowledge of differential equations. A good grasp of Calculus is required however.In a right triangle, the secant of an angle is the length of the hypotenuse divided by the length of the adjacent side. In a formula, it is abbreviated to just 'sec'. Of the six possible trigonometric functionssecant, cotangentand cosecantare rarely used.
In fact, most calculators have no button for them, and software function libraries do not include them. They can be easily replaced with derivations of the more common three: sin, cos and tan. Secant can be derived as the reciprocal of cosine:. For every trigonometry function such as sec, there is an inverse function that works in reverse.
These inverse functions have the same name but with 'arc' in front. So the inverse of sec is arcsec etc. When we see "arcsec A", we interpret it as "the angle whose secant is A".
But we can in fact find the secant of any angle, no matter how large, and also the secant of negative angles. For more on this see Functions of large and negative angles.
Because the secant function is the reciprocal of the cosine function, it goes to infinity whenever the cosine function is zero.
In calculus, the derivative of sec x is sec x tan x. This means that at any value of xthe rate of change or slope of sec x is sec x tan x. For more on this see Derivatives of trigonometric functions together with the derivatives of other trig functions. See also the Calculus Table of Contents.
Home Contact About Subject Index.Mr Foong is a success story. Once a struggling student in his early years, he worked his way to junior college, then university, and ultimately, a stellar career. Today, Mr Foong is a true-blue veteran of the education industry, with a portfolio ranging from editorship and curriculum development to teaching. His personal academic journey means he knows exactly what difficulties students face, and makes him a powerful presence in the classroom.
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Secant (sec) - Trigonometry function
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All Courses Secondary 1 Mathematics. Johan Foong Mr Foong is a success story. Contents Factors and Multiples 6. Factors and Multiples. Try quiz. Chapter 1. Concept: Multiples and factors. Practice: Evaluate square roots and cube roots using prime factorisation. Application Q: What time will the buses leave together.
Application Q: Number of tiles needed for bedroom. Worksheet PDF. Answer PDF.
Real Numbers, Approximation and Estimation. Chapter 2. Concept: Classify integers on the number line. Concept: Different types of decimals. Concept: How to classify real numbers. Short answer: Which of the following are natural, irrational, etc. Short answer: Which of the following are perfect cubes, prime numbers, etc. Chapter 3. Key things to take note when we multiply or divide numbers. Practice: Combined operations of numbers. Short answer: Combined operations of numbers.
Application Q: Distance travelled, temperature, others. Chapter 4. Concept: Significant figures.We flew into Stockholm and they had a driver meet us at the airport and take us to our hotel (we could have taken the train but preferred with all our bags to have a car).
CIE A Level Mathematics 9709
Our driver was great, even after she dropped us off she came into the hotel until we were checked in and made sure we had our welcome packet from Nordic Visitor. For our trip we upgraded to stay in nicer hotels (well worth the money). Every hotel they got us was great, right in the city center so we could walk everywhere and they all included wifi and breakfast which at all 3 hotels was a 5-star buffet.
From Stockholm we took a train to Copenhagen, Denmark, from there an overnight cruise to Oslo, Norway (upgraded on the ship and again, it was well worth it, great cabin, free wifi, free drinks and snacks in the VIP lounge).
Secondary 1 Mathematics
While in Oslo we stayed at the grand Hotel, which is the most renowned hotel in the city. From Oslo we took a train back to Stockholm (we had Nordic upgrade us on all trains to 1st class. A minimal fee but again well worth it). Communication was great, every time I had a questions Cecilia or someone from their team answered straight away. I highly recommend Nordic Visitor to anyone who is looking to take a vacation in Scandinavia. The nothometoday, United States Iceland Complete, August 2012 Wonderful!.
In August, we completed the Iceland Complete tour, arranged by Thordis of Nordic Visitor in Reykjavik. What a wonderful experience. We were met at the airport in Keflavik by the most hospitable, informative cab driver in the world, which was a great start. Rental car, GPS and cell phone were also arranged for us. Part of the reason for that is the widely varying style of each place - from elegant, to rustic, and always scenic. We loved that an itinerary was provided, with suggestions of what to see and do each day, but we had complete freedom to decide which we wanted to do.
Because of the great flexibility, we often had the opportunity to discover unexpected delights, like a wonderful horse show on a Sunday afternoon. When we returned our car in Reykjavik, there was a huge festival going on, and many streets (including the one our hotel was on) was blocked, but the creative young man from the rental agency was able to deliver us to within a block, and we were soon able to join the party.
A great trip arranged by a great travel agent and company. Any Nordic trip we plan in the future will have us contacting Nordic Visitor. My wife and I chose Nordic Visitor to arrange this self drive tour for us.
We travelled in July and were very lucky with the weather. Iceland is one of the most beautiful countries we have ever visited, and we were impressed by the friendliness and hospitality of the people ( and also by the fact that almost everybody spoke English).