Andrew's IB Maths Vault

Hiya! Welcome back to Trigonometric functions and equations v2.5. High quality content that you signed up for. Three standards: trig functions, trig equations and MORE trig equations! AAHL: AAHL MS: AASL: AASL MS: Andrew  

Hiya! This is probably the last unit test for 2025. We'll be working on trig identities. For AA students, mastering these is CRUCIAL as they show up time and time again in differentiation and integration, as even more if you decide to pursue a STEM path in engineering.  If you're looking for more personalised support, don't hesitate to reach out and complete the form ! I'm @adventurousandrew on Discord.     AAHL: AAHL MS: AASL: AASL MS: Merry Christmas!  Andrew  

Hiya! Waves. Today's test is on trigonometric functions and basic trigonometric equations/inequalities.     As usual, the test features a large number of questions, providing students with ample opportunities to demonstrate mastery. Some questions are trickier... so be prepared to lose a few brain cells. ;p AAHL: AAHL MS: AASL: AASL MS: If you're looking for more personalised support, don't hesitate to reach out and complete the form ! I'm @adventurousandrew on Discord.   Andrew  

Hiya! As the school year's starting for a lot of y'all, it's the perfect timing for a unit test - on a topic that's usually covered in the first semester of DP1. This time, we'll look at problems on trigonometric relationships - solving problems using the sine rule, the cosine rule and the area of a triangle in a wide variety of applications. Some of the items are quite demanding - enjoy!   If you're looking for more personalised support, don't hesitate to reach out and complete the form ! I'm @adventurousandrew on Discord. AAHL: AAHL MS: AASL: AASL MS: Andrew  

Hiya! It's Andrew and once again we're back with my FAVOURITE topic in the entire course - trig identities! You'll have a chance to experience what it's like to be Vietnamese (yes, we take trig equations VERY seriously) and a dozen questions to flex your trig identities muscles. Today's tests feature reciprocal and inverse trig functions for HL and the Identities for all.  Test Walkthroughs: Trig Identities (v2.4) p1 Trig Identities (v2.4) p2    If you're looking for more personalised support, don't hesitate to reach out and complete the form ! I'm @adventurousandrew on Discord. AAHL: AAHL MS: AASL: AASL MS:   Andrew  

Hey y'all! Nothing screams Andrew more than ridiculous trig questions. Well fear not, I'm back with the unit tests on trig functions, to be taken right before the almighty trig equations! AASL: AASL MS: AAHL: AAHL MS: If you're looking for more personalised support, don't hesitate to reach out and complete the form ! I'm @adventurousandrew on Discord.   -Andrew

Hey y'all. My love for trigonometric identities just got me all hyped up and make the third round of Version 2 trig identities tests. The content is similar to last time, with a couple more questions for the SL students to give them more opportunities to show off what they want. The HL papers are long and demanding as always. Enjoy! AAHL:   AAHL MS:   AASL:   AASL MS:    

Hey y'all. This unit test is long  overdue; I just couldn't find the inspiration to write a decent unit test on trig relationships. The SL version will be uploaded soon; it's mostly identical to the HL paper, maybe one fewer question and lower "grade boundaries". Enjoy! AAHL/AASL Unit Test: AAHL/AASL MS:

Hey y'all! A little different from my regularly scheduled posts, this time around I'm just gonna make some quick announcements! For many, a new school year is right around the corner (or already started!) and some of you have apprehensions going into the course, especially AAHL, perhaps due to your friends and upperclassmen scaring you (they're not entirely wrong) or you just realised you're totally out of your depth since day one (oop-). It's not too late to get help. For new DP1s, a solid foundation of algebra will save you SO MANY MARKS on exams. Every high-performing student will tell you to focus on algebra earlier on because it's worth half of the marks on some questions. Quadratics in trigonometry, simultaneous equations in sequences and series, you name it. The gaps in your basics will come back and bite you if you aren't careful. For current DP2s, lots of you have a hard time with trig functions, equations and identities. Unfortunately, there's ...

Trigonometry. Is. Back. Two unit tests, AASL and AAHL, on trigonometric identities!! If you’ve been here for any amount of time you know that I am obsessed with disgusting-looking trigonometric equations. I’m happy to report that a couple more nasty trig equations are on the way!   Advice for AAHL students who are not aiming for 7: do not bother attempting every questions, you will run out of time.   AASL: (30 minutes, 4 questions)   AASL MS:   AAHL: (1 hour, 2 sections, 12 questions – very long )   AAHL MS:   It’s been a while since I posted my three booklets on trigonometric functions and identities – go to Triangles become Circles page for more details!   Have a wonderful week. C:   Andrew    

Hi y’all! After letting AISL take the stage for the previous month, today I am back with something I’m a little better at: writing AA trigonometry tests.   We’re currently doing trigonometric equations with my students and I thought there’s no better time to start a brand new AA unit tests than this. Welcome back to v2.2 of Trigonometric Quartet!   Let’s kick this off with trigonometric functions test. As usual, both versions have more than half of the questions in common, but of course there are more challenges on the AAHL version as you guys are ready to take on even more maths!   AAHL Trig Functions v2.2:   AAHL Trig Functions v2.2 MS:   AASL Trig Functions v2.2:   AASL Trig Functions v2.2 MS:        

Hey y’all.   Just under 7 weeks and N23s are gonna take their final IB exams. Y’all are about to become members of the old people gang, congrats!   I noticed that I already posted Unit Tests v2 for all of trigonometry except trigonometric relationships, so now’s the time to correct that. As usual, there’s considerable challenge (I hope) at the top end, especially the time pressure, but students of all abilities have opportunities to show off what they know.   Some quick words before we get to the tests.   1) November 2023 mocks N23 mocks will be coming next weekend! Buckle up, we’re preparing for takeoff.   RShields is proofing the paper a 2 nd round before they’re sent off to y’all.   AASL, I think the papers reflect the difficulty of the actual papers. AAHL, they’re definitely on the harder end, especially Paper 3.   (Speaking of that I gotta start writing the MS too oop-)   2) Revision Sessions (on IB Discord) As exams are quick approaching ...

Hello hoomans. With less than two weeks before the M23 mocks, I hope everyone's getting ready for the heat. It always shows how long I've been on the server after each exam season: some people were just pre-IB but now are graduating in three months! Today I'd like to present my absolute favourite: trig identities unit test! Some of you already know I have an abusive relationship with trig: I like it way more than I should. But allow me to put it this way: dealing with trig identities is like solving a puzzle. Yes, it's hard. Yes, sometimes you're stuck. Yes, it's annoying. But it's fun and rewarding when you get it right! AAHL: AAHL Answers: AASL: AASL Answers: Good luck have fun! Andrew

Hello hello hello! After the calculus sequence we shall now commence on my second favourite journey: trigonometry. For long-time followers on the site, I have massive booklets to guide you through the whole of trigonometry apart from the very basics (sine rule, cosine rule, area of a triangle, unit circle), which you can find here . Trig functions is the first time you understand why I say "triangles become circles" the more you know about trigonometry - the function repeats itself after a certain period. You'll have sufficient practice on it by the time you finish the papers - enjoy! AAHL AASL AAHL Answers AASL Answers

This is it, ladies and gentlemen. The last section in the trig quartet. After brushing it off for 4? 5? months, I've finally sit down and finished this unit. It's quite a lot of work writing these booklets, so I'd really appreciate if y'all could buy me a coffee here and there. Every journey has to come to an end, and I'm sad that this is all the trigonometry that IB has to offer. But hey, further down the line you'll learn more  ways to prove trig identities (wink wink: complex numbers), which only emphasise the importance of knowing your trig well.  Enjoy!  P/S: I'll take a short break, maybe a month or two, cause I'll be travelling. Promise that after the break my brain will be free of clutter - I took a brief break (couple days or so) not writing questions and I'm blown away by my eagerness to come back to it. Be nice to yourself, your friends and your loved ones. Your favourite wolf will be back in August/September! Credits:   AdventurousAndrew#...

Second collection of unit tests: trigonometry and vectors. Occasionally featuring questions from endless inspirational sources. Answers included. Unit Tests Version 1 Part 1: Trig relationships (AASL/AAHL)  The trio (sine/cosine rules and area of a triangle), sectors and the unit circle. Part 1: Trig relationships (AISL/AIHL)  Same as above, just slightly modified. Part 2: Trig identities and equations (AASL/AAHL)  Trig identities and equations, including Pythagorean identities and compound angle identities for AAHL. Vectors (AAHL) : lines and planes in 3D. Version 2 Trig relationships (AASL/AAHL) Sine rule, cosine rule, area of a triangle and sectors. Trig functions (AASL/AAHL)  The start of triangles become circles, v2. Trig identities (AASL/AAHL)  Second part of triangles become circles. And graphs. Vectors : lines and planes in 3D.   Version 2.2 Trig relationships v2.2 Sine rule, cosine rule and area of a triangle, and other things. Trig functions v...

Hello hello hello! As you know we'll talk about trig equations after trig functions.  After a short hiatus due to me unable to comprehend thermo, I'm now temporarily  back with an ENTIRE (yes, entire) module on trig equations. Have fun with it. Answers included at the end. Link: Where are we going, where have we been? In our journey on trigonometry so far, we started with Pythagorean theorem and right-angled trigonometry. Extending our definition to larger angles, we develop the sine and cosine rules for non-right triangles and then to the entire unit circle.  The "point on the circle" model gives rise to our trigonometric functions, namely, sine and cosine functions. We did a bunch of transformations to fit our function with our data, which is then used to predict future values. The question arises: is there a way we could solve some  equations without using a calculator? Answer: special trig values. More details on that soon. Why are we interested in special trig v...

Here it is, the last part of this module. It is the summary of everything we've done so far, from identifying features to sketching devilish functions. And no way is better than ending this module with MORE questions that y'all can have a go at. Disclaimer, as usual: the questions are inspired by the books I've got my hands on, so it's normal if you find some questions similar to your textbook. The next module on trigonometric equations should be posted soon. I'm still in the process of writing the answers to the questions argh . It's gonna be a good ride. Thanks for tuning in with what I've posted over the last two weeks! Credits: AdventurousAndrew#7499

Thi s part of the module is on reciprocal and inverse trig functions, reserved for AAHL students only. From my experience, the IB doesn't ask tricky questions related to reciprocal and inverse trig, considering we haven't covered a lot of trig identities at this stage of the booklet. Consider this some downtime before the big game of trigonometric equations. Preview of next section:  End-of-Module Review and a practice quiz. Credits: AdventurousAndrew#7499

First post in 2022! Hey there. If you're looking for more trig functions torture fun, hang on tight. Today we'll put the properties of trig functions into solving more realistic problems. Surprisingly these questions are generally very poorly  done, simply because Kids cannot map the relative height on the wheel with the height of the trig functions Kids cannot interpret the properties of trig functions properly because the wordings are bad Kids' understanding of functions is weak, leading to their inability to recognise what  to do and what to substitute where and 7749 other reasons. Here's my two cents that might help y'all to avoid the common misconceptions, especially the second bullet point. You should be very  solid at properties of trig functions before reading on. Credits:  AdventurousAndrew#7499