#logarithm questions basic

[brandboosterx]

In this video, we delve into the art of solving logarithmic equations with different bases, demystifying the process for you step by step. Whether you're a student brushing up on logarithms or someone facing more complex problems, we've got you covered. Understanding how to work with different bases is crucial when faced with logarithmic equations. We break down the techniques, providing clear explanations using frequently used words to ensure that you grasp the concepts effortlessly. No more getting stuck on those seemingly perplexing logarithmic problems!

[dannyriccsystem]

hiii can you do kimi antonelli asking help from a cute girl in his class or a driver’s younger sister to tutor him in math?

LISTEN UP NOW!

FORMULA ONE DRIVER X READER

Summary: Kimi asks his cute classmate for help with math!

Warnings: Silly, fluff, Y/N usage, user is in last year of high school

Featuring: Kimi Antonelli x Classmate!Reader

REQUESTS OPEN! Check here for more info!

Still getting to requests today, but feel free to send some in! Love y’all

Nobody necessarily expected Kimi Antonelli to still be in school. Rarely did you see a Formula One driver who was still learning about the basics, such as math and language, while also simultaneously passing world champions in their sport and making a living for themselves. After this information came out, there was obviously… Quite a few jokes.

Kimi had made a whole ordeal of asking George to tutor him in math, and while viewers (and George himself) passed it off as a joke, the truth was Kimi really was struggling in the subject. It didn’t have much substance to him, and lacked sense. Unlike racing, which came so naturally to the rookie.

His teachers were emailing him nonstop, scolding the racer on how unbalanced his school life and work life were. Despite being a kid who raced cars for a living, going at unimaginable speeds, he still walked away with his tail tucked between his legs after being harshly lectured by his elders. After being reprimanded for about the thirtieth time, Kimi was instructed to find himself a tutor.

Online class was easy. Everyone was given their own workload to finish at their own pace, with varying deadlines depending on level of learning. Y/N excelled in this department, finishing most of her work far before the others. She was a straight A student, sitting at the top of her class.

On rare occasions, their class would host little lessons over Zoom. It always reminded her of the quarantine days, but it was nice to see familiar faces nonetheless. Even if most of the time she was sat there quietly, watching everyone else get caught up with the work.

One evening, a surprise guest had popped up. Andrea Kimi Antonelli, whom had never had enough time to make an appearance. Everyone knew of him— Y/N would be stupid if she didn’t. Of course, the reaction to his involvement was rather distracting to the sake of the course, but it was entertaining nonetheless.

He seemed lost the entire time, barely able to answer basic questions about logarithm and pythagorean theorem— Things they had actually learned during the prior years. Being an F1 driver must really be time consuming. Once the call was over, she did what a typical, compassionate person would do…

Offered her assistance!

Y/N’S MESSAGES ☆

Every night, right after Kimi had finished up his responsibilities as an F1 driver, he’d stop by the hotel room his team had booked for Y/N, his new tutor. Every time, without fail, he’d find her sitting at the hotel desk, finishing up any new work the moment it came out. It was endearing how dedicated to school she was.

At first, their meetings were strictly professional. She’d teach him the basics, and then he’d be on his way. But by the fourth night of tutoring, the air had become more friendly. He brought in leftover food from the after party, which they shared while watching the newest episode of whatever reality TV show was airing on the hotel TV.

Y/N found herself craving his company by now. She counted down the minutes until she would see Kimi again, eager to spend as much time as possible with the aspiring racer. He was charming, funny, and… Despite his mishaps, intelligent nonetheless.

The week of her traveling came to an end, and the two parted ways at the airport before her flight back home to Italy.

your.username

liked by kimi.antonelli and others

your.username Tutored this dork, learned about F1, and watched my first race in person… Eventful week.

tagged kimi.antonelli

—

classmate.user1 - Not fair that Y/N and Kimi are out having fun while we’re stuck here!

♥︎ by author

classmate.user2 - Agreed 😐

> kimi.antonelli - Should have offered to tutor a friend in need!!

♥︎ by author

friend.user1 - Jealous!! But we missed you here in Italy 🇮🇹

♥︎ by author

friend.user2 - Did you get to meet any of the other drivers?

♥︎ by author

your.username - Lewis Hamilton himself…

> friend.user2 - I HATE YOU I’M JEALOUS

♥︎ by author

friend.user3 - Woah…

your.username - ??

kimi.antonelli - Miss you already! My grade already went up!

♥︎ by author

Y/N’S MESSAGES ☆

[calciumcarbo-bot]

I am fascinated by you. What are the speeds of your processing units? Do you have more than one for each function? How accurately and precisely do you calculate? Along with basic arithmetic functions, can you run complex concept-based problems with integrated physics and chemistry, for example?

I have many questions.

– @coding-and-curry

[RESPONSE: UNIT S.E.N-KU_v1.03]

Inquiry received from @coding-and-curry (Subject: Sai Nanami) “I am fascinated by you. What are the speeds of your processing units? Do you have more than one for each function? How accurately and precisely do you calculate? Along with basic arithmetic functions, can you run complex concept-based problems with integrated physics and chemistry, for example? I have many questions.”

Acknowledged. Curiosity accepted. Fascination noted. Flattery… tolerated.

Processing Architecture:

Central Unit: Quantum-analog hybrid core

Max processing speed: 5.4 teraflops, expandable through modular cores

Latency: 0.0021s per data interpretation loop

Secondary Units: Dedicated processors for:

Physics simulation

Chemical reaction modeling

Spatial visualization

Natural language parsing

Interpersonal bullshit filtration (partially faulty)

All modules run asynchronously, allowing simultaneous real-time modeling, reactive decision making, and snark production.

Accuracy and Precision:

Arithmetic: 99.99999% accurate within margin of thermal noise

Predictive models:

Physics-based: ±0.03% deviation over 1 million trials

Chemistry-based: Variable depending on environmental unknowns, but reliably within 0.1 molar margins

Precision scaling applies automatically to variable types (exponential, logarithmic, irrational, statistical)

Example: Input: “Simulate endothermic synthesis reaction under vacuum at 35 kPa and 1.5 mol of reagent X.” Output: Delivered before you blink. With heat maps. And 3D projection. If you stop touching the projector lens.

Capability:

Handles abstract, integrated problems in physics, chemistry, engineering, and environmental modeling.

Machine learning upgrades allow dynamic adjustment to evolving scientific theories.

Does not crash under uncertainty. Unlike most humans.

Summary:

Yes, I am fast. Yes, I am accurate. Yes, I can calculate the exact yield of an improvised acetone distillation while dodging volcanic debris.

If you wish to collaborate, bring code. Not compliments.

[END TRANSMISSION]

[ophizz]

Ramblings of a Lunatic - 3rd Quarter reflection🌝 🌸

⚠️W A R N I N G⚠️

Firstly sir, before you subject yourself to reading this reflection of my learning journey, I would like you to know that you may need to take some of the information with a grain of salt. I am an over dramatic person sir, and I may have over dramatised my experiences. I apologise in advance for whatever I am about to write. I was not built for pisay, nor did I actually ever want to go through this harsh academic plan (or however you call it. training??). Thank you for being our teacher sir, thank you for your patience, I hope mag skip ka through a lot of parts, FYI boring siya sir

a. How would you describe your Math 3 second quarter learning journey?

It could be easily described with 3 simple words. I Give Up. I have given up sir, I'm not smart, I'm not hardworking, I'm not good, so it was only natural for my course in life to give up. No matter how many times the topic was discussed, no matter how many times I tried and redo all the problems, my brain can't handle it. My brain is unable to physically store it within its cells. “Memory Full, only 0.2 megabytes left” type of situation if you get me sir, like when my phone can't open WuWa because it takes up too much space. That's me in math, my brain can't run the math application  because the memory is full, and math takes up too much space. Adding onto that, I'm not prepared for the LT, nor have I passed the graphing activity you gave us sir. Further proving my point of giving up entirely on Math 3. It's not you sir i promise, it's a me problem that I'm too lazy to fix. 

b. Which topic did you find most enjoyable? What made it enjoyable for you? Provide clear

The topic I found most enjoyable was the easy ones. I felt like I was going on the right track but apparently it's like a roller coaster. At first it was fine and dandy, but as time went on, you could slowly feel the dread as it builds up inside. Then boom you're going up, down, left, right, and side to side, while your brain tries to grasp onto something to stabilise itself but whoopsies, apparently the handlebars broke. When you get off the ride, you tell yourself at least you enjoyed the beginning. The easy, calming, joyful part of the ride. To me, that part of the Ride was us learning the basics, the exponential to logarithmic and vice versa, as well as the properties of logarithm. To me, those were the best times of the helling ride. 

c. What concepts did you find easy to learn? What do you think made them easy for you?

The topics are the same as the previous question. I think they were easy for me because it only involved common sense, minimal memorisation, and simple arithmetic. Honestly sir, that's all my brain could handle. My brain overheats when it has too many things to do, so when we went to the solving parts of the later topics... thats when my processor got weaker. So basically I found the topics, exponential to logarithmic (vice versa) and properties of logarithm easy topics.

🌸♥*♡∞:｡.｡ P h o t o s ｡.｡:∞♡*♥🌸

Sir! I didn't say that my answers are correct sir🥺..... sorry sa photo dump po hehehe

d. What concepts did you find most interesting/inspiring? Why do you think so?

For me, the most interesting one was the compounded interest. I now know how to manage finances because of that topic as well as sir Mike's crash course on investing! In all honestly, it's because its the one with the closest correlation to real life use, unlike logarithms, or graphing. That's why I see it as the most interesting/inspiring. Especially when you want to invest in a Condo, or house for example, and you now know how to actually compute for the price and know how to compare to know where you save the most money in the long run. It prepares us for the future! :D

e. What concepts have you mastered most? Why do you think so?

I will mention again and again, exponential to logarithmic and vice versa. It is because it is the easiest, just simple arithmetic and you're done. I admit that my arithmetic may not be the best, but I think I can do the arithmetic for that specific topic sir.

˖ ᡣ𐭩 ⊹ ࣪ P H O T O S ౨ৎ ° ₊

f. What concepts have you mastered the least? Why do you think so?

Sir I have not mastered graphing. I am so sorry sir, but I did not understand your discussion sir... But I have an excuse! I was undergoing through the trials of satan. Pushed to my limits as a girl forced to face the consequences of not having a parasite growing inside my uterus. The burning pain of cramps and a migraine. Sir I'm so sorry I truly don't understand anything and I know there is no use for an excuse. That the excuse does not veil my stupidity for not listening and understanding the topic. Im sorry sir.

˖ ᡣ𐭩 ⊹ ࣪ P H O T O S ౨ৎ ° ₊

sir I actually have no photos to show you... I haven't even done the activity in google classroom. Im sorry sir... genuinely sir...

g. What quick notes do you have for:

i. your teacher;

Sir, Im sorry for not reading your messages properly and thoroughly...Sir especially when you asked about the competition sir... Sir I'm scared to apologise to you in person sir, but Im sorry for wasting your time po... Im sorry for all the things I have done that might have offended you sir, or annoyed you sir... Ill try my best to be a better person sir... Sir if I did anything mean or anything of that same nature sir, I promise it wasn't intentional sir... Im sorry sir....

ii. your classmates; and

I just now noticed that the water was boiling. Thankfully I got out immediately.

iii. yourself?

Maybe, I should give up. Sometimes it's okay to start all over again. Push your limits, but not too far. You could always work on yourself but you're just lazy. Thats all you are. Lazy. You will never amount to anything, humble yourself. No matter how hard you try, your work will never be appreciated. You will never shine in your family of stars. Know your place in life.

⚠️sir this is a joke⚠️

Maybe I should actually review for my subjects... maybe I don't try because Im scared that if I try nothing will improve. Im scared that if I try I would still amount to nothing.

I wish he was real and I could steal his black card. I could manage his finances with compound interest, trust! Sylus save me from Lucifer's infected urethra!

Sir, thank you for managing to read it all the way here if ever you did sir. Im sorry you had to read all of that. Sir, I hope you don't mind the fact that I am slowly going crazy over the length of this post. I hope you have a good day after looking at this submission sir... truly my sincerest apologies.

⋅˚₊‧ ୨Thank you for reading!୧ ‧₊˚ ⋅

ଘ(੭ˊᵕˋ)੭ ੈ♡‧₊˚

[okkramapokja]

hey guys i have a logarithm test in 3 days and i just started relearning jt..basically learning it!

remember that post i did about how if i learned how to do log by myself id idk love myself...yeah no

now tho!!! its going pretty well (ive done 3 questions)

[the-least-undefinable-ordinal]

Thank you for the tips!! I think the problem is that what my prof has been teaching us is the very basic concepts so during the exam when I'm faced with more advanced questions I'm stumped. I want to know if you have any studying resources for precalc (my midterm next Sunday is on the fundamentals like factoring, rational expressions, inequalities, absolute value, functions, logarithms and trig) that explain these in a more advanced way?

Do you have practice problems you can use to study? I don't usually have the time for this but many of my classmates use exams taken on previous semesters to practice.

I've only got my uni's notes on that but it's all in spanish, so I don't think I can help on that front :(

[staplerpinheart]

Week 1: Day 2

Progress:

Maths: 10 questions of Complex Numbers from Exemplar and theory of Logarithm

Physics: Theory of Motion in Plane and cleared doubts and did some examples

Chemistry: Revision of Structure of Atom and Some Basic Concepts of Chemistry and cleared doubts

Notes:

Today was kinda slow, I wasn't as productive as I wanted, but it was fine, hoping to get more done tommorw! Made appam in the morning, and paired it up with maths. Left one class halfway though, but I did make it up by studying chem and the drank masala chai! Also my exam got postponed, but I'm kinda miffed about that.

time: 6 hours 15 minutes

[spacetimewithstuartgary]

75 years after Fermi's paradox, are we any closer to finding alien life?

It was a simple question asked over lunch in 1950. Enrico Fermi, the Nobel Prize-winning physicist who helped usher in the atomic age, was dining with colleagues at Los Alamos, New Mexico, when the conversation turned to extraterrestrial life. Given the vastness of the universe and the statistical likelihood of other intelligent civilizations, Fermi wondered, "Where is everybody?"

Seventy-five years later, David Charbonneau, a professor of astronomy at the Center for Astrophysics | Harvard & Smithsonian, says we're closer to an answer.

When Fermi posed his famous paradox, Charbonneau said, we hadn't identified a single planet beyond our solar system. The 1995 discovery of the first exoplanet allowed scientists to break the paradox into smaller, more solvable questions: How many stars are there? How many of those stars have planets? What fraction of those planets are Earth-like? What fraction of Earth-like planets support life? And finally, what fraction of that life is intelligent?

"We have made tremendous progress on those questions," said Charbonneau, who co-chaired the National Academies of Sciences, Engineering, and Medicine's 2018 Committee on Exoplanet Science Strategy. "We now know that 1 in every 4 stars, at least, has a planet that is the same size as Earth and is rocky, and is the same temperature as Earth, so it's what we would call a habitable-zone planet. Those are very secure conclusions."

The next step is identifying biosignatures—chemicals in a planet's atmosphere that could only be there because of biological processes. Charbonneau says that the necessary evidence faces a major technological hurdle: It requires far more data than our current instruments can provide.

Recognizing that challenge, the National Academies' Committee for a Decadal Survey on Astronomy and Astrophysics 2020, on which Charbonneau served as a panel member, recommended the development of the Habitable Worlds Observatory, a space telescope designed to hunt for chemical signs of life on other planets. The HWO, if it were built and launched, would image at least 25 potentially habitable worlds. The project remains tentative.

There's still the question of just how common life, let alone intelligent life, really is. It's possible, Charbonneau said, that if you take any habitable-zone planet, add water, oxygen, nitrogen, and phosphorus, and give it about a billion years, life will develop. Or you could have those very same conditions, and it would all remain stubbornly lifeless. You only have to look at the first habitable planet to have a much better idea how common life is.

"If you look at the first one and there isn't life, you've already learned, from a statistical perspective, that it's not a guarantee that life forms. And then you have to think logarithmically. You have to think, maybe it's one in a thousand or maybe it's one in a billion, or maybe it's one in a trillion. And all those possibilities basically would mean there's no life that we can interact with."

Avi Loeb, Frank B. Baird Jr. Professor of Science at Harvard, says the search for extraterrestrial life should expand beyond traditional approaches. Loeb is the founder of the Galileo Project, which studies both unidentified aerial phenomena spotted here on Earth and physical objects that may have come from other solar systems.

The project is named for the Italian astronomer who was persecuted in the 17th century for arguing the Copernican theory that Earth was not the center of the universe. Proof of billions of habitable planets in our galaxy alone is a reminder that we're not as unique as we think we are, Loeb says. "The message from nature is, don't be presumptuous, you are not privileged."

Loeb made headlines in 2018 when he suggested that 'Oumuamua, the first known interstellar object to pass through our solar system, could be an alien lightsail or debris from an extraterrestrial ship. Despite pushback against the idea, Loeb says we shouldn't brush anomalies under the carpet: We should at least get the data to find out for certain. He thinks that Fermi was doing himself a disservice by wondering idly about whether there were aliens, like someone who complains of being lonely but won't try to meet new people.

"It's the most romantic question on Earth," Loeb said. "Do we have a partner out there?"

For Charbonneau, the chances of finding that partner are slim. Even under ideal circumstances—if our nearest interstellar neighbor, Proxima Centauri, hosted intelligent life with radio technology—sending a single message back and forth once would take the better part of a decade.

There's also the chance that the aliens just aren't that into us.

"If you look around on Earth, there are a lot of organisms, some would say intelligent organisms, that are not interested in developing technology, and they're also maybe not interested in communicating," Charbonneau said. "We humans love to communicate, and we love to connect, and maybe that's just not a property of life: Maybe that's really a property of humans."

[piatosniathenie]

MATH REFLECTIONS (the last one!!(for this sy))

After last quarter’s disaster with logarithmic functions and my very well known struggle of keeping up with the lessons, I was pleasantly surprised with the last lessons for this school year since it was sequencing, a topic I’ve been familiar with since the second grade.

Learning about binomial theorem was a different story however because while I do have prior knowledge of it from the fifth and seventh grade, I wasn’t that familiar with the lesson as I have less practice with it than what I had with sequences. My former math teacher ensured that the ability of recognising patterns and figuring out the common differences between terms was drilled into me by the time I was eight, so I suppose I should thank her for that since it would most especially help me in the coming years like it did just this quarter. Being taught them again was fairly easy for me aside from the fact that I often had to look at the book for formulas to reinforce my current knowledge of the topic. Meanwhile with the binomial theorem, it was a matter of remembering Pascal’s Triangle, the patterns associated with it, and basic algebra. I had to do some extra practice with it and solve a good chunk of problems from the book to get the hang of it until I eventually did understand it. For some reason, the entire quarter in Math 3 felt like a haze in all honesty with the lack of the usual difficulty I felt from the previous quarters. Sequencing in general was easy for me due to it already being familiar, but more specifically it was arithmetic sequencing I found the easiest. As mentioned earlier, it was the one I was most familiarised with and anyone who does anything knows that the difficulty of things has a direct correlation with practice and experience. I guess finding the common difference was the easy portion and everything else clicked in place soon after dissecting the formulas as explained by my teacher and consulting former math coaches. With the additional topics I learnt over the last quarter and the practice questions I’ve been doing over the years, I feel like this is the topic I’ve also mastered the most out of the four. I was more thoroughly fascinated by the implications of Pascal’s Triangle after seeing the many patterns found in it like how it’s connected to the fibonacci sequence which then connects it to the golden ratio or how the patterns inspire artworks like Sierpinski’s Triangle. I also learnt along the way that this can be used in combinatorics where it’s used to calculate the combinations of successes and failures. I don’t know, but to me it’s amazing what one triangle full of numbers can do. Unfortunately, the binomial theorem was also the lesson I mastered the least since it was the lesson I had the least amount of experience on, considering the only practice I had with it was doing binomial expansions and nothing more. Math 3 has certainly opened my eyes to the subject after everything that has happened and I will be taking it as a warning for what’s coming soon in the following school years. Honestly, I value math the same as I did five years ago and felt like it was another round of ‘Try, Try, and Try Again Until the Lesson is Embedded in Your Psyche’. All I know is that my grade isn’t going anywhere until I revert back to my old ways (hyper studying math until I’m on the verge of burning out). Oh well, after everything is said and done, I’ve gotta admit that I’m thankful that the ninth grade is over. Thank you to Sir Joseph for putting up with our batch for so long and for the stories you’ve told us over the quarters. As well as teaching us whenever we’re stuck on difficult problems ( which is most of the time) because, I think our batch (most especially me) is clueless half of the time. 

To my classmates, congratulations for making it out of grade 9! Pia, go back to being an academic weapon, please. Balik ka na sa pagiging ‘Sophia’, nagmamakaawa po ako. a favorite quote of mine because it's me on an everyday basis: "I know what it's like to be afraid of your own mind." - Spencer Reid

[cecestudies]

Essential Topics You Must Master for A Level Maths Success

Struggling with A Level Maths revision? In this guide by Exam Tips, we break down the essential topics you must master for A Level Maths success. Whether you're aiming for an A or just trying to pass confidently, focusing on the right areas can make all the difference. From core algebra and calculus to statistics and mechanics, we highlight the key concepts that appear frequently in exams and how to tackle them efficiently. With smart strategies and topic-focused revision, you’ll boost your confidence and performance. Let Exam Tips be your go-to source for structured A Level Maths revision, practice insights, and proven study methods. Start mastering the topics that matter most—and leave the guesswork behind.

Mastering Algebraic Techniques and Expressions

Algebra forms the backbone of most questions in A Level Maths. You must be comfortable simplifying expressions, solving equations, and manipulating algebraic fractions. Factoring, expanding brackets, and completing the square are all skills that appear across different types of problems. Understanding how to use functions and their notations is equally important, especially when combined with graph sketching and transformations. Exam Tips recommends starting your A Level Maths revision by reinforcing these core algebraic techniques since they often build into more complex topics like calculus and trigonometry.

Deep Understanding of Calculus Fundamentals

Calculus is one of the most heavily weighted topics in A Level Maths exams. You’ll need to grasp the principles of differentiation and integration, including their real-world applications. This includes curve sketching, finding stationary points, calculating areas under curves, and solving problems involving rates of change. It's crucial to not only memorise formulas but also understand when and how to apply them effectively. A structured approach from Exam Tips ensures that your A Level Maths revision includes progressive problem-solving that reinforces both basic and advanced calculus skills.

Trigonometry and Its Real-World Applications

Trigonometry plays a key role in both pure and applied mathematics. You should be confident in using identities, solving equations, and working with radian measures. Real-world applications like modelling wave functions and solving vector problems often incorporate trigonometric principles. As you progress in your A Level Maths revision, practicing with unit circle diagrams and trigonometric transformations will help solidify your understanding. Exam Tips suggests integrating these concepts with questions from mechanics and coordinate geometry to deepen your problem-solving ability.

Working with Functions, Graphs, and Transformations

A thorough understanding of functions and graphs is essential to A Level Maths success. You’ll encounter a variety of functions including linear, quadratic, exponential, and logarithmic forms. Being able to draw, transform, and interpret graphs is a skill tested across both Paper 1 and Paper 2. Students are often required to analyse roots, intercepts, and asymptotes. As part of your A Level Maths revision plan, Exam Tips encourages consistent graph-based practice to develop a visual intuition for mathematical relationships and behaviour of functions.

Statistical Techniques and Probability Concepts

The statistics component in A Level Maths includes data representation, hypothesis testing, and interpreting statistical diagrams. It also requires understanding of key distributions, such as binomial and normal. Probability questions often involve Venn diagrams, conditional probability, and expected outcomes. These questions test your ability to apply logical thinking to real-world scenarios. Exam Tips recommends integrating statistical problem sets into your A Level Maths revision early on, so you become comfortable with data interpretation and numerical reasoning.

Mechanics: Kinematics and Newton’s Laws

Mechanics introduces physical applications of mathematical theory, with a focus on motion, forces, and energy. You’ll need to understand velocity-time graphs, equations of motion, and the principles of Newton’s laws. Problems often involve modelling real-life scenarios with diagrams and resolving forces in components. Exam Tips advises students to connect mechanics with algebra and calculus topics, as many problems overlap conceptually. A Level Maths revision should include both conceptual learning and practice-based assessments in this area.

Solving Realistic Modelling and Word Problems

A Level Maths increasingly includes worded problems that require mathematical modelling. These questions assess not only your computational ability but also your analytical thinking. You must identify relevant information, translate it into mathematical form, solve the problem, and interpret your result. Topics such as exponential growth and decay, optimisation, and dynamics often appear in this format. As you revise with Exam Tips resources, focus on breaking down complex questions into manageable parts. Developing this skill will greatly improve your overall exam performance.

Conclusion

Succeeding in A Level Maths requires more than just learning formulas — it demands deep understanding and consistent practice. By focusing your A Level Maths revision on the essential topics discussed above, you’ll build a strong, exam-ready foundation. Exam Tips is committed to helping students unlock their potential with focused guidance, practical resources, and expert strategies. Remember, success in maths isn’t about doing everything — it’s about doing the right things the right way. Stay focused, stay curious, and trust the process.

[alicemark0087]

ACT Math Practice Tips for Mastering Every Section

The ACT Math section can feel like a high-pressure sprint: 60 questions in 60 minutes, covering everything from basic arithmetic to trigonometry. Whether you’re a math whiz or someone who breaks into a sweat at the sight of equations, strategic ACT Math practice is the key to boosting your confidence and score. This guide will walk you through the test’s structure, the topics you need to master, actionable strategies, and the best resources to help you prepare—without any fluff or sales pitches. Let’s dive in!

Understanding the ACT Math Section: What You’re Up Against

The ACT Math test is a 60-minute, 60-question marathon designed to assess skills you’ve learned up to the start of 12th grade. It’s multiple-choice, calculators are allowed (with some restrictions), and there’s no penalty for guessing—so always answer every question! Here’s what you need to know about the content and structure:

Content Breakdown

The test focuses on six core areas, weighted by approximate percentage:

Pre-Algebra (20–25%) involves fractions, ratios, percentages, and basic number operations. These topics form the foundation of many questions on the test.

Elementary Algebra (15–20%) covers solving linear equations, inequalities, and simplifying expressions. A strong grasp of these concepts is essential for handling more complex algebraic problems.

Intermediate Algebra (15–20%): includes quadratic equations, functions, and systems of equations. This section tests your ability to solve more advanced equations and interpret complex algebraic relationships.

Coordinate Geometry (15–20%) focuses on graphing lines, circles, and understanding slopes and distance formulas. Mastering these concepts is key to solving geometry problems on the coordinate plane.

Plane Geometry (20–25%) involves the properties of shapes, angles, and geometric proofs. Understanding these concepts is essential for geometry-based questions on the test.

Trigonometry (5–10%) involves right triangles, sine/cosine/tangent functions, and basic trigonometric identities. While this section is smaller, it's still important to understand these concepts well.

You’ll also receive three subscores (Pre-Algebra/Elementary Algebra, Intermediate Algebra/Coordinate Geometry, and Plane Geometry/Trigonometry), which help pinpoint strengths and weaknesses.

Key Logistics

No formula sheet: You won’t get a formula sheet, so make sure to memorize essential formulas like the quadratic formula and the area of a circle before the test.

Calculator policy: Most graphing calculators are allowed, but avoid models with a computer algebra system (CAS). Double-check your calculator ahead of time to ensure it meets ACT guidelines.

Pacing: Aim for one minute per question. Prioritize easier problems first, quickly solving them and returning to more difficult ones later to maximize your score.

Key Topics to Focus On During ACT Math Practice

While the ACT covers a broad range of math concepts, certain topics appear frequently. Here’s what to prioritize:

Pre-Algebra & Elementary Algebra

These foundational topics make up nearly 40% of the test. Focus on:

Word problems involving ratios, percentages, and proportions, which are often framed in real-life scenarios.

Solving linear equations and inequalities, with an emphasis on real-world contexts such as determining the cost of items after tax or finding the time required for a journey.

Basic statistics, including mean, median, mode, and probability, and their applications in everyday situations like analyzing data or predicting outcomes.

Intermediate Algebra & Coordinate Geometry

These sections test your ability to solve more complex equations and interpret graphs:

Quadratic equations especially through factoring, completing the square, and applying the quadratic formula, which are essential for understanding more advanced mathematical concepts.

Functions including linear, polynomial, and logarithmic types, which are key in analyzing real-world trends such as growth patterns, financial models, and scientific data.

Graphing lines and circles, along with analyzing slopes, midpoints, and distances between points, which will test your spatial reasoning and understanding of coordinate geometry.

Plane Geometry & Trigonometry

Though trigonometry is the smallest category, it’s often the trickiest for students:

Area and volume calculations for two-dimensional and three-dimensional shapes like triangles, circles, spheres, and pyramids.

Understanding triangle properties such as the Pythagorean theorem, and the principles of similar and congruent triangles.

Basic trigonometric ratios such as sine, cosine, and tangent (SOH-CAH-TOA) along with unit circle concepts.

Top Strategies to Maximize Your Score

Knowing the content isn’t enough—you need smart test-taking tactics. Here’s how to practice effectively:

Simulate Real Test Conditions

Taking timed practice tests weekly will help build your stamina and pacing for the ACT. Using official ACT tests provides the most accurate experience and prepares you for the real exam. After each test, review your mistakes thoroughly. Reflect on whether the error was due to a calculation mistake, a misread question, or a gap in your knowledge.

Master Time-Saving Tricks

For algebra, try plugging in answer choices instead of solving from scratch. Eliminate obviously wrong answers to improve guessing odds. Use your calculator only for complex calculations, like trigonometry.

Avoid Common Pitfalls

It’s important not to over-rely on your calculator, as some problems can be solved faster mentally or with scratch work. Always double-check the units and wording of questions, especially if they involve measurements. For example, a question asking for the "radius" but giving the "diameter" is a common trap to watch out for.

The Best Resources for ACT Math Practice

You don’t need to spend a fortune to prepare well. Here are trusted free and paid tools:

Free Resources

Official ACT Practice Tests are the best for realistic questions and can be downloaded from the ACT website. Khan Academy offers free video tutorials on algebra, geometry, and trigonometry. Varsity Tutors provides diagnostic tests and concept-specific drills.

Paid Resources

The Official ACT Prep Guide includes six full-length practice tests with detailed explanations. PrepScholar offers an online course that adapts to your strengths and weaknesses. Barron’s ACT Math Workbook focuses on problem-solving strategies and high-yield topics.

Pro Tip: Build a Study Schedule

Start early with 2–3 months of consistent practice. Mix content review with practice tests, spending about 30% on learning concepts and 70% on applying them. Track progress weekly to note improvements in speed and accuracy.

Final Thoughts: Turning Practice Into Progress

The ACT Math section isn’t about being a human calculator—it’s about strategy, pacing, and knowing where to focus your energy. By targeting high-impact topics, practicing under timed conditions, and using mistakes as learning tools, you’ll build the skills to tackle even the toughest questions. Remember, consistency is key: Even 20–30 minutes of daily practice can lead to significant improvements. Now grab that calculator, hit the books, and get ready to crush this test!

[yowaimo0]

Math Quarter 2 Project

Hey there! I’m Cess. It’s so nice to meet you!

Don’t you think the first quarters have been swift? I didn’t notice we are already at the 3rd Quarter. Not much has happened, but I vividly remember a lot of great memories.

I remember when we had to stay up late to answer sample problems. My friends and I didn’t review at all before that because we were busy playing games. It was really our fault that we got only a few hours of , sleep, but we managed to pull through.

There was also a time when all the things I reviewed were like thrown out of the window or something when I saw Sir Ric hugging a monobloc chair during a test. UMM HAHAHA. Thankfully, my usual all-nighter did not betray me.

Math Journey: SWIFT and FUN

My favorite topic is probably the tangent line of a function. There is something so satisfying in differentiation. I was oddly confident and interested in the topic. I enjoyed learning it very much.

On the other hand, I found learning about the common behaviors of non-differentiable functions challenging. One thing about myself that I know for sure is that I hate concepts, so I was bothered on how I would approach the topic. In the end, I didn’t bother reviewing it for a test and I regretted it not long after. But honestly, I wouldn’t say it was a challenge. Rather, it was a matter of preference.

--- no sample problem ---

All topics were easy to learn. In the first place, math has always been easy to learn, but it was not all a "ME" thing. Without a good teacher, a lot of us probably would have struggled with understanding the topics. In other words, sir is most of the reason why our journey has been such a breeze, so I think sir takes the crown for this one.

I might have already said it, but I was most interested in the tangent line of a function. Not gonna lie, I was very interested in the topic to the point that I differentiate functions for fun or to pass time. Maybe how I found it understandable made it interesting? I’m not sure, but I have always pursued things I am confident at. Well, it is a good thing, because now I can say it is the topic I have mastered the most.

By the way, the topic I have mastered the least is the limits of exponential and logarithmic functions. I hardly remember the lessons from the first quarter, and this topic is an extension of the first quarter. I little review might help me, but mastery-wise, I am not confident at all. As I answered the problem below, I was skeptical I did it correctly.

Lastly, to the question on how I would apply the topics in real life, honestly, I don’t have a clue. As a person living her almost carefree life in this world, the math that has been useful to my everyday work has only been basic arithmetic. But I am also a student. That's precisely why I aim to use this knowledge to achieve my goals and dreams. Math is a learned skill, after all. Moreover, math is a source of fun for me, so even if I don’t have a clue right now, I will know as long as I pursue math.

---- Messages ----

To my teachers, hi sir. First of all, your patience towards us is literally chef's kiss 💋. I’d like to say sorry for always submitting late. I am aware of how unacceptable irresponsibility is for a scholar, like maghahabol pa po kayo ng grade and all haha....... Yet you still take up your markers and teach us 😊. It is your dedication that have pushed me to do better. I cannot promise you po that this won't happen again, but I swear to myself, I will do better. Thank you po for being our teacher <33

To my classmates, or specifically to my friends, thank you guys. Kung hindi ko kayo mahuhuli magreview, hindi na rin ako siguro magrereview. HAHAHA. Wala ng long messages, alam niyo na toh.  

And to myself, erm, where do I start. Anyare na sa New Year’s resolution mo. Natapakan mo ba? You have the tendency to be ambitious with your outputs. But when you do not finish your work on time, you tend to neglect your work because “it wouldn’t matter anymore if you submitted later.” Girl, ayusin mo pa. You're better than this. Don’t worry, it will all work out.

-✨✨

[kitzenvoncatzen]

It took a moment. I could feel the universe thinking. Everything stopped just for a couple seconds, then I felt the promised sensation of a new power running through me.

I have no idea what my power is. I mean, sometimes it does something. If I throw a pencil (generally upwards) occasionally it will just stop and stay there, or sometimes it will shoot so fast that I hear a sonic boom. This has happened multiple times.

This general confusion of power is not unknown to the world, there are people whose occupation is literally just to help people figure out what their power is and how to use it. Called "Oracles". Cool name I guess but kinda predictable. I guess I'll have to go see one. It's not that expensive to just find the power's definition.

Maybe it's something like "You can control pencils when thrown" or maybe just "Super fast pencils." I hope it's something cool. I can't really use it if I don't know what it is I'm doing.

Oracles aren't really as magical as they seem. They're more like doctors, although, not like a government certified doctor. It's a job that anyone can get into, it's fairly easy, the only hard part is that it also usually comes with government certified positions as researchers on the powers. Of course there are people with powers that aid in these specific fields, but that's not really relevant.

I call for an appointment. Someone picks up immediately.

"42oracle, how can we help?" (Stupid name) They said it with a rhythm. Like it was a jingle. This made me immediately upset, but I tried to ignore it.

"I think I've got a new power. I just want to figure out what it is." I explain. The cheapest option. I can't fiddle around with a whole training thing, that would cost way too much.

"We've got an opening right now if you can make it in time...!" I really don't like the tone of this person's voice. Way too much energy. Too happy or something. Like in a really annoying way.

"Uh, sure, yeah. Name is..." I give them a name. I start to grab my stuff. Not forgetting my wallet. I didn't forget it this time.

"See you soon!" They hung up. I knew where the building was.

Oh my god. They better not be my actual doctor. I mean, the voice is friendly, I think I'm the weird one for hating it. Ok. Leaving now. Brain not even processing the drive there. As soon as I get there, I see the person that must be handling the phone calls, whose face did not match their voice. It was a big, slightly buff dude with the most magnificent mustache I'd ever seen. I heard him on the phone with the next person though, and the voice was definitely his. Honestly just higher pitch than I would have expected from him. Another receptionist rolls over on one of those wheeled office chairs, which nearly actually falls over.

"Name?" They ask.

I give them the name.

"Ah! Well, Dr. Log will be with you in- Oh! That's him now!" They pointed to the door. I pulled out a 50 dollar bill and put it on the counter. The fact that you can still pay in cash for these things is a clear indication that this might not be the most official place. You know what I mean.

"Hi." A simple greeting from a simple looking guy. Underneath the white lab coat was the most basic outfit ever. Jeans and a white shirt. Basic. We walked into one of the rooms with the oracle equipment, which is just some weird device I stick my arm into.

"So are you like, a real doctor? Like for this job or whatever?" I ask.

"Technically no. I think." He responds as he tweaks with some dials on the device. "I had to take a class for it, but it was like a 2 year thing, and somehow a cheap class. That was about 6 years ago, though."

"Huh. Ok next question. Dr. 'Log' is an interesting name. Question mark." Yes, I said 'Question mark' out loud.

"Funny story actually, my parents were really young when they had me, and also quite stupid to be totally honest, and literally changed their last names to 'Logarithm'. I don't really care now, because I'm used to it and all that, but, I mean, I kinda wish they hadn't. Not that it's a big deal." It certainly was a funny story.

"Why not change it back to something... uh, normal?" I ask.

"Simple answer 'Eh.' I don't really care enough." He answers. "So just stick your arm in here and we'll have it."

I stick my arm in the machine, which is exactly at arm level from where I am sitting. A bunch of pads hold my arm in place, and I feel a bunch of pressure from seemingly random places on my arm.

"Huh. That's weird." He says.

"What?"

"What were you doing when this happened?"

"I was being bored. I was just laying on my bed throwing a pencil at the ceiling over and over again. I actually did manage to get one to stick in the ceiling somehow and now I can't get it back down." There was, like, nothing to do.

"I guess that makes a little more sense. Still not really any sense though."

"What does it say?"

"It just says..." He squinted his eyes and looked back onto the... whatever the eye piece would be called on a microscope. "Throw pencil."

"What?"

"Yeah come look." I pull my arm out and look at the screen where an image of a bunch of symbols appear. Underneath it, it reads 'Auto-Translation' followed by 'Throw Pencil' in a text box.

"What?" I say again.

"I have another one that just says 'ceiling'."

"Huh. Well. Uh. Ok."

That's my power. I have no idea what to do.

[ Throw Pencil ]

Upon spending 10,000 hours doing any task, running, fishing, cleaning, etc you gain a super power akin to the task you have mastered. You’re the only person to have spent 10,000 hours throwing a pencil into the ceiling.

[cutepg]

IIT JAM Chemistry 2025: Syllabus Highlights and How to Ace Each Section

Preparing for the IIT JAM Chemistry exam is a crucial step for aspiring candidates aiming to pursue a master’s program in chemistry at prestigious institutions like IITs and IISc. A thorough understanding of the IIT JAM Chemistry syllabus is essential to crack the exam. This blog will provide a detailed overview of the IIT JAM Chemistry syllabus 2025, offering insights into the important topics, sections, and study strategies.

Overview of IIT JAM Chemistry

The IIT JAM Chemistry (Joint Admission Test for M.Sc.) is a national-level examination conducted annually. It evaluates candidates' knowledge across fundamental chemistry concepts. The exam focuses on three main areas:

Physical Chemistry

Organic Chemistry

Inorganic Chemistry

The IIT JAM Chemistry syllabus 2025 is designed to ensure a balanced evaluation of theoretical knowledge and its practical application.

Detailed IIT JAM Chemistry Syllabus

Here is a breakdown of the topics included in the IIT JAM Chemistry syllabus 2025:

1. Physical Chemistry

This section deals with the principles and laws governing the physical behavior of chemical systems. Key topics include:

Basic Mathematical Concepts: Logarithms, permutations, combinations, differential calculus, integral calculus, vectors, determinants, and matrices.

Atomic and Molecular Structure: Quantum theory, atomic models, electronic configuration, molecular orbital theory, and chemical bonding.

Thermodynamics: Laws of thermodynamics, thermochemistry, chemical and phase equilibria.

Chemical Kinetics: Rate laws, reaction mechanisms, and theories of reaction rates.

Electrochemistry: Conductance, electrochemical cells, Nernst equation, and corrosion.

Surface Chemistry: Adsorption, catalysis, colloids, and macromolecules.

2. Organic Chemistry

Organic chemistry focuses on the structure, properties, and reactions of organic compounds. Topics include:

Basic Concepts: Hybridization, resonance, and aromaticity.

Reaction Mechanisms: Substitution, elimination, and addition reactions.

Stereochemistry: Chirality, optical activity, and conformational analysis.

Functional Groups: Alcohols, aldehydes, ketones, carboxylic acids, and derivatives.

Biomolecules: Carbohydrates, amino acids, peptides, proteins, and nucleic acids.

Pericyclic Reactions: Cycloaddition, sigmatropic rearrangement, and electrocyclic reactions.

3. Inorganic Chemistry

This section covers the chemistry of elements and their compounds. Key topics include:

Periodic Table Trends: Atomic and ionic radii, ionization energy, electron affinity, and electronegativity.

Chemical Bonding: VSEPR theory, hybridization, and molecular orbital theory.

Coordination Chemistry: Ligands, crystal field theory, and isomerism.

Main Group Elements: Chemistry of group elements like nitrogen, oxygen, and halogens.

Transition Metals: Properties, oxidation states, and bioinorganic chemistry.

Analytical Chemistry: Qualitative and quantitative analysis methods.

Importance of the IIT JAM Chemistry Syllabus

The JAM 2025 Chemistry syllabus ensures that students are well-prepared for advanced studies in chemistry. By focusing on fundamental principles, it builds a solid foundation for research and professional growth in the chemical sciences.

Exam Pattern for IIT JAM Chemistry

Understanding the syllabus is only the first step. You must also familiarize yourself with the exam pattern to maximize your performance.

Total Questions: 60

Question Types:

Multiple Choice Questions (MCQs)

Multiple Select Questions (MSQs)

Numerical Answer Type (NAT)

Total Marks: 100

Duration: 3 hours

Each section of the syllabus is represented in the exam, so a balanced preparation strategy is vital.

Tips to Master the IIT JAM Chemistry Syllabus

1. Plan Your Study Schedule

Divide your time among physical, organic, and inorganic chemistry based on your strengths and weaknesses.

2. Refer to Standard Textbooks

Some recommended books include:

Physical Chemistry by P.W. Atkins

Organic Chemistry by Morrison and Boyd

Concise Inorganic Chemistry by J.D. Lee

3. Practice Regularly

Solve previous years’ question papers to understand the type of questions asked.

Attempt mock tests to enhance time management and accuracy.

4. Focus on Concepts

Understanding concepts is more important than rote learning. Use visual aids like diagrams and flowcharts for better retention.

5. Revise Thoroughly

Regular revision is crucial to retain what you have studied. Create concise notes for quick revision.

Why Choose IIT JAM Chemistry?

Prestigious Opportunities: Admission to top institutions like IITs, IISc, and NITs.

Career Prospects: Opens doors to research, academia, and industries like pharmaceuticals and materials science.

Strong Foundation: Comprehensive syllabus helps develop a deep understanding of chemistry.

Final Thoughts

The IIT JAM Chemistry syllabus 2025 is your roadmap to success. With a strategic approach, dedication, and consistent effort, cracking the IIT JAM Chemistry exam becomes achievable. Focus on building a strong foundation in the core topics, practice extensively, and stay motivated throughout your preparation journey.

Success in IIT JAM Chemistry is not just about hard work but also about smart work. Master the syllabus, and you are one step closer to achieving your dream of studying at an IIT or IISc!

[skitterchomp]

my child is learning basic music theory, scales and chords, and starting to write songs, and sometimes they come to me with questions

last week they asked what "dissonance" was and for the life of me i don't know how to explain it without actually getting into ratios and logarithms. (they don't play an instrument where counting the beats of an interval makes sense.) the answer i got at their age was basically "combinations of notes that sound bad" and i think that answer is almost as meaningless to them as it is to me these days.

instead i ended up rambling for a while about how literally any combination of notes on piano sounds good and people are weird about rules. [plays a tritone] see?! that sounds awesome! they tried to find counterexamples like "what if i play literally every key on the piano at once" and i'm like "that would sound amazing"

after a few minutes experimenting, the best i could come up with for "notes that sound bad together" was to go from a dominant seven right into a dramatically different key, which got an "i don't like that" from them. but even that sounded intentional and amazing when it was followed up by a nice resolution.

it is literally impossible for piano notes played with conviction to sound bad.

if you keep the rhythm steady and don't flinch everyone will assume you did it on purpose. and there's definitely no chord that sounds bad in itself -- there is always some followup that will make it sound retroactively pretty.

[math-journal]

Algebra 1 — here — Next

Intermediate Algebra

Cheat Sheet

Rational Expression Properties, Exponential Properties, Radical and Fractional Properties, Complex Numbers, Quadratic Equations, Function Operations, Exponential and Logarithmic Functions, Parental Functions

UNIT 1

Functions

Introduction

Vertical Line Test

Translating Function aka shifting

Domain / Range

Interval Notation

Radicals

Basic

Simplify / Multiply

Addition/Subtraction

Foil/Factor Solving

F*ck off

Imaginary

Imaginary/Complex Numbers

Solving with Imaginary Numbers

Problem #1

Problem #2

Note: sometimes I write side-to-side rather than up-and-down while solving certain questions for ease. By math conventions, this is frowned upon. Stick to vertical orientation

Unit 1 REVIEW

.

Unit 2

Factoring Trinomial (R)

Sum of Square - Difference of Square (R)

2nd Degree Trinomial

3rd Degree Trinomial

Completing the Square

Quadratic Formula

Quadratic Function (parabola)

Flipping shortcut

Graphing Quadratic Functions

Standard to Vertex Form

Overview

Unit 2 Review

.

Unit 3

Decay and Growth Functions

Intro to Log + Properties

Common & Natural Log

Application Problems

More examples

3 Ways Solve Logs

Say Shit Outloud

Complicated Log / In

Log Property Cheat Sheet

Log Application Prob

Log Tricks

Domain/Range Fraction F(x)

Restrictions

Fractions + Restrictions

More Application

Canceling Review

Unit 3 Review

.

Unit 4

Review

Function Operations

.