Expert Tips for Succeeding in High School Calculus

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To succeed in high school calculus, strong algebra skills are essential. Neatness in writing is crucial to avoid frustration and errors. It's important to avoid skipping steps in problem-solving, as this can lead to mistakes. Using multiple textbooks can provide different perspectives on challenging topics, enhancing understanding. Finally, always start with the easiest problems and gradually work up to more difficult ones to build confidence and skills effectively.
dekoi
I'm starting my first year of calculus at high school (grade 12 academic). I am wondering whether those of you with experience can suggest tips on doing well in this course. Any hints available would be very helpful (the most important skills as an example). Thank you.
 
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Algebra. If your algebra is good, you will do well in calculus.
 
Here's some that helped me:

1. Write neat (pretty would be a better word but don't want to sound peculiar). It's a big deal really. If you write messy you're in for a lesson in fustration.

2. Don't skip steps (I think Einstein said that one). You know, when you start getting good at it you have a tendency to do some of the simple steps in your mind. Try not to.

3. Try using several books (no I don't mean doing all the problems from all of them, just use them as reference. Sometimes one presents a topic better than the other.

4. Never attempt to "jump" to a high number in the problem set. Always start at problem 1 (the easiest one), then 2, then the rest. Try not to skip them. Their in an order for a reason. If your instructor tells you to do number 10, you guessed it, do the first nine first.


5. If you get to a problem you can't solve, put it up and try working on a simpler one. Do that one, add a little to it, solve it, do some more then gradually work up to the difficult one.
 
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Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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