$highschool class help$

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$highschool class help$

i only have the math level of a grade 11, which is pre calculus 11, would i be good to take a grade 12 level calculus course? im going to be passing pre cal 11 with a 98 but im not sure if thats enough for calculus 12. are the fundamentals of calculus taught in the course? Is calculus 12 like another type of math that pre cal 11 sets you up for? im also taking going to be taking pre calculus 12 in the same semester. if i am able to with my current knowledge, can you tell me what i need to know and what i should study to be more prepared?

Calculus

Taylor Fournel

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Given that you are passing Calculus 11 with a 98, I think you are absolutely ready and prepared for both pre calculus 12 and Calculus 12. Here are the guidelines for teaching Calculus 12 in BC, Canada:

file:///Users/new-imachome/Downloads/calculus.pdf

I suggest you to take a look at this file and it will give you a good idea about what topics are going to be covered. If you live in the USA or another part of Canada, or Europe the syllabus is going to be similar.

The topics in Calculus 12 generally cover the following concepts:

- Functions and their graphs. You should be good at understanding and graphing standard functions such as parabolas, trigonometric functions, exponential functions and lines.

- Limits of functions. To understand this concept, you need a good understanding of graphs of functions and have strong algebraic skills. So you may want to work on you algebra skills.

- Derivatives of functions. If you are good with functions and have strong algebraic skills you'll be fine and you can learn the concept of derivatives when it is taught in class.

- Anti-derivatives and Integrals. This is just doing derivatives in opposite direction and if you learn the concept of derivatives well, you would have absolutely not problem learning anti-derivatives.

_ You will also learn about applications of derivatives and antiderivatives in real life problems. (you should expect word problems).

My suggestion is that you try to see solutions to as many problems as possible for each concept first, then try to solve problems on your own. There is a famous quote by Einstein

"Example isn't another way to teach, it is the only way to teach."

By the same token

Example isn't another way to learn, it is the only way to learn.

The best way to learn Calculus is to learn from examples. Try to first see solutions to many solved problems and then try solving some on you own. You should absolutely avoid trying problems on your own before seeing solutions to at least a few similar problems first. This will help you learn much faster.

If you get stuck on problems, you may seek help from so many great mathematicians on the website. Most people who answer questions on this website have masters or PhD degrees and very knowledgeable.

Let me know if you have any additional questions or comments.

Here how you can rationalize:

\[ \frac{21}{3\sqrt{5}-\sqrt{3}}= \frac{21(3\sqrt{5}+\sqrt{3})}{(3\sqrt{5}-\sqrt{3})(3\sqrt{5}+\sqrt{3})} \]
\[=\frac{21(3\sqrt{5}+\sqrt{3})}{(3\sqrt{5})^2-(\sqrt{3})^2 }\]
\[=\frac{21(3\sqrt{5}+\sqrt{3})}{3^2. 5-3 }=\frac{21(3\sqrt{5}+\sqrt{3})}{45-3 }\]
\[=\frac{21(3\sqrt{5}+\sqrt{3})}{42 }=\frac{3\sqrt{5}+\sqrt{3}}{2 }.\]

Erdos

4.7K

Taylor Fournel

0

i didnt take calculus 11, i took pre calculus 11, but i was very good at everything in the class, we only looked at straight line formulas, parabola formulas, we didnt do anything other than that. we didnt deal with any 3d object questions, i know how to find volume but not a question like "a pool is 4 m tall, 3 meters long, and 5 meters wide. you have a hose thats outputting water at t/100 cubic meters per minute. after minutes how full with the pool be?"
Taylor Fournel

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i dont know the exact question but the volocity and the amount of water coming out was increasing. this was a question i was given by someone on reddit as an example of a question.
Taylor Fournel

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the amount of water coming out at 1 minute was 1/100 cubic meters per minute and at 2 minutes the rate of flow was 2/100 cubic meters per minute, after three minutes had elapsed the amount coming out was 3/100 cubic meters per minute
Erdos

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The problem you mentioned is an application of derivative. It is called related rates. See https://tutorial.math.lamar.edu/classes/calci/relatedrates.aspx
Taylor Fournel

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we didnt deal with any 3 d object questions about two intersecting prisms. im sure i can figure out the overlapping area of two shapes.
Erdos

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This is a good resource to learn about derivatives and related rates: https://tutorial.math.lamar.edu/classes/calci/DerivativeIntro.aspx
Taylor Fournel

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this is what we covered Ch2. Trigonometry -Standard Angles, Reference Angles, Quadrants -Exact trig ratios (SIN COS TAN) -Sine Law -Cosine Law Ch3. Quadratic Functions - Graphing quadratics in Vertex Form - Complete the square Ch4. Solving Quadratic Functions (must be =0) -Graphically (find x-intercepts) -Factoring -Quadratic Formula Ch5. Radical Expressions - Simplify Radical Expressions -Add an
Taylor Fournel

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Ch5. Radical Expressions - Simplify Radical Expressions -Add and Subtract Radical Expressions - Multiply and Divide Radical Expressions -Rationalize the Denominator - Solve Equations with Radicals Ch6. Rational Expressions - Simplifying (by factoring and cancelling) Non-permissible values -Multiplying and Dividing - Adding and Subtracting (common denominator) - Solving Equations Ch8. Systems of Equations - solving systems of equations using a graph - solving systems of equations using algebra Ch
Taylor Fournel

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Ch9. Graphing Inequalities -graphing a linear inequality -graphing a quadratic inequality
Taylor Fournel

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im sorry for the bad format, it cut off at 500 words
Erdos

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Great. I think you are prepared to take Calc 12. No need to be stressed out about it or get ahead of yourself!
Taylor Fournel

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are any aspects of calculus comparable to physics? i was good at that
Erdos

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Not really, the material is different. But of course Calculus has applications in Physics.
Taylor Fournel

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https://docs.google.com/document/d/1yjt40fNINiC_iYrsRfOsWGWEZJLoBs00HXMePOQqeyQ/edit?usp=sharing
Taylor Fournel

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thats the review
Erdos

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Can't view it.
Taylor Fournel

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give me a second, ill give an example of a question i would have a harder time with
Taylor Fournel

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actually there wasnt really any question i had problems with, just me overthinking. but heres a question i took a while
Taylor Fournel

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(21)/(3root5-root3)
Taylor Fournel

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theres no root button
Taylor Fournel

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is that in any way on the same level of math as calculus?
Taylor Fournel

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i was asked to rationalize
Taylor Fournel

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actually i found one that i couldnt get
Taylor Fournel

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(4x-1/x+2)-(x+1/x-2)=(x^2-4x+24/x^2-4) solving this
Taylor Fournel

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i now realize i make the denominators the same and that would probably make the final numerator factorable
Erdos

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I added the solution to your first question. I have spent so much time on this post. If you have additional questions you may ask them in a separate post.
Erdos

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See the body of my answer above.
Taylor Fournel

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unless i had to use the complete the square, i think thats what its called, am i supposed to (X^2-4x+4)+24-4
Erdos

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As I mentioned, if you have additional problems you may ask them in a separate post.
Taylor Fournel

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ill make another one for $20
Erdos

0

Make sure to ask your question very clearly. You can use the editor to type equations or just simply upload a picture.

$highschool class help$

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