Move onto Calculus?

[LisaKinVA]

My daughter is finishing up the AoPS Intermediate Algebra Book.  She has already completed LoF Trigonometry.  She will have approximately 3 months between finishing AoPS Intermediate Algebra and school starting in the fall.

 

Options:

 

1) Test through the Larson Precalculus Text I have... going back through anything she isn't sure of; or

 

2) Run through the shorter AoPS Precalculus text and then just go onto Calculus; or

 

3) Just go to Calculus (We'll be using the Larson Text here with Chalkdust and Educator.com, although I have AoPS -- it will help *me* tremendously if she and my oldest son are using the same textbook next year...she will most likely go back to AoPS to go deeper afterwards (for fun, as mathematics is a probable major)

 

**She's already completed the Counting & Probability books, and the Number Theory Book**

[Mike in SA]

Option 2.  Trigonometry is absolutely essential in calculus, and shouldn't be brushed over.  AoPS is pretty brief, but covers the trig well, and focuses on topics that many precalc texts miss.  If you worry it is too short, she can add additional trig and analytic geometry, and be all the better for it.

 

Really, you can't skip the trig content.  She needs to be comfortable with trigonometric identities, or the substitutions in calculus will be brutal.

[regentrude]

If AoPS works well for her, I recommend that she goes through the trigonometry portion of AoPS precalculus. If she has to complete it in a few months, she can focus on the trig chapters and skip the vectors and matrices.

Edited April 28, 2016 by regentrude

[Julie of KY]

If you want to move on to calculus, I'd spend the three months doing as much of the AoPS precalc book as you can. Concentrate on the trig and logarithm chapters.

[regentrude]

If you want to move on to calculus, I'd spend the three months doing as much of the AoPS precalc book as you can. Concentrate on the trig and logarithm chapters.

 

Logarithms are not covered in AoPS precalculus

 

[Julie of KY]

Sorry, I was thinking of the logarithm chapter in the Intermediate Algebra book.

In other words, make sure you know the trig (of precalc) and logarithms, which I think she's already done.

 

I thought the precalc book was an excellent book, by the way.

[LisaKinVA]

Option 2.  Trigonometry is absolutely essential in calculus, and shouldn't be brushed over.  AoPS is pretty brief, but covers the trig well, and focuses on topics that many precalc texts miss.  If you worry it is too short, she can add additional trig and analytic geometry, and be all the better for it.

 

Really, you can't skip the trig content.  She needs to be comfortable with trigonometric identities, or the substitutions in calculus will be brutal.

 

She has completed Life of Fred Trigonometry...it hasn't been skipped.

[LisaKinVA]

Okey dokey...AoPS Precalculus it is...I'm pretty sure since she's done trig already it won't be overly difficult and a good review.  

[Julie of KY]

I realize you haven't skipped trig and the is why you can move on to calculus. However, AoPS does go much more in depth and this would be "helpful" for calculus.

 

If you are going at your own pace rather than with a class, you can always back off and learn more trig if needed along the way. (Not sure if you are committed to another's schedule or not).

[Lilaclady]

Aops precalculus but I am not sure she can cover it in 3 months. It is quite in depth and also has some linear algebra in it which I think will be beneficial later.

[Kathy in Richmond]

AoPS precalculus is more worthwhile in my book than a typical calculus course like Larson. Much more thinking involved, harder problems to chew on, & the trig is much more in depth than LoF. I insisted that my own kids spend a year on this material, especially since they were considering math majors. The linear algebra chapters prepare well for upper level college math concepts.

[8filltheheart]

Agree 100% with Kathy. My ds spent a school yr going through the pre-cal book (with her, no less! Awesome teacher that she is! What a blessing that was for ds. :) ) Not sure how the text qualifies as shorter, though. It is a thick book.

 

He has commented a few times that the foundation from that book has been helpful in his upper level math courses and that he is glad he spent that yr with it.

[regentrude]

 The linear algebra chapters prepare well for upper level college math concepts.

 

... but are not a prerequisite for calculus 1 and can be postponed if the student has to start a calculus class at the beginning of the new school year. These concepts will be needed prior to multi variable calculus.

 

[LisaKinVA]

Yes, the goal is to have her ready to start calculus with her brother in the fall.  I kind of believe she'd be there *without* the AoPS Precalc book, but see the benefit in going through the trig portion again.  And yes...my goal is to make it a bit easier on *me* next year.  These two do well studying together, and they've done very well in more difficult classes (AP Chem) with each other to lean on/study with, etc.  What she finds easy, she explains to DS, what DS finds easy he explains to DD.

 

She will also go through the AoPS Calculus book, and can come back and hit the linear Algebra sections in the Precalc book (probably next summer and into the following year).  Her happy places are Math, Swimming and Marine Biology...although there is no convincing her that math competitions might be fun!

 

If she needs more time, that's fine, too.  She enjoys circling back around, and has been known to do so for fun.

Edited April 28, 2016 by LisaK in VA is in IT

[Arcadia]

You can do option 1 and 2. Option 1 might take you a week. The aops calculus book is the thin one though, the precalc book is as thick as the other books. My oldest is doing the precalc book now and some days he spend four hours because he want to. He does math daily because he wants to. Else it is a hard book to go fast on.

 

I have the Larson books and my kids aren't interested after using the aops books. However my kids are unfortunately rebellious like me.

[LisaKinVA]

You can do option 1 and 2. Option 1 might take you a week. The aops calculus book is the thin one though, the precalc book is as thick as the other books. My oldest is doing the precalc book now and some days he spend four hours because he want to. He does math daily because he wants to. Else it is a hard book to go fast on.

 

I have the Larson books and my kids aren't interested after using the aops books. However my kids are unfortunately rebellious like me.

 

Some days, her idea of crawling in bed with a "good book" is her AoPS text ;)  However, she's done well with every text she's used.  She does prefer AoPS to other texts...she's not my rebellious child, though.  That's reserved for PokeMan and Blondie.  

[Mike in SA]

After having done intermediate algebra, the precalculus text could be completed over the summer.

 

Just saying...

 

Eta: older DS has already been through two different precalculus texts and will start calculus in the fall (he has actually been through a calculus text, too). He just started AoPS precalculus this week. It's that worthwhile.

Edited April 28, 2016 by Mike in SA

[Grantmom]

So do you think one could start the AoPS Precalc book over the summer, start Calculus in the fall, and then still continue to work through the AoPS Precalc?

[Brad S]

So do you think one could start the AoPS Precalc book over the summer, start Calculus in the fall, and then still continue to work through the AoPS Precalc?

 

I think comments 2 and 3 address your question: with proper prep before precalc, you need to do the trig before the calc, then can do matrices whenever it fits but before multivariable calc (around the 3rd semester of calc).

 

[LisaKinVA]

I'm not 100% sure where she'll wind up, but since mathematics (teaching) is one of her two desired major areas, a thorough understanding is best.  She has worked pretty quickly through AoPS and has done double programs in Pre-algebra, Algebra 1, Algebra 2 and Geometry.  I'll probably work up a couple of math plans for her for the next 2 years (I'm pacing her older brother through BC over two years, because of swimming and intensive studies in other areas -- there's just not time to cover BC thoroughly and quickly in one year).  She's a different math student, and even if she does the whole AoPS Precalculus book, she'll probably catch back up to her brother in Calculus by the end of her sophomore year/his senior year.  After that, I believe she has multivariable calculus, differential equations and linear algebra, and statistics thrown in there somewhere.

[Mike in SA]

So do you think one could start the AoPS Precalc book over the summer, start Calculus in the fall, and then still continue to work through the AoPS Precalc?

 

Yes, or simply do them back-to-back.  Calculus can move surprisingly quickly.  We do precisely one section per day, then add two days for review and testing.  At that pace, it takes just under 6 months to complete the content from calculus 1 & 2.  Precal over the summer may not bleed into the school year at all, but if it does, probably not enough to be a concern.

[Grantmom]

Thank you! I'm feeling worried about trying to do too much too soon. I feel like I did that a bit this year. DS actually loved it, and is not the kind of kid to be concerned about grades. He just liked the challenge of the courses. But I'm worried about not setting him up to be successful, and then having that on his transcript if it's too much.

[kiana]

Thank you! I'm feeling worried about trying to do too much too soon. I feel like I did that a bit this year. DS actually loved it, and is not the kind of kid to be concerned about grades. He just liked the challenge of the courses. But I'm worried about not setting him up to be successful, and then having that on his transcript if it's too much.

 

If you start calculus and need to slow down for him to make optimal understanding, you can always complete it over two years -- this is commonly done in PS as well and will raise no eyebrows. If he has only one year left, you can complete differentiation and a chapter of integration and easily justify calling it Calculus I on a transcript.

[JanetC]

LoF Trig bills itself as a complete precalc program and AOPS Intermediate Algebra also includes many precalc topics. You are likely ready for most calculus programs.