I am going in AP Calc BC next year and I wanted a good head start. I am reviewing the AP Calculus Prep books as well as videos on khanacademy.org. What else should I do?
One more thing, I have NOT take AP Calculus AB.
One more thing, I have NOT take AP Calculus AB.
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First don't worry. Calculus BC is doable....most people who take Calculus BC across the country do NOT take AB. Basically, AB = 1 semester of college calculus, and BC = 2 semesters of college calculus, which INCLUDES BC Calculus.
Khan academy's a good site. MIT OCW also has good math videos. Their curriculum may not match up 100% to the AP curriculum...in fact, it goes faster, but may have a few holes in it, particularly towards the end. Their "first semester" calc class covers BC Calculus, and their "second semester' calculus class covers what would normally be the first college math class you'd take after BC calculus, plus some basics of linear algebra stuck in at the beginning.
Stay focused on your current math class.
Know how to solve polynomial inequalities like (x-1)(x+2) > 0. You will see stuff like these very, very often. Also know how to solve stuff like (sin^2 x) * e^x * (x+2) < 0 using similar methods.''
I know this will sound like review, but be VERY proficient at finding the equation of a line given a point and a slope. Trust me, you'll do this ad-nausem in calculus.
Get used to the basics of sigma notation.
If you've looked at the "end properties" of rational functions like f(x) = (x^3 + 2) / (-x^4 + 9x), great...review those.
If you've done anything involving "limits" or "tangents", look at that.
IMO, advanced high school students are done a bit of a disservice by rushing into Calc. There are so many GOOD problem solving/proof opportunities that you pass up that can be done just using the stuff you already know. Get involved in your school's math team. Look on the site Art of Problem Solving at the AMC 12, AIME, or USAMO. You won't be able to do these problems at first...which is GOOD! Try to figure out how to do some of the AMC ones, then advance yourself to the AIME problems. It's not calculus, but it will prepare you to problem solve.
Also, for future math reading, be -SURE- to know:
1) The conditions of a theorem. People often ignore these as givens. For example, the pythagorean theorem is NOT a^2 + b^2 = c^2. The pythagorean theorem is, "In a right triangle with side c the hypotenuse, and sides a and b legs, a^2 + b^2 = c^2". The pythagorean theorem doesn't work on random numbers, and it doesn't work on non-right triangles. It also won't work if you mislabel 'b' as the hypotenuse.
2) The difference between "if", "only if", and "if and only if". LIkewise, know the difference bewteen "necessary" and "sufficient". If I have $100, it's sufficient to buy lunch. But it's not necessary...usually about $10 is necesssary (or $1.99 if I go to McD's.)
Khan academy's a good site. MIT OCW also has good math videos. Their curriculum may not match up 100% to the AP curriculum...in fact, it goes faster, but may have a few holes in it, particularly towards the end. Their "first semester" calc class covers BC Calculus, and their "second semester' calculus class covers what would normally be the first college math class you'd take after BC calculus, plus some basics of linear algebra stuck in at the beginning.
Stay focused on your current math class.
Know how to solve polynomial inequalities like (x-1)(x+2) > 0. You will see stuff like these very, very often. Also know how to solve stuff like (sin^2 x) * e^x * (x+2) < 0 using similar methods.''
I know this will sound like review, but be VERY proficient at finding the equation of a line given a point and a slope. Trust me, you'll do this ad-nausem in calculus.
Get used to the basics of sigma notation.
If you've looked at the "end properties" of rational functions like f(x) = (x^3 + 2) / (-x^4 + 9x), great...review those.
If you've done anything involving "limits" or "tangents", look at that.
IMO, advanced high school students are done a bit of a disservice by rushing into Calc. There are so many GOOD problem solving/proof opportunities that you pass up that can be done just using the stuff you already know. Get involved in your school's math team. Look on the site Art of Problem Solving at the AMC 12, AIME, or USAMO. You won't be able to do these problems at first...which is GOOD! Try to figure out how to do some of the AMC ones, then advance yourself to the AIME problems. It's not calculus, but it will prepare you to problem solve.
Also, for future math reading, be -SURE- to know:
1) The conditions of a theorem. People often ignore these as givens. For example, the pythagorean theorem is NOT a^2 + b^2 = c^2. The pythagorean theorem is, "In a right triangle with side c the hypotenuse, and sides a and b legs, a^2 + b^2 = c^2". The pythagorean theorem doesn't work on random numbers, and it doesn't work on non-right triangles. It also won't work if you mislabel 'b' as the hypotenuse.
2) The difference between "if", "only if", and "if and only if". LIkewise, know the difference bewteen "necessary" and "sufficient". If I have $100, it's sufficient to buy lunch. But it's not necessary...usually about $10 is necesssary (or $1.99 if I go to McD's.)
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Here's an awesome online guide.