So I was searching the internet for a breakdown of the AP Calculus AB test and I was shocked when I realized that there are 28 multiple choice questions without a calculator. Now, I can get all the multiple choice questions with calculator right, but the non-calculator section just gets to me. Does anyone else have this problem and how do you guys manage to solve the problems?
Know how to do calculus--particularly integrating and differentiating by hand. The AP exam will probably have just a simple derivative, derivative at a point, definite integral, or indefinite integral on the non-calculator portion, because a question like that on the calculator portion would be silly (though I wouldn't mind it at all).
For example on a test I had a question that said if the U substitution u=radical(X-1) on the integral from 2 to 5 Radical(X-1)/x dx. I just couldn't get the answer. Can anyone try to show me how to do this? Sorry I don't have the answers I don't remember them. Also what would you guys recommend I practice these kinds of questions with?
jerrry4445Posts: 2,741Registered UserSenior Member
I'm assuming dx would be the numerator.
Btw, did the question ask you to find the exact value or just plug in the number and simplify? I'm just asking since I got 2sq(x-1)-2arctan(sq(x-1))+C as the antiderivative. (I did it by hand and verified it with the TI-89).
Oh if you want to know how i did it:
u=sq(x-1)
x=u^2+1
dx=2u du
So, plug it in: and you get int(u/(u^2+1) x 2u) du
So, i multiply it and I got int(2u^2/(u^2+1)) du. I have to separate by dividing 2u^2 by u^2+1. So, I have int(2-2/(u^2+1))du. Finally integrate and I got 2u - 2 arctan u + C. Substitute the u and you get 2sq(x-1)-2arctan(sq(x-1))+C. And you can plug in 2 and 5 to find the value from there.
And non-calculator MC shouldn't be that hard. It's just simple calculus computation. If you know the differentiation, integration, and other rules of calculus, you can do well enough to ace that portion.
purplepotatoPosts: 223Registered UserJunior Member
For example on a test I had a question that said if the U substitution u=radical(X-1) on the integral from 2 to 5 Radical(X-1)/x dx. I just couldn't get the answer. Can anyone try to show me how to do this?
u = (x-1)^(1/2)
u^2 = x-1
u^2 + 1 = x
dx/du = 2u
dx = 2u du
u(2) = (2-1)^(1/2) = 1
u(5) = (5-1)^(1/2) = 2
So, changing the limits from 2, 5 to 1, 2 and substituting the expressions above, the integral becomes the integral from 1 to 2 of [u/(u^2 + 1)]*2u*du = [2u^2/(u^2 + 1)]du.
Thanks Purplepotato. I really can't believe I made a stupid mistake like that. So now I'm starting to realize that I should think outside the box and carefully look at the question. Also can you find the derivative of sec(xy)=x^2? My answer was (2x-sex(xy)tan(xy))/xsec(xy)tan(xy), I just want to make sure if it's right.
Replies to: AP Calculus Multiple Choice
Btw, did the question ask you to find the exact value or just plug in the number and simplify? I'm just asking since I got 2sq(x-1)-2arctan(sq(x-1))+C as the antiderivative. (I did it by hand and verified it with the TI-89).
Oh if you want to know how i did it:
u=sq(x-1)
x=u^2+1
dx=2u du
So, plug it in: and you get int(u/(u^2+1) x 2u) du
So, i multiply it and I got int(2u^2/(u^2+1)) du. I have to separate by dividing 2u^2 by u^2+1. So, I have int(2-2/(u^2+1))du. Finally integrate and I got 2u - 2 arctan u + C. Substitute the u and you get 2sq(x-1)-2arctan(sq(x-1))+C. And you can plug in 2 and 5 to find the value from there.
And non-calculator MC shouldn't be that hard. It's just simple calculus computation. If you know the differentiation, integration, and other rules of calculus, you can do well enough to ace that portion.
u = (x-1)^(1/2)
u^2 = x-1
u^2 + 1 = x
dx/du = 2u
dx = 2u du
u(2) = (2-1)^(1/2) = 1
u(5) = (5-1)^(1/2) = 2
So, changing the limits from 2, 5 to 1, 2 and substituting the expressions above, the integral becomes the integral from 1 to 2 of [u/(u^2 + 1)]*2u*du = [2u^2/(u^2 + 1)]du.