Calculus AB Review

Derivatives

100

The derivative of 2x-5

What is 2?

200

The derivative of 4x³-13x²+8x

What is 12x²-26x+8?

300

The derivative of 4x²(4-x)

What is 32x-12x²?

400

The derivative of 4arctan(x²+2)

What is 8x/((x²+2)²+1)?

500

The derivative of (9x³+18x)/(3x²+3)

What is 3(x⁴+x²+2)/(x²+1)² ?

Integrals

100

The integral of x+1dx

What is x²+x+C ?

200

The integral of 3/(x+9)dx

What is 3ln(x+9)+C?

300

The integral of ln(x)dx

What is xln(x)-x+C?

400

The integral of (x-1)/(sqrt(x²-2x+4))dx

What is sqrt(x²-2x+4)+C?

500

The integral of e^xcos(2x)dx

What is e^x(2sin(2x)+cos(2x)/5+C?

Limits

100

Lim x->1 (x²-2x+1)

What is 0?

200

lim x->-3 (x²-9)/(x²+3x-18)

What is -2?

300

The lim x->-infinity x^1/3-7x²+14x

What is -infinity?

400

The limit x->infinity (6+x-3x²)/(5+x²+9x⁴)^1/2

What is -1?

500

The limit x->-infinity (6+x-3x²)/(5+x²+7x⁴)^1/2

What is -3/7^1/2?

Differential Equations

100

The solution to the differential equation dy/dx=4x+5y

What is y=-4/5x-25/4 ?

200

The rate that money $ flows into a bank account is directly proportional to the value of total sales in $ times the number of hours, t, worked by Worker X. 

What is d$/dt=$t ?

300

True or false: y=-e^{x^2-6x} is a solution to the differential equation dy/dx=y(2x-6)

What is true?

400

The solution y=f(x) to dy/dx=x²y+3 when f(1)=0

What is y=-7/3e^{x^3/3+3x} ?

500

The position equation for a falling object pushed off a 40m cliff whose acceleration due to gravity is -9.8 m/s²  and the velocity of the object is -2 m/s when t=0. 

What is P(t)=1/2(-9/8)t²-2t+40 ?

Exponential Growth and Decay

100

The amount of money in my bank account one year after I make an initial deposit of $1,000 with 7% interest compounded monthly. 

What is $1072.29 ?

200

The amount of garbage in a landfill after 5 years of continuously growing 25% if it originally had 7,438 pieces of trash.

What are 25,961 pieces of trash?

300

The initial amount of an element X (half-life=50 years) if only 4.68g are left after 100 years of radioactive decay. 

What is 18.72g of element X?

400

The time in years it will take for 99% of a 150.39g sample of Radon (half-life 3.8 days) to decay.

What is .069 years?

500

The temperature T(t) of a cookie in degrees C t hours after it is removed from the oven satisfies the equation T'(t)=7/9e^-t/90. If T(0)=35 degrees C, what is T(10)?

What is 7.09 degrees Celsius?