Calculus of Periodic Functions - and review of probability

Unit Circle Properties

100

The radius of the unit circle is equal to:

1

200

At x=-1, what is the reference angle in radians?

pi

300

The center of the unit circle is at the:

origin

400

After one full rotation of the unit circle, the reference angle is:

2pi

500

In quadrant 4, which function/s are positive?

Cosine

Derivatives (Chain Rule)

100

What is the derivative of sin(x)?

cos(x)

200

What is the derivative of cos(x)

-sin(x)

300

What is the derivative of sin(6x)

6cos(6x)

400

Find the derivative of cos(2x+4)

-2sin(2x+4)

500

Find the derivative of [sin(2x-5)]²

4sin(2x-5)cos(2x-5)

Derivative Lucky Dip

100

Find the derivative of sin(2x)

2cos(2x)

200

Find the derivative of 6cos(2x)

-12sin(2x)

300

Find the derivative of xsin(x)

sin(x)+xcos(x)

400

Find the derivative of x²cos(x)

2xcos(x)-x²sin(x)

500

Find the derivative of (2x-6)cos(x+1)

2 cos(1 + x) - 2 (-3 + x) sin(1 + x)

Integrals

100

What is the integral of -cos(x)

-sin(x)+c

200

Find the integral of 2sin(2x)

-cos(2x)+c

300

Find the integral of 2cos(4x)

0.5sin(4x)+c

400

Find the integral from 0 to 0.5pi of sin(x)

1

500

What do we always have to remember at the end of an indefinite integral?

+c

Probability

100

What is a compound event?

Where one or more trials take place within one "event"

200

What is the probability of rolling two sixes in a row when tossing an ordinary die twice?

1/36

300

What is the theoretical probability of giving birth to 4 girls in a row?

1/16

400

A square of side length 1 is inside a square of side length 2 as shown in the diagram alongside.  A point inside the larger square is chosen at random.  What is the probability that the point chosen is also inside the smallest square?

1/4

500

Find the probability that a randomly chosen number in the interval from 0 to pi is less than 1.

1/pi