Geometry

Trigonometry

100

What shape does Trigonometry go over

Triangles

200

In a right triangle, which trigonometric ratio is defined as sin(θ)?

Opposite side divided by hypotenuse

300

If sin⁡(θ)=3/5 and θ lies in the second quadrant, what is the value of tan⁡(2θ)?

-24/7

400

Which identity is most useful to simplify the expression sin⁡(2θ) cos(θ) into a sum or difference of sines or cosines?

Product to sum identities

500

A right triangle has hypotenuse length 10 and an angle of θ such that sin⁡(θ)=4/5.What is the length of the side adjacent to angle θ?

6

Sequence and Series

100

What is arithmetic sequence

Arithmetic is adding or subtracting a constant value to create a linear pattern. 

200

Find the common difference of the arithmetic sequence 14, 5, -4...

-9

300

Find the common ratio of the geometric sequence 

12, 96, 768,...

8

400

What's the explicit formula for An, the nth term of the sequence 

24, 16, 8,...

An= 24-8(n-1)

500

Find the sum of the following series?

5+10+20+...+320

635

Polar, Vector, Parametric

100

Find the sum of the vectors

(2,5) +  (3,1)

(5,6)

200

Find the magnitude of the vector  (3,4)

5

300

A particle moves according to the parametric equation

x=t+2 y=t-1

Find the point when t=3.

(5,2)

400

convert polar equation to rectangular form.

x=r cos(0)

x^2+y^2=4x

500

Convert the rectangular point (0,5) into polar coordinates.

(5,pi/2)

Limits

100

limx>3(2x+5)

11

200

lim>2(x2-4)

0

300

limx>1 x2-1/x-1

2

400

limx>4 sqrtx-2/x-4

1/4

500

lim X>0 sinx/x

1

Derivative

100

What is the derivative of f(x)=x³

What is 3x²

200

Find the derivative of f(x)=5x⁴-2x

What is 20x³-2?

300

A function has a derivative of zero at a point.What does this usually mean about the graph there? 

What is a horizontal tangent line?

400

Find the equation of the tangent line to f(x)=x²+1 at x=2

What is y=4x-3

500

Use the product rule to find the derivative of f(x)=x²(x+4)

What is 3x²+8x