Pre-cal

trigonometry

100

Find the value of sin(30°) + cos(90°)

1/2 or 0.5

200

Find the value of: sin(30^o)+ cos(60^o)

1

300

Solve for x: tan(x)=1,  for 0^o <x<360^o

x=45^o , 225^o

400

A right triangle has a hypotenuse of 15 and an angle of 35⁰ . Find the length of the side opposite the angle. Round to the nearest tenth.

8.6

500

A tree casts a 5-foot shadow. The angle of elevation from the tip of the shadow to the top of the tree is 45°. How tall is the tree?

5 feet

sequence and series

100

Find the next number in the sequence

2,4,6,8,......

10

200

Find the formula for the arithmetic sequence 

5,9,13,17,...

a_n=5+4(n-1)

300

Find the arithmetic sequence:

3,7,11,15...

39

400

Find the 15th term of the arithmetic sequence 

12,17,22,27,...

82

500

A geometric sequence has a first term of 6 and a common ratio of 3. What is the 8th term?

a₈=13122

polar,vector,parametric

100

Given:x=t², Y=2t+1

eliminate the parameter and write an equation in terms of x and y

y=2 square root x+1

200

find the magnitude of the vector {6,8}

10

300

Convert the polar coordinate (4,π/3) to rectangular form

(2,2 square root 3)

400

Convert the polar coordinate (4,n/2) to rectangular coordinates. 

(0,4)

500

A football player runs 6 yards east and 8 yards north. What is the magnitude of the player's movement vector?

10 yards

limits

100

lim as x approaches 2(x+3)

5

200

lim x→2 (3x + 1)

7

300

lim as x approaches 0, 1-cosx/x²

1/2

400

Evaluate the limit: limit as X approaches 2 

x²-4/x-2

4

500

lim as x approaches 0, sinx-x/x³

-1/6

derivative

100

What is a Derivative?

A Derivative is the rate of change of a function or the slope of the question of the tangent line at a point

200

f(x)=3x²-4x+7

6x-4

300

Find the derivative of 

f(x)=4x³-7x²+5x-9

f^'(x)=12x²-14x+5

400

Find the derivative of 

y=(3x²+1)(x-4)

y^'=9x²-24x+1

500

Find the derivative of f(x)=x^2+4x

f’(x)=2x+4