Pre-Calculus Honors Final Review

Unit Circle & Trig

100

sin((-7pi)/6)=?

1/2

200

Give the period of the graph of 

-3sin(pi/2)+1

4pi

300

What is the phase shift of the graph 

1/2cos(2theta-pi/4)

pi/8

400

Simplify this expression completely:

costheta/(1+sintheta)+costheta/(1-sintheta)

2sectheta

500

Solve for θ :

sintheta-2cos^2theta=-2

theta={0,pi,(7pi)/6, (11pi)/6}+2pik

Polar

100

Give the coordinates of this point

(6, (3pi)/4)

200

Give another representation of the point

(3,(5pi)/6)

with r<0

(-3,(11pi)/6)

300

What shape does this equation make?

r=3+sin(6theta)

Rose

400

Give another representation of

(-5,(5pi)/3)

with r>0 and θ <0

(5,-(4pi)/3)

500

Convert this point to polar coordinates 

(-6sqrt3,18)

(12sqrt3, (2pi)/3)

or

(20.8,120^o)

Vectors

100

Give the vector in component form with the initial point

(-2,-12)

and terminal point

(9,-7)

⟨11,5 ⟩

200

Give the magnitude of the vector 

vecv=-10i-j

|v|=sqrt101approx10.05

300

Give the direction of the vector 

vecu=7i-15j

thetaapprox295^o

400

Give the direction from the y-axis of the vector 

vecw=⟨ 2,-5,21 ⟩

betaapprox103.3^o

500

A bird flies S 30^o W at a speed of 40 mph. At some point in the migration, the bird catches a tailwind of 25 mph blowing in the south direction. What is the real speed and direction of the bird at this moment?

True speed: 62.9 mph

Real direction: 251.5^o (or S 18.5^o W or W 71.5^o S) 

Sequences

100

The 15th term of the sequence: 

a_n=6n^2-4

1346

200

Give the n^th term of the sequence:

1/2,4/3,9/4,16/5,25/6,...a_n

a_n=n^2/(n+1)

300

sum_(k=3)^6 k^2-k

68

400

An arithmetic sequence has a 19^th term of -181 and a 42^nd term of -434. Find the sum of the first 120 terms.

S_120=120/2(17-1292)=-76500

500

Find the sum of the partial sequence shown:

5,10,20,40,...327680

655355

Limits

100

lim_(x→3)x^2-3x+1

1

200

lim_(x→0)f(x)

2

300

lim_(x→-∞)x^2-3x+2

oo

or DNE

400

lim_(x→oo)(1-x^2)/(-x+x^2+2x^3)

0

500

lim_(x→-1)(x^3-3x^2-4x)/(2x^2+x-1)

-5/3