Intro to Calculus 2nd Semester Review

Trig

100

You are 300ft from the base of a building. Your angle of elevation is 22^o. How tall is the building?

The building is about 121ft tall.

200

How many triangles can be formed if B=37^o, a=12 and b=15?

One triangle

300

Solve the triangle a= 22cm, b=19cm and c=14cm

A=82.113^o, B = 58.811^o, C=39.076^o

400

Solve the traingle with C=38^o, a=9 and c=4

What is no triangles

500

Solve B=43^o, b=12 and c=16

What are 2 triangles

C₁=65.41^o, A1=71.59^o, a₁=16.69

C₂=114.89^o, A₂=22.41^o, a₂=6.71

C6

100

If u = <-2,2> and v=<7,-2> then 2u – v is

What is <-11,6>?

200

The actual ground speed and bearing of an airplane traveling at 460mph on a bearing of 170^o with an 80mph wind blowing on a bearing of 200^o

What is 530.791mph on a bearing of 174.322^o?

300

The angle between F and AB is 60^o The work done by 75lb force, F, in moving object 5ft.

What is 187.5ftlb?

400

The exact rectangular coordinates for P (5,-5pi/6) 

What is (-5 Sqrt(3)/2, -5/2)

500

The rectangular equation for x=t²/3  and y=t⁴-7

What is y=9x²-7

C7

100

Can you add a 4x5 matrix a and a 4x8 matrix?

What is NO?

200

Given matrix A is a 3x3 and Matrix B is a 3x3, what matrix operations can you do? Is order important here?

You can add, subtract, multiply in any order.

300

Solve x-2y+3z=11

        4x + y - z = 4

        2x  - y  + 3z = 10

 What is (2,-3,1)?

400

Solve 2x + 4y + 10z = 42

          x + 2y + 5z = -18

          x + y + z = -2

What is no solution?

500

Find the partial fraction decomposition for        (2x³+4x-6)/(x²+4)²

What is 2x/(x²+4) - (4x+6)/(x²+4)²

C8

100

What conic is represented by 4x² - 2x - 5y² + 10y -3=0

What is a hyperbola?

200

Give the equation in standard form for a parabola with focus at (-4,7) and directrix y=5.

What is (x+4)² = 4(y-6)

300

Find the equation of the ellipse with foci at (2,1) and (2,-5)  with a major axis of length 10. 

What is (y+2)²/25 + (x-2)²/16=1

400

Find the equation of the hyperbola with vertices at (+/- 3,0) and foci at (+/-9,0)

x²/9 - y²/72 = 1

500

Find the equation for the asymptotes of the hyperbola with (y-3)²/4 - (x+1)²/8 = 1

What is y-3=+/-[Sqrt(2)/2](x+1)

U10

100

Find the lim x->2 (x-5)³

What is -27?

200

f(x)=(x²+x-2)/(x²+8x+12) has this type of discontinuity(ies) at this/these x-value(s)

What is a removable discontinuity at x=-2 and an infinite at x=-6?

300

The lim as x ->5^- [f(x)]=9 the lim as x -> 5⁺ [f(x)]= 9 f(5)=-9, what is lim x->5[f(x)]?

What is 9?

400

The slope of the tangent line for f(x)=3x²-5 

What is 6x?

500

The equation of the tangent line for f(x)=7-2x through (3,-2) in point slope form.

What is y+2=-2(x-3)?