Precalculus

# Practice Test

PrecalculusPractice Test

### Practice Test

1.

Assume $α α$ is opposite side $a,β a,β$ is opposite side $b, b,$ and $γ γ$ is opposite side $c. c.$ Solve the triangle, if possible, and round each answer to the nearest tenth, given $β=68°,b=21,c=16. β=68°,b=21,c=16.$

2.

Find the area of the triangle in Figure 1. Round each answer to the nearest tenth.

Figure 1
3.

A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15° to the right of his original course, and flies 1 hour in the new direction. If he maintains a constant speed of 575 miles per hour, how far is he from his starting position?

4.

Convert $( 2,2 ) ( 2,2 )$ to polar coordinates, and then plot the point.

5.

Convert $( 2, π 3 ) ( 2, π 3 )$ to rectangular coordinates.

6.

Convert the polar equation to a Cartesian equation: $x 2 + y 2 =5y. x 2 + y 2 =5y.$

7.

Convert to rectangular form and graph: $r=−3cscθ. r=−3cscθ.$

8.

Test the equation for symmetry: $r=−4sin( 2θ ). r=−4sin( 2θ ).$

9.

Graph $r=3+3cosθ. r=3+3cosθ.$

10.

Graph $r=3−5sinθ. r=3−5sinθ.$

11.

Find the absolute value of the complex number $5−9i. 5−9i.$

12.

Write the complex number in polar form: $4+i. 4+i.$

13.

Convert the complex number from polar to rectangular form: $z=5cis( 2π 3 ). z=5cis( 2π 3 ).$

Given $z 1 =8cis( 36° ) z 1 =8cis( 36° )$ and $z 2 =2cis( 15° ), z 2 =2cis( 15° ),$ evaluate each expression.

14.

$z 1 z 2 z 1 z 2$

15.

$z 1 z 2 z 1 z 2$

16.

$( z 2 ) 3 ( z 2 ) 3$

17.

$z 1 z 1$

18.

Plot the complex number $−5−i −5−i$ in the complex plane.

19.

Eliminate the parameter $t t$ to rewrite the following parametric equations as a Cartesian equation: ${ x(t)=t+1 y(t)=2 t 2 . { x(t)=t+1 y(t)=2 t 2 .$

20.

Parameterize (write a parametric equation for) the following Cartesian equation by using $x( t )=acost x( t )=acost$ and $y(t)=bsint: y(t)=bsint:$ $x 2 36 + y 2 100 =1. x 2 36 + y 2 100 =1.$

21.

Graph the set of parametric equations and find the Cartesian equation: ${ x(t)=−2sint y(t)=5cost . { x(t)=−2sint y(t)=5cost .$

22.

A ball is launched with an initial velocity of 95 feet per second at an angle of 52° to the horizontal. The ball is released at a height of 3.5 feet above the ground.

1. Find the parametric equations to model the path of the ball.
2. Where is the ball after 2 seconds?
3. How long is the ball in the air?

For the following exercises, use the vectors u = i − 3j and v = 2i + 3j.

23.

Find 2u − 3v.

24.

Calculate $u⋅v. u⋅v.$

25.

Find a unit vector in the same direction as $v. v.$

26.

Given vector $v v$ has an initial point $P 1 =( 2,2 ) P 1 =( 2,2 )$ and terminal point $P 2 =( −1,0 ), P 2 =( −1,0 ),$ write the vector $v v$ in terms of $i i$ and $j. j.$ On the graph, draw $v, v,$ and $−v. −v.$ Do you know how you learn best?
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