Honors Precalculus - Chapter 6 Test
Part A:
FORM A
NO CALCULATOR MAY BE USED FOR THIS PART. Choose the best answer for
each question. Angles without the degree symbol (°) are assumed to be in radians.
Pictures are not drawn to scale.
1. In the diagram shown, ABCD is a parallelogram. If AB =
x and AD = y, express BD in terms of x and y.
€
a) y – x
c) -x – y
€
C
B
E
x
b) 2x
d) x – y
€
A
D
y
2. A 2000 pound car is parked on a street that makes an angle of 10° with the horizontal. Which
of the following expressions represents the magnitude of the force (in pounds) required to keep
the car from rolling down hill?
a) 2000 sec10°
b) 2000 cos10°
c) 2000 sin10°
d) 20,000
3. Which of the following is/are true for any two nonzero vectors u and v?
I. u – v = v – u
II. u . v = v . u
III. u . u = |u|2
IV. 2(u . v) = u . (2v)
a) II & IV only
b) I, III, & IV
c) II, III, & IV
d) All are true
4. A child pulls a wagon along level ground by exerting a force of 20 pounds on a handle that
makes an angle of 30° with the horizontal. How much work is done pulling the wagon 10 feet?
a) 20 2 ft-lbs
b) 100 ft-lbs
c) 200 3 ft-lbs
d) 100 3 ft-lbs
5. What is the projection vector of u onto v if u = 2i + j and v = 3i?
a) 2i + 4j
b) 5i + j
c) j
€
€
6. Find u • (v + w) if u = 3i, v = 6i – 2j and w = i + j?
a) 20ij
b) 21
7.€ Write the complex number -1 +
a) 2(cos 150° + i sin 150°)
c) 2 (cos 120° + i sin 120°)
€
d) 2i
c) -21 – 3ij
d) -21
3 i in trigonometric (polar) form.
b) 2 (cos 120° + i sin 120°)
d) 4(cos 300° + i sin 300°)
€


π
π
7π
7π 
w
8. If z = 2  cos + isin  and w = 10  cos €+ isin  , find
in standard form.


4
4
4
4
z
a) − 5 i
b) −2 5 i
c) 2 5 i
d) 2 + 5i
3

π
π  €
€
9. Find 2cos + isin  .
3

€
€3 
a) 8(cosπ + isinπ)
€
€
€
€
  π 3
 π
 π 
 π 3
b) 8 cos  + isin  c) 8 cos  + isin  
 3 
 3 
  3
  3
€
€ _A
Honors Precalculus – Ch. 6 Test
€
pg 1 of 1
€
d) 6(cosπ + isinπ)
10. Which of the following points in polar coordinates is NOT the same as the other three?
 π

 5π 
 23π 
11π 
a) 2,− 
b) −2,−
c) −2, 
d) 2,





 6 
6
6 
6
11. Which of the following is NOT a complex fourth root of 1?
 π
  3π 
 π 
 3π 
a) cos  + isin €
b) cos  + isin €
€
€

 2 
 2 
  2
 2
 π
 π 
c) (cosπ + isinπ )
d) cos  + isin 
 4 
  4
€
€
12. Transform the equation y = x2 to polar form.
sinθ
€
a) r = (sinθ) cos2 θ
b) r =
€
cos2 θ
(
)
(
)
c) y = r 2 cos2 θ
d) r = 16
13. The graph of r = 2 + cos θ is symmetric to
a) the pole.
b) the y-axis.
€
€
c) the polar axis. €
d) None of the above.
€
14. The graph of the parametric equations x = 4 + 2sin t and y = 2cos t – 1 is
a) line with slope 2 and y-intercept 4.
b) a circle with center (2, -1) and radius 4.
c) a parabola with vertex (4, -1).
d) a circle with center at (4, -1) and radius 2.
15. 6Which of the following is the correct graph of r = 4csc( θ)?
6
a)
b)
4
c)
4
4
€
6
d)
6
2
2
4
2
10
5
5
10
2
10
5
5
2
2
10
5
10
4
5
5
2
2
6
4
4
6
4
6
8
6
Honors Precalculus – Ch. 6 Test _A
10
pg 2 of 2
15
Part B: A calculator is necessary for some problems. Show work and answer for the
following problems. Partial credit will be given for partially correct work. Include
units whenever applicable.
REMEMBER TO CHECK THE MODE OF YOUR CALCULATOR.
1. After 1 hour in the air, an airplane arrives at a point 200 miles due south of its departure point.
There was a steady wind of 30 miles per hour from the east.
a) Draw a diagram using vectors to illustrate the situation. Find the velocity vector of the airplane
in still air.
b) What compass heading (bearing) was maintained? Round to the nearest whole degrees.
c) What was the average airspeed of the airplane? Round to the nearest whole number.
2. Grant hits a baseball when it is 4 ft above the ground with an initial velocity of 120 ft/sec. The ball
leaves the bat at 25° with the horizontal and heads toward a 30-ft fence 350 ft from home plate.
a) Write the parametric equations that describe the path of the ball.
b) Write the parametric equations that describe the position of the fence.
c) Draw the path of the ball over time and the position of the fence.
d) Does the ball clear the fence? Show algebra.
3. a) Graph the line described by the parametric equations x = 3t – 1, y = t + 2 for -∞ < t < ∞.
b) Find the slope and y-intercept of the line. Show algebra.
c) Find the polar equation of the line. Solve for r in your final answer.
Bonus:
Find the smallest angle at which Grant should hit the ball to clear the fence in problem #2, assume
the same initial velocity. No guessing and checking allowed here. Show reasoning. Round
answer to the nearest whole degrees. No partial credit.
Honors Precalculus – Ch. 6 Test _A
pg 3 of 3