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Math 124C-4
1.
a
14
SAMPLE Test 3: Trigonometry, Linear Systems, Conics
In the right triangle shown, find:
C
a. The measure of side C _________________
10.5
b
b. The secant of angle a ______________
c. The measure of angle b _______________
2. Solve the following system for w, x, y, and z:
w+x+y+z=0
w = __________
-w + 2x + 2y + z = 5
x = ___________
-w + 3x + y – z = -4
y = ___________
-2w + x + y – 3z = -7
z = ___________
3. A quadratic function of form d = at2 + bt + c is to be used to model the distance d an
accelerating object moves in time t. Using data from the table below, find the values for a, b,
and c that fit the function to the data.
t
5
15
25
d
47.7
379.7
1011.7
_______t2 + ________ t + ________ = d
4. Given the linear equation A: 3x + 2y = 7
Find the following:
a. An equation in x and y that makes a dependent system with A:
b. An equation in x and y that makes an inconsistent system with A:
c. An equation in x and y that makes a consistent and independent system with A:
d. The x and y values that solve the system in answer c.
5. For each equation, tell which conic (circle, ellipse, parabola, hyperbola) it describes:
a. y2 – 3x + 7 = 0
_______________________________________
b. x2 – 2x = y2 + 2x
_______________________________________
c. 2×2 + 5y = 4x – 3y2
_______________________________________
6. For a parabola with vertex (-3, 2) and directrix x = –5
a. Find the focus: _____________________
b. Write the equation of the parabola: ___________________________________________
7. For the conic described by (x + 4)2 – 4(y – 2)2 = 16
a. Find the center: ___________________
b. Find the focuses: _______________________ and _________________________
c. Find the equation of the transverse axis: __________________________________________
8. An architect is designing a “whispering gallery” 100 feet long. If the distance between the
location where a person whispers and the location where the whisper can be heard clearly
is to be 80 feet, how high should the ceiling of the gallery be at its center?
9. Meteorologists measure cloud height ay night by shining a spotlight straight up at the
cloud. A meteorologist standing 1350 feet away from the light source notes the angle of
elevation of the illuminated spot on the cloud as 67.35°. To the nearest whole foot, how
high is the cloud?
10. A mail order firm charges $6.50 for each standard package, and $10 for each express
package. On Monday, the firm shipped 120 packages, and billed shipping fees of $934. How
many of each kind of package were shipped?
Standard Packages: __________
Express Packages: ____________
…
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