1. Use the given vectors below to find the scalar u • v.
u = -8i + 5j and v = -15i - 8j
A. 120
B. 160
C. 80
D. -40
2. Solve the triangle below, rounding to the nearest tenth.
A. B = 40°, a = 12.7, c = 8.1°
B. B = 45°, a = 8.2, c = 12.7°
C. B = 50°, a = 8.2, c = 12.7°
D. B = 45°, a = 12.7, c = 8.1°
3. Use Demoivre's Theorem to find the indicated power of the complex number below. Write the answer in rectangular form.
4. A vector v has initial point P and terminal point P . Write v in terms of ai + bj.
1 2
P = (0, 0); P = (-5, 6)
1 2
A. v = 6i + 6j
B. v = -6i + 5j
C. v = -5i + 6j
D. v = 5i - 6j
5. Find the product of the complex numbers below.
6. Use the dot product to determine whether the vectors below are parallel, orthogonal, or neither.
v = 4i + 3j and w = 3i - 4j
A. Parallel
B. Not enough information
C. Orthogonal
D. Neither orthogonal nor parallel
7. Use Heron's formula to find the area of a triangle in which a = 19 yards, b = 19 yards, and c = 14 yards.
A. 124 square yards
B. 133 square yards
C. 127 square yards
D. 130 square yards
8. Use the vectors below to find the specified scalar.
u = -8i + 5j and v = -11i - 6j; Find u • v.
A. 118
B. 58
C. 88
D. -30
9. A vector v has initial point P = (0, 0) and terminal point P = (4, -6). Write v in terms of ai + bj.
1 2
A. v = 6i - 4j
B. v = -6i - 6j
C. v = -4i + 6j
D. v = 4i - 6j
10. A surveyor standing 52 meters from the base of a building measures the angle to the top of the
building and finds it to be 35°. The surveyor then measures the angle to the top of the radio tower on the
building and finds that it's 50°. How tall is the radio tower?
A. 13.93 meters
B. 10.01 meters
C. 9.17 meters
D. 25.56 meters
11. Convert the polar equation r = 9 csc θ to a rectangular equation.
12. Convert the polar equation r = 4 csc θ to a rectangular equation.
A. x = 4
B. y
C. x
13. Find the unit vector having the same direction as v if v = 12i + 5j.
14. Convert the rectangular equation y = 3 to a polar equation (that is,
in terms of r and θ).
A. sin θ = 3
B. r = 3
C. r cos θ = 3
D. r sin θ = 3
15. Two sides and an angle (SSA) of a triangle are given below. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results.
Round lengths to the nearest tenth and angle measures to the nearest degree.
A = 30°, a = 22, b = 44
A. B = 60°, C = 60°, c = 38.1
B. B = 60°, C = 90°, c = 38.1
C. No triangle
D. B = 90°, C = 60°, c = 38.1
16. Convert the rectangular equation y = 1 to a polar equation that expresses r in terms of θ.
A. r = 1
B. sin θ =1
C. r cos θ = 1
D. r sin θ = 1
17. Which of these is a complex fourth root of cos 120° + i sin 120°?
A. cos 190° + i sin 190°
B. cos 200° + i sin 200°
C. cos 210° + i sin 210°
D. cos 220° + i sin 220°
18. Solve the triangle in the figure below.
A. B = 50°, a = 8.25, c = 6.55
B. B = 55°, a = 6.55, c = 8.25
C. B = 60°, a = 6.55, c = 8.25
D. B = 55°, a = 8.25, c = 6.55
19. Using the polar coordinates of the point given below, find the rectangular coordinates of the point.
20. Use Heron's formula to find the area of a triangle in which a = 16 yards, b = 13 yards, and c = 16 yards. Round to the nearest square unit.
A. 98 square yards
B. 95 square yards
C. 101 square yards
D. 104 square yards
