Final Study Guide MATH 1150
NAME:
COURSE:
SECTION:
1. Determine the interval(s) on which the given function is increasing.
2. Determine the average rate of change of the function f (x) = 4 − 5x2 between x = −2
and x = 0.
3. Sketch the graph of the function y = 1 −
√
x + 5 using transformations.
4. Determine whether f (x) = x4 + 3x2 is even, odd, neither, or both
5. Find g ◦ f for f (x) =
√1
x
and g(x) = x2 − 5x, and determine its domain.
6. Find the inverse function of f (x) =
7. Evaluate the expression,
20i
1−3i ,
1
5x+10
and write the solution in the form a + bi
8. If $ 4000 is borrowed at a rate of 3.75 % interest per year, compounded quarterly, find
the amount due at the end of 5 years.
9. Evaluate the expression log36
√
6
2 3
10. Use the Laws of Logarithms to expand the expression log( xz 4y )
11. Find the solution of the equation 101−x = 5x (Round to 4 decimal places.)
12. Find the solution of the equation log2 (x + 14) − log2 (x − 3) = 1
MATH 1150
13. If Radium-221 has a half-life of 30 seconds, how long will it take for 96% of a sample
to decay? (Round to the nearest second.)
14. Find an angle between 0◦ and 360◦ that is coterminal with −260◦
15. From the top of a 225 ft lightbouse, the angle of depression to a ship in the ocean
is 27◦ . How far is the ship from the base of the lighthouse? (Round to the nearest foot.)
16. Find the exact value of sin 3π
2
17. Find the exact value of tan(sin−1
24
25 )
18. Find all possible solutions of the triangle using the Law of Sines for
c = 130, ∠B = 11◦ , ∠C = 102◦
19. A pilot flies in a straight path for 1 12 hours. She then makes a course correction, heading 15◦ to the right of her original course, and flies 2 hours in the new direction. If
she maintains a constant speed of 625 mph, how far is she from her starting position?
(Round to the nearest mile.)
20. Sketch the graph of y = 4 + 2 sin(3x + 3)
21. Sketch the graph of y = 5 tan( 21 x + π8 )
22. Verify the identity
sin x
cos x+sin x
=
tan x
tan x+1
23. Use an Addition or Subtraction Formula to find the exact value of the expression
tan 19π
12
24. Prove the identity cot 2x =
25. Prove the identity
1−tan2 x
2 tan x
sin 3x+sin 7x
cos 3x−cos 7x
= cot 2x
26. Solve the equation cos 5θ − cos 7θ = 0 on the interval [0, 2π)
27. Sketch the graph of the polar equation r = − cos 7θ
MATH 1150
28. Find the indicated power using De Moivre’s Theorem and write in the form a + bi for
(1 − i)14
29. Find the indicated roots of the complex number: cube roots of −8i
30. A jet is flying through a wind that is blowing with a speed of 50 mph in the direction
of N30◦ E (see figure). The jet has a speed of 775 mph relative to the air, and the pilot
heads the jet in the direction N45◦ E. Find the true speed of the jet. (Round to the
nearest integer.)
31. Find the angle between the vectors ~u = î + ĵ and ~v = î − j
32. Find the component of ~u = h3, 0i along ~v = h8, 6i
MATH 1150
Answer Key
1. (−∞, 0] ∪ [20, 50]
2. 10
20.
3.
21.
4. even
5. (g ◦ f )(x) =
6. f −1 (x) =
1
x
−
√5 ;
x
domain: (0, ∞)
1−10x
5x
7. −6 + 2i
8. $4820.71
9.
1
4
22. Uses Ratio identities
√
23. −2 − 3
24. Uses Double Angle identities
25. Uses Sum-to-Product identities
5π
7π 4π 3π 5π 11π
26. 0, π6 , π3 , π2 , 2π
3 , 6 , π, 6 , 3 , 2 , 3 , 6
10. 2 log x + 3 log y − 4 log z
11. 0.5886
12. 20
27.
13. 139 seconds
14. 100◦
15. 442 ft
28. 128i
16. -1
√
√
29. w0 = 2i, w1 = − 3 − i, w2 = 3 − i
17.
24
7
30. 823 mph
18. a = 122, b = 25, ∠A = 67◦
31. 90◦
19. 2169 miles
32.
12
5