FINAL EXAM REVIEW
PC 11
18. For each angle in standard position, determine the reference angle.
a. 48˚
b. 242˚
c. 198˚
d. 337˚ after being reflected in the x-and y- axis
19. Determine the exact values of each of the following angles.
a. cos 0˚
b. sin 45˚
c. tan 90˚
d. cos 30˚
e. sin 90˚
f. tan 60˚
20. Determine the exact values of each of the following angles.
a. cos 210˚
b. sin 315˚
c. tan 135˚
d. cos 150˚
e. sin 135˚
f. tan 300˚
21. Point P (-7, -24) lies on the terminal arm of angle θ, in standard position. Determine the exact values of sin θ,
cos θ, and tan θ
22. If the terminal arm of θ is in quadrant 2, and cos θ = − 12 , determine the exact values of sin θ and tan θ.
37
1
b. sin θ = 0
c. cos θ = 1
a. tan θ = −
23. Determine θ, if 0˚≤ θ < 360˚.
2
3
24. Solve the following triangles.
a.
b.
c.
a = 36 cm,
c = 42 cm,
∠A = 38˚
25. How does the graph of a quadratic function in the form y = a ( x − p ) 2 + q change when
a. The value of p is decreased by 5 and the value of q increased by 4.
b. The value of a is multiplied by a factor 0.5 and the value of q is decreased by 9.
26. State which graph corresponds to each function.
2
2
a) y = (x + 3) + 1
b) y = −2(x + 4) 2 + 3 c) y = 12 (x − 2) − 5
d) y = −(x − 3) + 2
2
27. Graph y = −0.25( x + 5) 2 − 1 . State the vertex, equation of axis of symmetry, x-and y- intercepts, domain and
range, and the maximum or minimum value
28. Determine the equation of the parabola that has a vertex of (-3, -5) and passes through (1, 20).
29. Convert y = −4( x + 2.5) 2 + 20 to standard form ( y = ax 2 + bx + c ).
30. If the point (-3, 30) is on the graph y = ( x − 1) 2 + 14 , where will the point be on y = ( x − 8) 2 − 6 ?
31. Complete the square.
32. Solve
a. y = −0.5 x 2 + 3x − 4
b. y = 6 x 2 + 24 x + 17
a. The sum of two numbers is 46. Their product is a maximum. Find the numbers.
b. Two numbers have a difference of 6. The sum of their squares is a minimum. Find the numbers.
c. A rental business charges $12 per canoe and averages 36 rentals a day. For every 50-cent increase
in rental price, it will lose two rentals a day. What price would yield the maximum revenue?
d. You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting
a rectangular enclosure in half. What are the dimensions of the largest such enclosure?
33. Solve 0 = x 2 + 6 x − 72 graphically.
34. Factor a. 4 x 2 − 81
b. 125 − 5 x 2
c. 9 x 2 − 12 x + 4
35. Solve the following. a. x 2 − 8x + 15 = 0
d. 4x 2 − 8x = 0
d. 3x 2 − 17 x + 24
b. 0 = x 2 + 6 x − 16
e. 36 x 2 − 144 = 0
e. 5( x + 3) 2 + ( x + 3) − 22
c. 6x 2 − x − 15 = 0
36. Solve using the quadratic formula. Leave answers in exact form. Also, determine the nature of the roots.
2
b. x(x − 2) = 4
c. 8x 2 − 3 = 0
a. 4x + 4x − 5 = 0
37. Solve. a. The length of a rectangle is 3 greater than its width and its area is 28. Find its dimensions.
b. When 4 times a number is subtracted from its square, the remainder is 21. Find the number.
c. Find a number such that its square plus the number itself is equal to 20.
38. Multiply:
a.
b.
7× 8
39. Express as mixed radicals in simplest form:
40. Express as an entire radical:
a.
2
(
5− 7
36
2
c.
b. 6 2 − 4 2 + 2
)
44. Rationalize the denominator:
b.
(
3+2
a. 2
b.
)(
)
x +7= 4
c.
12 x( x − 1)
9 x 2 ( x − 1)
b.
9x2
27 x 2 + 18 x
c.
48. Simplify: a.
20 xy 2 4 x 2 y
×
x2
10 xy
b.
8 xy  10 xy 
÷−

15 y 2  16 x 2 
c.
4 x − 20 6 x + 30
×
3
25 − x 2
4a a
−
9 6
2
4
e.
+
4x + 4 2x − 6
e.
b.
e. 3 16 + 3 3 54
1
2
+
2 x 3x
f.
)(
2 +3
3−2
c.
x +3=9
d.
d.
6x −1
x2 + 4
8 x + 12
4 x + 20
d.
)
3x + 1 = − 5 x − 4
2
e. x 2 − x − 20
x − 6x + 8
2d − 6
3− d
e.
x2 − 4
x 2 − 11x + 18
y 2 + 7 y + 10
y2 − 4
× 2
3y − 6
y + 4y + 4
r 2 −1
r2 − r − 2
÷
r2 − r − 6
r2 − 4
c. x +
y
5y
− 2
y + 4 y − 16
3
2x
x−4 x
b.
−
= −2
+ =6
2x x + 1
4
3
4
x
1
e. 2
=
+
x − 8 x + 12 x − 2 x − 6
50. Solve: a.
d. 4 18 − 8
(
3
5− 2
b.
47. Simplify: a.
49. Simplify: a.
d. 3 108
c. 4 + 5 4 − 5
3 +1
46. State the non-permissible values for each expression.
x2 − 2x − 8
x−6
a.
b. −3 x
c.
3
2x
x −8
d.
c. 3 16
9 24
2 18
c. 4 6 + 2 10
5
45. Solve. a. 2x − 5 = 4
b. 80
b. 3 11
b.
42. Add/Subtract: a. 2 3 + 3 3
43. Simplify:
a. 54
a. 2 7
a. 2 5
3
41. Divide:
c. 4 8 × 3 6 × 7 3
24 × 18
c. x −
3a
a
−
a − 4 a −1
2
3
g. 2
− 2
x − 9 x + 20 x − 10 x + 25
3
−2
x
d.
2
x −1
=
x −3 3− x
d.
2m
m−5
− 2
=1
m +1 m −1
51. Solve the following problems
a. One positive integer is 5 more than the other. When the reciprocal of the larger number is subtracted
from the reciprocal of the smaller the result is 5 . Find the two integers.
14
b. Bill’s garden hose can fill the pool in 12 hours. His neighbor has a hose that can fill the pool in 15
hours. How long will it take to fill the pool using both hoses?
c. The first leg of Mary’s road trip consisted of 120 miles of traffic. When the traffic cleared she was able
to drive twice as fast for 300 miles. If the total trip took 9 hours how long was she stuck in traffic?
d. Brett lives on the river 45 miles upstream from town. When the current is 2mph he can row his boat
downstream to town for supplies and back in 14 hours. What is his average rowing speed in still
water?
58. Medium drinks cost $2 and large drinks cost $3. Let x be the number of medium drinks sold and y be the
number of large drinks sold. Write the inequality to show how many drinks the vendor must sell to have at
least $60 in sales?
59. Solve:
a. x 2 + 5 x + 6 > 0
60. Graph: a. y < x 2 + 4 x
b. 3x 2 − 4 x − 5 ≤ 2 x 2 − 7 x − 1
c. − x 2 + x + 1 ≥ 0
b. y ≥ 4 x 2 + 9 x + 2
c. y > 3x 2 − 9
FINAL EXAM REVIEW ANSWERS
18a. 48˚ b. 62˚ c. 18˚ d. 23˚
19a. 1 b.
1
c. undefined d.
2
21. sin θ = − 24 cos θ = −
25
3 e. 1 f.
2
24
7
tan θ =
7
25
3
20a. − 3
2
b. −
22. sin θ = 35 tan θ = − 35
12
37
1
c. -1 d. − 3 e.
2
2
1
f. − 3
2
23a. 150˚, 330˚ b. 0˚, 180˚ c. 60˚, 300˚
24a. ∠D= 65.7˚ ∠C = 35.58˚ BD = 3.61
b. AB = 3.1 ∠A = 33.0˚ ∠B = 97.6˚
c. ∠C = 45.9˚ ∠B = 96.1˚ b = 58.1 OR ∠C = 134.1˚∠B = 7.9˚ b = 8.0
25a. The graph moves 5 to the left and 4 up. b. The graph is vertically compressed by half and moved down 9
26a.
b.
c.
d.
27. Vertex: (-5, -1) ; Axis of Symmetry: x = -5 ; x –int: none ; y-int: -7.25 ; Domain: ARN Range: y ≤ -1 ; max of -1
28. y =
25
( x + 3) 2 − 5
16
29. y = −4 x 2 − 20 x − 5
32a. 23 and 23 b. 3 and -3 c. $10.50
30. (4, 10)
1
31a. y = − ( x − 3) 2 + 0.5 b. y = 6( x + 2) 2 − 7
2
d. 200 ft by 300 ft
34a. (2 x + 9 )(2 x − 9 ) b. 5(5 + x )(5 − x ) c. (3x − 2 )2 d. ( x − 3)(3x − 8) e. (5 x + 26)( x + 1)
33.
c. x = − 3 , 5
35a. x = 3, 5
b. x = -8, 2
36a. − 1 ± 6
2
b. 1 ± 5 c. ±
6
4
28
b.
43a.
10 − 14
99
41a. 2 15 b. 3 2 c. 3 3
3
b. 5 + 3 3
c. 11
e. x = ±2
37a. 4 by 7 b. -3 or 7 c. 4 or -5
38a. 2 14 b. 12 3 c. 1008
40a.
d. 0, 2
2 3
39a. 3 6 b. 4 5 c. 23 2 d. 33 4
42a. 5 3 b. 3 2 c. 4 6 + 2 10 d. 10 2 e. 113 2
44a. 2 5
5
45a. x = 10.5 b. no solution c. x = 36 d. no solution 46a. x ≠ 0
b.
5+ 2
b. x ≠ 8
c. − 6 − 2 2 − 3 3 − 6
c. No NPV d. No NPV e. x ≠ 2,4
47a. 4
3x
e. r − 1
r−3
49a. 5a
18
50a. x = 12
b.
x
c. 2 x + 3
3x + 2
x+5
b. 7
6x
2
c. x − 2 x + 3
x
b. x = − 3
7
c. x = -1
d.
58. 2x + 3y ≥ 60
48
x
3x + 2
2a 2 + a
(a − 1)(a − 4)
d. No Solution
54a.
55a.
e. x + 2
x−9
d. -2
e.
e. x = -1
a. 8 y 2
5x + 1
2( x + 1)( x − 3)
51a. 2, 7
2
b. − 64 x 2
75 y
f.
c. y + 5
3
y2 − 9y
( y + 4)( y − 4)
b. 6 2 hrs
3
c. 4 hrs
b.
b.
56a. No Solution b. x = 1, 2
59a. x < -3 or x > 2 b. -4 ≤ x ≤ 1 c. 1 − 5 ≤ x ≤ 1 + 5
2
2
g.
d. -8
2− x
(x − 4 )(x − 5)2
d. 7 mph