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Trig/Math Anal
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LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON _____
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HW NO.
SECTIONS
LE-1
3-3/3-4
LE-2
3-5
LE-3
3-6
LE-4
9-9
LE-5
3-9
LE-6
Review
ASSIGNMENT
Practice Set B #1-12
Practice Set C #1-3, 6-10, 12, 13
Practice Set A #1, 2
Practice Set D #1, 5-16, 18
Practice Set A #7-25 odd
Practice Set A #3, 4, 8, 12, 16, 20, 24
Practice Set D #2, 3
Practice Set A #5, 10, 14, 18, 22, 26, 29, 30
Practice Set E #1-3
Practice Set A #6, 32, 33, 34
Practice Set B #13, 14
Practice Set C #4, 5, 11, 14
Practice Set D #4, 17, 19
Practice Set E #4
DUE
√
Practice Set A: Word Problems
1. On Saturday, Jill’s sidewalk stand sold lemonade at 35 cents a glass and cookies at 25 cents
each, and took in $3.50. On Sunday Jill set both prices at 30 cents, sold exactly the same
numbers of each item, and took in $3.60. How many lemonades and how many cookies were
sold each day?
2. If a particle starting with initial speed v0 has constant acceleration a , then its speed v after t
seconds is given by v  v0  at
Find v0 and a if v  25 m/s when t  5 and v  33 m/s when t  7 .
3. Amy has $1, $5, and $10 bills in her wallet worth $87. She has as many $1 bills as $5 and $10
bills combined, and she has 24 bills in all. How many of each denomination has she?
4. A parabola with vertical axis passes through the given points. Find its equation. (Hint: The
parabola has an equation of the form y  ax 2  bx  c . Substitute the coordinates of the given
points in turn and solve the resulting system for a, b, and c.) (1, 0), (1, 6), (2, 0)
5. A load of 2.5 kg stretches a coil spring to a length of 70 cm, and a load of 4.5 kg stretches it to
a length of 82 cm. Find the natural (un-stretched) length of the spring.
6. The riverboat Alert takes six hours to travel 120 km upstream but only four hours to return.
Find the speed of the current and the speed of the riverboat in still water.
7. The degree measure of one of two complementary angles is 30 less than twice that of the
other. What are the degree measures of the angles?
8. The degree measure of one of two supplementary angles is 6 more than one-half that of the
other. What are the degree measures of the angles?
9. A collection of dimes and quarters has a total value of five dollars and contains 29 coins. How
many of each kind of coin are there in the collection?
10. Tickets for a benefit performance of a new movie sold at $5.50 for the orchestra section and
$3.25 for the balcony. If the receipts from the sale of 1800 tickets totaled $7110, how many
tickets were sold at each price?
11. A glass manufacturer makes two grades of glass which differ in silica content. If she has 2400
kilograms of silica with which to make one batch of each type, and she uses 510 more kilograms
of silica for one type than for the other. How many kilograms of silica are used for each type?
12. In five years a boy will be two-thirds as old as his uncle will be. Three years ago he was half
as old as the uncle is now. How old are the boy and his uncle?
13. With an 80 km/h head wind, a plane can fly a certain distance in four hours. Flying in the
opposite direction with the same wind blowing, it can fly that distance in one hour less. What is
the plane’s airspeed?
14. Traveling downstream, a boat can go 18 km in 2 hours. Going up-stream, it makes only 23 this
distance in twice the time. What is the rate of the boat in still water, and what is the rate of the
current?
15. Find values of A and B so that the line whose equation is Ax  By  6 will contain the points
whose coordinates are (6, 8) and (15, -4).
16. Find values for a and b so that the set of ordered pairs  x, y: y  ax 2  b will contain (2, 3)
l
and (-3, 13).
17. If  x , y : y  mx  b contains (1, 7) and (-1, 1), find m and b.
18. If  x , y : y  mx  b contains (-4, -1) and (2, -4), find m and b.
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q
19. A chemist wants to make 200 mL of acid solution with a concentration of 48%. He wants to
make this from two solutions with 60% and 40% concentrations respectively. How much of each
solution should he use? (Hint: The amount of acid in the final mixture is the sum of the amounts
contributed by each solution).
20. The final velocity of a uniformly accelerated particle is linearly related to the elapsed time by
the equation v  vo  at , where a and v o are constants. If v=15 when t=10, and v=35 when t=25,
find values for a and vo .
In problems 21-24, the original number is a positive two-digit integer. In each problem, find
this integer.
21. The sum of the numbers named by the digits is 8. When the digits are interchanged, the
resulting numeral names a new number that exceeds the original number by 18.
22. The sum of the numbers named by the digits is 10. The original number is 2 less than three
times the number represented when the order of the digits is reversed.
23. The number named by the units digit is 1 more than twice the number named by the tens
digit. The number represented when the order of the digits is reversed is 7 less than 8 times the
sum of the numbers named by the digits.
24. The number named by the tens digit is 5 more than the number named by the units digit. If
the digits are interchanged and the number represented by the resulting numeral is added to the
original number, the sum is 143.
25. A river steamer travels 48 km downstream in the same time that it travels 32 km upstream.
The steamer’s engines drive in still water at a rate that is 16 km/h greater than the rate of the
current. Find the rate of the current.
26. Jean finds that in still water her outboard can drive her boat 3 times as fast as the rate of the
current in Pony River. A 16 km trip up the river and back requires 4 hours. Find the rate of the
current.
27. Two railroad workers are together in a 1.2 km mountain tunnel. One walks east and the
other west in order to be out of the tunnel before the Bad Creek Express comes through at 60
km/h. Each man reaches his respective end of the tunnel in 6 minutes. If the man walking east
reaches the east entrance just before the train enters, and the train passes the other man 0.24
km beyond the west end of the tunnel, at what rate did each man walk?
28. Two kilometers upstream from his starting point, a rower passed a log floating with the
current. After rowing upstream for one more hour, he rowed back and reached his starting point
just as the log arrived. How fast was the current flowing?
29. With a tail wind a plane traveled 120 km in 2.0 hr, but the return trip against the same wind
took 0.5 hr longer. Find the wind speed and the plane’s air speed.
30. Tony flew his ultra-light plane to the next town against a head wind of 10 mph, the trip taking
2 ½ hours. The return trip, under the same wind conditions, took 1 ½ hours. How far is the next
town, and what is the speed of the ultra-light?
31. Two temperature scales are established, one, the R scale where water under fixed conditions
freezes at 5º and boils at 405º, and the other, the C scale where water freezes at 0º and boils at
100º. If the R and C scales are linearly related, find an expression for any temperature R in terms
of a temperature C.
32. A load of 6 kg stretches a coil spring to a length of 30 cm, and a load of 10 kg stretches it to a
length of 40 cm. Find the length of the spring when there is no load.
33. A chemist has 100 mL of a 20% ammonia solution. How many milliliters of water must she
add to reduce the ammonia concentration to 8%?
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34. Four bags of apples and five cartons of yogurt cost $7.76. Three bags of apples and two
cartons of yogurt cost $2.85 less. What does a bag of apples cost?
Practice Set B: Slope
Find the slope of the line containing the given points if the line is not vertical. If the line is
vertical, so state.
1. (2,3), (5,9)
2. (7,0), (7,4)
3. (4,-3), (4,13)
Find the slope of the line with the given equation.
4. x  y  3
5. 3  2 y  6 x
x y
6.   1
3 2
Draw the line passing through the point P and having slope m. Find the coordinates of two other
points on the line.
7. P (2, 0), m  1
1
2
8. P(4,1), m  
9. P(0, 6), m  
2
3
10, Determine whether or not the points whose coordinates are given in the table lie on a line. If
they do, find the slope of the line.
y
x
0
2
2
5
4
8
8
14
Determine k so that the given line will have slope m.
11. kx  2 y  8, m  3
12. (k  1, k ), (3, 2); m  2
13. (k  6) x  3 y  1, m  k
14. (k ,3k ), (k  2, k  4); m  k
Practice Set C: Equation of a Line
Find an equation in standard form and with integers as coefficients of the line through P having
the given slope.
1. P (3,1), m  1
2. P(3, 5), m  3
3. P(2, 6), vertical
4. P(4, 0), m  1
5. P(1, 5), m  0.2
Find an equation in standard form and with integers as coefficients of the line having slope m and
y  intercept b.
6. m  2, b  1
7. m  0.4, b  1.2
Find an equation in standard form of the line containing the given points.
8. (4, 0), (0, 3)
9. (1, 4), (1,5)
11. (1, 3), (3,3)
 1 2  1 
10.  ,   1, 
 2 3  6 
Find equations in standard form of the lines through the point P that are (a) parallel to, and (b)
perpendicular to, the line L.
12. P(0, 3); L : 2 x  y  4
13. P(2, 3); L : 3x  5 y  1
14. P(4, 0); L : 3 x  2 y  7
Practice Set D: Solving Systems
Each system has a unique solution; find it.
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3x  2 y  2 z  1
2. 2 x  5 y  5 z  7
3u  2v  w  4
1 3 4
  6
x y z
4. 5u  3v  w  2
1 2 1
4 x  3 y  z  3
2u  w  1
3.    10
x y z
2 3 1
   12
x y z
Graph both equations of each system in the same coordinate plane and state whether they are
consistent or inconsistent.
3 x  4 y  12
2
y  x6
6.
5.
4 x  3 y  12
3
2x  3y  6
Write each equation of the system in slope-intercept form. By comparing slopes and
y  intercepts, determine whether the equations are consistent or inconsistent.
4x  5 y  5
6x  y  7
7.
8.
4 y  5x  2
6x  y  2
For each of the following systems, if the system has a unique solution, find it; if the system has an
infinite solution set, describe it and give three particular solutions; if the system has no solution,
so state.
3x  5 y  6
6 x  9 y  21
16s  6t  3
11.
9.
10.
6 y  4 x  14
2x  3y  4
6s  4t  5  0
2( x  y )  5  2 y
x  y  4( y  2)
2 x  3 y  3( x  y  2)
12.
13.
14.
2( x  y )  5  2 x
x  y  2( y  4)
3 x  2 y  2( x  y  3)
6 3
3 8
1 1
 5
 2
 1
u v
u v
u v
15.
16.
17.
5 3
2 9
5 4
  3
 4
 1
u v
u v
u v
Determine A and B so that the graph of the equation will contain the given points.
18. Ax  By  13;(1,3), (4, 1)
19. y  Ax 2  B;(1, 3),(3,5)
Practice Set E: Functions
Find a formula of the form f ( x)  mx  b for the linear function f
1. f (0)  1; f (1)  3
2. f (3)  1; f (4)  0
3. Assume that f is a linear function. If f (3)  5
4. Find  (3) , given that  is a linear
and f (8)  20 , find f (5) and f (98) .
function with  (1)  2 and  (4)  7
Practice Set W: Writing
1. Write a distance word problem involving wind or current. Include a topic sentence (i.e., “A
canoe rows up a river…”), supporting details (the facts), and a conclusion (the question to be
solved). State your problem and solve it.
ANSWERS
Practice Set A
1. 5 lemonades, 7 cookies
3. 12-$1, 9-$5, 3-$10
2. v0  5, a  4
1.
5s  9t  6  0
3s  4t  2
4. y  x 2  3x  2
7. 40º, 50º
8. 64º, 116º
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5. 55 cm
9. 15 d, 14 q
6. current 5 km/h, boat 25 km/h
10. 560 orch., 1240 bal
11. 1455 kg, 945 kg
12. 17, 28
13. 560 km/h
17. y  3x  4
14. 6 km/h; 3 km/h
15. 21 , 83
16. y  2 x 2  5
19. 80 mL of 60%, 120 mL of 40%
20. v0  53 ; a 
4
18. y   12 x  3
3
21. 35
22. 82
23. 37
24. 94
25. 4 km/h
26. 3 km/h
27. 10 km/h W; 2 km/h E 28. 1 km/h
29. wind 6 km/h; air speed 54 km/hr
30. 75 mi, 40 mph
31. 19. R  4C  5
32. 15 cm
33. 150 mL
34. $1.29
Practice Set B
1. 2
2. vertical 3. vertical 4. -1
5. -3
7. sample: (4,2) (3,1)
6.  23
8. sample: (4,1) (8,-1)
Practice Set C
1. x  y  2
5. x  5 y  24
9. x  1
13a. 3x  5 y  9
Practice Set D
1. (6,-4)
9. sample: (-3,-4) (3,-8)
10.
3
2
11. 6
12. -10
13. 3
14. 1
2. 3x  y  14
4. x  y  4
3. x  2
6. 2 x  y  1
7. 2 x  5 y  6
8. 3 x  4 y  12
10. 6 x  6 y  7
11. 3 x  y  6
12a. 2 x  y  3
12b. x  2 y  6
13b. 5 x  3 y  19
14a. 3 x  2 y  12
14b. 2 x  3 y  8
4. (-1,2,3)
3. (3,  13 , 113 )
6. consistent
7. consistent
8. inconsistent
3 7
11. ( 2 , 2 )
12. ( 32 ,  12 )
10. infinite sol:  x, y  ;2 x  3 y  7
2. (1,3,2)
5. inconsistent
9. (2,0)
13. inconsistent
15. (2,-3)
16. (7,14)
18. A=4, B=3
19. A=1, B=-4
14. ( 65 , 65 )
17. ( 23 ,  72 )
Practice Set E
1. f ( x)  2 x  1 2. f ( x)   x  4
3. f ( x)  3x  4; f (5)  11; f (98)  290
4. -4
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