1. science
2. mathematics
3. algebra

MTH 05
WeBWork
Problem Book
(Spring 2015 - Ojakian)
TA TEST
Assignment HW 01-Review of Fractions due 05/15/2015 at 06:00am EDT
4. (1 pt) Replace the letters with natural numbers so that the
resulting equations are true.
1. (1 pt) The following questions reinforce the vocabulary
for the four basic arithmetic operations. Don’t use words like
”minussing” or ”timesing”, they are juvenile. Use the proper
terminology employed in this class.
3
A
18
C
57
=
=
=
=
4 12
B
44
D
A=
B=
C=
D=
Match the verbs below with the letters labeling particular
nouns.
1.
2.
3.
4.
subtract
add
multiply
divide
A.
B.
C.
D.
sum
difference
quotient
product
MTH05 Spring2015 Ojakian
5. (1 pt) Choose the appropriate symbol (<, >, =) so that we
get a true statement:
3
7
?
11
5
6. (1 pt) Choose the appropriate symbol (<, >, =) so that we
get true statements:
6
14
?
23
23
23
23
?
6
14
2. (1 pt)
This is a problem with multiple parts. When you complete a
part and are told that your answers are correct then click to go on
to the next part and resubmit your answer. When you do this ignore the statement that there are unanswered questions and just
answer the new questions.
The picture above shows a part of the number line with the
numbers 0, 1, and 2 marked (below the number line)by the
longer vertical lines.
There are four short colored lines. Each of these corresponds to
a fraction and is put at the point on the number line that represents that fraction.
The four short colored lines correspond to the fractions 13 , 23 , 12 , 14
The red line corresponds to the fraction
The blue line corresponds to the fraction
The green line corresponds to the fraction
The black line corresponds to the fraction
7. (1 pt) Simplify the fraction to the simplest form.
9
=
15
8. (1 pt) Simplify the fraction completely to its simplest
form.
13
=
91
9. (1 pt) Express each of the following as a fraction in simplest form.
a) 0.75=
b) 0.5=
10. (1 pt) Change the given fraction to mixed numbers.
Here is an example of how to put your answer in an answer box.
If your answer is 2 35 then put 2 3/5 into the answer
Make sure that you leave a space between the whole number and
the fraction.
1) 74 =
2) 18
5 =
39
3) 9 =
3. (1 pt) Replace the letters with natural numbers so that the
resulting equations are true.
0 A B
= =
6
7
8
A=
B=
1
17. (1 pt)
Complete the factor tree for the composite number 1287. Enter numbers from lowest to highest (when there is a choice).
11. (1 pt) Perform the following multiplication. Give your
answer in the simplest form.
7 6
·
=
12 14
12. (1 pt) Perform the following multiplication. Give your
answer in the simplest form.
A × B ×C × D =
66 32
·
=
6 77
×
×
×
= 1287
18. (1 pt)
Complete the factor tree for the composite number 110. Enter your answers from lowest to highest.
13. (1 pt) Perform the following division. Give your answer
in the simplest form.
4
3
÷
=
4 21
A × B ×C =
5 13
÷
=
7 35
c)
5
9
3
7
5
8
=
21. (1 pt) Perform the following addition. Give your answer
in the simplest form.
2
4+
=
13
.
=
.
d) (5 79 )(3 83 ) =
22. (1 pt) Write each sum in simplest form (as a mixed number).
13 58 + 12 61 = .
5
3
.
5 +77=
1
15 8 + 9 43 = .
27 45 + 18 53 = .
.
16. (1 pt) Perform the operation and then write the answer in
lowest terms as a mixed number.
12
5
4
7
23. (1 pt) Perform the following addition. Give your answer
in the simplest form.
11
3
13
+
+
=
8
32 40
• A. 2 17
24. (1 pt) Perform the following subtraction. Give your answer in the simplest form.
6
17
−
=
19 19
• B. 4 15
• C.
35
48
• D. 1 13
35
• E.
= 110
20. (1 pt) Perform the following addition. Give your answer
in the simplest form.
3 9
+ =
4 8
15. (1 pt) For each problem perform the operation and then
write the result as either 1) A reduced fraction, or 2) A mixed
number with a reduced fractional part.
a) ( 73 )(1 38 ) =
.
2 61
×
19. (1 pt)
1) The least common multiple of 40 and 3 is
2) The least common multiple of 140 and 28 is
14. (1 pt) Perform the following division. Give your answer
in the simplest form.
b)
×
25. (1 pt) Perform the following subtraction. Give your answer in the simplest form.
14
7
−
=
15 24
5
21
2
The perimeter is
26. (1 pt) Perform the following subtraction. Give your answer in the simplest form.
15
8−
=
4
centimeters.
The area is
square centimeters.
27. (1 pt) Find the perimeter and the area of the rectangle in
the following figure.
28. (1 pt)
Courtney walks 5 laps around a 14 -mile track.
[1 mile is 5280 feet].
How far does she walk?
feet.
c
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 02-Real Numbers–Introduction due 05/15/2015 at 06:00am EDT
5. (1 pt) Simplify:
a) | − (−(−10))| =
b) −(−(−15)) =
1. (1 pt) Identify the points shown on the given number line.
Separate your answers by commas.
6. (1 pt) Choose the appropriate phrase so that we get each
statement true:
a) −24 ? 6
b) −5 ? −17
c) | − 5| ? | − 17|
Points in order from low to high =
2. (1 pt) Order −1, 18, 13, −14 from least to greatest.
(Separate your answers by commas.)
3. (1 pt) Simplify:
a) |6| =
b) | − 4| =
7. (1 pt) Choose the appropriate phrase so that we get each
statement true:
a) 16 ? −(−25)
b) | − 1| ? −8
c) 25 ? | − 25|
4. (1 pt) Simplify:
a) | − 12.6| =
b) −| − 1| =
c
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 03-Real Numbers–Adding and Subtracting due 05/15/2015 at 06:00am EDT
1. (1 pt) Assuming that white tiles equal +1 and solid blue
tiles equal −1, write a numerical expression for the model and
find the sum.
+
9. (1 pt) Perform the following operations: (Note: Your answer is a fraction.)
a) − 12 − (− 16 ) =
b) 45 − 18 =
c) − 18 + 1 =
d) −1 + (− 45 ) =
=
2. (1 pt) A football team gains 4 yards on first down, loses 8
on second down and then gains 4 on third down.
An appropriate expression describing this result is
+
+
and the result of the three plays is a total of
yards.
(It is possible for the answer to be a negative number.)
10. (1 pt) a) The temperature dropped from 4 degrees to −9
degrees. The drop in temperature is
degrees.
b) The temperature is −15 degrees. It dropped 15 degrees
from the temperature two days ago. The temperature two days
degrees.
ago was
3. (1 pt) An elevator started at floor 27. It then went down 14
floors, then up 5 floors and then down 11 floors. The elevator is
at floor
.
11. (1 pt) As of the year 2014, the lowest subway station in
New York City is the 191street 1 station; it is 180 feet below
street level. Suppose you are 84 feet above street level. What is
the difference in height between you and this subway station?
feet.
4. (1 pt) Add as indicated:
a) −5 + (−3) =
b) −9 + 11 =
c) 20 + (−16) =
d) 7 + (−15) + (−7) =
12. (1 pt) As of the year 2014, the lowest subway station in
New York City is the 191street 1 station; it is 180 feet below
street level. Suppose you are in a subway car that is 16 feet below street level. What is the difference in height between you
and this subway station?
feet.
5. (1 pt) Subtract as indicated:
a) 4 − 25 =
b) 3 − (−14) =
c) 7 − (−7) =
d) (−7) − (−2) =
13. (1 pt) As of the year 2014, the highest subway station in
New York City is the Smith-9 Street Station (F and G trains); it
is 88 feet above street level. Suppose you are in a train that is 58
feet below street level. What is the difference in height between
you and this subway station?
feet.
6. (1 pt) Compute the value of
26 − 10 − 8
Answer =
7. (1 pt) Use rules to find the sum
38 + (−28) + (−11)
14. (1 pt) As of the year 2014, the highest subway station in
New York City is the Smith-9 Street Station (F and G trains);
it is 88 feet above street level. Suppose you are 25 feet above
street level. What is the difference in height between you and
this subway station?
feet.
8. (1 pt) Use addition and subtraction rules to find the sum
39 + (−30) + (−12) + 70
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 04-Real Numbers–Multiplying and Dividing due 05/15/2015 at 06:00am EDT
a) Reciprocal of − 120
80 =
b) Reciprocal of −40 =
1. (1 pt) Multiply as indicated:
a) 13(−9) =
b) (−7)(−11) =
8. (1 pt) Divide or state that the division is undefined.
a) − 13 ÷ (− 45 ) =
b) 20 ÷ (− 13 ) =
2. (1 pt) Multiply as indicated:
a) −4(0) =
b) −4(2)(2) =
9. (1 pt) Divide or state that the division is undefined:
3. (1 pt) Divide or state that the division is undefined. (When
the division is undefined, enter undefined .)
0
a)
=
−6
−11
b)
=
0
4
5
=
−4
19
−
b) 10
=
− 17
10
a)
10. (1 pt) UNTESTED!
The average of −10◦ , −11◦ , −16◦ , −6◦ , 16◦ =
decimal if necessary)
4. (1 pt) Divide or state that the division is undefined. (In this
case, enter undefined .)
28
a)
=
−4
−170
b)
=
−5
◦
(Use
11. (1 pt)
5.3 × 0.3=
57.2 ÷ 0.5=
12. (1 pt) The cost of a single fare on an MTA subway or bus
is $2.5 (in the year 2014).
5. (1 pt) Multiply: (Note: Use fractions not decimals.)
a) 31 (−2) =
b) 79 ( 18 ) =
How much will 14 rides cost?
6. (1 pt) Multiply: (Note: Use fractions not decimals.)
a) (−3)(0)(−2) =
b) 12 (− 79 )( 21 ) =
Answer=
13. (1 pt) The cost of a single fare on an MTA subway or bus
is $2.5 (in the year 2014).
7. (1 pt)
Find the reciprocal of the number (your answer should be
in reduced form ).
With $42.5, how many rides can you take?
Answer=
c
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 05-Exponents and Order of Operations due 05/15/2015 at 06:00am EDT
1. (1 pt) Evaluate each expression:
a) (−9)2 =
b) −92 =
8. (1 pt) Evaluate each expression:
a) 62 − 27 ÷ 32 · 4 − 5 =
5 · 3 − 32
=
b) 2
[2 − (−1)]2
2. (1 pt) Evaluate each expression:
a) (−10)3 =
b) (−1)8 =
9. (1 pt) Evaluate each expression:
a) 6 − 2[−3(3 − 9) − 6(10 − 2)] =
4(−4) − 4(−6)
b)
=
3−9
3. (1 pt) Evaluate each expression:
a) (4 · 5)2 =
b) (−4)2 52 =
4. (1 pt) Evaluate each expression:
a) 4 · 3 + 2 · 9 =
b) 1 · 10 − 5 · 9 =
10. (1 pt) Evaluate.
| − 5|(−6) − (5)(2)3
√
9 − 81
5. (1 pt) Evaluate each expression:
a) (−3 + 2) · 4 =
b) −4(−3 − 2) =
6. (1 pt) Use the order of operations to simplify:
a) 2(−2) − 3(−3) =
b) 2(−3)2 − 3(−1)2 =
• A. 0
• B. − 79
• C. − 35
36
7. (1 pt) Evaluate each expression:
a) −2
− |2 − | − 2|| =
b) (−2)3 − 22 =
• D.
35
36
• E. Undefined
c
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TA TEST
Assignment HW 06-Transition to Algebra due 05/15/2015 at 06:00am EDT
1. (1 pt) Write a variable expression for the phrase
The sum of 15 and a
MTH05 Spring2015 Ojakian
11. (1 pt) Write variable expressions for
The value in cents of a nickels =
The value in cents of a dimes =
The value in cents of a quarters =
The value in cents of a dimes and one quarter =
The value in cents of 17 dimes =
2. (1 pt) Write a variable expression for the phrase
m more than 20
3. (1 pt) Write the following English phrase as an algebraic
expression.
Let x represent the unknown number.
The product of five and an unknown number.
Answer:
4. (1 pt) Write a variable expression for the phrase
7 less than a number y
12. (1 pt) Write the following English phrase as an algebraic
expression.
Let x represent the unknown number.
The difference of eight times a number and four times its
square.
Answer:
5. (1 pt) Write a variable expression for the phrase
n divided by 3
13. (1 pt) Write the following English phrase as an algebraic
expression.
Let x represent the unknown number.
Ten less than the cube of the difference of twice a number
and seven.
Answer:
6. (1 pt) Write a variable expression for the phrase
7 subtracted from a number k
7. (1 pt) Write the following English phrase as an algebraic
expression.
Let x represent the unknown number.
Six fifths of an unknown number.
Answer:
8. (1 pt) Write the following English phrase as an algebraic
expression.
Let x represent the unknown number.
The quotient of an unknown number and six.
Answer:
9. (1 pt) Write a variable expression for the length of the
bottom black bar with a being the length of the orange bar:
14. (1 pt) Write the following English phrase as an algebraic
expression.
The difference of the product of -6 and z and negative one.
Answer:
15. (1 pt) Write the phrase as a mathematical expression.
Use x to represent the number.
Which equation is a correct translation of the phrase?
The sum of 5 times a number and −2, divided by 4 less
than the same number
5x − 2
x−4
5x − 2
B.
4−x
5x − 2
C.
−4
x
−2
D. 5x +
4−x
−10x
E.
x−4
• A.
(Click on image for larger view)
Formula for length of black bar =
•
10. (1 pt) Write a variable expression for the length of the
bottom black bar with a being the length of the orange bar:
•
•
(Click on image for larger view)
Formula for length of black bar =
•
1
TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 07-Evaluating Algebraic Expressions due 05/15/2015 at 06:00am EDT
8. (1 pt) Indicate whether the following statements are True
(T) or False (F).
1. −y2 + 5y = −6y; y = 11.
2. x2 + y2 < 72; x = 5, y = 6.
3. 6x + 5y = 19; x = 0, y = −5.
4. |5x − 4y| = 25; x = −1, y = 5.
5. 6x
= −11xy; x = −1, y = 0.
y2
1. (1 pt) Evaluate the expressions for x = 6, y = 9 and z = 3:
x+8 =
2z − 8 =
xyz =
y+z =
2. (1 pt) Evaluate the expressions for x = 5, y = 8 and z = 0:
9. (1 pt) The area A of a triangle with base b and height h is
given by the formula
16 − 4xz =
14xy =
1
A = bh
2
3. (1 pt) Evaluate the expressions for x = 15 and y = 60:
450
x+y
y−x
5
=
=
The area of a triangle with 8 in and height 6 in is
inches.
square
10. (1 pt) The volume of a sphere of radius r is given by the
formula
4. (1 pt) Evaluate each of the following expressions when
a = 0 and b = −1:
a) (a + b)2 =
b) a2 + b2 =
c) a2 + 2ab + b2 =
4
V = πr3
3
where π is the area of a circle of radius 1 (this is a number
approximately equal to 3.1415926536). The volume of a sphere
of radius 6 cm is
π cubic cm.
5. (1 pt) Evaluate each of the following expressions when
a = −2 and b = −5:
a) (a + b)2 =
b) a2 + b2 =
c) a2 + 2ab + b2 =
11. (1 pt) In the formula
r=
I
Pt
P stands for the principal, I for the total interest earned, r for the
rate of interest, and t for the time, in years, that the money was
invested. If the principal is $3250 and the total interest earned
in 4 years is $520, then the interest rate is
6. (1 pt) Evaluate each of the following expressions when
a = 21 and b = −2. Leave a fraction as an improper fraction if
possible (Do not convert it to a mixed number).
a) (a + b)2 =
b) a2 + b2 =
c) a2 + 2ab + b2 =
12. (1 pt) Use the formula F = 95 C + 32 for converting degrees Celsius into degrees Fahrenheit. Find the Fahrenheit measure of the Celsius temperature C = 5.
7. (1 pt)
Evaluate each of the following expressions.
Your answer must be in simplest form [ as a proper fraction or
mixed number ]
If p = (1/5) and q = 5 17 then p2 q =
If s = (1/7) and t = 1 67 then t 2 /s =
•
•
•
•
•
c
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A. 33
B. 169
C. 77
D. 41
E. 15.4
TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 08-Adding and Subtracting Algebraic Expressions due 05/15/2015 at 06:00am EDT
1. (1 pt) Fill in the blanks below by choosing from the available options to get the correct definition.
Term: A number or the product of a number and one or more
? and their exponents.
Coefficient: In each term, the variable is multiplied by this
?
Like Terms: Terms which have the same ?
Constant: A term without a ?
Simplify: The process of replacing an expression with an
equivalent one that has a smaller number of ?
10. (1 pt) The expression 2(4x2 + 5x + 5) − 5(5x2 + 3x + 7)
equals
x2 +
x+
11. (1 pt) The expression 3(2x3 + 4x2 − 7x + 3) − (2x2 + 5x −
2) equals
x3 + x2 +
x+
12. (1 pt) A rectangle has length 14x + 5 and width 4x − 2.
Which of the following expressions represents the perimeter of
the rectangle?
2. (1 pt)
Consider the expression 4r + 11r .
(separate by a comma)
The coefficients =
and 4r + 11r =
3. (1 pt)
Consider the expression 5 j − 12 j + 3 j .
(separate by a comma)
The coefficients =
and 5 j − 12 j + 3 j =
•
•
•
•
A. 18x + 3
B. 36x + 6
C. 36x − 6
D. 18x − 3
13. (1 pt) Subtract 10t − 8 from 10t 2 − 3t
4. (1 pt)
•
•
•
•
6x + 13 + 10x − 4x − 4
=
x+
.
5. (1 pt)
Simplify (8 − 4x) + (9x − 5).
A. −10t 2 − 7t − 8
B. 10t 2 − 7t − 8
C. 10t 2 − 13t + 8
D. −10t 2 + 13t + 8
14. (1 pt) Simplify Completely.
8xy3 − xy − −3xy3 − xy − 6xy + 8xy3
6. (1 pt)
7(4x) + 9(x − 4)
=
x+
.
•
•
•
•
•
7. (1 pt)
8x + 9y + 6x + 10y
=
x+
y.
A.
B.
C.
D.
E.
13xy3 + 4xy
13xy3 − 8xy
3xy3 − 6xy
19xy3 + 6xy
3xy3 + 6xy
8. (1 pt)
The expression (8x2 − 7x + 5) + (5x2 + 3x − 2) equals
x2 +
x+
15. (1 pt) Add: (4a5 b4 − 1) + (−2a5 b4 + a4 b5 + 4)
Answer:
9. (1 pt) When multiplied and simplified, the expression
16. (1 pt) Subtract: (5a6 b3 −2a4 b4 +5)−(−6a6 b3 −6a4 b4 −
1)
7 (6x2 + 4x + 2) + 3 (6x2 + 7x + 2) =
Answer:
c
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TA TEST
Assignment HW 09-Solving Linear Equations due 05/15/2015 at 06:00am EDT
1. (1 pt) Is x = −1 a solution to the equation
4 − x = 4 + x?
?
MTH05 Spring2015 Ojakian
10. (1 pt) In each of the following equations, solve to find the
value of x.
a) If 2x = 6 then x =
b) If 85 x = 74 then x =
c) If 0.35x = 0.375 then x =
2. (1 pt) Is x = 75 a solution to the equation
4(2x − 7) = 9x − 12?
?
11. (1 pt)
Solve each equation:
a) If 2x − 6 = 10 then x =
b) If 3z − 14 = 10 then z =
c) If 2s + 6 = 30 then s =
3. (1 pt) Is x = − 11
6 a solution to the equation
3x + 6 = 12 ?
?
12. (1 pt) Solve the following linear equation.
If possible, simplify your answer.
− 12 x + 16 = − 16
x=
4. (1 pt) Consider the equation x3 − x2 = 9x − 9.
a) Is x = −3 a solution to the equation?
?
b) Is x = 1 a solution to the equation?
?
13. (1 pt)
−8x + (−13) x + 18 = 13 + 12 has solution:
5. (1 pt) Solve each equality and express your answer in the
form x =
x =
14. (1 pt) Find x where x is the number of movies actress
Megan Fox has appeared in as of 2014:
(for example, if the solution is 7, enter x = 7 not just 7).
1. −6 + x = 17 has the solution
2. 9 + x = 13 has the solution
3. x + 5 = −19 has the solution
4. x − 6 = −21 has the solution
x − 5 = 2x − 24
x=
6. (1 pt) Solve the following linear equation.
If possible, simplify your answer.
x + 21 = 15
x=
15. (1 pt) Find the solution to the below equation. If this solution is multiplied by 3, it is a number that is one less than the
number of siblings Michael Jackson has. Determine how many
siblings Michael Jackson has.
7. (1 pt)
Solve each equation:
a) q × 12 = 192
q=
.
b) r ÷ 18 = 21 r =
.
2x − 2 + 5x = 4 + 4x + 2
x=
Total siblings=
8. (1 pt)
Solve each equation:
a) If 4x = 36 then x =
b) If 7y = 56 then y =
c) If −1a = 9 then a =
16. (1 pt) When four times a number is decreased by 4, the
result is 20.
a) Write an equation to model the problem. Use x to represent the number.
Answer:
b) Solve the equation to find the number:
Answer:
9. (1 pt) Solve the following linear equation.
If possible, simplify your answer.
2
3 x = −1
x=
1
17. (1 pt) One positive number is 12 times another number.
The difference between the two numbers is 583, find the numbers.
The two numbers in increasing order are
and
209 − 7x = 4x − 9(−5x − 5) − 4
24. (1 pt) Solve.
•
•
•
•
•
.
18. (1 pt) In the 2012-2013 NBA season, Dwayne Wade and
LeBron James combined for 711 free throws. If James made 95
more free throws than Wade, determine how many free throws
each player had.
A. 4
B. 2
C. 3
D. No Solution
E. All real numbers are solutions
−27x − 46 = 5x − 8(4x + 6) − 7
25. (1 pt) Solve.
•
•
•
•
•
Dwayne Wade=
LeBron James =
A. −3
B. −4
C. −6
D. No Solution
E. All real numbers are solutions
26. (1 pt) Consider the equation 0.011 = 0.156x + 0.038.
19. (1 pt) In the 2012-2013 NBA season, Dwight Howard
and Blake Griffin had the same number of personal fouls. DeAndre Jordan and Amir Johnson both had five personal fouls
less than Howard (and hence Griffin). If the total number of
personal fouls of the four players was 762, determine how many
fouls each player had at the end of the season.
To clear the decimals, we multiply by 10∧
When we clear the decimals, we get the following equation:
Dwight Howard=
Blake Griffin =
DeAndre Jordan =
Amir Johnson =
=
.
0.011 = 0.156x + 0.038 has solution: x =
20. (1 pt) In the 2012-2013 NBA season, Jason Kidd had
4 fewer steals than LeBron James. If the average of their total
steals is 127, find the total number of steals each player had in
the season.
27. (1 pt) Find the LCD of all the fractions present in the
equation. LCD =
Jason Kidd =
LeBron James =
Re-write all fractions as equivalent ones with denominator =
LCD.
Then by multiplying both sides of equation by the LCD to clear
7x 1
5
the denominators of − + = ,
12 9 18
we get the following equation:
21. (1 pt) Find x, where x is the subway train Jennifer Lopez
would ride that shuttled her between the Bronx and her Manhattan dance auditions:
5(9x − 9) − 4(11x − 11) + 1 = 6
=
x=
22. (1 pt)
4x − 13 = − (9x + 21) has solution: x =
ANSWER: −
23. (1 pt)
Solve (for this problem there are two options: No solution or
All real numbers are solutions).
−4(−7x − 1) − 9x + 5 = 19x + 9
.
7x 1
5
+ =
has solution: x =
12 9 18
28. (1 pt) Solve for x, where x is the number of cars Kanye
West owned in 2012:
2
1 1
(x + 3) − = x
5
2 2
• A. No Solution
• B. All real numbers are solutions
2
b) Solve the equation to find the width of the pool. (Note:
Include the units , in this case m ).
Answer:
x=
29. (1 pt) The sum of 29 and the solution to the equation
below is the total number of Grammy awards won by Michael
Jackson. Find both.
34. (1 pt)
According to one mathematical model, the average life expenctancy for American men born in 1900 was 55 years. Life
expectancy has increased by about 0.2 year for each birth year
after 1900. If this trend continues, for which birth year will the
average life expentancy be 71 years?
a) Write an equation to model the problem. Let t represent
the number of years after 1900. For example, t = 12 would represent the year 1912.
Answer:
b) Solve the equation, then answer the question given above.
(Note: You are asked for a year, not a value for t. )
Answer:
3
1
+ 7x − − 4x = −1 + 4 + 4x + 1
2
2
x=
total Grammys=
30. (1 pt) Find x where x is the number of movies actor Brad
Pitt has appeared in as of 2014:
3
1
(x − 1) = (x − 5) + 13
4
8
35. (1 pt)
In 2003, the price of a certain automobile was approximately
$30,600 with a depreciation of $1,490 per year. After how many
years will the car’s value be $21,660?
a) Write an equation to model the problem. Let t represent
the number of years after 2003. For example, the year 2005
would be represented by t = 2.
Answer:
b) Solve the equation to find the answer to the question
above. (Note: Include the units , in this case years. )
Answer:
x=
31. (1 pt) The sum of three consecutive natural numbers is
1704, find the numbers.
The three numbers in increasing order are
.
,
, and
32. (1 pt) The oldest child in a family of four children is three
times as old as the yougest. The two middle children are 23 and
25 years old. If the average age of the children is 29, how old is
the youngest child?
36. (1 pt)
Video Store A charges $7 to rent a video game for one week.
Although only members can rent from the store, membership is
free. Video Store B charges only $3 to rent a video game for one
week. Only members can rent from the store and membership
is $120 per year. After how many video game rentals will the
total amount spent at each store be the same?
a) Write an equation to model the problem. Let x represent
the number of video game rentals.
Answer:
b) Solve the equation to find to answer the question. (Note:
Include the units , which in this case is ”rentals”; for example,
if you find of a solution of 29, write: 29 rentals. )
Answer:
Answer:
33. (1 pt)
The length of a rectangular pool is 6 meters less than twice
the width. If the pool’s perimeter is 72 meters, what is the
width?
a) Write an equation to model the problem. Use x to represent the width of the pool.
Answer:
c
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TA TEST
Assignment HW 10-Formulas due 05/15/2015 at 06:00am EDT
1. (1 pt) Solve for w :
9. (1 pt) Solve i = Prt for t, given that P = $400, r = 8%,
and i = $192.
Answer: t =
A = lw
w=
2. (1 pt) Solve the equation PV = nRT for R.
Your answer is :
Note: The answer is case sensitive. P, V and T are capital
letters!
3. (1 pt) Solve the equation P = 2l + 2w for w.
Your answer is :
Note: The answer is case sensitive!
4. (1 pt) Solve for n :
10. (1 pt) Consider the formula to calculate Body Mass Index
(BMI)
Consider the formula to calculate Body Mass Index (BMI)
mass
BMI = height
2
where mass is measured in kilograms and height is measured in
meters.
L = a + (n − 1)d
Determine the height of an individual that has a BMI of 28.5
and weighs 50 kg. Round your answer to the nearest tenth.
n=
5. (1 pt) Solve for t when
p
= 6tc
d
Answer=
p
− 6c
d
p
t=
6dc
p
t = 6c −
d
p
t = + 6c
d
pc
t=
6d
• C.
• D.
• E.
m
11. (1 pt) Consider the formula to calculate Body Mass Index
(BMI)
BMI = 703∗weight
.
height 2
where the weight is measured in pounds and height in inches.
Determine the height of an individual that has a BMI of 30.4
and a height of 77 in. Round your answer to the nearest tenth.
• A. t =
• B.
MTH05 Spring2015 Ojakian
Answer=
6. (1 pt) The area inside a rectangle is its length times the
width. A formula describing this relationship is A = Lw.
Your friend has a basketball goal in his driveway with a rectangular concrete playing area with length 20 feet and width 33
feet. The playing area for the game is
feet-squares.
in
12. (1 pt) Consider the formula to calculate the Estimated
Blood Alcohol Content (EBAC):
EBAC = 0.086·SD·1.2
− (MR · DP)
BW ·Wt
where
SD is the number of drinks containing 10grams of ethanol
Wt is body weight in kilograms
BW is the body water content (females=0.49, males=0.58)
MR is the metabolism constant (females = 0.017, males =0.015)
DP is the drinking period in hours.
7. (1 pt) Distance is the product of rate and time. A formula
describing this relationship is d = rt.
If your family drives 2380 miles in 35 hours, then the average
rate of speed is
miles per hours.
8. (1 pt) The volume of a pyramid is given by the equation
1
V = Bh.
3
Solve for B.
Answer: B =
Note: This is case sensitive.
Determine the EBAC of a 54.9 kg man drinking 3 standard
drinks in 1 hours. Round your answer to the nearest tenth.
Answer=
If V = 180 and h = 20, then what is the value of B?
Answer: B =
1
MR is the metabolism constant (females = 0.017, males =0.015)
DP is the drinking period in hours.
13. (1 pt) Consider the formula to calculate the Estimated
Blood Alcohol Content (EBAC):
− (MR · DP)
EBAC = 0.086·SD·1.2
BW ·Wt
Determine the EBAC of a 70.1 kg woman drinking 3 standard
drinks in 4 hours. Round your answer to the nearest tenth.
where
SD is the number of drinks containing 10grams of ethanol
Wt is body weight in kilograms
BW is the body water content (females=0.49, males=0.58)
Answer=
c
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TA TEST
Assignment HW 11-Ratio and Proportion due 05/15/2015 at 06:00am EDT
1. (1 pt) Find each unit rate and express your answer as a
decimal:
miles per hour.
112 miles in 8 hours is
1251 miles in 24 hours is
miles per hour.
MTH05 Spring2015 Ojakian
7. (1 pt) Solve the proportion:
X
44
=
51
1122
2. (1 pt) Write each ratio as a fraction in simplest form:
35 to 266 is the fraction
112 to 44 is the fraction
Your fraction should be entered in the form a/b and needs be
be reduced.
3. (1 pt) In the 2012-2013 NBA season, Chris Paul averaged
9.7 assists per game and 2.4 steals per game. Russel Westbrook
averaged 7.4 assists per game and 1.8 steals per game. Who has
the higher steals to assist ratio? Enter ”Paul” or ”Westbrook”.
1122
8. (1 pt)
Your father is planning to cook for 40 people using a recipe
that specifies three-fourths cups of sugar for each three people.
For the larger group, your father will require
cups
of sugar.
When necessary, round to three decimal places.
Ans=
4. (1 pt) In the 2012-2013 NBA season, LeBron James averaged 7.2 assists per game and 1.7 steals per game. Russell Westbrook averaged 7.4 assists per game and 1.8 steals per game.
Who has the higher steals to assist ratio? Enter ”James” or
”Westbrook”.
9. (1 pt) Peter bought 3 toy cars for $39.
How much do 11 cars cost?
•
•
•
•
Ans=
5. (1 pt) In a grocery store there are three choices of size for
your favorite laundry detergent.
1) A 28 ounce bottle for $ 5.49
2) A 44 ounce bottle for $ 6.49
3) A 64 ounce bottle for $ 8.49
The bottle that costs the least per ounce is
)
Choose between choices 1,2,3
A. $31
B. $33
C. $50
D. $143
10. (1 pt) 17 workers take 2 months to repair 40 miles of
road. How many miles of road can be repaired by 23 workers in
2 months?
6. (1 pt) Solve the proportion:
•
•
•
•
•
X
5
=
2
16
16
c
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1
A. 2 12
17
B. 29 13
23
C. 460
31
D. 9 40
2
E. 54 17
TA TEST
Assignment HW 12-Percentage due 05/15/2015 at 06:00am EDT
8. (1 pt) 90% of what number is 27?
a) Write an equation to model the problem. Use x to represent the number.
Answer:
b) Solve the equation to find the number:
Answer:
9. (1 pt) When a number is decreased by 30% of itself, the
result is 49. What is the number?
a) Write an equation to model the problem. Use x to represent the number.
Answer:
b) Solve the equation to find the number:
Answer:
10. (1 pt) The size of Manhattan is 23 square miles. The size
of Staten Island is 58 square miles.
1. (1 pt) Convert the number 0.8777 into its equivalent
percent.
Answer=
%
3
2. (1 pt) Convert the (mixed) fraction 5 into its equivalent
4
percent.
Answer=
MTH05 Spring2015 Ojakian
%
3. (1 pt) In the 2012-2013 NBA season (82 games) Kevin
Durant made 90.5
Answer=
1) The area of Manhattan is what percent of the area of Staten
island?
%
4. (1 pt) The population of New York City is 8200000 (in
the year 2010). Suppose that 2% of the population are wearing
Yankee hats. How many people are wearing Yankee hats?
2) The area of Staten Island is what percent of the area of
Manhattan?
%
Answer=
3) What is the percent increase in area?
%
4) What is the percent decrease in area?
%
5. (1 pt) 17 kilometres is what percent of 20 kilometres?
Answer=
%
6. (1 pt) The population of New York City is 8200000 (in the
year 2010). Suppose 656000 people are wearing Yankee hats.
What percent of the population are wearing Yankee hats?
11. (1 pt) Since the US re-instated the death penalty in 1976,
there have been a total of 510 executions in Texas and 5 executions in Maryland. Calculate by what percent the number of
executions in Texas exceeds those in Maryland.
Answer=
Answer=
7. (1 pt) Angela gets a 9 % cut. Her original salary was $
29400 per year. What is her new salary?
•
•
•
•
•
%
12. (1 pt) Since the US re-instated the death penalty in 1976,
there have been a total of 470 black defendants executed and 767
white defendants executed. Calculate by what percent the number of white defendants executed exceeds the number of black
defendants executed. Round your answer to the nearest tenth.
A. $29391
B. $2646
C. $26754
D. $28500
E. $32046
Answer=
1
%
16. (1 pt) In the 2012-2013 NBA season (82 games) Kobe
Bryant had attempted 1595 field goals, while LeBron James attempted 1354. By what percent did Kobe Bryant’s field goal
attempts exceed LeBron James’ attempts? Round your answer
to the nearest tenth.
13. (1 pt) The total number of individuals stopped and frisked
in 2003 was 160851, and 601285 in 2010. Calculate the percent
increase of individuals stopped and frisked from 2003 to 2010.
Round your answer to the nearest tenth.
Answer=
Answer=
%
17. (1 pt) In 2013, the average cost of a Yankee’s ticket cost
$ 51.55, while the average cost of Mets’ tickets cost $ 25.3 .
Calculate by what percent Yankee tickets cost more than Mets
tickets. Round your answer to the nearest tenth.
14. (1 pt) The total number of individuals stopped and frisked
in 2012 was 532911 and dropped to 191558 in 2013. Calculate the percent decrease of individuals stopped and frisked from
2012 to 2013. Round your answer to the nearest tenth.
Answer=
Answer=
18. (1 pt) As of 2014, Beyonce has won a total of 17 Grammy
awards whereas Mariah Carey has won 5. Calculate by what
percent Beyonce’s wins exceed Mariah Carey’s. Round your
answer to the nearest tenth.
%
15. (1 pt) Of the 532911 total individuals stopped and frisked
in 2012, 165140 were Latino. Calculate the percentage of
Latino individuals stopped and frisked in 2012. Round your
answer to the nearest tenth.
Answer=
Ans=
19. (1 pt) As of 2013, Michael Jackson’s ”Thriller” album
sold 50000000 copies, while his ”Bad” album sold 30000000.
Calculate the percent decrease in record sales. Round your answer to the nearest tenth.
%
Ans=
c
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Assignment HW 13-Solving Linear Inequalities due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
8. (1 pt) Simplify each inequality. ( )
1. (1 pt) Express the graph below as an inequality:
1.
2.
3.
4.
For greater than or equal to, type ¿=
For less than or equal to, type ¡=
2. (1 pt) Express the graph below as an inequality:
−4x ≥ −48 has the solution
−4x > −48 has the solution
−4x < −48 has the solution
−4x ≤ −48 has the solution
9. (1 pt) Simplify each inequality. ( )
1. A solution for −4x < −96 is
2. A solution for −2x ≤ 96 is
3. A solution for −2x > 72 is
4. A solution for 4x ≥ 24 is
For greater than or equal to, type ¿=
For less than or equal to, type ¡=
3. (1 pt) Express the graph below as an inequality:
10. (1 pt) UNTESTED
Solve the inequality
2(x + 3) ≤ 5x + 5
Answer: x
Instructions: Enter either <, >, >= or <= in the first answer
box. Enter a number in the second answer box.
For greater than or equal to, type ¿=
For less than or equal to, type ¡=
4. (1 pt) Express the graph below as an inequality:
11. (1 pt) UNTESTED
Solve:
5b − 27 + 2(b − 4) < 0
For greater than or equal to, type ¿=
For less than or equal to, type ¡=
Answer:
12. (1 pt) UNTESTED
Solve:
2x − 6 < −2(2x − 1) + 2
5. (1 pt) Determine which inequality symbol matches each
expression:
? x is more than 12
? x is less than 12
? x is at most 12
? x is no less than 12
? x is at least 12
? x is no more than 12
Answer:
13. (1 pt) UNTESTED
Solve:
a−
4 6
> a−2
5 5
Answer:
14. (1 pt) Consider the following table with the number of
defendants executed in the US since 1976, based on race.
6. (1 pt) Simplify each inequality. ( )
Race
Black
Latino
White
Other
Total
1. 5 + x > 17 has the solution
2. x − 3 ≤ −17 has the solution
3. −8 + x < 21 has the solution
4. x + 3 ≥ −19 has the solution
7. (1 pt) Simplify each inequality. ( )
Executed
470
108
767
24
1369
a) Solve the inequality:
1.
2.
3.
4.
4x < −72 has the solution
4x ≤ −72 has the solution
4x ≥ −72 has the solution
4x > −72 has the solution
6x + 2(2x + 1) < 8 + 2(3x − 1)
1
b) In the above inequality, suppose that x represents the number of white individuals executed. Is the solution to a) TRUE or
FALSE?
16. (1 pt) Find the graph of the solution to the inequality.
c) In the above inequality, suppose that x represents the number of latino individuals executed. Is the solution to a) TRUE or
FALSE?
15. (1 pt) Find the graph of the solution to the inequality.
−9 − 8(9 + x) ≤ 7x − 141
−5x+ 86 < −4(−2x−2)
?
A
A
B
B
C
C
D
D
E
E
c
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?
TA TEST
Assignment HW 14-Two Variable Equations due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
• A. (− 13 , 4)
1. (1 pt) Determine whether the given points are on the graph
of y = 2x + 3.
Enter Yes or No for your answers:
Is (4,11) on the graph?
Is (-3,-3) on the graph?
Is (0,2) on the graph?
Is (0,-2) on the graph?
• B. (−2, 4)
• C. (4, 4)
• D. (−3, 4)
• E. Cannot be solved
2. (1 pt) Find a number y, so that the pair (1, y) is a solution
to the equation 6x − y + 1 = 0.
y=
6. (1 pt) Find five solutions of the equation x + y = 5.
(x, y) =
(x, y) =
(x, y) =
(x, y) =
(x, y) =
3. (1 pt) Find a number x, so that the pair (x, 0) is a solution
to the equation x − 7y = −1.
x=
4. (1 pt) Complete the ordered pair (−19, ), so that it is a
solution for the given equation −7x −8y = −22
7. (1 pt) Find three solutions of the equation 3y − 7x − 1 = 0.
(x, y) =
(x, y) =
(x, y) =
• A. (−19, −7)
8. (1 pt) Let F denote a certain temperature in degrees
Fahrenheit, and C the same temperature in degrees Celsius.
Then you can convert between F and C by the formula
• B. (−19, 19 38 )
8
• C. (−19, 155
)
9
F = 32 + C.
5
• D. (−19, −8)
• E. Cannot be solved
Suppose the temperature is 5 degrees Celsius.
5. (1 pt) Complete the ordered pair ( , 4), so that it is a solution for the given equation −2x + 4y = 22
Enter here
the corresponding temperature in degrees
Fahrenheit.
Hint: Substitute the value of C in the given formula.
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MTH05 Spring2015 Ojakian
Assignment HW 15-The Cartisian Coordinate System due 05/15/2015 at 06:00am EDT
The coordinates of point F are (
The coordinates of point B are (
The coordinates of point E are (
The coordinates of point D are (
The coordinates of point C are (
The coordinates of point A are (
1. (1 pt) Identify the proper quadrants for each of the points
shown on the given coordinate system.
,
,
,
,
,
,
).
).
).
).
).
).
4. (1 pt)
A=
B=
C=
D=
E=
F=
G=
?
?
?
?
?
?
?
Use the graph above to find the following points:
The point with coordinates (5,1) is ? .
The point with coordinates (5,4) is ? .
5. (1 pt)
2. (1 pt)
The coordinates of the point labelled A are (
The coordinates of the point labelled B are (
The coordinates of the point labelled C are (
,
,
,
).
).
).
3. (1 pt)
In the graph above, the x and y values are shown on the axes.
Find the coordinates of each of the marked points.
The point with coordinates (-1,0) is
.
The point with coordinates (-2,-5) is
.
The point with coordinates (-1,5) is
.
The point with coordinates (3,-3) is
.
The point with coordinates (2,1) is
.
The point with coordinates (0,-1) is
.
In the graph above, the x and y values are shown on the axes.
Find the coordinates of each of the marked points.
1
TA TEST
Assignment HW 16-Lines–Graphing due 05/15/2015 at 06:00am EDT
1. (1 pt) Determine whether the given points are on the graph
of y = 2x + 3. Enter Yes or No for your answers:
Is (-6,-9) on the graph?
Is (-5,-7) on the graph?
Is (-5,-8) on the graph?
Is (3,4) on the graph?
MTH05 Spring2015 Ojakian
4. (1 pt) Match the linear equations with one of the graphs
below.
2. (1 pt) Complete the table of values for the equation y = 7
−1
x
y
−7
2
A
B
C
D
• A. 7 ; 7 ; 7
• B. −1 ; −7 ; 2
• C. −7 ; −49 ; 14
• D. −7 ; −1 ; 2
• E. Cannot be completed
3. (1 pt) Complete the table of values for the equation x = 5
x
y
−2
−8
−1
1.
2.
3.
4.
• A. −2 ; −8 ; −1
3x + 2y = −8
y=x
3x − 3y = −12
y = −3x
• B. −8 ; −2 ; −1
Note: You can click on the graphs to enlarge the images.
• C. −10 ; −40 ; −5
• D. 5 ; 5 ; 5
• E. Cannot be completed
5. (1 pt) Match the linear equations with one of the graphs
below.
1
Without a calculator, match each equation with its
graph A-G.
? y = x−4
? −4x + 4 = y
? 4=y
A
? y = −4x − 4
B
? y = x+3
? y=
x
4
? 2=x
C
1.
2.
3.
4.
A
B
C
E
F
G
D
D
y = 4x − 2
y = − 12 x − 2
y=2
y = − 14 x − 2
(Click on a graph to enlarge it)
7. (1 pt) UNTESTED!
Find the x- and y-intercepts of the graph of the equation
y = x + 6.
Note: You can click on the graphs to enlarge the images.
The x-intercept is:
6. (2 pts)
The y-intercept is:
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TA TEST
Assignment HW 17-Lines–Slope due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
Enter the labels of the graphs (A, B, C, and D) in order of
increasing slope:
<
<
<
.
1. (1 pt) UNTESTED!
3. (1 pt) Find the slope of the line determined by the two
points (1, −1) and (4, 6).
Slope: m =
4. (1 pt) Find the slope, if possible, of the line passing
through the points, (0, −4) and (0, 5) and describe the line. If
the slope does not exist, please type ”undefined”.
a) m =
b) The line ? .
5. (1 pt) Write the linear equation 80x + 90y = 350 in slopeintercept form y = mx + b. Enter your answer as an equation in
slope-intercept form.
Use the graph, given above, to find the slope of each line.
a) Slope of Line 1 (blue) =
b) Slope of Line 2 (red) =
b) Slope of Line 3 (green) =
6. (1 pt) Write the equation for the line y − 4 = −4(x − 3) in
the form y = mx + b, and enter your answer in this form.
2. (1 pt) UNTESTED!
Order the following graphs by increasing slope of the line
being displayed:
7. (1 pt) Rewrite the equation in slope-intercept form by solving for y. Find the slope and the y-intercept.
2x + y = 2
a) The equation is: y =
b) The slope is m =
c) The y-intercept is b =
8. (1 pt) Rewrite the equation in slope-intercept form by solving for y. Give the slope and y-intercept.
−2x + y = 0
A
B
.
a) The equation is: y =
b) The slope is m =
c) The y-intercept is b =
9. (1 pt) Write the equation of a line with the slope, −3
2 ,
which passes through the origin. Write the answer in slopeintercept form.
Answer:
C
10. (1 pt) Write the equation of a line with the slope, 14 ,
which passes through the point (0, −3). Write the answer in
slope-intercept form.
Answer:
D
1
11. (1 pt) UNTESTED!
Find an equation y = mx + b for the line whose graph is
sketched (click on the graph to view an enlarged graph ):
12. (1 pt) UNTESTED!
Use the graph, given above, to find the slope and equation
for the line.
a) Slope of the line: m =
b) The equation of the line in slope-intercept form: y =
The number m equals
The number b equals
13. (1 pt) Find y if the line through (5, 4) and (−4, y) has a
5
slope m = − .
9
Answer: y =
;.
;.
c
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Assignment HW 18-Lines–Equations due 05/15/2015 at 06:00am EDT
1. (1 pt) Find the equation for the vertical line passing
through the point (−18, −6).
The equation for the line:
9. (1 pt) Find the equations of the line that passes through
the points (−6, −2) and (−9, −1).
2. (1 pt) Find the equation for the horizontal line passing
through the point (19, 4).
The equation for the line:
• A. y = − 13 x − 2
3. (1 pt) Write the equation of a line with the slope, − 23 ,
which passes through the point (−6, 0). Write the answer in
slope-intercept form.
Answer:
4. (1 pt) Write an equation for the line through the points
(8, 3) and (3, 10) in point-slope form y = y0 + m(x − x0 ).
y=
MTH05 Spring2015 Ojakian
• B. y = 31 x − 4
• C. y = −3x − 20
• D. y = − 13 x − 4
• E. None of the above
+
5. (1 pt) UNTESTED!
Find the slope and the equation for the line passing through
the points: (5, −6) and (3, −2).
a) m =
b) The equation for the line:
10. (1 pt) UNTESTED!
Are the lines below perpendicular, parallel, or neither?
y = 3x − 9
6. (1 pt) UNTESTED!
Find the slope and the equation for the line passing through
the points: (3, 1) and (3, −1).
a) m =
b) The equation for the line:
• A. Perpendicular
• B. Parallel
• C. Neither
7. (1 pt) Find the equation of the line passing through the
points (−6, 19) and (3, −17). Write the equation in slope intercept form.
•
•
•
•
1
y = x−6
3
11. (1 pt) UNTESTED!
Are the lines below perpendicular, parallel, or neither?
A. y = 4x − 29
B. y = 4x + 43
C. y = −4x − 5
D. y = −4x + 19
2y = 21 − x
8. (1 pt) Find the equations of the line that passes through
the points (8, 6) and (1, 6).
2y = −10 − 8x
• A. Perpendicular
• B. Parallel
• C. Neither
• A. y = 6x + 8
12. (1 pt) UNTESTED!
Write an equation for the line through the point (−2, −7)
and parallel to the line y = 3x − 6 in point-slope form y =
y0 + m(x − x0 ).
• B. x = 6
• C. y = 6x + 1
• D. y = 6
y=
• E. None of the above
1
+
• B. y =− 13 x − 23
13. (1 pt) Find an equation in the slope-intercept form of the
line passing through the point (4, −2) and
parallel to the line given by the equation 6x−2y = 7.
• C. y =6x −26
• D. y =3x −14
• A. y =− 16 x − 34
• E. No such equation exists.
c
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 19-Linear Inequalities in Two Variables due 05/15/2015 at 06:00am EDT
A
B
C
D
E
F
1. (1 pt) Graph the linear inequality in two variables
−3x ≤ −3 ?
A
C
E
B
D
F
2. (1 pt) Graph the linear inequality in two variables y < −6
3. (1 pt) Graph the linear inequality in two variables
3x − 3y < 15 ?
?
1
A
B
A
B
C
D
C
D
E
F
E
F
4. (1 pt) Graph the linear inequality in two variables
3x − 3y ≤ 6 ?
5. (1 pt) Graph the linear inequality in two variables
−3x + 3y > 9 ?
2
A
B
A
B
C
D
C
D
E
F
E
F
6. (1 pt) Graph the linear inequality in two variables
6x − 9y ≥ 36 ?
7. (1 pt) Graph the linear inequality in two variables
−x + y ≤ 0 ?
3
A
B
C
D
E
F
c
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*************** HW #20 **************
1. (1 pt)
The graphs of two linear equations in a system are shown above.
Solve the system of the equations. Please write your solution(s)
in the ordered-pair form. If there is no solution, please type
”None”. If there are infinitely many solutions, then enter x for x
and give y as a function of x.
Answer:
2. (1 pt)
The graphs of two linear equations in a system are shown above. Solve the system of the equations. Please write your solution(s) in the ordered-pair form. If there is no solution, please type ”None”. If there are infinitely many solutions, then enter x for x
and give y as a function of x.
Answer:
1
3. (1 pt)
TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 21-Solving Systems of Linear Equations due 05/15/2015 at 06:00am EDT
6. (1 pt) Solve the following system of equations.
1. (1 pt) For the system of equations given below, determine
whether each ordered pair is a solution of the system. Type Yes
or No .
3x − 3y = 3
2x + 4y = −16
5x − 5y
−15x + 15y
Please write your solution(s) in the ordered-pair form. If
there is no solution, please type ”None”. If there are infinitely
many solutions, then enter x for x and give y as a function of x.
Answer: (x, y) =
a) Is (−2, −3) a solution? Answer:
b) Is (−4, −4) a solution? Answer:
7. (1 pt) Solve the following system of equations.
2. (1 pt) Solve the following system of equations.
4x − 2y
5x − y
3x + 2y
6x + 4y
= −30
= −30
3. (1 pt) Solve the following system of equations.
= −20
=8
8. (1 pt) Solve the following system of equations.
1
4x+
−1
2 x+
Answer: (x, y) =
= −16
= 12
Answer: (x, y) =
5. (1 pt) Which ordered pair is the solution to the system of
equations?
Note that there may be no solution or infinitely many solutions.
2x − y
6x − 3y
•
•
•
•
•
−3
4 y
−1
6 y
= 23
=1
Answer:
9. (1 pt) An important application of systems of equations
arises in connection with supply and demand. As the price of a
product increases, the demand for that produce decreases. However, at higher prices, suppliers are willing to produce greater
quantities of the product. Suppose a chain of electronics stores
sells hand-held color televisions. The weekly demand and supply models are given as follows
4. (1 pt) Solve the following system of equations.
4x + 3y
−3x − y
=9
= −2
Please write your solution(s) in the ordered-pair form. If there
is no solution, please type ”None”. If there are infinitely many
solutions, then enter x for x and give y as a function of x.
Answer: (x, y) =
Answer: (x, y) =
4x − 3y
2x + 3y
= −5
= 15
Demand model:
Supply model:
= −9
= −18
N = −3p + 2660
N = 4p
where N is the number of televisions sold each week and at price
p. (Note: Answer with the appropriate units.)
a) How many hand-held color televisions can be sold at $ 470
per television?
Answer:
b) How many televisions will be sold when supply and demand are equal?
Answer:
c) Find the price at which supply and demand are equal.
Answer:
A. (1, 5)
B. No Solution
C. Infinitely Many Solutions
D. (−3, 5)
E. (−3, 3)
c
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MTH05 Spring2015 Ojakian
Assignment HW 22-Postitive Integer Exponents due 05/15/2015 at 06:00am EDT
9. (1 pt) Find the quotient
1. (1 pt) Write each expression using exponents.
Remember that the way to enter an in answer box is to type an .
1. x · x · x · x · x · x · x =
2. (5 · 5 · 5) · (5 · 5)
r2 s5t 4
r4 s2t 4
in the form ra · sb · t c .
2. (1 pt) Write out the following as successive multiplication
with the correct number of terms in a and b.
a4 b6 =
The exponents are a =
12. (1 pt) UNTESTED!
Simplify the expression:
8
x
=
y3
5. (1 pt) Evaluate each of the following expression:
a) (−2)5 =
b) (−3)3 =
c) (−10)4 =
d) (−5)2 =
d) (−1)35 =
13. (1 pt) Find the area of a rectangle whose dimensions are
5b7 feet by 6b8 feet.
•
•
•
•
•
6. (1 pt) UNTESTED!
Evaluate:
(6a10 )(3a10 ) =
7. (1 pt)
Find the product
A.
B.
C.
D.
E.
30b15 square feet
11b56 square feet
11b15 square feet
30b56 square feet
22b30 square feet
14. (1 pt) Suppose we have 696 = 36a . What is a?
Answer: a =
15. (1 pt) UNTESTED!
Divide using the quotient rule:
30a19 b15 c11
=
3a17 b13 c7
16. (1 pt) UNTESTED!
Simplify the expression:
4a 2
− 5
=
b
(−6x3 y4 )(−20xy4 )
in the form C · xa · yb .
, and the exponents are a =
.
11. (1 pt) UNTESTED!
Simplify. Do not leave negative exponents in your answer:
(−2a2 )2 =
4. (1 pt) UNTESTED!
Evaluate each exponential expression:
a) (−2)2 =
b) −22 =
The coefficient C =
.
, and c =
10. (1 pt) UNTESTED!
Simplify:
(b7 )3 =
3. (1 pt) Evaluate each of the following expression:
a) 22 =
b) 34 =
c) 103 =
=
,b=
and b
8. (1 pt) UNTESTED!
Divide using the quotient rule:
x15
=
x10
17. (1 pt) UNTESTED!
Multiply using the product rule:
(10x10 y12 )(9x12 y5 ) =
c
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 23-Negative Integer Exponents due 05/15/2015 at 06:00am EDT
1. (1 pt) UNTESTED!
Use the zero-exponent rule to simplify:
(−14)0 =
5. (1 pt) UNTESTED!
Write the expression with positive exponents and simplify:
a5 b−5 =
6. (1 pt) UNTESTED!
Simplify the expression:
(3x4 )(−2x−6 ) =
2. (1 pt) UNTESTED!
Simplify the numerical expression
0
4
.
5
Answer:
7. (1 pt) Find the quotient
r2 s5t 3
r6 s4t 3
Note: You cannot use any operations except division (/) and
negation (-).
in the form ra · sb · t c .
The exponents are a =
3. (1 pt) UNTESTED!
Use the zero-exponent rule to simplify:
−20 =
4. (1 pt) UNTESTED!
Express the number 2−3 as a reduced fraction.
Answer:
,b=
, and c =
8. (1 pt) UNTESTED!
Simplify the expression:
−5a5 b−5 c−3
=
−25a−1 b9 c−3
9. (1 pt) REVIEW: Simplify the expression:
1
(− a−2 b5 )(8a−4 b−2 ) =
4
Note: You cannot use any operations except division (/) and
negation (-).
c
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.
TA TEST
Assignment HW 24-Scientific Notation due 05/15/2015 at 06:00am EDT
9. (1 pt) Divide. Give the answer in scientific notation.
1. (1 pt) In 2013, JayZ’s annual salary was $ 42000000. Convert his salary into scientific notation.
$ 42000000=
6 × 102
8 × 109
×10ˆ
2. (1 pt) Consider the following table of select celebrities and
the cost of their engagement rings:
•
•
•
•
Celebrity
Cost
Kate Middleton 137200.00
Jennifer Lopez 2500000.00
Beyonce
5000000.00
Kate Middleton:
×10ˆ
Jennifer Lopez:
×10ˆ
Beyonce:
×10ˆ
11. (1 pt) UNTESTED!
Perform the computation and write the result in scientific notation:
(1.5 × 106 )(3.8 × 10−3 ) =
3. (1 pt) In 2013, Madonna’s annual salary was $ 125000000.
Convert her salary into scientific notation.
12. (1 pt) UNTESTED!
Perform the computation and write the result in scientific notation:
−4.2 × 10−8
=
2.8 × 103
13. (1 pt) UNTESTED!
Perform the computation and write the result in scientific notation:
−3.04 × 10−5
=
3.8 × 104
14. (1 pt) In 2013, Oprah Winfrey’s annual salary was $
77000000, while Madonna’s salary was $ 125000000. Calculate the sum and difference of their salaries. Write your answer
in scientific notation.
×10ˆ
4. (1 pt) In 2013, Oprah Winfrey’s annual salary was $
77000000. Convert her salary into scientific notation.
$ 77000000=
×10ˆ
5. (1 pt) Write in decimal notation without the use of exponents:
5.8 × 102 =
6. (1 pt) Write in decimal notation without the use of exponents:
3.2 × 10−3 =
7. (1 pt) UNTESTED!
Write the following number in scientific notation.
SUM = $
×10ˆ
DIFFERENCE = $
×10ˆ
15. (1 pt) In 2013, Ellen Degeners’ annual salary was $
56000000, while Rihanna’s salary was $ 43000000. Calculate
the product and quotient of their salaries. Write your answer in
scientific notation. Round your answer to one decimal place.
0.0038
Answer:
8. (1 pt) Multiply. Give the answer in scientific notation.
(4 × 10−10 )(7 × 106 )
•
•
•
•
•
A. 7.5 × 10−7
B. 7.5 × 10−8
C. 0.75 × 10−7
D. 7.5 × 10−6
10. (1 pt) UNTESTED!
Perform the computation and write the result in scientific notation:
(−2.8 × 10−6 )(9.0 × 10−6 ) =
Write the values in Scientific Notation:
$ 125000000=
MTH05 Spring2015 Ojakian
×10ˆ
56000000 × 43000000 =
56000000
=
×10ˆ
43000000
16. (1 pt) In 2013, Lady Gaga’s annual salary was $
80000000, while Madonna’s salary was $ 125000000. Calculate
the product and quotient of their salaries. Write your answer in
scientific notation. Round your answer to one decimal place.
A. 2.8 × 10−2
B. 2.8 × 10−5
C. 28 × 10−4
D. 2.8 × 10−4
E. 2.8 × 10−3
1
80000000 × 125000000 =
80000000
=
×10ˆ
125000000
×10ˆ
TA TEST
Assignment HW 25-Polynomial–Introduction due 05/15/2015 at 06:00am EDT
1. (1 pt) Determine the following for: 5x2 − x6 − 3x + 9
a) Determine the coefficient and the degree of each term.
a) g(2) =
Term Coefficient Degree
5x2
−x6
−3x
9
b) The degree of the polynomial is
the leading term is
,
.
and the leading coefficient is
MTH05 Spring2015 Ojakian
b) g(0) =
,
c) g(−3) =
x7 + x5 − x − 2
2. (1 pt) Determine the following for:
a) Determine the term and coefficient of each degree.
Term
4. (1 pt) Evaluate f (−7) for f (x) =−3x2 −x−1
Coefficient Degree
7
5
1
0
b) The degree of the polynomial is
the leading term is
,
and the leading coefficient is
.
•
•
•
•
,
A. −141
B. 155
C. 153
D. −153
5. (1 pt) Evaluate h(−4) for h(x) =−x2 −5x−9
3. (1 pt) Find the indicated functional values.
•
•
•
•
•
g(x) = x2 + x − 6
c
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A. 45
B. −5
C. 27
D. −27
E. None of the above
TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 26-Polynomials–Adding Subtracting Multiplying Dividing due 05/15/2015 at 06:00am EDT
9. (1 pt) Multiply the monomial and the polynomial: 4x(3x +
1. (1 pt) Add: (2a5 b3 + 2a4 b4 − 5) + (−6a5 b3 + 3a4 b4 − 2)
Answer:
1)
Answer:
10. (1 pt) Multiply the monomial and the polynomial:
5x2 (5x4 − x3 + 1)
Answer:
11. (1 pt) Multiply the monomial and the polynomial:
4xy(5x − 3y)
Answer:
12. (1 pt) Multiply the monomial and the polynomial:
ab3 (5a3 b4 − 2ab)
Answer:
13. (1 pt) Multiply the monomial and the polynomial:
−3x2 (3x5 − 2x4 + 2)
Answer:
14. (1 pt) Multiply the polynomials: (x − 1)(x + 5)
Answer:
15. (1 pt) Multiply the polynomials: (7x + 2)(6x + 5)
Answer:
16. (1 pt) Multiply the polynomials: (x − 5y)(4x + 3y)
Answer:
2. (1 pt) Subtract: (3a6 b3 + 3a5 b5 − 1) − (6a6 b3 + 6a5 b5 + 6)
Answer:
3. (1 pt)
Simplify completely.
•
•
•
•
•
−16u17 − 16u6 − 4u4
−4u4
A. 4u13 − 16u6 − 4u4
B. 4u13 + 4u2 − 1
C. 4u13 − 16u6 + 4u4
D. 4u13 + 4u2 + 1
E. None of the other responses
4. (1 pt)
Simplify completely.
•
•
•
•
•
−24a11 b10 − 16a6 b7 − 4a2 b2
−4a2 b2
17. (1 pt) Multiply the polynomials: (4x + 5)(x2 + 3)
Answer:
A. 6a9 b8 + 4a4 b5 + 1
B. −6a9 b8 + 4a4 b5 − 1
C. −6a9 b8 − 4a4 b5 − 1
D. None of the other responses
E. 6a9 b8 − 16a6 b7 − 4a2 b2
18. (1 pt) Square the binomial: (x − 5)2
Answer:
19. (1 pt) Square the binomial: (2x − 3y)2
Answer:
5. (1 pt) Perform the indicated division of a polynomial by a
monomial.
6x3 − 12x2
3x2
Answer:
20. (1 pt) Multiply the polynomials: (x − 4)(x2 + 2x − 3)
Answer:
21. (1 pt) Multiply the polynomials: (x − 1)(2x2 + 2x + 3)
Answer:
22. (1 pt) Multiply the polynomials: (a+2b)(a2 +2ab+2b2 )
Answer:
23. (1 pt) Find the product of the sum and difference of two
terms: (x + 3)(x − 3)
Answer:
24. (1 pt) Find the product of the sum and difference of two
terms: (5y2 + 4)(5y2 − 4)
Answer:
25. (1 pt) Find the product of the sum and difference of two
terms: (6 + 5y5 )(6 − 5y5 )
Answer:
6. (1 pt) Perform the indicated division of a polynomial by a
monomial.
6xy − 8x2 y2 − 12x3 y4
−xy
Answer:
7. (1 pt) Multiply the monomials: (−3x4 )(−x2 )
Answer:
8. (1 pt) Multiply the monomials: (−1x6 y3 z5 )(3x5 yz5 )
Answer:
c
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Assignment HW 27-Factoring–Introduction due 05/15/2015 at 06:00am EDT
1. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
a2 − 4a =
2. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
6x2 − 15x =
3. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
12x4 + 3x3 =
4. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
9x2 y4 + 15xy − 18x =
MTH05 Spring2015 Ojakian
11. (1 pt) Factor:
2x(x − 1) + 3(x − 1) =
12. (1 pt) Factor:
3a(a − 3b) − 5(a − 3b) =
13. (1 pt) Factor:
5a3 (2a − b) − 4b2 (2a − b) =
14. (1 pt) Factor:
5a(s − 2t) + 3b(s − 2t) + 4(s − 2t) =
15. (1 pt) Factor by grouping:
a2 + 2a + 5a + 10 =
16. (1 pt) Factor by grouping:
t 2 − 7t + 4t − 28 =
17. (1 pt) Factor by grouping:
s2 + 3s + 2st + 6t =
18. (1 pt) Factor by grouping:
xz + x − 4yz − 4y =
5. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
20y5 + 15y3 − 35y2 =
6. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
18x3 y4 + 30xy5 =
19. (1 pt) Factor by grouping:
12ac − 28bc + 3a − 7b =
20. (1 pt) Factor by grouping:
x4 z − 6yz − x4 + 6y =
7. (1 pt) Factor out the greatest common factor (GCF). Please
write the GCF as the first factor.
10x4 y4 + 4x3 y3 =
8. (1 pt) Factor out the negative of the greatest common factor (GCF). Please write the GCF as the first factor.
−15x2 − 10x =
9. (1 pt) Factor out the negative of the greatest common factor (GCF). Please write the GCF as the first factor.
−20y2 + 5y =
21. (1 pt) Factor by grouping:
12sx − 21tx + 20sy2 − 35ty2 =
22. (1 pt) Which of the following is a factor of the polynomial?
6ac − 5ad + 18bc − 15bd
• A. a − 3b
• B. 6c + 5d
• C. c + 3d
• D. a + 3b
10. (1 pt) Factor out the negative of the greatest common
factor (GCF). Please write the GCF as the first factor.
−20s2t + 24st − 20s =
c
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Assignment HW 28-Factoring–Special Products due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
9x3 − 4x =
9. (1 pt) Factor completely. Please write the greatest common factor as the first factor.
If there is a complete square, please write in the square format
(e.g. (a+b)2 ).
I f thepolynomialisnot f actorable, pleaseinputthepolynomialitsel f orinput”
1. (1 pt) Factor the difference of squares:
x2 − 4 =
2. (1 pt) Factor the difference of squares:
x2 − 16 =
3. (1 pt) Factor the difference of squares:
9 − 16y2 =
48a3 b − 27ab =
10. (1 pt) Factor completely. Please write the greatest common factor as the first factor.
If there is a complete square, please write in the square format
(e.g. (a+b)2 ).
I f thepolynomialisnot f actorable, pleaseinputthepolynomialitsel f orinput”
4. (1 pt) Factor the difference of squares:
16x2 − 9 =
5. (1 pt) Factor the difference of squares:
16x2 − 9y2 =
6. (1 pt) Factor the difference of squares:
4x10 − 9 =
243x5 y2 − 768xy2 =
7. (1 pt) Factor the difference of squares:
16x8 − 9y4 =
11. (1 pt) Factor completely:
t 3 + 4t 2 − 9t − 36 =
12. (1 pt) Factor completely.
8. (1 pt) Factor completely. Please write the greatest common factor as the first factor.
4x2 y − 16y3
If there is a complete square, please write in the square format
• A. 4 x2 y − 4y3
(e.g. (a+b)2 ).
• B. 4y x2f−
4y2
I f thepolynomialisnot f actorable, pleaseinputthepolynomialitsel f orinput”Doesnot
actor”.
• C. 4y(x − 2y)2
• D. 4y(x − 2y)(x + 2y)
c
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Assignment HW 29-Factoring–Trinomials due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
• D. x + 3
• E. x − 12
1. (1 pt) Factor:
x2 + 5x + 4 =
2. (1 pt) Factor:
x2 − 9x + 20 =
9. (1 pt) Factor completely. If there is a complete square,
please write in the square format (e.g. (a+b)2 ).
x4 − x2 − 30 =
3. (1 pt) Factor:
x2 − x − 2 =
10. (1 pt) Factor:
12x2 + 13x + 3 =
4. (1 pt) Factor:
x2 − x − 20 =
11. (1 pt) Factor:
2x2 + x − 28 =
5. (1 pt) Factor:
x2 + 5xy − 6y2 =
6. (1 pt) Factor the polynomial.Factor completely. If there
12. (1 pt) Factor:
is a complete square, please write in the square format (e.g.
4x2 − 11x + 6 =
2
(a+b) ).I f thepolynomialisnot f actorable, pleaseinputthepolynomialitsel f orinput”Doesnot f actor”.
13. (1 pt) Factor:
x2 + 4xy + 16y2 =
3x2 − 11x − 4 =
7. (1 pt) Factor completely. Please write the GCF as the first
factor.
14. (1 pt) Factor:
x3 − 5x2 − 6x =
2x2 + 3xy + y2 =
8. (1 pt) Which of the following is a factor of the polynomial?
15. (1 pt) Factor:
2x2 − 7xy + 3y2 =
x2 − 13x + 12
• A. x − 3
• B. x − 3
• C. x − 4
16. (1 pt) Factor:
24x3 + 44x2 + 20x =
c
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MTH05 Spring2015 Ojakian
Assignment HW 30-Factoring–Solving Quadratic Equations due 05/15/2015 at 06:00am EDT
1. (1 pt) Solve the equation
11. (1 pt) Solve for x.
4x(6x − 33) = −180
2
y − 10y = 0.
•
•
•
•
•
Solutions (separate by commas): y =
2. (1 pt) Solve the equation
4x = 15x2 .
Solutions (separate by commas): x =
3. (1 pt) Solve the equation
A. {− 52 , −3}
B. { 52 , 3}
C. {− 25 , 3}
D. {0, 11
2 }
E. {0, − 11
2 }
12. (1 pt) UNTESTED!
At time t = 0, in seconds, a pair of sunglasses is dropped
from the Eiffel Tower in Paris. At time t, its height in feet above
the ground is given by h(t) = −16t 2 + 1000.
z − 8z2 = 0.
Solutions (separate by commas): z =
4. (1 pt) Find all real number solutions for the equation
x5 − 81x = 0.
(a) What does the function tell us about the height from which
the sunglasses were dropped? Include units in your answer.
Solutions (separate by commas): x =
5. (1 pt) Find all real number solutions for the equation
45 − 5x2 = 0.
(b) When do the sunglasses hit the ground? Include units in
your answer.
Solutions (separate by commas): x =
6. (1 pt) Find all real number solutions for the equation
n2 + 17n + 66 = 0.
13. (1 pt) UNTESTED!
A coin, thrown upward at time t = 0 from an office in the
Empire State Building, has height in feet above the ground t
seconds later given by
h(t) = −16t 2 + 32t + 560 = −16(t − 7)(t + 5).
(a) From what height is the coin thrown? Include units in
your answer.
Solutions (separate by commas): n =
7. (1 pt) Find all real number solutions for the equation
n(n − 24) = −128.
Solutions (separate by commas): n =
8. (1 pt) Find all real number solutions for the equation
2x3 = 32x.
Solutions (separate by commas): x =
(b) At what time does the coin hit the ground? Include units
in your answer.
9. (1 pt) Find all real number solutions for the equation
3w3 − 21w2 + 36w = 0.
14. (1 pt) UNTESTED!
An object is propelled upward, starting at a height of 200
feet. Suppose its height h after t seconds is given by the equation h = −20t 2 + 60t + 200. After how many seconds does the
object hit the ground?
Solutions (separate by commas): w =
10. (1 pt) Find all the solutions to the equation
−3y2 − 15y = 0
•
•
•
•
•
•
•
•
•
A. Only y = 5
B. y = 0 or y = -5
C. y = 0 or y = 5
D. Only y = -5
c
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A. 4 seconds
B. None of the others
C. 2 seconds
D. 5 seconds
E. 3 seconds
TA TEST
Assignment HW 31-Radicals–Introduction due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
√
describe by the equation 3 = 9.]
Those numbers that are the areas of squares whose sides have
lengths that are integers are called per f ect squares.
The first few perfect squares are 1, 4, 9, 16, 25, 36.
Now suppose we have a square whose area is 2 square units.
First, you might ask yourself whether or not it is possible to have
such a square.
You might be surprised to find out that this is really an important question to mathematicians, but here we will just assume
that there is such a thing.
Well, if there is such a thing as a square whose area is 2
square units, what is the length of its side?
Its length must be more than 1 unit since a square whose side
has length 1 unit has area 1 square unit.
Its length must be less than 2 units, since a square whose sides
have length 2 units has area 4 square units.
√
We can, of course, say that its length is 2 units, but how long
would that be? √
Surprisingly, 2 is not only not a whole number, it is not
even a fraction. We can find better and better approximations to
it, but we can never find a fraction whose square is 2.
In fact, it turns out that if a number is not a perfect square its
square root can never be equal to a fraction.
But, since there are squares whose areas are 2 units,
these square roots are really numbers and we must figure out
how to deal with them.
√
1. (1 pt) Simplify the numerical expression − 121.
Answer:
Note: You cannot use any operations except negation (-).
2. (1 pt) Change the radical
√
−5 8
√
into simplest radical form A C, where A and C are all integers.
Answer: A =
and C =
3. (1 pt) Change the radical
√
3 27
√
into simplest radical form A C, where A and C are all integers.
Answer: A =
and C =
One of the things that we do is to simplify things somewhat.
For example, suppose we have found approximate values for the
square roots of the√numbers
than 8.
√ smaller
√
Since
8
=
4*2,
8
=
4
∗
2
but
4 is a perfect square and
√
4√= 2
√
√
so 8 = 2 ∗ 2. [We will usually write this as 2 2] and we can
just double the value we have used to approximate the square
root of 2.
This gives the idea that we can make our calculations with
square roots somewhat easier by taking out the largest square in
under the square root sign.
√
For example if we want to simplify 4608 we√should just notice
√
that 4608 = 2 × 2304 and 2304 = 482 . Thus 4608 = 48 2.
But most of us can’t notice things like that quite so easily. But
we can use prime factorization to make that job much easier.
4608 = 2 × 2304 = 22 × 1152 = 23 × 576 = 24 × 288 = 25 ×
144 = 26 × 72 = 27 × 36 = 28 × 18 = 29 × 9 = 29 × 32 . Now
28 = 24 × 24 since if we multiply four 2’s together and multiply
them by four more 2’s we have multiplied
√ So
√ eight 2’s together.
4 ) ∗ (24 ) ∗ 2 and thus 4608 = 24 × 3 × 2 =
4608
=
3
×
3
×
(2
√
48 2. If we were writing this as the answer to a problem we
4. (3 pts)
If we start with the idea that if a square with sides of length
one unit then its area is one square unit.
We call this a square whose sides have length one unit a
unit square Now, if a square has sides lengths are whole numbers of units we can see how to find the area by breaking it into
unit
squares (see the diagram). Thus, we can see that if a square had
sides of length 3 units we can exactly fit 9 unit squares into it.
Suppose we have measured a square in square units, for example, if its area is 9 square units. Then we say that the length
of a side of the square the is the square root of the area of the
square.
So, in the case of a square of area 9 square units, the length of
the side is 3 units and 3 is called the square root of 9 [which we
1
would write 48*sqrt(2) because the answer box cannot make a
√
and the * separates the number from the s in sqrt.
Simplify
each of the following:
√
1) √32=
.
2) √27=
.
.
3) √18=
4) √50=
.
.
5) √72=
6) 300=
.
Sometimes things are a bit√more complicated. For example
suppose we want to simplify 1080. When we factor we find
that
1080 = (23 ) × (33 ) × 5 = (22 ) ∗ ×32 ) ∗ 2 ∗ 3 ∗ 5. The only factors
that are perfect squares are 22 and 32 .
√
So we can √
take out 2 and 3 and we are left with 2×3× 2 ∗ 3 ∗ 5
which is 6 30.
Simplify:
√
1) √24=
.
2) √420=
.
.
3) √375=
4) √96=
.
.
5) 27000=
5. (1 pt) Express the number
r
3
−
27
64
as a reduced fraction.
Answer:
Note: You cannot use any operations except division (/) and
negation (-).
c
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TA TEST
Assignment HW 32-Radicals–Simplifying due 05/15/2015 at 06:00am EDT
1. (1 pt) Change the radical
√
2 80
√
into simplest radical form A C, where A and C are all integers.
Answer: A =
and C =
MTH05 Spring2015 Ojakian
4. (1 pt) Change the radical
2√
80
3
√
into simplest radical form AB C, where A, B, and C are all integers.
,B=
, and C =
Answer: A =
2. (1 pt) Change the radical
√
3 8
√
into simplest radical form A C, where A and C are all integers.
Answer: A =
and C =
5. (1 pt) Change the radical
3√
125
4
√
into simplest radical form AB C, where A, B, and C are all integers.
Answer: A =
,B=
, and C =
3. (1 pt) Change the radical
√
−5 28
√
into simplest radical form A C, where A and C are all integers.
Answer: A =
and C =
c
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TA TEST
Assignment HW 33-Radicals–Operations due 05/15/2015 at 06:00am EDT
1. (1 pt) Find the product
MTH05 Spring2015 Ojakian
6. (1 pt) UNTESTED!
Find the product
√
√
(−3 3)(4 5)
√
and express your answer in simplest radical form A C, where
A and C are integers.
and C =
Answer: A =
√ √
√ 3 2 4 12 + 6 6
√
√
and express your answer in the form A B +C D, A, B, C, and
D are all integers and B > D.
,B=
,C=
, and D =
Answer: A =
2. (1 pt) UNTESTED!
Use the distributive property to help simplify the numerical
expression
√
√
3 8 − 8 18
√
into the form A C, where A and C are all integers.
Answer: A =
and C =
7. (1
√ pt) Multiply and simplify
(7 + 2 3)2
•
•
•
•
•
3. (1 pt) Use the distributive property to help simplify the
numerical expression
√
√
6 8 − 8 18
√
into the form A C, where A and C are all integers.
Answer: A =
and C =
A. 27
√
B. 55 + 28√3
C. 61 − 28 √3
D. 61 + 28 3
E. 61
8. (1
√ pt) Multiply
√ and simplify
(4 − 2 5)(4 + 2 5)
4. (1 pt) Simplify.
•
•
•
•
•
√
√
√
3 90 + 5 360 + 3 1000
•
•
•
•
•
√
A. 69√ 10
B. 11√10
C. 11 √30
D. 11√ 90
E. 69 90
9. (1 pt) UNTESTED!
Let a and b represent the lengths of the legs of a right triangle, and c represent the length of the hypotenuse. Find b if a = 6
meters and c = 12 meters.
√
Express your answer in simplest radical form b = A C,
where A and C are all integers.
and C =
Answer (in meters): A =
5.
√ (1√pt) Simplify
√ completely.
6( 78 + 2 6)
•
•
•
•
•
A. 60
B. −4
√
C. 36 − 16 5
D. 36
√
E. 36 + 16 5
√
A. 13
√
√ 6 + 12
B. 6√13 + 2 6
C. 6 √
13 + 12
D. 36√ 13 √
E. 13 6 + 2 6
10. (1 pt) What is the value of x in the right triangle?
1
•
•
•
•
•
√
A. 4 2
B. 4√
C. √
2
D. 2 2
E. Cannot be solved
• A.
• B.
• C.
• D.
• E.
√
6 17
17
6
5
√
102
17
36
17
√
2 15
5
12. (1 pt) Olivia runs 9 meters diagonally across a rectangular field that has a width of 6 meters. Find the length of the
rectangular field,
•
•
•
•
•
11. (1 pt) What is the value of x in the right triangle?
2
√
A. 5 3 meters
B. 3 meters
C. 45 meters
D. 1 21 meters
√
E. 3 5 meters
16. (1 pt) UNTESTED!
Rationalize the denominator of expression
r
2
,
9
i.e., write it in the form of
√
a
.
b
13. (1 pt) UNTESTED!
Suppose you are given a triangle with hypotenuse of length
3 and legs of length x − 1 and x + 1.
Your answer for a is :
Your answer for b is :
17. (1 pt) UNTESTED!
Change the radical
r
7
√ 8
into simplest radical form AB C, where A, B, and C are all integers.
,B=
, and C =
Answer: A =
Determine the numerical length of the two legs.
Shorter leg =
Longer leg =
18. (1 pt) UNTESTED!
Evaluate the expression
14. (1 pt) UNTESTED!
The expression
√
9
√
4
equals
/
√
72
√
2
Your answer is
19. (1 pt) UNTESTED!
Use the distributive property to help simplify the numerical
expression
5√
1√
5+
80
7
4
√
into the form BA C, where A, B, and C are all integers.
Answer: A =
,B=
, and C =
.
15. (1 pt) UNTESTED!
Rationalize the denominator of expression
1
√
3
i.e., write it in the form of
20.
(1 pt) Simplify completely.
√ √
2 84
√
7
√
• A. √
6 2
• B. √
24
• C. 4 6
• D. 24
√
• E. 2 6
√
a
.
b
Your answer for a is :
Your answer for b is :
c
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TA TEST
Assignment HW 34-Complex-Numbers due 05/15/2015 at 06:00am EDT
•
•
•
•
√
1. (1 pt) Simplify −63. Write your answer as the product
of a real number and i.
•
•
•
•
•
√
A. √
−3 7 i
B. √
63 i
C. 7 √
3i
D. −7
√ 3i
E. 3 7 i
MTH05 Spring2015 Ojakian
√
B. 2√ 3 i
C. √
18 i
2i
D. 3 √
E. −2 3 i
3. (1 pt) Write the following expression in terms of i, perform
multiplication, and simplify
√ √
−4 −25.
Answer:
4. (1 pt) Find the following product and express the answer
in standard form of a complex number.
√
2. (1 pt) Simplify −18. Write your answer as the product
of a real number and i.
(−9i)(−4 − 3i)
√
• A. −3 2 i
Answer:
c
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TA TEST
MTH05 Spring2015 Ojakian
Assignment HW 35-Solving-Quadratic Equations by Completing the Square due 05/15/2015 at 06:00am EDT
a=
h=
k=
1. (1 pt) Consider the quadratic equation y = 7x2 − 8x.
Complete the square to express the quadratic in standard form
y = a(x − h)2 + k.
a=
h=
k=
3. (1 pt) Consider the quadratic equation y = −7x2 − 168x +
3.
Complete the square to express the quadratic in standard form
y = a(x − h)2 + k.
a=
h=
k=
2. (1 pt) Consider the quadratic equation y = x2 + 12x + 2.
Complete the square to express the quadratic in standard form
y = a(x − h)2 + k
c
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1
TA TEST
Assignment HW 36-The Quadratic Formula due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
The zeros are x =
4. (1 pt) UNTESTED!
A ball is thrown into the air. Its height (in feet) t seconds
later is given by
h(t) = 96t − 16t 2
Based on the two equivalent forms of the function h(t) = 96t −
16t 2 = t · (96 − 16t), answer the following questions:
a) What is the height of the ball 1 second after it has been
(include in your answer)
thrown?
b) After how many seconds does the ball hit the ground?
(include in your answer)
c) At what time(s) is the ball 20 feet above the ground? If
there is more than one answer, give your answer as a comma
separated list of values. Note that you do not have to include
units in this answer.
seconds
After
1. (1 pt) UNTESTED!
Solve the quadratic equation x2 − 12x − 4 = 0. If there is
more than one correct answer, enter your answers as a comma
separated list. If there are no real solutions, enter NONE.
x=
2. (1 pt) UNTESTED!
Find the zeros of y = 6x2 + 37x + 6. If there is more than
one zero or a zero is repeated, enter your answers as a comma
separated list. If no (real) zeroes exist, enter NONE.
The zeros are x =
3. (1 pt) UNTESTED!
Find the zeros of y = 5x2 + 48x + 64. If there is more than
one zero or a zero is repeated, enter your answers as a comma
separated list. If no (real) zeroes exist, enter NONE.
c
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1
TA TEST
Assignment HW 37-Introduction to Parabolas due 05/15/2015 at 06:00am EDT
MTH05 Spring2015 Ojakian
1. (1 pt) Given the function f (x) = x2 − 11x + 28,
what is its vertex? (
,
);
its y-intercept is y =
.
List its x-intercept(s) as a comma separated list. If there are
none, type none .
3. (1 pt) Given the function f (x) = −2x2 + 16x − 24, algebraically determine the vertex, x-intercepts, and y-intercept.
List its y-intercept(s) as a comma separated list. If there are
none, type none .
Its vertex is (
,
).
Its x-intercepts are
.
Note: If there is more than one answer enter them separated by
commas (i.e.: (1,2),(3,4)).
2. (1 pt) Given the function f (x) = −3x2 + 23x − 14,
its vertex is (
,
);
its x-intercepts are x =
Note: If there is more than one answer enter them separated by
commas.
Its y-intercept is
c
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.