Download 3 - Bunnell High School

1) How can you verify factoring is
correct?
2) factor: x2 – 9x + 18
3) factor: x2 – 7x – 18
4) factor: 49x2 – 81y2
11/6/09
Given the point (6 , 6) is on f(x), what
point must be on:
a) f(x + 3)
b) f(x) + 3
c) –3f(x)
d) f(-3x)
11/6/09
Given the point (6 , 6) is on f(x), what
point must be on:
a) f(x + 3)  (3 , 6)
b) f(x) + 3  (6 , 9)
c) –3f(x)  (6 , -18)
d) f(-3x)  (-2 , 6)
11/6/09
Add one line to make this a true
statement.
5 + 5 + 5 = 550
11/5/09
Add one line to make this a true
statement.
5 + 5 + 5 = 550
(no, not ≠)
11/5/09
Add one line to make this a true
statement.
5 + 5 + 5 = 550
11/5/09
If x and y are positive odd integers, which of
the following MUST be even?
I. (x + y) / 2 II. xy + 1 III. (xy + 1) / 2
A) None B) I only C) II only D) I & II only
E) I , II , and III
11/4/09
If x and y are positive odd integers, which of the following
MUST be even?
I. (x + y) / 2 II. xy + 1 III. (xy + 1) / 2
A) None B) I only C) II only D) I & II only
E) I , II , and III
Try numbers:
1 & 3  (1 + 3) / 2 , 1*3 + 1 , and (1*3 + 1) / 2
are all even
BUT… try 1 & 5  (1 + 5) / 2 is odd
1*5 + 1 is even, but (1*5 +1)/ 2 is odd
C) II only
11/4/09
Let
jk
jk 
jk.
If 2  1 = 1  x, then what is
the value of x?
A) 2 B) 1 C) ½ D) -1/2 E) -1
11/2/09
Let
j  k.
jk 
jk
If 2  1 = 1  x, then what is
the value of x?
A) 2 B) 1 C) ½ D) -1/2 E) -1
2  1 = (2 – 1) / (2 + 1) = 1/3
1 x = (1 – x) / (1 + x) = 1/3
3(1 – x) = 1 + x
3 – 3x = 1 + x
2 = 4x
x = 1/2
11/2/09
What is the shaded area, if the rectangle is 2
by 4? (in terms of π)
10/29/09
What is the shaded area, if the rectangle is 2
by 4? (in terms of π)
=
10/29/09
-
If m § n = mn + n, and 5 § 7 = x § 3, what is
the value of x?
A) 5 B) 7 C) 9 D) 11 E) 13
10/27/09
If m § n = mn + n, and 5 § 7 = x § 3, what
is the value of x?
A) 5 B) 7 C) 9 D) 11 E) 13
5 § 7 = 5(7) + 7 = 42 (5 = m and 7 = n)
x § 3 = 3x + 3 (x = m and 3 = n)
If 3x + 3 = 42, then x = 13
10/27/09
If j@k=jk-1, what is the value of 3@(2@1)?
A) 6 B) 5 C) 4 D) 3 E) 2
10/26/09
If j@k=jk-1, what is the value of 3@(2@1)?
A) 6 B) 5 C) 4 D) 3 E) 2
2@1 = (2)(1) – 1 – 1
3@(2@1) = 3@1 = (3)(1) – 1 = 2
10/26/09
If 3 yaps equals 4 yips, and 5 yips equals 6
yups, than what is the ratio of yups to yaps?
A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1
10/23/09
If 3 yaps equals 4 yips, and 5 yips equals 6
yups, than what is the ratio of yups to yaps?
A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1
Need “common denominator”
3 yaps = 4 yips
15 yaps = 20 yips = 24 yups  24/15 = 8/5
5 yips = 6 yups
10/23/09
If 3 yaps equals 4 yips, and 5 yips equals 6
yups, than what is the ratio of yups to yips?
A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1
or, another way:
(4yips/3yaps)(6yups/5yips)=24yups/15yaps
(the yips / yips cancels)
10/23/09
All of the following can be written as the sum
of two consecutive integers EXCEPT:
A) 27 B) 30 C) 33 D) 37 E) 45
10/21/09
If 3 < x < 7, and 4 < y < 7, which of the
following best describes x – y?
A) -1 < x – y < 0 B) -4 < x – y < 1
C) -7 < x – y < 7 D) -4 < x – y < 3
E) 3 < x – y < 4
10/19/09
If 3 < x < 7, and 4 < y < 7, which of the
following best describes x – y?
A) -1 < x – y < 0 B) -4 < x – y < 1
C) -7 < x – y < 7 D) -4 < x – y < 3
E) 3 < x – y < 4
10/19/09
If 3 < x < 7, and 4 < y < 7, which of the
following best describes x – y?
A) -1 < x – y < 0 B) -4 < x – y < 1
C) -7 < x – y < 7 D) -4 < x – y < 3
E) 3 < x – y < 4
Smallest x – biggest y is 3 – 7 = -4
Biggest x – smallest y is 7 – 4 = 3
All others will be between -4 and 3
10/19/09
Which of the following could not be the sides
of a triangle?
A) 1 , 1 , 1 B) 1 , 1 , 17
C) 1 , 17 , 17
D) 3 , 4 , 5
E) 5 , 6 , 10
10/16/09
Which of the following could not be the sides
of a triangle?
A) 1 , 1 , 1 B) 1 , 1 , 17
C) 1 , 17 , 17
D) 3 , 4 , 5
E) 5 , 6 , 10
The sum of the smaller two sides must be
greater than the largest side in a triangle
1 + 1 is not > 17
10/16/09
If 10x – y = 37, and 10y – x = 8, what is the
value of x + y?
A) 3 B) 5 C) 7 D) 9 E) cannot be
determined
10/15/09
If 10x – y = 37, and 10y – x = 8, what is the
value of x + y?
A) 3 B) 5 C) 7 D) 9 E) cannot be
determined
Let’s add the equations (don’t need to find x
and y separately)
10x – y = 37
-x + 10y = 8
9x + 9y = 45
x +y = 5
Note: the answer will virtually never be E)
10/15/09
If 3x + 2y = 10, and x + 4y = 2, then what is
the value of 2x – 2y?
A) -8 B) -6 C) 6 D) 8 E) cannot be
determined
10/14/09
If 3x + 2y = 10, and x + 4y = 2, then what is
the value of 2x – 2y?
A) -8 B) -6 C) 6 D) 8 E) cannot be
determined
You virtually never have to solve for x and y
separately in these types of problems. Combine the
information you’re given to find what you’re looking
for. In this case, subtract…
3x + 2y = 10
x + 4y = 2
2x – 2y = 8 (D)
10/14/09
If the 3rd Tuesday of the month is the 21st,
what date is the second Friday?
A) 10th B) 14th C) 17th D) 21st E) 24th
10/13/09
If the 3rd Tuesday of the month is the 21st,
what date is the second Friday?
A) 10th B) 14th C) 17th D) 21st E) 24th
Sketch a calendar, and count backwards…
Friday before is the 17th
Before that is the 10th
Before that is the 3rd
2nd Friday must be the 10th…
10/13/09
One number is four times another. If the
sum of the two numbers is -1, what is
the smaller of the two numbers?
A) -.8 B) -.75 C) -.25 D) -.2 E) 4
10/09/09
One number is four times another. If the sum of the two
numbers is -1, what is the smaller of the two numbers?
A) -.8 B) -.75 C) -.25 D) -.2 E) 4
x + 4x = -1
5x = -1
x = -1/5 = -.2
4x = -.8
Trap: here, 4x is smaller than x
the smaller number is -.8
“Killer Rabbit”
10/09/09
The digits 7 , 8 , and 9 are used to create a
one-digit number and a two-digit number,
with no digit repeated. What is the largest
possible product of the resulting one-digit
and two-digit numbers?
10/08/09
The digits 7 , 8 , and 9 are used to create a
one-digit number and a two-digit number,
with no digit repeated. What is the largest
possible product of the resulting one-digit
and two-digit numbers?
7
Try 1 , 2 , and 3:
1 * 32 = 32
2 * 31 = 62
3 * 21 = 63
Thus 9 * 87 = 783 will be largest product (largest digit
is the one digit number; the other two will be the twodigit number in decreasing order.
10/08/09
8
3
A book collector has a collection of 1200 books,
of which 900 are hardcover and 300 are
paperback. If 1000 of the books are nonfiction
and 50 of the paperbacks are fiction, how many of
the books are hardcover and non-fiction?
10/07/09
A book collector has a collection of 1200 books,
or which 900 are hardcover and 300 are
paperback. If 1000 of the books are nonfiction
and 50 of the paperbacks are fiction, how many of
the books are hardcover and non-fiction?
PB
F
10/07/09
Tot
50
NF
Tot
HC
1000
300
900 1200
A book collector has a collection of 1200 books,
or which 900 are hardcover and 300 are
paperback. If 1000 of the books are nonfiction
and 50 of the paperbacks are fiction, how many of
the books are hardcover and non-fiction?
7
10/07/09
PB
HC
Tot
F
50
150
200
NF
250
750 1000
Tot
300
900 1200
5
0
In Pet-town, the 46 residents all own a dog, a cat,
or both. If there are 36 dog owners, and 26 cat
owners, then how many dog owners have no cat?
A) 5 B) 8 C) 10 D) 16 E) 20
10/06/09
In Pet-town, the 46 residents all own a dog, a cat,
or both. If there are 36 dog owners, and 26 cat
owners, then how many dog owners have no cat?
A) 5 B) 8 C) 10 D) 16 E) 20
Dog
Cat
36 - x
x
26 - x
(36 – x) + x + (26 – x) = 46  62 – x = 46  x = 16
10/06/09
BUT… answer the question: 36 – 16 = 20
The Bunnell Math Club has 15 members, and the
Culinary Arts Club has 12 members. If 13
students belong only to one club or the other, how
many belong to both?
10/05/09
The Bunnell Math Club has 15 members, and the
Culinary Arts Club has 12 members. If 13
students belong only to one club or the other, how
many belong to both?
Math
CA
15 - x
x
12 - x
(15 – x) + (12 – x) = 13  x = 7
10/05/09
7
What is the square root of the absolute
value of the product of the integers from
-6 to 3, inclusive?
0
10/01/09
0
What is the square root of the absolute
value of the product of the integers from
-6 to 3, inclusive?
10/01/09
How many different committees of
three people can be formed out of a
group of 5 people (gosh, let’s call them
A, B, C, D, and E again!)
A) 10 B) 15 C) 30 D) 60 E) 120
This time, let’s list the groups:
ABC ABD ABE ACD ACE ADE
BCD BCE BDE CDE
(note that ABC is the same as BAC, and
we don’t need to list it (or count it)again
9/30/09
How many different committees of
three people can be formed out of a
group of 5 people (gosh, let’s call them
A, B, C, D, and E again!)
A) 10 B) 15 C) 30 D) 60 E) 120
9/30/09
Five runners–let’s call them A , B , C ,
D , and E–are in a race. In how many
different ways can they finish if either A
or B win the race?(assume no ties)
A) 12 B) 15 C) 30 D) 48 E) 120
2 * 4 * 3 * 2 * 1 = 48
9/29/09
Five runners–let’s call them A , B , C ,
D , and E–are in a race. In how many
different ways can they finish if either A
or B win the race?(assume no ties)
A) 12 B) 15 C) 30 D) 48 E) 120
9/29/09
How can you make 7 even?
Take away the ‘S’!
9/25/09
How can you make 7 even?
9/25/09
A restaurant offers 3 different appetizers, 5
different entrees, and 4 different desserts
(yum… dessert). How many different meals
can be served with one of each course?
A) 5 B) 12 C) 19 D) 60 E) 120
3 * 5 * 4 = 60
multiply the different choices for each
course
9/23/09
A restaurant offers 3 different appetizers, 5
different entrees, and 4 different desserts
(yum… dessert). How many different meals
can be served with one of each course?
A) 5 B) 12 C) 19 D) 60 E) 120
9/23/09
When r is divided by 5, the remainder is 3.
What is the remainder when 3r is divided by
5?
A) 4 B) 3 C) 2 D) 1 E) 0
9/21/09
When r is divided by 5, the remainder is 3.
What is the remainder when 3r is divided by
5?
A) 4 B) 3 C) 2 D) 1 E) 0
Strategy: plug in a number for r
Let’s try 8 (8 / 5 has a remainder of 3)
3r/5 = 24/5  remainder of 4
another? r = 13
3r/5 = 39/5  remainder of 4
9/21/09
What is the value of
(1/2) * (2/3) * (3/4) * (4/5) * ….* (14/15)?
1
/
1
5
.
0
6
7
(NO calculators!)
9/18/09
What is the value of
(1/2) * (2/3) * (3/4) * (4/5) * ….* (14/15)?
(NO calculators!)
9/18/09
In at least 2-3 grammatically correct
sentences (to hand in), answer the following:
Are the functions f(x) = x – 1 and
g(x) =
9/17/09
x2 1
x 1
the same?
I rode my bike to school at 20 km / hr, and the
same distance back home at 30 km / hr. If my
total travel time was 1 hour, how far was my total
ride?
A) 22 B) 24 C) 25 D) 26 E) 28
Let’s guess the distance was 60 km each way
(why?) That means it took 3 hours to get to
school, and 2 hours to get back home.
Total distance: 120 km
Total time: 5 hours  120 / 5 = 24 km / hr
And since I traveled a total of 1 hour, the distance
9/17/09
was 24 km.
I rode my bike to school at 20 km / hr, and
the same distance back home at 30 km / hr.
If my total travel time was 1 hour, how far
was my total ride?
A) 22 B) 24 C) 25 D) 26 E) 28
9/17/09
I rode my bike up a 1-mile hill at 6 mph (it
was steep!), and then 1 mile downhill at 30
mph (whee). What was my average speed
for the two miles?
A) 10 B) 12 C) 15 D) 18 E) 24
Average speed = total distance / total time
time up the hill = 10 minutes
time down the hill = 2 minutes
total time: 12 minutes
total distance: 2 miles (1 up, 1 down)
2miles / 12 minutes = 10 miles / 60 minutes
9/16/09
I rode my bike up a 1-mile hill at 6 mph (it
was steep!), and then 1 mile downhill at 30
mph (whee). What was my average speed
for the two miles?
A) 10 B) 12 C) 15 D) 18 E) 24
9/16/09
On the first 3 quizzes, Jose got a 94, 84, and
86. What does he need on his last quiz to
reach an average of 90?
A) 88 B) 90 C) 92 D) 94 E) 96
94 + 84 + 86 = 264
4*90 = 360
360 – 264 = 96
9/15/09
On the first 3 quizzes, Jose got a 94, 84, and
86. What does he need on his last quiz to
reach an average of 90?
A) 88 B) 90 C) 92 D) 94 E) 96
9/15/09
The average of a set of 4 numbers is 8. When one
of the four numbers is removed, the average
increased by 1. What number was removed?
A) 5 B) 7 C) 9 D) 11 E) 13
This is a job for “Total Man!”
4 * 8 = 32
3 *9 = 27 (average increased 1)
difference = 32 – 27 = 5
9/14/09
The average of a set of 4 numbers is 8.
When one of the four numbers is removed,
the average increased by 1. What number
was removed?
A) 5 B) 7 C) 9 D) 11 E) 13
9/14/09
On a math quiz, the average score
for 12 students was 40. If 2
students averaged 45, what was the
average for the other 10?
A) 35 B) 36 C) 37 D) 38 E) 39
total for class is 12 * 40 = 480
total for 2 students is 2 * 45 = 90
that leaves 390 for the other 10 students
9/10/09
On a math quiz, the average score
for 12 students was 40. If 2
students averaged 45, what was the
average for the other 10?
A) 35 B) 36 C) 37 D) 38 E) 39
9/10/09
If the average (mean) of p and q is
6, and the average of p , q , and r is
8, then r = ?
A) 2 B) 10 C) 12 D) 14 E) 18
Use totals when working with averages.
p + q = 12 (why?)
p + q + r = 24
so r = 12
PS What’s special about today?
9/9/09
If the average (mean) of p and q is
6, and the average of p , q , and r is
8, then r = ?
A) 2 B) 10 C) 12 D) 14 E) 18
9/9/09
I rode 500 miles in 7 days this
summer. If my average speed was
14 mph, how many hours per day
did I ride (estimate!)?
A) 3 B) 4 C) 5 D) 6 E) 7
9/8/09
I rode 500 miles in 7 days this
summer. If my average speed was
14 mph, how many hours per day
did I ride (estimate!)?
A) 3 B) 4 C) 5 D) 6 E) 7
500 / 7 = 71 miles / day
71 / 14 is about 5 (C)
9/8/09
When does 11 + 2 = 1?
1) two hours past 11:00
2) two months past November
3) 11 + 2 = 1 baker’s dozen
any others?
9/4/09
When does 11 + 2 = 1?
(there are at least three possible
answers)
Hint: I’ll tell you in ten minutes
or maybe next year
9/4/09
When does 11 + 2 = 1?
(there are at least two possible
answers)
9/4/09
What is the next letter in this
sequence?
OTTFFSS
ENTETTFFSSE
9/3/09
What is the next letter in this
sequence?
OTTFFSS
Hint: Spelling class?
9/3/09
What is the next letter in this
sequence?
OTTFFSS
Hint: Count the letters…
9/3/09
What is the next letter in this
sequence?
OTTFFSS
9/3/09
9/2/09
Add 5 segments to the 6 to make 9.
| | | | | |
9/2/09
Add 5 segments to the 6 to make 9.
| | | | | |
9/2/09