what is the shaded area, if the rectangle is 2 by 4? (in terms of π )
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What is the shaded area, if the rectangle is 2 by 4? (in terms of π ). What is the shaded area, if the rectangle is 2 by 4? (in terms of π ). =. -. Don’t worry about moving slowly, worry about standing still. -- Chinese Proverb. - PowerPoint PPT PresentationTRANSCRIPT
10/23/13
What is the shaded area, if the rectangle is 2 by 4? (in terms of π)
10/23/13
What is the shaded area, if the rectangle is 2 by 4? (in terms of π)
= -
10/23/13
Don’t worry about moving slowly, worry about standing still.
-- Chinese Proverb
10/22/13
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 < 1C) -7 < x – y < 7 D) -4 < x – y < 3
E) 3 < x – y < 4
10/22/13
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 < 1C) -7 < x – y < 7 D) -4 < x – y < 3
E) 3 < x – y < 4Smallest x – biggest y is 3 – 7 = -4Biggest x – smallest y is 7 – 4 = 3All others will be between -4 and 3
10/22/13
The most difficult thing is to just start the ball rolling. Once it starts, it is actually more
difficult to stop it!
---Butch Lovelace
10/21/13
For how many positive numbers b is it true that b x b x b = b + b + b ?
A) 0 B) 1 C) 2 D) 3 E) more than 3
10/21/13
For how many positive numbers b is it true that b x b x b = b + b + b ?
A) 0 B) 1 C) 2 D) 3 E) more than 3
b3 = 3b b3 – 3b = 0 b(b2 – 3) = 0 This has one positive root (√3)
10/16/13
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 onlyE) I , II , and III
10/16/13
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 onlyE) I , II , and III
Try numbers:1 & 3 (1 + 3) / 2 , 1*3 + 1 , and (1*3 + 1) / 2
are all evenBUT… try 1 & 5 (1 + 5) / 2 is odd
1*5 + 1 is even, but (1*5 +1)/ 2 is oddC) II only
10/16/13
Your actions speak so loud, I can't hear what you say.
10/15/13
If two sides of a triangle are 7 and 13, what could the length of the third side be?
10/15/13
Opportunity is missed by most people because it is dressed in overalls and looks like
work.
-- Thomas Edison
10/14/13
Which of the following could not be the sides of a triangle?
A) 1 , 1 , 1 B) 1 , 1 , 17 C) 1 , 17 , 17D) 3 , 4 , 5 E) 5 , 6 , 10
10/14/13
Which of the following could not be the sides of a triangle?
A) 1 , 1 , 1 B) 1 , 1 , 17 C) 1 , 17 , 17D) 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
10/11/13
If 3 yaps equals 4 yips, and 5 yips equals 6 yups, then what is the ratio of yups to yaps?
A) ½ B) 5/8 C) 2/3 D) 8/5 E) 2/1
10/11/13
If 3 yaps equals 4 yips, and 5 yips equals 6 yups, then 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
10/11/13
If 3 yaps equals 4 yips, and 5 yips equals 6 yups, then 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)
10/11/13
What do you throw away the outside and cook the inside, then eat the outside and throw away
the inside?
10/10/13
For all positive numbers a and b, let aΔb = √(ab). If n > 1, what does nΔ(1/n)
equal?
A) √n B) √n2 C) 1/√n D) 1/√n2 E) 1
10/10/13
Neither you nor the world knows what you can do until you have tried.
----Ralph Waldo Emerson
10/9/13
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
10/9/13
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…
10/8/13
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
10/8/13
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 = -15x = -1
x = -1/5 = -.24x = -.8
Trap: here, 4x is smaller than xthe smaller number is -.8
“Killer Rabbit”
10/8/13
Follow these steps and see if you can figure this out.
1) Get a brown, cardboard box.2) Get purple, orange, and turquoise paints.
3) Paint the box orange.4) Paint on purple spots.
5) Paint on turquoise stripes.7) Turn it upside down.
8) Lie on your side.
What is missing from this sequence?
10/8/13
What happens once a minute, twice in a moment, but never in a thousand years?
10/7/2013
Let . If 2 1 = 1 x, then what is the value of x?
A) 2 B) 1 C) ½ D) - ½ E) -1
kj
kjkj
10/7/2013
Let . If 2 1 = 1 x, then what is the value of x?
A) 2 B) 1 C) ½ D) - ½ E) -12 1 = (2 – 1) / (2 + 1) = 1/31 x = (1 – x) / (1 + x) = 1/3
3(1 – x) = 1 + x3 – 3x = 1 + x
2 = 4xx = ½
kj
kjkj
10/7/13
What is the next letter in this sequence?
OTTFFSS
10/7/13
What is the next letter in this sequence?
OTTFFSS
Hint: Spelling class?
10/2/13
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
10/2/13
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
10/2/13
How can you make 7 even?
10/1/2013
If j@k=jk-1, what is the value of 3@(2@1)?
A) 6 B) 5 C) 4 D) 3 E) 2
10/1/13
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 – 13@(2@1) = 3@1 = (3)(1) – 1 = 2
9/30/13
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
9/30/13
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
x
Dog Cat
36 - x 26 - x
(36 – x) + x + (26 – x) = 46 62 – x = 46 x = 16
BUT… answer the question: 36 – 16 = 20
9/27/13
A book collector has a collection of 1200 books, of which 900 are hardcover and the rest 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?
9/27/13
A book collector has a collection of 1200 books, or which 900 are hardcover and the rest 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 HC Tot
F 50
NF 1000
Tot 900 1200
9/27/13
A book collector has a collection of 1200 books, or which 900 are hardcover and the rest 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 HC Tot
F 50 150 200
NF 250 750 1000
Tot 300 900 1200
7 5 0
9/26/13
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
9/26/13
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 rLet’s try 8 (8 / 5 has a remainder of 3)
3r/5 = 24/5 remainder of 4another? r = 13
3r/5 = 39/5 remainder of 4
9/25/13
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
9/25/13
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 = 22x – 2y = 8 (D)
9/24/13
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
9/24/13
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 = 89x + 9y = 45
x +y = 5Note: the answer will virtually never be E)
9/18/13
On my bike, I ride up a steep 2 mile hill at 6 miles per hour. How fast must I ride down the hill to average 12 miles an hour for the entire
trip?
A) 12 B) 18 C) 24 D) 36 E) Call Einstein
9/18/13
On my bike, I ride up a steep 2 mile hill at 6 miles per hour. How fast must I ride down the hill to average 12
miles an hour for the entire trip?
A) 12 B) 18 C) 24 D) 36 E) Call Einstein
6 mph 10 min / mile 20 min for 2 miles12 mph 5 min / mile 20 min for 4 miles
It is impossible to average 12 mph for the trip…
9/18/13
Every man is a damn fool for at least five minutes every day; wisdom consists in not
exceeding the limit.
--- Elbert Hubbard
9/18/13
Bonus riddle: If removing the appendix is called an appendectomy, and
removing tonsils is called a tonsillectomy, what is the procedure
called to remove growth from the head?
9/17/13
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
9/17/13
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 timetime up the hill = 10 minutes
time down the hill = 2 minutestotal time: 12 minutes
total distance: 2 miles (1 up, 1 down)2miles / 12 minutes = 10 miles / 60 minutes
9/17/13
The greatest mistake you can make in life is to be continually fearing you will
make one.
--- Elbert Hubbard
9/16/13
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
9/16/139/19/12
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) 28Let’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 / hrAnd since I traveled a total of 1 hour, the distance
was 24 km.
9/16/13
The secret of getting ahead is…
getting started!
9/13/13
On the first 3 quizzes, Emily got a 94, 84, and 86. What does she need on her last quiz
to reach an average of 90?
A) 88 B) 90 C) 92 D) 94 E) 96
9/13/13
On the first 3 quizzes, Emily got a 94, 84, and 86. What does she need on her last quiz
to reach an average of 90?
A) 88 B) 90 C) 92 D) 94 E) 9694 + 84 + 86 = 264
4∙90 = 360360 – 264 = 96
9/13/13
Add 5 segments to the 6 to make 9.
| | | | | |
9/13/13
Add 5 segments to the 6 to make 9.
| | | | | |
9/12/13
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
9/12/13
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) 39total for class is 12 * 40 = 480
total for 2 students is 2 * 45 = 90that leaves 390 for the other 10 students
9/12/13
Listen. Don’t just wait to talk.
--- Donald Trump
9/11/13
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
9/11/13
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
9/10/13
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
9/10/13
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 = 24so r = 12
9/10/13
Make your mistakes work for you by learning from them.
--- Donald Trump
9/9/13
What is the value of (1/2) ∙ (2/3) ∙ (3/4) ∙ (4/5) ∙ …. ∙ (14/15)?
(NO calculators!)
9/9/13
What is the value of (1/2) ∙ (2/3) ∙ (3/4) ∙ (4/5) ∙ …. ∙ (14/15)?
(NO calculators!)1 / 1 5 . 0 6 7
9/9/13
The phenomenal power of the human mind
I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg The phaonmneal pweor of the
hmuan mnid! Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer inwaht
oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit
pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh? Yaeh, and I awlyas thought slpeling was ipmorantt.
9/6/13
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
9/6/13
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 / day71 / 14 is about 5 (C)
9/6/13
9/4/13
What is the square root of the absolute value of the product of the integers from
-6 to 3, inclusive?
9/4/13
What is the square root of the absolute value of the product of the integers from
-6 to 3, inclusive?00 0
9/3/13
1) True or False: (x + 3)2 = x2 + 9
2) True or False: -72 = 49
9/3/13
1) True or False: (x + 3)2 = x2 + 9False: (x + 3)2 = x2 + 6x + 92) True or False: -72 = 49
9/3/13
1) True or False: (x + 3)2 = x2 + 9False: (x + 3)2 = x2 + 6x + 92) True or False: -72 = 49
False: -72 = -49(-7)2 = 49
1) Without changing anything, make this a true statement:
8 + 8 = 91
2) Add one line to make this a true statement
5 + 5 + 5 = 550(You don’t need to write this down)
1) Without changing anything, make this a true statement:
8 + 8 = 91
2) Add one line to make this a true statement
5 + 5 + 5 = 550(and it’s not turning it into an inequality)
Title: 3, 76, 49, 24, 59, 36Category: Trick
What’s the next number in the sequence?
3 , 76 , 49 , 24 , 59
(don’t shout out the answer if you know it)
9/3/13
2013-2014
10/25/12
If 7a = (91)(13), what is the value of √a ?
(No Calculator)
10/19/12
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
10/19/12
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) 120This time, let’s list the groups:
ABC ABD ABE ACD ACE ADEBCD BCE BDE CDE
(note that ABC is the same as BAC, and we don’t need to list it (or count it)again
10/18/12
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
10/18/12
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
10/18/12
When does 11 + 2 = 1?
(there are at least two possible answers)
10/18/12
When does 11 + 2 = 1?
(there are at least three possible answers)
Hint: I’ll tell you in ten minutesor maybe next year
10/18/12
When does 11 + 2 = 1?
1) two hours past 11:002) two months past November
3) 11 + 2 = 1 baker’s dozenany others?
10/3/12
Add one line to make this a true statement.
5 + 5 + 5 = 550
10/3/12
Add one line to make this a true statement.
5 + 5 + 5 = 550(no, not ≠)
10/3/12
Add one line to make this a true statement.
5 + 5 + 5 = 550
10/2/12
In at least 2-3 grammatically correct sentences (to hand in), answer the following:
Are the functions f(x) = x – 1 and
g(x) = the same?1
12
x
x
9/18/12
What is the next letter in this sequence?
OTTFFSS
Hint: Count the letters…
9/18/12
What is the next letter in this sequence?
OTTFFSSENTETTFFSSE
11/4/11
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?
11/4/11
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?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 two-digit number in decreasing order.
7 8 3
10/31/11
10/21/11
Given the point (6 , 6) is on f(x), what point must be on:
a) f(x + 3)b) f(x) + 3c) –3f(x)d) f(-3x)
10/21/11
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)
10/05/11
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?
10/05/11
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?
x
Math CA
15 - x 12 - x
(15 – x) + (12 – x) = 13 x = 7
7
9/24/10
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
9/24/10
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 = 60multiply the different choices for each
course
11/6/09
1) How can you verify factoring is correct?
2) factor: x2 – 9x + 183) factor: x2 – 7x – 184) factor: 49x2 – 81y2
10/21/09
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