Problem-Solving Strategies:"Date" Word Problem

1, Mathcounts chapter–coundown-50-2007(52)

January 1, 2007 was a Monday.  In 2007, how many Friday are there?

2,AMC8-2002-5

Mary was born on Sat. Nov. 9, 2002, on what day of the week will Mary be 706 days old

3,AMC8-2008-3

If Feb. is a month that contains Friday the 13th, what day of the week is Feb. 1


Worksheet1

Mean, Median and Mode

1, school-sprint-21-2008(94)

Thomas took three 100-point quizzes, and the mean score for three quizzes was 87 points.  If the highest score is taken away, the mean of remaining two scores would be 83.5 points.  If the lowest score is taken away, the mean of the remaining two scores would be 89 points, What is the highest score?

2, school-sprint-9-2008(4796)

A set of five distinct positive integers has a mean of 1000 and a median of 100.  What is the largest possible integer that could be included in the set?

3, chapter-target-4-2007(13)
Six years ago a vacant lot was turned into a park.  At that time 46 trees were planted.  Three years ago 50 trees were planted in the park, and 60 trees were planted in the park today.  Each tree was planted as a seed.  Assuming that all of these planted trees survive and no other tree are added in the next 10 years, what will be the average age of the trees in the park 10 years from today?  Express your answer to the nearest whole number.

4, chapter-sprint -7-2007(1)

The mean of four distinct positive integers is 5,  If the largest integer is 13, what is the smallest integer?

More study:

Mean, Median and Mode

Mean, Median Mode and Range


Worksheet
Mean, Median and Mode -dad
Mean, Median and Mode --Math Aid
Mean, Median and Mode

Problem-Solving Strategies: "Distance" and "Work" Word Problem

Distance= Rate X Time
D = RT

"Distance" Word  problem

1, chapter-sprint-24-2007(10)

Grady rides his bikes 60% faster than his little Noah.  If Grady rides 12 miles further than Noah in two hours, how fast does Noah ride?

If the rate of Noah is R, the rate  of Grady is 1.6R

1.6R x2 =2R + 12

Therefore, The rate of Noah is 10 

2, AMC10A-2002-12(48)

Mr. Earl E. Bind leaves for work at exactly 8:00 A. M. every morning. When he average 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?

Since D = RT 

40(t+3/60)= 60(t- 3/60) , therefore t=1/4(hour), d=24(mile)

R=d/t=24/(1/4) = 48 (mile)

"Work" Word Problem

1, chapter-team-10-2007(462)

Bricklayer Ben places 42 bricks per hour. Bricklayer Bob places 36 bricks per hour. Bricklayer Bob worked twice as many hours as Bricklayer Ben, and the two of them placed a total of 1254 bricks. How many bricks did Bricklayer Ben place?

If Bricklayer Ben works for t hours, then

Bricklayer Ben places 42t (bricks)

Bricklayer Bob places 36 x2t=72t(bricks)

Together

42t + 72t =1254,   therefore t= 11

Then we knowBricklayer Ben places 42t =42 x11=462 

More study

D=RT

Worksheet1

Mid Point and Distance of a Line Segment

Midpoint of a Line Segment 

A Mid point of a segment  with endpoint (x1,y1) and (x2,y2) are
((x1+x2)/2, (y1+y2)/2)
Distance Formula

Direct and Inverse Proportion

Two types of proportions
Direct proportion;
Y=f(x)=kx  k is a constant
or Y/X=k
Y and X are direct proportion
The more X is, the more Y is
ex: buy one book costs $2, two books costs $4, 3 books costs $6.......
(given k=2, when x=1then y-=2,x=2then y=4 ,x=3 then y=6.............)
the more  x is, the more y is
the more the books, the more  the cos is
x and y are direct proportion (books and cost are direct proportion)

Inverse proportion:
Y=f(x)=k /X             k is a constant
or XY=k
X and Y are inverse proportion
The more X is, The less Y is
ex: D=RT
if D is a constant.
The faster the rate is , the less  the time it will take
EX1: k=xy (D=RT)                                                                      k=xy (D=RT)
 Given 120 miles, rate at 30 mph, it takes 4hours(given k=120   120=30x4)
                           rate at 60 mph, it takes 2 hours(given k=120, 120=60x2)
                          rate ate 120 mph, it takes 1hour(given k=120  120=120x1)
                       
The more x is, the less y is (k=xy)
The more R is, the less T is (D=RT)
x and y are inverse proportion (R and T are inverse proportion)

Ex2: It takes 10 workers and works 100 hours to finish a project(Given k=1000=10x100 )
        It takes 20 workers and works  50 hours to finish a project (k=1000, 1000=20x50)
        It takes 40 workers and work 25 hours to finish a project   (k=1000, 1000=40x25)

Problem Solving Strategy:
Step1: to recognize if it is direct or inverse proportion
Step2: If it is direct proportion: y=f(x)=kx
          If It is inverse proportion: y=f(x)=k/x
Step3: find k=? and put the value in the known variable, and solve the unknown variable.

Q1, For the function f , y=f(x) is inversely proportional to x, when x>0.  If f(3) =6, what is the value of f(2)?

Since it is  inversely proportional- xy=k, y=k/x
 y=f(x)=f(3) =k/3=6, so k=18
f(2)=k/x=18/2=9


Q2, If y is directly proportional to x square and y=1/8 when x=1/2 what is the positive value of x when y=9/2
Since it is directly proportional , y=k(x)(x)
1/8=k(1/4), so k=1/2
9/2=k(x)(x)=1/2(x)(x)
so x=3


Q3, If 5 chickens lay 5 eggs in 5 days. How many eggs will 25 chickens lay in 25 days?
The more chicken, the more eggs, and the less days
Chicken(C) and eggs (E)are direct proportional, and chicken(C) and days(D) are inverse 
proportional ,
Therefore, k=CD/E , k=(5x5)/5=5
k=5=(25x25)/D
D= 125


More Study:

Math Word Problem of the Day

Problem Solving Strategies-proportion, ratio

1, chapter-coundown-3-2007(22)-ratio

The ratio of butter:flour:sugar in a recipe is 1:6:4.  When using 8 cups of sugar in this 
recipe, how many total cups of these three ingredients will be used?

2, school-coundown-25-2008(96.8)-rate

If 60 miles per hour is 88 feet per second, how many feet per second is 66 miles per hour?  Express your answer as a decimal to the nearest tenth.

3, school-coundown-35-2008(10)-proportion

If 5 lunks can be traded for 3 kunks, and 2 kunks will buy 4 apples.  How many lunks are needed to purchase one dozen apples?

4, school-coundown-54-2008(7/12)-ratio

Points A, B, C and D lie on a line, in the order. If AB=2 units, BC=5units and AD=14 units, what is the ratio of AC to BD?  Express your answer as a common fraction

More Study:
Ratio and proportion
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/index.shtml

Ratio and Proportion

Special topics: Ratios and Proportion

direct proportion and inverse proportion

Math meeting 5-22-11

Dear all,

We have finished all odd number  , some even number questions of worksheet and discussed the problem -solving strategy for "percent off sale price"

More study:

1, problem solving strategy for "percent off sale price"

2,percent-Word Problems

Please finish the rest problems we haven't done in the meeting .

Finish it and e-mail to me I will check for you.

Some children can't  attend  the meeting, please finish the worksheet at home and check the club blog.

Ya-Chi

Problem Solving Strategies-percent off sale price

10%off means 90% of the original price
25%off means 75% of the original price
80%off means 20% of the original price 


For this kind of problems:
Always go directly to calculate the percentage of the original price after discount
 That is the Remaining Value 


Step1: find what percentage  of the original price after discount(%)
Step 2: find the discount price (the remaining value)
            the original price x (1- discount percentage) 


EX: A ball sells for $10, There 's 30% off on Friday.  How much you need to pay after discount?


10x(1-0.3)=7


Application Word Problems :


1, school-coundown-47-2008(99)

If Jimmy increases a number by 10% and then decreases this new value by 10%, what 

percent of the original number will the final result be?

2, At Pacific Middle School, 40% of the students are boys. 20% of the boys play a musical instrument. Half of these boys play brass instruments. If there are 14 boys who play brass instruments, what is the total number of students at Pacific Middle School?

3, An oil tanker containing 108,000 gallons of oil releases one third of its remaining volume every two hours. How many gallons have been released after the first six hours?(76000)

4,A computer virus destroys computer memory. On the first day it destroyed ½ of this memory. On the second day it destroyed 1/3 of the memory remaining after the first day; on the third day it destroyed ¼ of the memory remaining after two days and on the fourth day it destroyed 1/5 of the memory remaining after three days. What part of all the computer memory was left after those four days? (1/5)

Solution : 

Problem Solving Strageties: Fractions

More Study :

Mathcounts Notes

Problem-Solving Strategies: Venn Diagram

Principle of Inclusion-Exclusion：Venn Diagram

More Study : Mathcounts note

“Average Speed “ v.s. “Average Number”

Average speed = total distance divided by total time= total distance / total time

1, chapter-coundown-19-2007(55)

Stan drove 300 miles in 5 hours, 20minutes.  Next, he drove 360 miles in 6 hours, 40 minutes.  What was Stan’s average speed in miles per hour for the total trip?

The average (arithmetic mean) is the sum of the values divided by the number of values.

Example : 5, 9, 10
Their sum is 5+9+10 = 24 and there are 3 numbers
The average is 24/3 = 8

1, school-sprint-20-2008(94)

Thomas took three 100-point quizzes, and the mean score for three quizzes was 87 points.  If the highest score is taken away, the mean of remaining two scores would be 83.5 points.  If the lowest score is taken away, the mean of the remaining two scores would be 89 points,  What is the highest score?

2, chapter-sprint -7-2007(1)

The mean of four distinct positive integers is 5,  If the largest integer is 13, what is the smallest integer?

a@b

1, If a #b = 2a + b for all a and b, then what is the value of 4#3?

2x4+3 =11

2, school-coundown-28-2007(-4)

If x@y-=xy-2x, what is the value of (5@3)-(3@5) ?

(5x3-2x5)-(3x5-2x3)=-4

3,,AMC8-2001-12

if a@b=(a+b)/(a-b) then (6@4)@3=?

4, The operation # is defined as a # b = a + a/b. What is the value of 6 # 2?

Problem-Solving Strategies: Counting Coins

Application Word Problem

1, chapter-sprint-18-2007(20)

A customer ordered 15 pieces of gourmet chocolate.  The order can be packaged in a small box that contains 1,2, or 4 pieces of chocolate.  Any box that is used must be full.  How many different combinations of boxes can be used for customer’s 15 chocolate pieces? One such combination to be included is to use seven 2-piece boxes and 1-piece box.

2, schoolr-sprint-24-2008(13)

In how many ways can U.S. coins be combined to total 26cents?

How to solve this kind of problems?

Start with the largest value, 

More study:

Problem-Solving Strategies: Counting Coins

Ratio of two similar figures:

Ratio of Two Similar figures:

If the ratio of the measures of corresponding side length is A:B,

Then the ration of the perimeter is A:B,

the ratio of the area is A^2:B^2

the ratio of the volume is A^3:B^3

Ratio og two similar figures

View more documents from ly3247.

More study

Ratio of two similar figures

Factorials and Trailing Zeros

Application problems

1,Find the number of trailing zeros in the expansion of 23! (4)

2, Find the number of trailing zeros in 101!(24)

3,Find the number of trailing zeros in the expansion of 1000!(249)

4, chapter-coundown-5-2007(2)

What is the hundred digit in the following product: 5x6x7x8x9x10?

5, chapter–coundown-37-2007(12)

Suppose that 50! Is written in the form N x10^x, where N is an integer. What is the largest possible value of x?

More Study:

Factorials and Trailing Zeros-purple Math
Mathcounts note-finding zeros