Number Sense and Operations

June, 1999

 

#41  The housewares store at the shopping mall is promoting a new floor scrubber.  The chart below shows how much money you save depending on how many floor scrubbers you buy.  The amount of money you save increases with the number of floor scrubbers you buy.

 

                  SAVINGS CHART

Number of Floor

Scrubbers Bought

Amount

of Savings

3

$ 5.00

6

$10.00

9

$15.00

12

$20.00

 

 

You purchase 21 floor scrubbers, spending a total of $299.95 after the discount.  What was the price, p, of each floor scrubber before the discount?

 

Show your work.

 

 

 

 

 

Answer  $__________________

 

June 1999

 

# 31  Dina wrote the following facts about three different numbers: a, b, and c.

 

                                Dina’s Math Facts

 

                                Fact 1:  a ÷ c = a

      

                                Fact 2:  a ÷ b = a

 

                                Fact 3:  abc = 1

 

Part A

If Fact 1 and Fact 2 are true, explain why Fact 3 is NOT true.

 

 

 

 

 

 



Part B

What are the values of each of the variables in Fact 1 and Fact 2 ?

 

a  = _________                 b =_________      c  =___________

 

 

May, 2001

 

#34  The  Queen Mary is a large cruise ship that has 8,123,700 cubic feet of cargo space.  Express this number in scientific notation.

 

 

Answer______________________

 

Explain in words how you converted the number of cubic feet into scientific notation.

 

 

 

 

 

 

 

May, 2002

 

# 29  The temperature on the moon can vary from 243  F to –261  F.  By how many degrees can the temperature vary on the moon?

 

Show all work.

 

 

 

 

 

 

 

Answer_________________________  F

May, 2002

 

#34  The statements below are examples of the commutative property of addition.

 

                           134 ( x + 17) = 134 ( 17 + x )

 

                            8 + y + 0.25 = y + 8 + 0.25

 

Part A 

 

On the lines below, explain in words why these statements are examples of this property.

 

 

 

 

 

 

 

______________________________________________________________________________________

 

 

Part B

 

Write a different mathematical statement that demonstrates this same property.

 

Answer__________________________

 

May 2003
 

#31 Justin says that if he adds any two negative integers, the result will always be a negative integer, but if he subtracts the same two negative integers, the result will be a positive integer.

Part A 

 

On the lines below, explain why you agree or disagree with Justin's statement..

 

 

 

 

 

 

 

______________________________________________________________________________________

 

 

Part B

 

On the lines below, give one example of adding two integers and one example of subtracting the same two negative integers that support your explanation.

 

Example 1__________________________

 

 

 

Example 2__________________________

May, 2004

#34

 

 

Statistics and Probability

 

#42  Marina studied the number of people using the escalator and the elevator in the mall for one hour per day for 6 days.  Her figures are listed in the table below.

 

ESCALATOR AND ELEVATOR USAGE

Day

Number of People Using Escalator

Number of People Using Elevator

Monday

30

12

Tuesday

23

15

Wednesday

19

17

Thursday

17

11

Friday

33

23

Saturday

40

24

 


 

Part A

 

Using the information from the table, create a bar graph on the grid showing the number of people using the escalator and the elevator for one hour per day over the 6-day period.

 

Be sure to

·         title your graph

·         label your axes

·         use appropriate and consistent scales

·         accurately graph the data

·         use an appropriate key

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Part B

 

Make one conclusion based on the information from Marina’s study and write it on the lines below.

 

 

 

 

 

 

 

 

May, 2003

#28 Todd made the following measurements of each day's snowfall.

SNOWFALL MEASUREMENTS

Day

Snowfall

Friday

3.25 inches

Saturday

5.75 inches

Sunday

2.4 inches

What is the mean snowfall, in inches, for the 3 days shown?

Show your work.

May, 2004

#43


 

June, 1999

#29  Ahmir is doing a project on snowfall.  The table below shows snowfall data for six New York cities in November 1995.

 

SNOWFALL DATA FOR SIX NEW YORK CITIES IN NOVEMBER 1995

City

Total Snowfall

(in inches)

Departure from

Normal (in inches)

Albany

5.8

+0.8

Binghampton

34.1

+26.6

Buffalo

15.4

+5.5

New York City

2.9

-0.4

Rochester

23.4

+17.0

Syracuse

34.2

+25.1

 

Part A

What was the mean snowfall for all of these cities in November 1995?

 

Show your work.

 

 

 

 

 

Answer___________________inches

 

 

Part B

Using the information in the table above, calculate the normal November snowfall, in inches, for Syracuse.

 

 

Answer__________________inches

 

Algebra


May 2000

 

#34  An advertisement for a new car states that the cat travels 17 to 20 miles for every gallon of gasoline.  The fuel tank on the car holds 18 gallons of gasoline.  On the number line below, represent the possible range for the distance this new car could travel on one full tank of gasoline.

 

_______________________________________________________________________
 
/        /        /        /        /       /        /       /        /        /        /        /       /        /       /       /        /       /        /

300   305   310   315   320   325   330    335   340   345   350   355   360   365   370   375   380   385   390

 

#45  Georgina is collecting data on the growth of E. coli bacteria.  Each E. coli sell reproduces by dividing in half every 20 minutes.

 

Part A

 If Georgina starts with one E.coli cell, how many cells will be in the sample after 1220 minutes?

 

Show your work.

 

 

 

 

 

 

 

 

Answer________________________

 

Part B

 

After how many minutes will there be 256 cells in the sample?

 

Show your work.

 

 

 

 

 

 

Answer_______________minutes

 

May 2000

 

 #36  Maya’s class is selling ice cream cones for $0.75 each at the spring fair.  The class spent $60.00 for the ice cream and cones.  The equation below can be used to find the amount of profit the class will make.

 

      Profit = $0.75 x number of ice cream cones sold - $60.00

 

Use the equation above to find how many ice cream cones Maya’s class must sell to make a profit of $30.00

 

Show your work.

 

 

 

 

 

Answer___________________________

 

 May, 2000

 

 

#38  The school planning committee wants to rent as many tents as they can for the spring fair.  The committee has received from three rental companies the following information:

 

·         Rent- a –Roof charges $325 for the first 3 tents, and $125 for each additional tent.  There is no charge for delivery and setup.

 

·         Parties –R-Us has a one time charge of $100 for delivery and setup, plus $100 for each tent.

 

*  Tents-‘n – More charges $125 for each tent.  There is no additional charge for delivery and setup.

 

The committee has $600 to spend on tents.  What is the maximum number of tents it can rent?

 

 

 

 

 

Answer­­­­____________________

 

What company will give the best price for the maximum number of tents?  Explain your answer on the lines below.

 

 

 

 

 

 

May, 2001

 

#38  Tony is selling hot dogs at a football game.  He sold 26 hot dogs in his section during the first half of the game.  During the second half of a game, Tony usually sells about half as many hot dogs as he does in the first half.  Shown below is a diagram of the stadium.  All the sections are about the same size as Tony’s section, and there are about the same number of people seated in out each section.

 

The company Tony works for estimates that 300 hot dogs will be sold during the game.  Could the estimate be correct?  Explain your answer on the lines below.

 

 

______________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

______________________________________________________________________________________

 


May, 2000

#40   Kyle says that he can pick any number between 1 and 100, add 1 to it, multiply the result by 2, add 2 to that result, then subtract 2 times the number he started with, and he will always get the same answer.

 

Using x to represent any number between 1 and 100, write an expression that demonstrates the process described above.

 

Expression____________________________________________________________

 

Is Kyle correct?  Explain why or why not on the lines below.

 

 

 

 

 

 

 

_____________________________________________________________________________________

 

May, 2001

 

#44   Ron owns a flower shop in the shopping mall.  The flower most frequently ordered from his flower shop is the rose.  For each order of roses, Ron charges $3.00 for each rose plus $5.00 for delivery service.  Ron made a delivery of roses for which he charged $59.00.  Write an equation that you could use to find how many roses, r, he delivered.

 

 

 

 

Equation_____________________________

 

 

Solve your equation to find the number of roses he delivered.

 

 

 

 

 

 

 

Answer___________________

 

May, 2002

 

# 30  Dave wants to cut a 20-foot long piece into pieces that are either 5 feet, 4 feet, or 2 feet long.  He must have at least one of each length and have no wood left over.  What is the greatest number of pieces he can cut from this piece of wood?

 

 

 

 

Answer____________________pieces

 

 

 

On the lines below, explain the process you used to arrive at your answer.

 

 

 

 

 

 


May, 2002

 

 

#33  Mr. Adams will be serving 20 people at a barbeque.  He plans to make two hamburgers for each person.  Mr. Adams spent $27.00 at the store on the meat, which sells for $2.25 per pound.  If Mr. Adams wants to make all the hamburgers the same size, what will be the size, in pounds, of each hamburger?

 

Show your work.

 

 

 

 

 

 

Answer_____________________ pounds

 

#37  Antonio is building a bookshelf.  He has a piece of wood that measures 90 centimeters in length.  The directions require that this piece of wood be cut into two pieces, one piece 20 centimeters longer than the other.  He uses the equation below to determine where to make the cut. 

 

                                          x + ( x + 20 ) = 90

 

The shorter piece of wood must then be cut in half.  Use the equation above to help you determine the length of the shortest piece of wood.

 

Show your work.

 

 

 

 

 

 

 

 

 

 

 

Answer__________________________centimeters

 

 

 

 

 

May, 2003

 

#41 Solve the inequality below for y and graph the solution set on the number line provided.

 

                                                                3y + 45 = 54

 

 

Show your work.

 

 

 

 

 

 

 

 

 #44  Joey needs to travel 15 miles from Smithville to Clarksville and 5 miles from Clarksville to Elmwood. The table below shows two different taxicab companies' rates.

 

 

                                                   TAXICAB RATES

Sunshine Cab Co. Flat rate: $5.00 + $1.00 for every 5 miles

Freedom Cab Co.

Flat rate $2.50 + $0.50 for every mile over 10 miles

 

Joey will choose one of these four options:

    1. Travel with Sunshine Cab Co. to Clarksville, then with Freedom Cab Co. to Elmwood.

    2. Travel with Freedom Cab Co. to Clarksville, then with Sunshine Cab Co. to Elmwood.

    3. Travel nonstop with Sunshine Cab Co. the entire way.

    4. Travel nonstop with Freedom Cab Co. the entire way

 

Which is the least expensive way for Joey to make the trip?

 

Show your work.

 

 

 

 

 

 

 

 

 

 

 

Answer__________________________


May, 2004

#39


 

#44

 

May, 2001

 

#30  Gina programmed her computer to perform an algorithm.  At each step, her computer displays a number on the screen.  The table below shows the numbers the computer displays on the screen for the first 6 steps.

 

ALGORITHM STEPS

Step

Number on Screen

1

4

2

7

3

10

4

13

5

16

6

19

 

Part A

 

If the pattern in the table continues, what number will the computer display on the screen at Step 9?

 

Show your work.

 

 

 

 

 

 

Answer_____________________

 

Part B

 

If the pattern in the table continues, what number will the computer display on the screen at Step 50?

 

 

 

 

 

 

 

Answer________________________

 

Part C

 

Explain how you know which number will be displayed on the screen after each step.

 

____________________________________________________________________________________

 

______________________________________________________________________________________

 

____________________________________________________________________________________


 

 

 

Geometry

 

 

# 37  Alicia is making a pattern with equilateral triangles.  She started with one equilateral triangle and is adding equilateral triangles to the perimeter of each design.  The first four designs in her pattern are shown below.

 

 

 

If Alicia continues the pattern shown above, how many equilateral triangles will she add to get Design 6?

 

Show your work.

 

 

 

 

 

 

 

 

 

 

 

Answer_____________________


 

 

Measurement

 

May, 2001

 

#28  Dante is driving 638  miles to his cousin’s house.  His car has a 12 gallon tank and goes 22 miles for every gallon of gasoline.  Dante started with a full tank of gasoline and will fill up the tank when it is empty.  How many times will he have to stop for gasoline?

 

Show your work.

 

 

 

 

 

 

Answer______________________

 

#36  Part A

 

At the bakery, the daily ratio of cookie sales to donut sales is 3 to 4.  Cookies and donuts cost the same amount.  If the bakery earned $225.00 an Tuesday from the sale of cookies, write a proportion that could be used to find the amount of money that came from the sale of donuts on Tuesday.

 

 

 

 

 

Proportion___________________________

 

 

Part B

 

Use your proportion to find how much money the bakery earned from the sale of donuts on Tuesday.

 

Show your work.

 

 

 

 

 

 

Answer  $_____________________


 

#39  In Social Studies class, eight-graders learned that each person in America, on average generate about 5.1 pounds of garbage per day.

 

Part A

 

How many pounds of garbage does a family of 5 generate in 365 days?

 

Show your work.

 

 

 

 

 

 

 

Answer__________________________pounds

 

Part B

 

How many tons of garbage does a family of 5 generate in 365 days?  Round your answer to the nearest ton.   

 

 

 

 

 

 

Answer__________________tons

 

Part C

 

Explain how you determined your answer to Part B.

 

______________________________________________________________________________________


______________________________________________________________________________________


______________________________________________________________________________________


 

# 41  Dana wants to lay a straight path of stepping stones from one end of her garden to the other.  Her garden is 12 feet long.  She wants to use rectangular stepping stones measuring 2.5 feet by 1 foot, and would like to lay them 6 inches apart from each other.

 

Part A

 

The grid below represents Dana’s 12 foot long garden.  On the grid, make a scale drawing to show how Dana should lay the stepping stones using the maximum number of stones.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SCALE

 

 

= 6 in.

 

 

 

 

 

 

 

 

 

 

Part B

 

What is the minimum number of stones Dana will need for her walkway?

 

Show your work.

 

 

 

 

 

 

 

Answer_____________________


 

May, 2002

 

# 31  Ben is hiking from Mt. Pleasant to Yorkville.  He is following the trail shown on the map below.

 

 

The darker section of trail shows how far Ben has hiked, a distance of approximately 4 miles.  Estimate how many more miles Ben has to get to Yorkville.

 

 

Estimate______________________ miles

 

 

 

 

 

 

On the lines below, describe the process you used to determine your estimate.

 

 

______________________________________________________________________________________

____________________________________________________________________________________

 

____________________________________________________________________________________


 

# 35  Mary  selected some students in her school at random and asked how they got to school each morning.  Her results are shown in the table below.

 

                 Mary’s Results

Way to School

Number of Students

Ride in car

23

Ride the bus

51

Walk

18

 

Part A

 

What percent of the students in the table above ride in a car ro school each morning?

 

Show your work.

 

 

 

 

 

 

 

 

Anwer_______________%

 

Part B

 

There are 440 students in Mary’s school.  The proportion of students who ride in a car to Mary’s school is equal to the proportion in the table shown above.  How many students in Mary’s school ride in a car to school?

 

Show your work.

 

 

 

 

 

 

 

 

Answer_______________________students

 


# 40  Look at the drawing of the  statue below.

 

 

Andre knows that the signpost next to the statue is 6 feet tall.  He wants to measure the height of the statue, but cannot reach the top to do so.  This scale drawing of the statue is the only thing he has to help him.

 

On the lines below, describe a method Andre can use to measure the height of the statue.

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

Using the method you described above, find the height of the statue.

 

 

Height_________________feet


 

 

#41  Martin has an office with a floor shaped like a rectangle, 12 feet by 20 feet.  He has a desk that is positioned against one of the 12-foot walls.  His desk measures 8 feet by six feet.  On the grid below, draw a scale diagram of martin’s office floor plan.  Make sure to include and label his desk in the drawing in a correct place.  Be sure to provide the scale that you used to draw your diagram.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

May, 2003

#32 The outboard engine on Jimmy's boat uses a fuel-to-oil mixture in  a 50:1 ration. If Jimmy puts 2.5 gallons of fuel in the tank, how many fluid ounces of oil does he need to add? (1 gallon = 128 fluid ounces)

Show your work.

 

 

 

 

 

 

 

Answer____________________fluid ounces


 

Chapter Six:  Percent

 

June, 1999

#30  Steven’s dad is researching an old family recipe.  He has found that members of the family do not agree on the amount of floor needed for the recipe.  The following is a list of measurements he received from different people for the number of cups of flour needed:

 

                        1 ¼  ,  1 ⅓ ,  1.5,   5/3,  1 ⅛

 

 

He wants to use the larger amount of flour.  Which measurement above should he use?

 

Answer___________

 

Explain how you determined which number was the largest.

 

 

 

#35  Shade in 5/8 of the rectangle below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

What  percent of the rectangle is shaded?

 

Show your work.

 

 

 

 

 

 

 

Answer____________________

 

#36  In the expression below, insert two sets of parentheses so that the expression is equal to 15.

 

3 x 18 + 32 - 6

 

2 - 1x 5

Now show the steps you used to simplify the expression so that it is equal to 15.

 

Show your work.

 

 

 

 

 

 

 

May 2000

 

#28  Bryan and Annie are going to a school dance.  Tickets cost $12.00 per couple at the door, but are only $10.50 if they are bought in advance.  What percent of the door price will Bryan and Annie save if they buy their ticket in advance?

 

Show your work.

 

 

 

 

 

 

 

Answer______________________%

 

#33  Joshua made $650.00 while working last year doing yard work for various people.  He decided to make a graph to record how he spent his money.  The graph is shown below.

 

ESTIMATE the total amount of money Joshua spent on CDs last year.

 

 

 

 

 

 

Estimate  $__________________

 

Explain in words how you determined your estimate.

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

#35  Each year approximately 28 million tons of yard waste ( mowed grass, dead leaves, etc.) are thrown away in the United States.  This is about 20 % of the total amount of garbage thrown away in the United States each year? 

 

Show your work.

 

 

 

 

 

 

 

 

Answer__________________tons

 


 

May, 2003

#33 Sweaters were on sale for 20% off of the original price. Kelly bought a sweater on sale that had an original price of $32.00. The sales tax was 7.25%. How much did Kelly pay for the sweater? 

Show your work.

 

 

 

 

 

 

 

Answer $____________________ 

 

 May, 2003

 

#36 On the line below, arrange these numbers in order from smallest to largest.

 

Answer_______________________________________________________________________________________

 

 

Explain the process you used to determine your answer.

 

___________________________________________________________________________________

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

 

 

 

#37 The equation below can be used to find the cost, including 8% tax, of p pairs of socks. Rachel wants to know how many pairs of socks she can buy for $8.91. Solve the equation and write your answer on the line below.

 

                                                                      $1.65p(1.08) = $8.91

 

 

 

Show your work.

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer ____________________ pair of socks

 

 

#45 Paul's class went to the zoo and counted the various types of animals they saw, as shown in the table below.

 

 

                                                     ZOO ANIMALS

Type of Animal

Number Seen

Birds

35

Reptiles

10

Grazing mammals

26

Insects

16

Carnivorous mammals

3

 

 

Using your protractor, make an accurate circle graph of the types of animals the class saw.

 

Be sure to

 

 

Show your work.

 

 

May, 2004

 

#32 

 

 

#36

 

 

Chapter Seven:  Number Sense:  Rational and Irrational Numbers

June, 1999

#44  Tony and his friends bought some snacks at a movie theater.  The table below shows the snacks and their prices.

 

MOVIE THEATER SNACKS

Item

Price

Popcorn 

$2.25

Candy bar

$1.20

Cold drink

$1.49

Cotton Candy

$1.39

Nachos

$3.69

Hot dog

$2.07

Lemonade

$0.99

 

Which items did Tony and his friends buy if together they spent exactly $8.00 and bought only one of each item they selected?

 

Show your work.

 

 

 

 

 

 

 

Answer_________________________


 

May, 2000

 

#29  On the line below, list all whole numbers from 1 to 100 that can be evenly divided by both 6 and 15.

 

 

 

 

Whole numbers_________________________________________________________

 

On the lines below, describe at least one pattern that you notice in the above set of whole numbers.

 

_______________________________________________________________________________

 

____________________________________________________________________________________

 

____________________________________________________________________________________

 

 

 

How many whole numbers between 290 and 410 can be evenly divided by both 6 and 15?

 

Show your work.

 

 

 

 

 

 

#30  In the equations below, each of the variables a, b, c, and d represents a different value.

 

                                                          a + c = b

                                            

                                                          b – a  = c

 

                                                          c  x d = -d

 

                                                          d + d = a

 

In a= 4, use the equations above to determine the value of each other variable.

 

Show your work.

 

 

 

 

 

 

 

 

Answers

 

b=____________                               c=________________                    d=____________________

 

 


#31  Look at the numbers on the index cards below.

 

Plot each number on the number line below.  Label each point with the letter from the index card.

 

__________________________________________________________________________________                   │| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│| | |│ 

-5   -4    -3    -2    -1     0     1     2     3      4     5     6      7     8     9     10

 

 

#39  Raoul and Clarence are writing questions for the “Name That Number” game.  They want to ask the players to find a number with the following properties:

 

·         The number is a one-digit positive integer

·         When 82 is divided by the number, the remainder is 3.

 

Does such a number exist?  If so, write the number and explain your answer on the lines below.  If not, explain in words why is no such number.

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________


May, 2001

 

#29  What is the smallest number that has prime factors of 2, 3, 5, and one other different prime number?

 

Show your work.

 

 

 

 

 

 

 

Answer_______________________

 

 

#42 A radio broadcasting tower is 80 feet high. Cables are attached to the top and anchored to the ground 60 feet from the base of the tower.

 

 

Show your work.

 

 

 

 

 

 

 

Answer_______________________


 

May, 2002

 

#38   Lauren  and Victoria are playing a number – guessing game.  Lauren   thinks of a whole number from 1 to 20, then Victoria tries to guess the number in as few tries as possible.  If she guesses wrong, Lauren tells her if the number is higher or lower than her guess.

 

On the lines below, explain a process Victoria could use to determine Lauren’s number that minimizes the number of guesses.

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________


 

# 39  Jimmy and his uncle left the shore in their boat from point A and continued on this course for 350 meters until they reached point B.  After fishing for awhile, they made a 90-degree turn and continued for 475 meters to point C.  The diagram below shows the course they took and the locations of the two different fishing spots on the lake.

 

 

 

What is the approximate distance, d, they will travel from point C to get back to point A?

 

Show your work.

 

 

 

 

 

Answer_____________________meters

 

 

May, 2003

#38 A window washer leans a ladder up against a wall so that the top of the ladder touches the base of the window, as shown below. The bottom of the ladder is 15 feet from the wall, and the base of the window is 26 feet from the ground.


What is the length of the ladder to the nearest foot?

Show your work.

 

 

 

 

 

Answer_____________________feet

 

May, 2004

#28


#31

#41

 

Chapter Eight:  Geometry and Measurement

 

June, 1999

 

# 37  The physical education department distributed a survey asking the students in which three sports they participate:  volleyball, soccer, or basketball.  They received the following results:

 

·         29 students participated only in volleyball

·         31 students participated only in soccer

·         5 students participate in all three sports

·         2 students participate in soccer and basketball, but NOT in volleyball

·         1 student participates in volleyball and soccer, but NOT in basketball

·         39 students participate in volleyball

·         102 students participate in at least one of the three sports

 

Part A

Complete the Venn diagram below to reflect the results of the survey.

 

 

 

Part B

 

On the lines below, explain how to find the total number of students that participate in basketball.

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

#38  Use the centimeter side of your ruler and your protractor to help you solve this problem.

 

Look at the polygons below.

 

 

Part A

Which of the polygons above are regular polygons?

 

__________________________________________________________________________________

 

Part B

Explain in words how you know a polygon is regular.

 

__________________________________________________________________________________

 

__________________________________________________________________________________


 

May, 2000

 

#41  Use the centimeter side of your ruler and our protractor to help you solve this problem.

 

Part A

  

Tyrone cut out a quadrilateral from a piece of cardboard.  One pair of opposite sides are parallel but not congruent, and the other pair of opposite sides are congruent but not parallel.  In the space below, draw the shape of the quadrilateral Tyrone cut from the cardboard.

 

 

 

 

 

 

 

What is the name of the quadrilateral that you drew above?

 

Answer_____________

 

Part B

 

In the space below, draw a quadrilateral in which both pairs of opposite sides are parallel and congruent

 

 

 

 

 

 

Part C

 

What is the name of this new quadrilateral?

 

Answer_________________


 

May, 2001

 

 

#35  The figure below shows a trapezoid intersected by a line.  The angles formed are represented by the numbers 1 through 12.

 

 

On the line below, list two angles in the figure that are congruent to    5.

 

 

__________________________________________________________________________________

 

On the line below, list two angles in the figure that are supplementary to     5.

 

__________________________________________________________________________________


May, 2002

 

Angle A and angle B are complementary.  In addition, angle A is supplementary to angle C.  What are the measures of angle A and angle C if angle B measures 37  ?

 

 

 

Angle A ____________________degrees

 

Angle C____________________degrees

 

Explain in words how you determined your answers on the lines below.

 

__________________________________________________________________________________

 

______________________________________________________________________________________

 

__________________________________________________________________________________


May, 2003

 

#34  Use your ruler and protractor to help you solve this problem.

Ingrid drew a polygon with 3 sides that has one angle that measures 90 degrees. In the space below, draw the shape that is like the one that Ingrid drew and indicate where the 90 degree angle is located.
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

What is the most specific name for the polygon that Ingrid drew?

 

Answer __________________

 

May, 2004

#29

#33

Chapter Nine:  Area and Volume

 

 

June, 1999   

 

 

#28   Heather is making a pair of bookends from a clay cone.  She will cut the cone in half, as shown below.

 

 

 

 

In the space below, draw the polygon that shows the shape of the cut face of each  half.

 

Show your work.

 

 

 

 

 

 

 

On the line below, write the name for the figure you drew.

 

Answer __________________

 


#40  Shown below is a floor plan of the west wing of the shopping mall.  The store that is shaded represents approximately 1,275 square feet.  ESTIMATE the total square footage of all the stores in this wing of the shopping mall.

 

 

Estimate_______________square feet

 

Explain the process you used to determine your estimate.

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________


#43 Plot and label the following points on the coordinate grid below.

 

A (-3,-2)    B (7,-2)     C (5,4)    D (-5,4)

 

 

Part B

 

Draw line segments between points A and B, B and C, C and D, and D and A.  Give the most precise name of the figure formed.

 

Answer______________________

 

Part C

 

Find the area, in square units, of the figure you drew on the coordinate grid.

 

Show your work.

 

 

 

Area_____________square units

 

 


May, 2000

 

#44  A large water tank in the shape of a right circular cylinder stands 25 meters high and measures 15 meters in diameter.

 

 

 

Part A

 

What is the volume of the water tank in cubic meters?  ( You may use 3.14 for )

 

Show your work.

 

 

 

 

 

Volume___________ cubic meters

 

Part B

 

 

For every cubic meter, the tank can hold 1,000 liters of water.  What is the maximum numbers of liters of water the tank can hold?

 

 

 

 

 

Answer_________________

 

 


May 2001

 

#32  Use the centimeter side of your ruler to help you solve this problem.

 

 

On the lines below, explain one way you could find the area of the figure above.

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

 

Find the area of the figure in square centimeters.

 

Show your work.

 

 

 

 

 

 

 

 

 

 

Area______________________________square centimeters

 


#43  Julie is making a poster of the Earth.  She wants the Earth to be a circle with a diameter of  10 inches.  She wants to outline the Earth with yarn.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

How many inches of yarn will Julie need to outline the Earth in her poster?  (You may use  =3.14)

 

Show your work.

 

 

 

 

 

 

 

Answer______________________inches


 

May, 2002

 

#44  The students in Ms. Lewis’s class have seashell decals to put around the border of their ocean project bulletin board, as shown below. 

 

 

Each paper decal is 4.5 inches long and 4.5 inches wide.  How many decals will it take to complete the border of the bulletin board?

 

Show your work.

 

 

 

 

 

 

 

 

Answer_______________________decals

 


43 A baker is decorating the top of a cake with a 3-inch border of chocolate frosting surrounding a 6-by-10-inch of vanilla frosting. A diagram of the top of the cake is shown below:

 

Part A

 

What is the total area in square inches of the chocolate frosting border?

 

Show your work.

 

 

 

 

 

 

 

Answer_______________________square inches

 

Part B

 

On a second cake of the same size and shape, the bake makes a 5-inch by 9-inch rectangle of vanilla frosting, and then covers the rest of the top of the cake with chocolate frosting. How many more square inches of chocolate frosting are on top of the second cake than are on top the first cake?

 

Show your work.

 

 

 

 

 

Answer_______________________square inches

 

 

 

May, 2003

#43 The city planning department wants to build a rectangular playing field in one of its parks. The perimeter of the entire field will be fenced, and the total area of the field will be 1,200 square feet.

Part A

 

If the length and the width can only be whole numbers, what dimensions for the playing field will require the minimum number of feet of fencing?

 

Show your work or explain in words.

 

 

 

 

 

 

 

Dimensions __________________feet by __________________feet

 

 

 

What is the perimeter of the playing field with the minimum number of feet of fencing?

 

 

 

Perimeter_______________________feet

Part B

Using the grid and scale below, accurately draw the playing field and label the dimensions.

 

 

                             
 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

May, 2004

#37

#38

Chapter Ten:  Algebra:  Functions and Relations

 

Not applicable


 

Chapter Eleven:  Similarity, Congruence, and Transformations

 

June, 1999

 

 

#33  In the figure below,   ADE is similar to   ABC.

 

 

Part A

What is the length in feet of BC ?

 

Show your work.

 

 

 

 

 

 

Answer_____________ feet

 

Part B

What is the length in feet of AB?

 

Show your work.

 

 

 

 

 

Answer_______________________feet

 


#39  A tree which is in danger of falling, stands 65 feet from a house.  The angle of elevation from the bottom of the house to the top of the tree is 40.

 

If the tree should fall directly toward the house, will it hit the house?

 

Show your work or explain in words.

 

 

 

 

 

Answer____________________


 

#32  Use the centimeter side of your ruler to help you solve this problem.  Miguel wants to make a kite with a shape similar to the one shown below.  The length of the sides of the new kite will be 15 times larger.

 

 

 

 

 

 

Part A

 

What would be the perimeter in the centimeters of the new kite?

 

Perimeter__________________ centimeters

 

Part B

 

Would the angles the new kite be larger, smaller, or the same as the angles of the kite pictured above?  Explain your answers on the lines below.

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________


 

May, 2000

 

#42  An engineer for an electric company is calculating the height of a tree.  She placed a flag on the ground 42 feet from the base of the tree and used her surveying equipment to find that the angle of elevation from the flag to the top of the tree is 55.

 

Find the height, x, of the tree to the nearest foot.

 

Show your work.

 

 

 

Answer_____________________feet


 

May, 2001

 

#31  The two triangles shown on the grid below are similar triangles.  Using point A as one of the vertices, draw a third triangle that is similar to both existing triangles, but that is not congruent to either one.

 

 

Explain in words how you know that the triangle you drew is similar to the two original triangles on the grid.

 

___________________________________________________________________________________

 

___________________________________________________________________________________

 

___________________________________________________________________________________

 

___________________________________________________________________________________


#45   On the grid below, draw the reflection of quadrilateral ABCD in the y-axis so that the y-axis is a line of symmetry.

 

 

Part B

 

On the lines below, write the coordinates of each new vertex.

 

(________________)        (__________________)    (__________________)    (____________________)


 

May, 2002

 

#33  Use the centimeter side of your ruler to help you solve this problem.

 

Part A

 

In the space below the triangle shown, drawn a new triangle with sides that have lengths  1.5 times the lengths of the sides of the original triangle.

 

 

 

Part B

 

Are the two triangles similar or congruent to each other?  Explain your answer in words on the lines below.

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

______________________________________________________________________________________

 

______________________________________________________________________________


#36  Figure A was transformed on a grid and renamed figure B.

 

On the lines below, name and describe the transformation that changed figure A to figure B.


______________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________

 

__________________________________________________________________________________


 

#45  Brady drew a rectangle and then drew a diagonal in that rectangle as shown below.

 

 

 

When Brady measured the width of the rectangle and the length of the diagonal, he found that the diagonal is twice as long as the width.

 

Part A

 

Express the width of the rectangle and the measure of the diagonal in terms of x.

 

 

 

Width____________                    Diagonal______________

 

 

Part B

 

On the lines below, explain how Brady can find the measure of the angle formed by the width of the rectangle and the diagonal.

 

______________________________________________________________________________________


_____________________________________________________________________________________


____________________________________________________________________________________


_____________________________________________________________________________________

 

 

Part C

 

If the width of the rectangle is 4 inches, find the measure of the angle formed by the width of the rectangle and the diagonal.

 

 

Answer_____________________degrees

 


May, 2003

#42 What value of x would make the two triangles shown below similar?

Show your work.

 

 

Answer ____________

May, 2004

#40

#42

#45

 

Chapter 12:  Counting and Probability

 

June, 1999

#34  A coin collector has a box that contains United States quarters.  The quarters have dates from 1954 to 1959, as shown in the table below.

 

                U.S. Quarters

Date

Number of Quarters

1954

19

1955

7

1956

6

1957

8

1958

5

1959

11

 

If  the coin collector chooses one quarter from the box without looking, what is the probability that the quarter selected is dated 1955, 1956, or 1957?

 

Show your work.

 

 

 

 

 

 

 

Answer___________________


 

 

May 2000

 

#37  The “Wheel of History” game uses a spinner divided into 20 equal sections, each labeled with a time period in American history.  A team member spins the spinner and is asked a question about the time period the spinner lands on.

 

 

Part A

 What is the probability that the spinner will land on the time period 1800-1899?

 

 

 

 

Probability___________________

 

Part B

 

The history department is planning to write 60 questions for the game.  Based on the probability you gave in Part A, how many questions should be written for the period 1800-1899?

 

Show your work.

 

 

 

Answer________________


 

May, 2001

 

 

#33  Jared went out to dinner with his mother, father, and 3 sisters.  The restaurant had choices of 2 different types of salads and 3 different main courses.  If each person ordered a salad and a main course, is it possible for each person in Jared’s family to order a different combination?

 

 

 

Show your work.

 

 

 

 

 

 

Explain your answer on the lines below.

 

______________________________________________________________________________________

____________________________________________________________________________________

_____________________________________________________________________________________

May, 2002

 

Mr. Bell’s class is playing a math game.  Mr. Bell randomly names an integer from the set of integers –15 to 15.

 

Part A

 

What is the probability that Mr. Bell names a positive integer?

 

 

 

Probability_________________

 

Part B

 

On the lines below, explain how you determined your answer.

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 


 

Logical Reasoning

 

May, 2000

 

 

#40  Jamal and Morgan are playing a game in which 7 objects are placed on a table.  Each player takes turns removing 1 or 2 objects.  The player who removes the last object on the table loses.

 

 

Morgan goes first and removes one object from the table on her first turn.  How many objects should Jamal remove next to be sure that he will win?

 

 

 

 

Answer________________

 

 

Explain in words why this is a winning strategy.

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________


 

 

May,  2002

 

#28  Tina, Carlos, April, and Malek will sit in these chairs according to the rules below.

 

 

Write a name on each chair above to show in what order Tina, Carlos, April, and Malek will be seated.

 

On the lines below, explain in words why Carlos cannot sit in chair 2.

 

______________________________________________________________________________________

______________________________________________________________________________________

 

______________________________________________________________________________________

 

______________________________________________________________________________________

May 2003

#30 For a game, Lisa created notes to be handed out. Each note was on blue or orange paper and had a "yes" or "no" written in red or green letters. No two notes were the same. How many combinations of notes could Lisa have created?

Show your work.

 

 

 

Answer________________  combinations

 

 

 

#35 The manager of a deli wants to list all of the possible sandwich combinations from the menu shown below.

 

                SANDWICH MENU

Bread Cheese

Meat

Sourdough Cheddar

Turkey

Wheat American

Ham

Rye

Pastrami

 

 

Part A

Construct a tree diagram that shows the number of possible sandwich combinations using one kind of bread, one kind of cheese and one kind o meat from the menu.

 

 

 

 

 

 

 

 

 

 

 

 

Part B

How many of the different sandwich combinations in your tree diagram above have cheddar cheese?

 

 

Answer________________  combinations

 

 

 

 

#39 Laura received a box of chocolates for her birthday. The chocolates in the box have five different fillings. The table below shows how many chocolates with each type of filling are in the box. The manager of a deli wants to list all of the possible sandwich combinations from the menu shown below.

 

                CHOCOLATES

Filling Number
Caramel 16
Coconut 10
Mint  12
Cherry 14
Toffee 8

 

 

The chocolates are all the same shape and size. Laura does not like coconut or toffee. What is the probability that Laura will pick a chocolate from the full box that has a filling she does like?

 

 

Probability ________________

 

 

On the lines below, explain how you determined your answer.

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

 

_____________________________________________________________________________________

May, 2004

#30