Objective 6: Mathematical Processes and Tools used in Problem Solving
2003 #25:
The Venn diagram shows how many of the 400 students at SmithMiddle School have a
scooter only, a skateboard only, or both a scooter and a skateboard.
Use the information in the diagram to find theprobability that 1 student chosen at randomhas neither a scooter nor a skateboard.
A
B*
C
D
2003 #48:
A camp leader plans to buy 3 hot dogs per person for a cookout. If 30 people are going onthe cookout and if hot dogs cost $3.99 perpackage, what other information is needed tofind the cost of the hot dogs?
F The number of meals at which hot dogs will be served
G The cost of mustard and relish
H The number of people who eat hot dogs
J* The number of hot dogs in a package
2004 #26:
Mr. Thomas is framing a 28-by-40-foot area for a concrete slab. If the concrete companycharges $120.00 per cubic yard of concrete,what other information is needed in order tofind c, the cost of the concrete slab?
F The area of the slab
G* The thickness of the slab
H The perimeter of the slab
J The price per cubic foot of concrete
2006 #29
The Sundown Parking Garage charges $5.00 to park a car for the first hour and $0.75 foreach additional hour or part of an hour afterthe first hour. What is the total charge forparking a car for 4 hours 42 minutes in thisgarage?
A $5.75
B $6.50
C $7.25
D*$8.00
2006 #48
Mr. and Mrs. Lee brought their 2 children, Cooper and Erin, to a museum. Only Mr. Lee received a discount on his ticket. The table below shows the admission prices at the museum.
Which person’s admission price can be found without any other information?
F*Mrs. Lee
G Mr. Lee
H Cooper
J Erin
2003 #5:
The Stars, the Tigers, and the Lobos scored a total of 56 goals during the hockey season.The Stars scored 4 more goals than the Tigers,and the Lobos scored twice as many goals asthe Tigers. Which is a reasonable conclusionabout the goals the teams scored?
A The Stars scored the least number ofgoals.
B The Stars and the Lobos scored an equal number of goals.
C The Tigers scored exactly half the totalgoals.
D* The Lobos scored the greatest number of goals.
2003 #33:
There are 4 children in the Carter family. Roger is 1 times as tall as Charlie. John is
3 inches taller than Roger. Grace is 58 inches tall, and she is 2 inches taller than Charlie.How tall is John in feet and inches?
A 5 ft 3 in.
B 5 ft 10 in.
C 6 ft in.
D* 6 ft 1 in.
2003 #35:
Antonio and his two brothers equally shared the cost of a new CD with a list price of $18.They received a 20% discount off the list priceand paid 8.25% sales tax on the discountedprice. Find the approximate amount that eachof the 3 brothers paid toward the cost of theCD.
A $4.80
B* $5.20
C $6.50
D $15.59
2003 #39:
Rectangle I is similar to rectangle II.
The area of rectangle II is 216 square centimeters. Find the area of rectangle I.
A 4 cm2
B 12 cm2
C* 24 cm2
D 108 cm2
2004 #12:
After careful consideration of the menu shown below, Mireya purchased Charlie’s Value Meal No. 2.
Mireya calculated her savings by finding the sum of $2.49 plus 2 times $1.29. What did Mireya do next to calculate her savings?
F Add $1.29 to the sum
G Divide the sum by 3
H Subtract $4.29 from the sum
J* Subtract $4.69 from the sum
2004 #20:
Roderick is building a model of an actual airplane with a length of 20 feet.
What other information is necessary in order to find x, the length of the model airplane?
F The ratio of the length of the modelairplane’s tail to the length of its wing
G The speed of the model airplane
H* The scale factor used
J The model airplane’s wingspan
2006 #34
On Monday Mandy bought a CD for 40% offthe regular price of $16.00, not including tax. The next day the CD that Mandy had boughtwas marked down to 65% off its regular price. How much more money would Mandy havesaved, not including tax, if she had waiteduntil Tuesday to buy the CD?
F*$4.00
G $6.40
H $9.60
J $10.40
2006 #42
Mrs. Díaz told her math class that a particular rectangle has a perimeter of
36 units and an area of 65 square units. Which of the following could be the
dimensions of the rectangle?
F 2.5 units by 26 units
G 4 units by 9 units
H*5 units by 13 units
J 6.5 units by 11.5 units
2003 #6:
The figure shows a rectangle inside a circle.
Which procedure should be used to find the area of the shaded region?
F* Find the area of the circle and thensubtract the area of the rectangle.
G Find the circumference of the circle and then subtract the perimeter of therectangle.
H Find the circumference of the circle and then subtract the area of the rectangle.
J Find the area of the rectangle and then subtract the perimeter of the rectangle.
2004 #34:
On Monday Cornelius’s mother gave him school money for the week. He spent $2.80 forlunch every day for 5 school days. He paid a$0.75 book fine at the library and boughtschool supplies for $3.50. If Cornelius had$1.75 left at the end of the school week, whichexpression can he use to find the amount ofmoney he received on Monday?
F* 1.75 + 5(2.80) + 3.50 + 0.75
G 5(2.80) + 3.50 + 0.75 − 1.75
H 1.75 + 2.80 + 0.75 + 3.50
J 5(2.80 + 3.50 + 0.75 + 1.75)
2004 #46:
Mr. Polanco purchased 12 boxes of tile. Each box contained 15 square tiles. If Mr. Polancowants to tile the wall 14 tiles high and 13 tileslong, which procedure can he use to determinewhether he has enough tiles to complete thejob?
F Multiply 14 by 12
G Subtract 14 from 15 and then multiplyby 12
H* Multiply 12 by 15 and then compare the product with the product of 13 and 14
J Add 15 and 14 and then multiply by 13
2006 #25
Nikki paid Dalton $15.50 for a combination of 15 baseball and football cards. The baseballcards were $1.50 each, and the football cardswere $0.50 each. How much did Nikki spendon the baseball cards?
A $3.50
B*$12.00
C $4.00
D $10.50
2003 #18:
Before the last game of the basketball season, Fernando had scored a total of 73 points. Hescored 20 points in the last game, making hisseason average 15.5 points per game. To findthe total number of games he played, first findthe sum of 73 and 20 and then —
F add the sum to 15.5
G subtract 15.5 from 73
H multiply the sum by 15.5
J* divide the sum by 15.5
2004 #9:
∆LMN is similar to ∆XYZ.
Which procedure can be used to find the number of degrees in ∠N?
A Subtract 100 from 360
B* Subtract 100 from 180
C Divide 100 by 2
D Divide 180 by 3
2004 #31:
The figure below shows three shaded equilateral triangles inside a rectangle.
Which statement about this figure is true?
A The shaded area is more than 50% of the area of the rectangle.
B The shaded area is of the unshaded area of the rectangle.
C The unshaded area is of the shaded area of the rectangle.
D* The shaded area is equal to the unshaded area of the rectangle.
2006 #6
Zeb used the rule listed below to rewrite the
expression 10 2 × 10 5.
10× 10= 10
Based on this rule, which of these isequivalent to the expression 8× 8?
F 8, because 8 x 8= 8
G 8, because 8 × 8 = 8
H 8, because 8 × 8 = 8
J*8, because 8 × 8 = 8
2003 #20:
The figures below have a repeating pattern.
Which shows a 180° rotation of the 19th figure in the pattern?
F H
G* J
2004 #10:
A pattern of equations is shown below.
1% of 800 = 8
2% of 400 = 8
4% of 200 = 8
8% of 100 = 8
16% of 50 = 8
Which statement best describes this pattern of equations?
F*When the percent is doubled and theother number is halved, the answer is 8.
G When the percent is doubled and the other number is doubled, the answer is 8.
H When the percent is increased by 2 and the other number remains the same, the
answer is 8.
J When the percent remains the same and the other number is increased by 2, the
answer is 8.
2006 #9
The table shows n, the number of sides of a polygon, and S, the sum of the measures ofthe interior angles of that polygon.
Based on the table, which statement is true?
A The sum of the interior angle measuresdecreases by for each side increase of 1.
B*The sum of the interior angle measures increases by 180° for each side increase
of 1.
C The sum of the interior angle measuresdoubles for each side increase of 1.
D The sum of the interior angle measures isa whole-number multiple of 360°.
2006 #39
This Venn diagram is used to classify counting numbers according to a set of rules.
Which one of the following numbers belongs in the region of the diagram marked by the question mark?
A 45
B 50
C*60
D 65
2003 #44:
The following statements are true about ∆XYZ.
• The measure of each angle is evenly divisible by 12.
• The measure of ∠Z is greater than the measure of ∠Y.
• The measure of ∠Y is greater than the measure of ∠X.
• The measure of ∠X is greater than 40°.
Which choice fits all 4 statements for anglesX, Y, and Z?
F m∠X = 72°
m∠Y = 60°
m∠Z = 48°
G m∠X = 60°
m∠Y = 72°
m∠Z = 48°
H m∠X = 50°
m∠Y = 60°
m∠Z = 70°
J* m∠X = 48°
m∠Y = 60°
m∠Z = 72°
2004 #29:
Mrs. Avery bought a 5-pound bag of white potatoes for $4.25. If red potatoes sold for
$0.89 per pound, why did Mrs. Avery believe that she made the better buy?
A The number of red potatoes in a5-pound bag is greater than the number
of white potatoes in a 5-pound bag.
B The cost for all kinds of potatoes in 5-pound bags is the same.
C* The cost per pound of white potatoes is$0.04 less than the cost per pound of red
potatoes.
D The cost per pound of white potatoes is $0.04 more than the cost per pound of redpotatoes.
2004 #41:
Valdemar has a spinner like the one shown below.
Valdemar would like to increase the chances of the following events:
• Spinning an even number
• Spinning a number less than 4
• Spinning the square root of 9
Valdemar decides to remove the 5 from the spinner. Which statement best supports his reasoning?
A The number 5 takes up more space on the spinner.
B Spinning the number 5 has the greatest probability.
C The number 5 is the greatest number.
D* Spinning the number 5 is not a desired event.
2006 #8
A set of parentheses is missing from the expression below.
15 − 5 + 7 · 2 + 4
Which of the following expressions has theparentheses in the correct place for the
expression to equal 52?
F 15 − (5 + 7 · 2) + 4
G (15 − 5 + 7) · 2 + 4
H 15 − (5 + 7 · 2 + 4)
J*15 − 5 + 7 · (2 + 4)
2006 #12
Raymond packs boxes for an appliance company. He can pack a large box in
10 minutes and a small box in 4 minutes. He needs to pack 10 large boxes and 20 small
boxes. If 2.5 hours remain before closing time, will Raymond have time to finish the workbefore closing time if he works withoutstopping?
F Yes, Raymond will finish the work in1.8 hours.
G No, it will take him 4 hours to finish.
H Yes, Raymond will finish the work in0.5 hour.
J*No, it will take him 3 hours to finish.
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