2014 Shoreline Math Olympiad (Answer Key) Fourth Grade Mental Math 1 · PDF file2014 Shoreline Math Olympiad Fourth Grade – Mental Math Test #1 Question #1: What is the largest multiple

Page 5 of 5

2014 Shoreline Math Olympiad (Answer Key)

Fourth Grade – Mental Math 1

Problem Number

Answer

Explanation

1 48 Largest factor of 48 is 48 itself which is a multiple of 8.

2 Less 9 x 8 = 72; 12 dozen = 144. 72 < 144.

3 25

8/(5+8+7) or 8/20 which is reduced to 2/5.

Fourth Grade – Mental Math 2

Problem Number

Answer

Explanation

1 494 6 x 100 = 600; 6 x 99 is 6 less than 600 which is 594. 594 – 100 = 494.

2 8 2 cups in 1 pint; 2 pints in a quart; 2 quarts in half a gallon. Thus, 2 x 2 x 2 = 8.

3 15

Two possible whole numbers that would produce a range of 20 are 45 (25 + 20) and 15 (35 – 20). Since 15 < 45, 15 is the smallest possible third number.

2014 Shoreline Math Olympiad Fourth Grade – Mental Math Test #1

Question #1: What is the largest multiple of 8 that is a factor of 48? Question #2: On a table, there were NINE rows of eggs. In each row, there

were EIGHT eggs. Were there MORE or LESS than 12 dozen eggs on the table?

Question #3: What is the probability of randomly picking an ORANGE ping pong

ball from a bag that contains 5 BLUE ping pong balls, 8 ORANGE ping pong balls, and 7 WHITE ping pong balls? Express your answer as a REDUCED FRACTION.

2014 Shoreline Math Olympiad

Fourth Grade – Mental Math Test #2 Question #1: What number is one hundred less than the PRODUCT of 6 and 99? Question #2: How many cups are there in a half-gallon?

Question #3: The range of THREE whole numbers is twenty. If two of the whole

numbers are 25 and 35, what is the smallest possible whole number that the third number could be?

Think Write

; largest factor of 48 is 48 ; is 48 a multiple of 8? yes → 48

9×8=72 = 6 dozen → LESS than 12 dozen

of 9×8=72 ; 12 dozen = 144; 72 is LESS than 144

:al balls : 5+8+7=20 ; P (orange

) : ± = 25

; 6×99 = 6×100 - 6×1=600 -6=594 ; 594 - 100 = 494

2 cups in a pint,2 pints in a quart, 2 quarts in a half gallon → 2×2×2 = 8

FtI gal = 128 oz ; tzgal = 64 oz ; 1

cup= soot → 6¥ = 8

If largest is 35,

smallest is 35 - 20 = 15

Page 1 of 5


Fourth Grade - Individual Test 1

Problem Number

Answer

Explanation

1 C 3 x 5 = 15, thus the units digit is 5.

2 C

3 D Since the result of flipping a single coin is an independent event, the probability of the result being heads or tails is the same.

4 B 6/8 = 3/4

5 D (2 x 6) x (2 x 4) = 12 x 8 = 96

6 C

7 A

8 B “5.5” appears twice while the each of the other numbers appears only once.

9 A

10 B Roy - 8/12 = 2/3; Sam – 9/15 = 3/5; Tom – 12/18 = 2/3, thus Roy & Tom

11 D 25 + 10 + 5 + 15 = 55 cents; 55/100 = 11/20

12 C (4,9) is 4 units vertically from (4,5).

13 A

14 D 24 x 18 ≈ 20 x 20 = 400

15 C 100 x 10 x 8 = 8,000

2014 Shoreline Math Olympiad Fourth Grade – Individual Test #1

1. What is the units (or ones) digit in the product of 123 and 65?

A. 0 B. 3 C. 5 D. 8

2. On the partial number line below, which number most closely represents point P?

A. 2.33 B. 2.50 C. 2.75 D. 3.75

3. A coin is flipped and it landed on tails. If it is flipped again, it will . . .

A. certainly be heads

B. likely be heads

C. unlikely be heads

D. have an equal chance to be heads or tails

4. Which one of the fractions below is NOT equivalent to 4/5?

A. 8/10 B. 6/8 C. 12/15 D. 40/50

5. If the length and width of the rectangle below were doubled, what would be the area of the enlarged rectangle?

A. 20 sq. cm. B. 40 sq. cm. C. 48 sq. cm. D. 96 sq. cm.

6. When M&M candies were divided equally among 10 friends, each person had less than 12 pieces. Which inequality, when solved, will help find possible numbers of M&M candies there were BEFORE being divided up? (M represents the number of M&M candies.) A. 12 ÷ 10 < M B. 12 ÷ M < 10 C. M ÷ 10 < 12 D. M ÷ 10 > 12

7. How wide (in cm.) is the umbrella at the right?

A. 110710

cm.

B. 1107

100 cm.

C. 1107

1000 cm.

D. 1107 cm.

- PLEASE TURN OVER – (page 1 of 2)

2 3 4

P

4 cm.

6 cm.

110.7 cm

/3×5=15

=

/A 13 C D

:Probability oneveryflipisindependentofeveryotherfip

.

✓=3

✓ ✓

/

:2×8=96 of 24×2×2=96

/

/

.

7=210

8. Using the Richter scale, if five earthquakes measured 5.2, 5.5, 6.4, 7.9, and 5.5, what would be the mode of those measurements? A. 2.7 B. 5.5 C. 6.4 D. 6.1

9. Which spinner pictured below most likely was used to produce the results in the table at the right?

SPINNER RESULTS

1 |||| |||| 10

2 ||| 3

3 |||| |||| 9

TOTAL 24

A.

B.

C.

D.

10. Roy, Sam, and Tom went to a carnival. If Roy spent $8 out of the $12 that he brought to the carnival, while Sam spent $9 out of his $15 and Tom spent $12 out of his $18, which boys spent the same fractional amount of the money that they brought to the carnival? A. Roy & Sam B. Roy & Tom C. Sam & Tom D. Roy & Sam & Tom

11. Annie found 1 quarter, 1 dime, 1 nickel and 15 pennies in her purse. What fractional part of a dollar did she find in her purse? A. 9/50 B. 1/2 C. 3/5 D. 11/20

12. In the coordinate plane, which one of the following ordered pairs represents a point that is 4 units from the point whose coordinates are (4, 5)?

A. (0, 4) B. (4, 0) C. (4, 9) D. (8, 9)

13. Gaye gave boxes of cookies away as gifts. She filled each of the boxes, b, with 12 cookies. Which expression below shows how many cookies in all that she gave away? A. 12 x b B. b ÷ 12 C. 12 ÷ b D. b + 12

14. Twenty-four students in the fourth grade each brought 18 cookies for a party. Which of the choices below is the closest estimate to the number of cookies that were brought to the party? A. 40 B. 100 C. 200 D. 400

15. Pikachu had 100 packets of Pokemon stickers. If each packet had 10 sheets of stickers and each sheet contained 8 stickers, how many stickers did Pikachu have? A. 80 B. 800 C. 8,000 D. 80,000

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED (page 2 of 2 – 2014 SMO 4th grade individual test #1)

1

3 2

1

3 2

1

3 2

1

3 2

✓only 5.5 occurs more thanoEe→F5isFmode( most frequent)

area fraction÷I <'

-

22 11 2

X

32:

-

[#3< ¥2 ) 22

.Needa spinnerX X where # is almostHof total

,and

¥3 is much bigger

#l > E) [ As >#1 ) than ¥2

✓

Roy :E= } ; Sam :Fs=2s ; Tom : ,Is=2z= =

/25+10+5+15=35+20--55 cents → 5¥ - zkoofadollar

/

±".edu's

ykllettilloner( slowed (4 higher) (4 right ,4 higher €i

12 cooky,

xbboxes = hxb cookies

/24×18×20×20=400

/100×10×8=1000×8--8000

Page 2 of 5


Fourth Grade - Individual Test 2

Problem Number

Answer

Explanation

1 A 31 x 13 = 403; tens digit = 0

2 B

3 C 3/4 = 75/100 = 0.75

4 A 6/16 = 3/8

5 A

6 B Every 7th day would be a Saturday. The twelfth multiple of 7 would be 84. Six needed to be added to 84 to get to the 90, thus the 6th day after a Saturday is a Friday.

7 D 144 ÷ 8 = 18 pages/night

8 B 12 x 365 ≈ 10 x 400 = 4,000 days

9 C To get to 4:00, add 0:17 to 3:43. From 4:00 to get to 4:14, add 0:14. 0:17 + 0:14 = 0:31 or 31 sec.

10 C

11 B Median = 3.5, Mode = 3, Range = 7, thus the mode has the smallest value.

12 C Since area is 4 sq. ft. and rectangle is a square, the length of one side must be 2 feet. Doubling 2 feet = 4 ft. Area would then be 4 x 4 or 16 sq. ft.

13 B “9” and “6” need to be switched to have the numbers sorted. Median would then be “6”.

14 D 20 x ? = 8,000,000; ? = 400,000

15 B

2014 Shoreline Math Olympiad Fourth Grade – Individual Test #2

1. In the product of 31 and 13, what is the value of the tens digit?

A. 0 B. 1 C. 3 D. 4

2. The weights of four watermelons were 5.2 lb., 5.03 lb., 5.12 lb., and 6.0 lb. What was the weight of the lightest watermelon? A. 5.2 lb. B. 5.03 lb. C. 5.12 lb. D. 6.0 lb.

3.

4. If a blindfolded person were to draw one ball from the sixteen balls shown below, what is the probability that a ball with a 2-digit number would be drawn?

A. 38

B. 35

C. 58

D. 1516

5. If 3.49, 3

4999

, and 3.5 were each rounded to the nearest whole number, what would be the rounded numbers?

A. 3, 3, 4 B. 3, 4, 4 C. 4, 3, 4 D. 3, 4, 3

6. If today was Saturday, what day of the week would it be 90 days from now? A. Thursday B. Friday C. Saturday D. Sunday

7. The book, The Cricket in Time Square, has 144 pages. If you want to read it in 8 days and read the same number of pages each night, how many pages would you have to read each night?

A. 8 B. 13 C. 16 D. 18

– PLEASE TURN OVER – (page 1 of 2)

Which one of the choices below is the measurement of the length of the paperclip shown in the one-inch ruler at the right?

A. 0.12 in. B. 0.34 in. C. 0.75 in. D. 3.4 in.

✓ :±:

0403/ =

5.20 5.03 5.12 6.00-

✓

24=75%-0:75of4¥2820=:

these 6outoflle

÷¥E

/

3.49<3.5 →3 ; 3479<34958-73; 3.5=3 'z→4

✓90=-7--12126

Rwaeksbdaysfom Saturday✓ tbdaysfom Saturday - Friday

k¥-7,÷=3¥ - 18

¥ 8*84÷4- 6:-

8. It takes the planet Jupiter about 12 earth years to complete an orbit around the sun. Using 365 days in an earth

year, about how many days does it take Jupiter to complete an orbit around the sun? A. 400 days B. 4,000 days C. 40,000 days D. 400,000 days

9. In 1913, the initial world’s record for running the mile was about 4 minutes, 14 seconds. Currently, the world’s record is about 3 minutes, 43 seconds. About how much faster is the current world’s record than the one that was set in 1913? A. 7 min., 57 sec. B. 1 min., 29 sec. C. 31 sec. D. 29 sec.

10.

11. Refer to the table below. Which measure, median, mode, or range has the smallest value?

Number 3 4 6 8

Frequency 5 3 1 2

A. median B. mode C. range D. They are all the same.

12. The area of a square is 4 square feet. What would be the area if the length of its sides were doubled? A. 2 sq. ft. B. 8 sq. ft. C. 16 sq. ft. D. 64 sq. ft.

13. What is the median of the following set of numbers: 4, 4, 4, 5, 9, 6, 10, 11, 11?

A. 4 B. 6 C. 7 D. 9

14. In the number, 8,000,020, how many times larger is the value of the digit “8” than the value of the digit “2”?

A. 4 B. 4,000 C. 40,000 D. 400,000

15. Which of the choices below is the closest estimate of the area (using the square units) of the handprint at the right?

A. 10 square units

B. 30 square units

C. 50 square units

D. 60 square units

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

(page 2 of 2 – 2014 SMO 4th grade individual test #2)

If the figure at the right were flipped over horizontally (left to right), which one of the choices shown below would be the same figure?

A. B. D. C.

r

rounding : 365×12×400×10=4000

/

4:14 . 3:43 = 4:14 - 4:00 1- 4:00 - 3:43 = 014+0.17=0 : 31

✓

⇒

✓mode : 3( largest frequency)

how many total range : 8.3=5 (biggest - smallest )times the -

Number occurs 's 11 median:4( needmiddleilembthoutofll, in order;first Stare }6this4 )

SUI 15 12 6 16 49

/ 4 3 5

4×2×2=16

✓inorder : 44456=910 11 4 ( 5th out of 9 items : 6)

r

8,00%000--8090200--400,000✓

.

i. =⇒÷

= .

2+6+8 +7+6+2 - 31×30

Page 3 of 5


Fourth Grade - Team Test 1

Problem Number

Answer

Explanation

1 12 50 x 12 = 600; 600/28 = 21 R 12.

2 2 Mode of 2nd lunch: $42; Median of 1st lunch: $40; $42 - $40 = $2 3 ¾ or 6/8 or

equivalent fraction

It takes 8 one-inch cubes to make one 2-inch cube. Eleven 2-inch cubes require 88 one-inch cubes, leaving 6 one-inch cubes left. Thus, 6/8 or ¾ of a 2-inch cube can be completed.

4 28 The whole number dimensions of a rectangle with area of 48 and their respective perimeters are: 1x48 with perimeter 98, 2x24 with perimeter 52, 3x16 with perimeter 38, 4x12 with perimeter 32, and 6x8 with perimeter 28. Thus, the smallest perimeter would be 28 inches.

5 273 68 – 2(21) = 26; 26/2 = 13. The area of the rectangle is 21 x 13 or 273 sq. in.

6 137 9 x 365 = 3,285; 3,285/24 ≈ 137 days. 7 $42 Flour: 2 x 5 x 40 = 400¢ or $4; Pecans: 2 x 5 x $2.50 = $25; Sugar: 5 x

25¢ = 125¢ or $1.25 ; Butter: 5 x $2 = $10; Vanilla: 5 x 35¢ = 175¢ or $1.75. $4 + $25 + $1.25 + $10 + $1.75 = $42.

2014 Shoreline Math Olympiad Fourth Grade – Team Test #1

1. It takes 28 inches of ribbon to make one ribbon bow. After making as many ribbon bows as possible from a 50-

foot roll of ribbon, how much ribbon (in inches) would be left over?

Answer: __________ inches

2. The table below shows how much student store sales were conducted during the first and second lunch periods during one week at a local middle school.

First lunch Second lunch Monday $45 $42 Tuesday $40 $42 Wednesday $23 $19 Thursday $34 $35 Friday $58 $38

What is the positive difference between the median sales at first lunch and the mode sales at second lunch for the week? Answer: $______

3. Anthony wanted to use all of the 94 one-inch cubic blocks that he found in a container to make larger two-inch cubic blocks. He found, however, after making as many two-inch cubic blocks as possible, that he had some blocks left over. With the left over blocks, what fractional part of a two-inch cubic block could he complete?

4. What is the smallest perimeter of a rectangle whose side lengths are whole number inches, and whose area is 48 square inches?

Answer: ________ inches


1”

1” 1”

2”

2” 2” Answer: ________

Area = 48 sq. in.

✓

50ft = 600 in

12zs #

RR

¥:8

✓ ' 2

In order : First lunch → 23 , 34 , 40,

45,

58

Median is 40

Second lunch → 19,

35, 38

,42

,42

Mode is 42

/ 40 - 42 / = 2

2

✓

using . HE

:T

✓

28To get smallest perimeter : area

ratio, get dose to a square .

I × 482×24

3¥:8 → 2 (6+8)=244 ) = 28

5. The length of the flat bottom of a rectangular cat box is 21 inches. If the perimeter of the box’s flat bottom is 68 inches, what is the area (in square inches) of the cat box’s flat bottom? Answer: ________ square inches

6. Carson sleeps about 9 hours per day. If he converted the number of hours he sleeps in a year into days, how many days would that be to the nearest day. Use 1 year as equal to 365 days.

Answer: _______ days

7. Using the recipe below as well as the table of costs for the ingredients, what would be the cost (in dollars) of the ingredients to make 5 batches of snowball cookies?

Answer: The cost of 5 batches of snowball cookies is $_______________

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED ( page 2 of 2 – 2014 SMO 4th grade team test #1)

Recipe for ONE batch of snowball cookies

2 cups all-purpose flour 2 cups finely chopped pecans 1/4 cup sugar 1 cup butter 1 teaspoon vanilla

Cost of ingredients

All-purpose flour 40¢ per cup

Finely chopped pecans $2.50 per cup

sugar 25¢ per ¼ cup

butter $2.00 per cup

vanilla 35¢ per teaspoon

✓

273Perimeter is 68in

lengthtwidthis

61=34in

2

Lengths 21in

→ width is34-21=13 in

Area is

21×13=273in2

✓

137 391×23×6=1085*3*5×137- 8

¥⇐a7

-Needed for 5 batches

Costforsbatd-

2×5=10 cups lox $0.40 -

$4.002×5=10 cups

10×5/2.50=5/25.00

tyx5=ETcups 5×510.25=151.25

1×5=5 cups 5×512.00=5/10.00

1×5=5 tsp 5x$O.35=$±$42.00

42.00

Page 4 of 5


Fourth Grade - Team Test 2

Problem Number

Answer

Explanation

1 D A C B

Changing the fractions in 24ths, Alisha completed 20/24 of the course, Beth completed 16/24 of the course, Carol completed 18/24 of the course, and Debbie completed 21/24 of the course.

2 (6, 1) (1, 4) (6, 4)

To create an area that is an odd number, both the length and width must be odd numbers. Thus the largest rectangle will have dimensions of 5 by 3 on the grid. The coordinates must then be (6,1), (1,4), and (6,4).

3 11:40 PM

From 8:33 PM to midnight is 3:27. From midnight to 2:47 AM is 2:47. 3:27 + 2:47 = 6:14. 6:14/2 = 3:07. 8:33 PM + 3:07 = 11:40 PM.

4 270 12 x 30 = 360; 360 – 2(3 x 15) = 270 sq. cm. 5 $285 The design contains two 5x10 tiled rectangles, thus each design contains

100 tiles. 3 x 100 = 300 tiles. 300 x 95 cents = 28,500 cents or $285. 6 3

Number of folds Thickness in mm 0 0.1 1 0.2 2 0.4 3 0.8

7 1/6 The multiples of 3 that are even are actually multiples of 6. These are 30, 42, 48, and 54. Since there are 24 numbers on the card, the probability is 4/24 = 1/6.

2014 Shoreline Math Olympiad Fourth Grade – Team Test #2

1. Alisha, Beth, Carol, and Debbie ran in a 10-kilometer race along a straight course. After half an hour, Alisha had completed five-sixth of the course, Beth had completed two-thirds of the course, Carol had completed three-fourths of the course, and Debbie had completed seven-eighths of the course. Using A for Alicia, B for Beth, C for Carol, and D for Debbie, list the order in which they find themselves in the race from closest to the finish line to farthest from the finish line. Closest to the finish line: ______ 2nd closest to the finish line: ______ 3rd closest to the finish line: ______ Farthest from the finish line: ______

2. In the grid at the right, using the point at (1,1) as a vertex, identify 3 other vertices on this grid (with whole numbers as coordinates) that forms the largest rectangle whose area is an odd number. Answer: (____, ____)

(____, ____)

(____, ____)

3. What is the time exactly half way between 8:33 pm and 2:47 am? Make sure to label your answer with “pm” or “am”. Answer: ___________


0 1 2 3 4 5 6

(1,1)

1

2

3

4

5

r

A = I = 20D 6 24

B=§=16

A 24C=¥=1824

CD= } = I

24B

D > A > c > B

?

× ,-.

. . - - - . - . . ...

;. |. ← area is only 15. ;

!

#→ area is # 2=17

50 : i

6 4'

- - - - -- - - - - - - - '

i [ answer key :( 6,1) ;(1.4); ( 6,4) ]

2 5

✓

833pmzt_247am.sc:33/m+l4:47pm_11:40pm 2

=22:80_pm2

= 11:40pm

11:40pm - 8:33pm = 3:07✓

2:47am - 11:40pm =3 : 07

4. Find the area (in square centimeters) of the figure below.

Answer: ______ square centimeters

5. Sue decided to tile three different walls in her home with the tiled design shown below. If each tile costs 95 cents, how much would just the tiles cost to complete the job? Write your answer in dollar ($) form.

6. A piece of paper is 0.1 mm thick. How many times must it be folded so that the folded paper is more than ½ mm thick? Answer: ________ times

7. Bingo is a game of chance played with randomly drawn numbers (from 1 through 75) that players match against numbers that have been pre-printed on cards. Using the card shown below, and assuming the first number drawn is on your card, what is the probability that this drawn number is a multiple of 3, and is an even number? Express your answer as a fraction in lowest terms.


( page 2 of 2 – 2014 SMO 4th grade team test #2)

Answer: $_______

12 cm

15 cm

15 cm

12 cm

3 cm

3 cm

3 cm

3 cm

Answer: _____________

✓

- - - - . . . .

A 12×(121.15+3) - 2( 3×15 )Assume this is

12cm ; could be-12×30-2×45

anything >6cm- - . . - - . . .

= 360.90

= 270

270

r

285 -(0×5)+(10×5)=50+50--100 tiles

^

F| 100×954=1595 per wall

5 10 For 3 walls :5195×3=51285±k÷io'

'→|3w=#×(ioxsi.io#hjtaIxftFe5xF*

d

k-5→l 3×1,0*95=3×95--285✓

Fold ¥1 : 0.1mm → 0.2mm < 0.5mm

2 : 0.2 → 0.4 <

33 : 0.4 → 0.8 >

lo8to¥)=z3z , ..→2 folds are insufficient;

log 2 3 folds are sufficient

✓

1-6

multiple of 3 and even - multiple of 1cm(2,31=6

/ "

¥¥§.dk/4outof5xs.i=z4-s4y=toD

(2014 SMO 6th grade answer key page 1 of 3)

2014 Shoreline Math Olympiad Sixth Grade – Answer Key

Note that parts of answers in parenthesis are NOT necessary for a correct answer. They are units, but if the wrong units are listed, then that makes the answer incorrect. Mental Math Test #1 #1: 12 A variety of ways to solve this; could multiply 3/5 x 20/1 which is 60/5 = 12. #2: 9 3 cubed would equal 27, and 3 is the square root of 9. #3: A trapezoid All types of trapezoids are acceptable answers. Mental Math Test #2 #1: -11 55 – 17 = 38; 38 – 13 = 25; 25 – 47 = -22; -22/2 = -11. #2: 0.75 (or .75) 3/1, 3/2, and 3/3 are not proper fractions; ¾ would be the greatest = 0.75. #3: 65 (degrees) The sum of all internal angles of a triangle = 180 degrees; a right triangle has

one 90 degree angle and this one has a second angle of 25; 180 – 90 – 25 = 65. Individual Test #1 #1: B. 1 7/8 5/2 x 3/4 = 15/8 = 1 7/8. #2: D. 85 10 + 12 + 14 + 15 + 16 + 18 = 85. 11, 13, 17, and 19 are prime and therefore not added. #3: C. 64 ounces for $125 By approximating, you can see that choices A, B, and D are all over $3 per ounce;

choice C is just under $2 per ounce. #4: A. 13 A cube has 8 vertices (corners) and a square pyramid has 5 (it doesn’t matter if the

pyramid is regular or irregular), 8 + 5 = 13. #5: C. 294 meters If 1 is at the beginning and 1 is at the end, 4 are in the middle creating 5 equal gaps

between the friends; 1470/5 = 294. #6: D. (Q – 2) ÷ 3 This is the only expression that accurately shows the value of Y when any of the

examples of the value of Q are substituted. #7: B. 2,086 24 hours for 1 day + 10 hours + 46 minutes; 34 hours & 46 minutes; 34 x 60 +46, 2,040 +

46 = 2,086 minutes.

#8: B. < 1.1 < In choice A, 1.8 is equal to not greater than 1 4/5; in choice C, 0.7 is not greater than ¾;

and in choice D, 0.29 is not greater than 2/6. #9: D. 2 : 5 There must be 10 Ghost (40 – 25 – 5 = 10), and there are 25 Carolina Reapers; 10 : 25

reduces to 2 : 5. #10: B. 1,800,000 miles² Base x Height = area of the parallelogram; 3,000 x 600 = 1,800,000; or could break the

shape up into rectangles and right triangles.; to simplify operations, could factor out by tens from the numbers and factor them back in later.

#11: C. -8 > -6 -6 is larger than -8 so this is false; choice D is true (mean of 2 middle numbers of a set with an even number of members is the median of that set; choice A is trueÆ least common denominator is 12.

#12: A. 22% Substitute X for amount Sheldon ate or any number, then Eugene ate 2X and Patrick ate 6X; X + 2X + 6X = 9X = total amount of pickles eaten; Eugene ate 2X/9X or 2/9ths of the pickles = 0.22222 . . . . which is closest to choice A which can be seen by approximation.

#13: D. 5/36 The length of the divisor bar indicates order of operations: you must first find the result of dividing 1 4/5 by 3/8 and then divide 2/3 by that result for the final answer; 1 4/5 divided by 3/8 = 9/5 x 8/3 = 72/15 = 24/5 in most reduced form; 2/3 divided by 24/5 = 2/3 x 5/24 = 10/72 = 5/36 in most reduced form.

#14: C. 18 cubic feet Convert all measurements to feet or inches then multiply; feet Æ 2 x 1.5 x 6 = 18 cubic

=


feet; inches Æ 24 x 18 x 72, don’t have to do since estimating shows the number to be much greater than any choice listed for cubic inches.

#15: A. 4 If one side is always 8 cm then the other 2 sides must total 16 cm; side lengths of 15-1-8, 14-2-8, 13-3-8, and 12-4-8 are not possible; 11-5-8, 10-6-8, 9-7-8, and 8-8-8 are possible = 4 different sized triangles; 7-9-8 would be the same size as 9-7-8.

Individual Test #2 #1: B. 200 Could add them one at a time or see that they average 20; 20 x 10 = 200, or see the pair

pattern where each add up to 40 (11 + 29 =40, 13 + 27 =40, etc. . . , 5 pairs of 40 = 200. #2: D. 1/2 What happens in any individual coin toss is not influenced by what happened before it;

there is a 1/2 chance it will be heads and a 1/2 chance it will be tails. #3: D. 71.53 Multiplying 3,576.2 with 0.02 = 71.528; rounding two places to the right of the decimal

point Æ round up to 71.53. #4: B. 18 inches 75% of 32 = ¾ (or 0.75) x 32 = 24 inches high on the first bounce; 75% of 24 = ¾ (or 0.75)

x 24 = 18 inches high on the second bounce.

#5: A. 8.3 (2 = 13/5, (4 x 13/5) – (3 x 0.7) = 52/5 – 2.1 = 10.4 – 2.1 = 8.3.

#6: C. circle A circle has an infinite number of lines of symmetry.

#7: A. 9 Order of operations: expressions in parenthesis, then multiplication and division, then

addition and subtraction; 6 x 4 = 6

4 = 10

= 9

.

#8: B. 90 cubic feet H x W x L = volume of a rectangular prism; tripled height and doubled width Æ 3H x 2W x L (or depth) = the previous volume x 6; 15 x 6 = 90 as the new volume. Could also substitute numbers to see affect on volume.

#9: D. 16 8 oz = 1 cup, 16 oz = 1 pint, 32 oz = 1 quart; 32 + 32/2 oz = 1 ½ quarts = 48 oz; 48/3 = number of 3 oz servings = 16.

#10: A. (0,2) (1,4) (3,8) (X,Y) points where no other choice follows a linear relationship; choice A shows for every 1 increase in X, Y increases 2.

#11: C. 2 x 2 x 3 x 5 x 7 All these numbers are prime and their product is equal to 420; choices A and D contain a non-prime number, choices B and D do not have products of 420.

#12: A. 112 0.6 x 40 games = 24 goals outscoring their opponents, 136 – 24 = 112. #13: C. 25 The floor covers 100 square feet and each 2 foot tile covers 4 square feet; 100/4 = 25. #14: B. 40 m.p.h. Traveling at 60 m.p.h. for 60 miles took 1 hour; Traveling at 30 m.p.h. for 60 miles took 2

hours; total trip took 3 hours and covered 120 miles for an average rate of 40 m.p.h. #15: D. 112 sq. ft. The object is a tetrahedron (4 congruent equilateral triangular faces); find the area of

one face and multiply by 4; area = ½ x h x b = ½ x 7 x 8 = 28 sq. ft. for the face; 28 x 4 = 112 sq. ft.

Team Test #1 #1: 1969 Trial and error method can be used,or could solve by calling her age “X”; then + 27 = x

and solve for x; multiply each side of the equation by 5 Æ 2x + 135 = 5x, subtract 2x from each side of the equation Æ 135 = 3x, divide each side of the equation by 3 Æ 45 = x, so she is 45; 2014 – 45 = 1969 is the year in which she was born.

#2: 4.1 (seconds) 1.2 minutes = 1.2 x 60 seconds (per minute) = 72 seconds, 300 feet = 100 yards; so:

= where solving for x finds seconds to run 100 yards; cross multiply 72 x 300 =

5,280x, 21,600 = 5,280x, dividing each side of the equation by 5,280 yields x = 21,600 / 5,280 or 4.09 seconds, rounding to 4.1.

#3: Roacho de Gama, by 3.9 (inches) If the pizza has an area of 254. 4 = πr², 254. 4/ .14 = r², 81 = r², 9" = radius and diameter is 18”; Roacho traveled a total of 2 diameters or 6 inches; Roachleigh traveled two radii plus 2/8 or ¼ of the circumference (πD); 18 ( .14 x 18)/4


= 18 56.52/4 = 18 14.1 = 2.1 ” traveled by Roachleigh; 6 – 32.13 = Roacho traveled longer by 3.87 inches which rounds to 3.9 inches.

#4: 7 ½ (hours or 7.5 hours) Weeding rate is 27 hours per 6 acres, 27/6 = 4.5 hours of weeding per acre, 4.5 hours/3 = time needed for 3 individuals to weed 1 acre = 1.5 hours per acre, 1.5 x 5 acres = 7.5 hours.

#5: 25 (binturongs) 18 had popcorn less those that had both(7) = 11 ate just popcorn; 13 had figs less those that had both (7) = 6 ate just figs; 11(popcorn) + 6(figs) + 7(both) +1(neither) = 25.

#6: 80 (kids) 1 represents 1/ of those who don’t like yellow jacket soup, 26 would be the other 2/ who do, 13 + 26 = 39; 39 represents 75% or ¾ of the remaining kids who don’t like mealworms, 13 would be the other ¼, 39 + 13 = 52; 52 represents 65% of all the kids, .65 times x (total # of kids) = 52, x = 52/.65, x = 80.

#7: 19 (slabs) Each slab covers 21 sq. ft. (7 x 3 = 21), 380/21 = number of slabs need = 18.095 so 18 not enough, need at least 19; can make a rectangular shape with just 19 by using 7 slabs oriented in one direction (covering a 21’ x 7’ area) and 12 slabs oriented in the other direction (covering a 21’ x 12’ area); area covered is 21’ by 19’ for a total area of 99 square feet ≥ the 80 sq. ft. minimum.

Team Test #2 #1: 144 Square Miles (sq. mi. or mi.²) A cube with a side perimeter of 24 has a side length of 6; half of a cube

with a side of 6 would have a top and bottom measuring 6 x 6 = 36 sq. mi. for top and 36 sq. mi. for bottom; the four other sides would each measure 6 x 3 = 18 sq. mi. per side; 36 + 36 + (4 x 18) = 72 + 72 = 144 square miles of total surface area for each half.

#2: 20(%) Weight of grease from 2 pounds = 1 lb. 3 1/4 ounces less jar weight of 12 7/8 ounces; 19 2/8 – 12 7/8 = 6 3/8 of grease from 2 lbs. of bacon; 3 3/16 grease per pound; 3.1875 ounces / 16 ounces = .1992187 which rounds to 20%.

#3: 12 (kilometers) The circumference of a circle = π x Diameter, so = πD/2, 66 = πD, D = 66/ .14 = 21.019… and so the diameter of the race half circle, which is the path Spear took, is very close to 21; 33 – 21 = 12 kilometers shorter than the race course.

#4: 3 : 6 : 1 Add up the total number of animals using variable x to represent number of koalas; 18 + 2x + x + 8 + 2x/6(simplified to x/3) = 56, 26 + 3x + x/3 = 56, 3x + x/3 = 30; could solve through trial and error or multiply each side of equation by 3, 9x + 3x/3 = 90, 10x = 90, x = 9 = number of koalas; therefore 18 wombats, 18 kittens, 9 koalas, 8 chinchillas, and 3 porcupines; ratio of koalas to wombats to porcupines is 9 : 18 : 3 which reduces to 3:6:1.

#5: 42 (miles per hour) Find total distance traveled first; at 60 mph you travel at 1 mile/minute, but the cheetah only was at that speed for 2/3 of a minute so it traveled 2/3 mile; at 5 mph you travel 5/60 miles per minute or 1/12 of a mile, but the cheetah was only at that speed for 1/3 of a minute so it traveled 1/36 of a mile; 2/3 + 1/36 = 25/36 of a mile traveled in a minute; multiply by 60 to convert to miles per hour = 1500/36 = 41.6666 which rounds to 42 mph.

#6: 44.4(%) There are 36 different combinations of what will show on the dice; add the combinations that have a 6 or add to 6; 1-6, 2-6, 3-6, 4-6, 5-6, 6-6, 6-1, 6-2, 6-3, 6-4, 6-5, 1-5, 2-4, 3-3, 4-2, 5-1; 16 of the 36 possible combinations work, 16/36 = 0.44444, which rounds to 44.4%.

#7: 0.006 Area of a circle is πr²; area of pen = .14 x 10 ft² = .14 x 100 = 14 sq. ft.; area of the bottom of a pizza = 3.14 x 0.75ft² = 3.14 x 0.5625 = 1.76625 sq. ft.; 1.76625 / 314 = 0.005625 which rounds to 0.006.

2014 Shoreline Math Olympiad Sixth Grade – Mental Math Test #1

Question #1: What is three fifths of twenty? Question #2: The square root of a number is cubed and is equal to 27. What is

the number?

Question #3: A figure has four sides with only one pair of sides being parallel to

each other. What is the figure?

2014 Shoreline Math Olympiad Sixth Grade – Mental Math Test #2

Question #1: Fifty-five (55), subtract seventeen (17), subtract thirteen(13),

subtract forty-seven (47). Divide that result by two (2). What is the final result?

Question #2: Convert the greatest proper fraction with a numerator of three

into decimal form.

Question #3: An interior angle of a right triangle is 25 degrees. What is the

measure of the smaller of the two other interior angles?


2014 Shoreline Math Olympiad Sixth Grade – Individual Test #1

1. What is five halves of three fourths? A. 15/4 B. 1 7/8 C. 3/10 D. 3 1/3 2. What is the sum of all composite two digit numbers less than 20? A. -7 B. 0 C. 60 D. 85 3. At the Mega Munchin’ Mart, pickled squid eyes come in cans of various sizes. Assuming you were going to eat it

all, which can listed below is the least expensive per ounce? A. 3 ounces for $10 B. 7 ounces for $25 C. 64 ounces for $125 D. 144 ounces for $450 4. At the vertex party, a cube showed up with an irregular square pyramid. How many total vertices did the couple

have? A. 13 B. 8 C. 11 D. 10 5. Stella Tonne slid head first down an icy track that was 1,470 meters long. If she had 6 friends evenly spaced

along the side of the track to cheer her on with one at the beginning and one at the end, how far apart would each friend be from the next closest friend?

A. 210 meters B. 245 meters C. 294 meters D. 367.5 meters 6.

Q 8 17 2 11 Y 2 5 0 3

Using the information in the chart above, which expression can be used to calculate the value of Y for any given

value of Q? A. (Q ÷ 2) – 2 B. 4 x Y + (Q ÷ 2) C. 2 x (Q ÷ 4) – 2 D. (Q – 2) ÷ 3

7. How many minutes must pass from the time of 7:21 p.m. on a Saturday until it is 6:07 a.m. of the next Monday? A. 2,486 B. 2,086 C. 806 D. 646

8. Which inequality expression below is correct?

A. 1.8 > 1 > 1.45 B.

< 1.1 < C. 0.6 <

< 0.7 D.

> 0.29 >

(page 2 of 2 - 2014 SMO 6th grade individual test #1)

9. There are 40 peppers of three different types (Carolina Reapers, Ghost, and Tiger Paw) in Madame la Boomba’s

spicy pot. 25 are Carolina Reapers and 5 are Tiger Paw. What is the ratio of Ghost Peppers to Carolina Reapers? A. 1 : 3 B. 10 : 40 C. 25 : 10 D. 2 : 5

10. 800 miles 600 miles Å 2,200 miles Æ The figure above represents the 3rd largest parallelogram in our solar system. What is its area? A. 1,320,000 miles² B. 1,800,000 miles² C. 2,280,000 miles² D. 2,040,000 miles² 11. Which statement listed below is false?

A. The least common denominator of the fractions and is not 24

B. = 0.1250

C. -8 > -6 D. The median of 4, 6, 1, and 0 is 2.5 12. A barrel full of squeaky pickles were eaten by three individuals. If Sheldon ate half as many as Eugene, and

Patrick ate three times as many as Eugene, then approximately what percentage of the squeaky pickles did Eugene eat?

A. 22% B. 33% C. 40% D. 15 %

13.

= ? 1 ÷

A. 9/20 B. 80/81 C. 3 1/5 D. 5/36

14. Count Dracula’s new traveling coffin is a bit too cramped for his liking. It is a rectangular prism shaped box that

is 24 inches wide, 18 inches tall and 6 feet long. What is the volume of the coffin? A. 12 cubic feet B. 114 cubic inches C. 18 cubic feet D. 216 cubic inches

15. A triangle has whole number side lengths with at least one side 8 centimeters in length. How many different

sized triangles could be formed if the triangle has a perimeter of 24 centimeters? A. 4 B. 2 C. 16 D. 8



2014 Shoreline Math Olympiad Sixth Grade – Individual Test #2

1. What is the sum of 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29? A. 167 B. 200 C. 227 D. 270 2. A fair coin is flipped high into the air and lands on the ground heads side up. It is tossed in the same way 8 more

times and each time lands with the heads side up. What is the probability that the tenth coin toss will also result with the coin landing with its heads side up?

A. 1/1,024 B. 1/1,000,000 C. 1/10 D. ½

3. What is the product of 3,576.4 and 0.02 rounded to the nearest hundredth? A. 100 B. 178,800 C. 400.420 D. 71.53 4. Mel’s meatballs don’t taste very good, but they do bounce well. In fact, they bounce upward 75% of the

distance of the height they fall from. If one rolls off a table that is 32 inches tall, how high will the meatball get after its second bounce?

A. 10 inches B. 18 inches C. 15 inches D. 24 inches

5. If R = 0.7 and K = 2 , then what is 4K – 3R equal to?

A. 8.3 B. -2.4 C. 2 D. 6

6. Which shape listed below has the most lines of symmetry? A. octagon B. right triangle C. circle D. regular pentagon

7. 6 = ?

A. 9 B. 19 C. 7

D. 12

(page 2 of 2 - 2014 SMO 6th grade individual test #2)

8. A rectangular prism shaped stick of butter has a height of 3 feet and a volume of 15 cubic feet. If the height of

the stick of butter is changed to 9 feet and its width is doubled while keeping its depth the same, what is the new volume of the stick of butter?

A. 75 cubic feet B. 90 cubic feet C. 180 cubic feet D. 195 cubic feet 9. Balok is down to his last 1 ½ quarts of Tranya and wants to know how many servings he has left. Since there are

8 ounces in a cup, 2 cups in a pint, and 2 pints in a quart, how many 3 ounce servings does he have left? A. 32 B. 48 C. 24 D. 16 10. Which set of points are on a straight line in a coordinate plane? A. (0,2) (1,4) (3,8) B. (2,1) (1,2) (2,3) C. (2,2) (3,5) (7,7) D. (3,0) (6,0) (0,3) 11. What is the prime factorization for the number 420? A. 5 x 7 x 12 B. 2 x 3 x 5 x 7 x 11 C. 2 x 2 x 3 x 5 x 7 D. 1 x 4 x 5 x 19 12. Over the course of a 40 game season, the Pataha Peacock Spiders hockey team scored a total of 136 goals. If

they averaged scoring 0.6 goals more than their opponents per game, how many total goals were scored by their opponents for the season?

A. 112 B. 124 C. 108 D. 122 13. The floor space at the “Things Found in the Back of the Refrigerator” e hibit at the museum is square and

measures 10 feet on a side. What are the fewest number of stink-proof square tiles that measure 2 feet on a side that are needed to completely cover the floor?

A. 100 B. 50 C. 25 D. 5 14. Samantha the Slow Loris, going to her ski chalet, traveled at an average rate of 60 miles per hour for 60 miles on

her rocket skateboard. She then ran out of rocket fuel and traveled on her solar powered unicycle at an average rate of 30 miles per hour for another 60 miles, and arrived at her destination. What was her average rate of speed for the trip?

A. 35 m.p.h. B. 40 m.p.h. C. 45 m.p.h. D. 50 m.p.h. 15. The giant 4-sided die that Gary is making in his garage is a triangular pyramid whose base measures 8 feet on

each edge, and each face is congruent. It is approximately 7 feet from the top of the pyramid to the midpoint on one of the edges of the base. What is the approximate total surface area of the giant die?

A. 176 sq. ft. B. 148 sq. ft. C. 140 sq. ft. D. 112 sq. ft.



2014 Shoreline Math Olympiad Sixth Grade – Team Test #1

1. At her birthday party on March 8, 2014, when Narcissus was asked how old she was, she would just reply that

she was only 2/5th of her age plus another 27 years old. In what year was Narcissus born? 2. Wanting to be more powerful than the Seahawks “Beast Mode”, the Bainbridge Barnacles football team have

found Trangor, a 17,000 pound, 42 foot tall monster who causes structural damage with every step taken. If Trangor can run a mile in 1.2 minutes, how long will it take him to run 100 yards, assuming he runs at a constant rate? Round your answer to the nearest tenth of a second. (note: there are 5,280 feet = 1 mile, and 3 feet = 1 yard).

3. “I have crossed the Great Pizza of Brad’s dorm room when it was whole and hot, crossing straight through its

centermost point and returned on the same path alive!”, proclaimed Roacho de Gama. “Big deal. I have explored the entire perimeter of the two remaining connected slices of the Great Pizza!”, boasted Sir Walter Roachleigh. The pizza, when whole, was circular with an area of 254.34 square inches, and cut into 8 equal slices. Which explorer covered the most distance AND, rounded to the nearest tenth of an inch, how much longer was that distance? (use π = 3.14)

4. Those pesky roses keep sprouting in the witch’s 6 acre garden. It would take the witch 27 hours to weed out all

of the roses if she has to do it herself. Instead of that, she uses her powers to force the Gingerbread Man, Pinocchio, and the so hot right now Hansel to do her evil weeding. If those three each weed at the same rate as the witch, how many hours will it take the three of them to weed out the roses in just 5 acres of her 6 acre garden?

5. Smelling popcorn coming from a movie theater, a group of hungry half-bear, half-cat like creatures called

binturongs, felt at home and wandered in to watch a midnight showing of “Manos, the Hands of Fate”. Once inside, 18 biturongs ate popcorn, 13 biturongs ate figs, 7 ate both popcorn and figs, and one hated the movie and left without getting anything to eat. How many biturongs wandered into the theater?

(page 2 of 2 - 2014 SMO 6th grade team test #1)

6. Thirty-five percent of the kids at Camp Mi-T-Hungry come running for the rich taste of squirrel. Twenty-five

percent of the remaining kids come running for the rich taste of mealworms. 2/3 of those who don’t come running for the rich taste of squirrel or mealworms, come running for the rich taste of yellow jacket soup. If thirteen (13) kids don’t come running for any of those rich tastes, how many kids are at Camp Mi-T-Hungry?

7. Han needs a new driveway surface for his Ford Falcon because his old one was not entirely stable. He wants to

build it out of slabs of carbonite that measure 3 feet wide by 7 feet long. The new driveway surface must be rectangular, at least 18 feet wide and at least 18 feet long, and cover a minimum of 380 square feet. What is the fewest number of carbonite slabs he must order from Bespin Enterprises to do the job?



2014 Shoreline Math Olympiad Sixth Grade – Team Test #2

1. A Vogon cruiser, the shape of a cube, hovers over Squidlandia with one face parallel to the ground. One face of

the cube has a perimeter of 24 miles. Taking no pleasure, Marvin slices the cube into two congruent halves with a horizontal cut parallel to the ground from his 42 mega-bleem laser. What is the surface area of one of the resulting halves?

2. Boss Hogg cooked up 2 pounds of bacon for his pre-breakfast snack, poured the liquid grease that came out of

the bacon into a jar, and found that jar with the grease in it weighed 1 pound and 3 ¼ ounces. If the jar weighs 12 7/8 ounces when empty, what percent of 1 pound of un-cooked bacon turns into liquid grease when cooked? Round your answer to the nearest percent (i.e. 85.4% would round to 85%) and note there are 16 ounces per pound.

3. In the Tour de Half-Arc, bicyclists must ride a 33 kilometer course that is half of a circle. Spear Strongleg decided

to use his mountain bike and rode a direct path from the starting point to the finish line. To the nearest kilometer, how much shorter was the distance Spear traveled than the other bicyclists? (use π = 3.14)

4. At the Cute-n-Fuzzy competition, 18 wombats were present. There were also twice as many kittens as koalas, 8

chinchillas, and some delusional porcupines, who came to the competition. The number of porcupines present were equal to 1/6 the number of kittens, and there were a total of 56 animals at the competition. In simplest form, what was the ratio of koalas to wombats to porcupines at the competition?

5. A cheetah is jogging along at 5 miles per hour for ten seconds until it spots an impala it wants to catch. The

cheetah then speeds up and averages 60 miles per hour for the next 40 seconds while it chases the impala. Its prey gets away and the cheetah slows back down to an average of 5 miles per hour for ten seconds. Rounded to the nearest mile per hour, what is the cheetah’s average speed for the entire minute?

(page 2 of 2 - 2014 SMO 6th grade team test #2)

6. Two fair, standard six-sided dice, each side with a single number 1 through 6, are rolled. What percent of the

time would one expect a number 6 to be showing or the sum of the two dice showing to be 6? Round your answer to the nearest tenth of a percent.

7. “The pie is falling, the pie is falling” cried Chicken Little while running around an open aired, circular-shaped free

range pen. Large, circular pizza pies, some with anchovies, with an 18 inch diameter where indeed falling flat, cheese side down, randomly inside at least part of the pen. If the pen is 20 feet in diameter, what is the probability, with 0 being impossible and 1 being certain, that a falling pizza pie landing flat on its cheese side will hit any given point in the pen? Round your answer to the nearest thousandth and use π = 3.14.


Page 1 of 9


7th/8th Grade Answer Keys

Individual Test #1

# Answer 1 D 2 C 3 B 4 B 5 C 6 C 7 A 8 C 9 D

10 A 11 A 12 D 13 D 14 B 15 B

Individual Test #2

# Answer 1 D 2 B 3 B 4 A 5 C 6 B 7 D 8 B 9 B

10 C 11 D 12 D 13 A 14 C 15 B

Mental Math #1 Mental Math #2

# Answer 1 14 2 13 (inches) 3 7

Team Test #1 Team Test #2

# Answer 1 1 hr, 51 mins 2 60 3 24.87 or 24.88 cm 4 68 5 1,224 6 1/13 7 18

# Answer 1 39 2 1/36 3 40 (degrees)

# Answer 1 1/10 (or 0.1) 2 3 3 68 degrees 4 4,096 5 195.5 6 Saturday 7 box

Page 2 of 9

2014 SMO 7th/8th GRADE INDIVIDUAL TEST # 1 -- SOLUTIONS

1. D 3x5x5 + 4x5 +12 = 75 + 20 + 12 = 107

2. C – =

and - = Then

=

x =

3. B x

= = 21.75

4. B =0.778, = 0.785, 0.80, = 0.833

5. C (1) Probability of drawing a 10 from a deck of cards = =

Probability of (1) and (2) = x

=

6. C 540 = 2x2x3x3x3x5

7. A Fish tank is 30x12x12. Subtract 1 inch for rock and 2 inches for space from height so that

water volume = 30x12x9=3240 cubic inches 3240 cu in x = 54 minutes

8. C slope = =

= =

9. D |2x1-5| = |-3| =3 and |2x4-5| = |8-5| =|3| = 3

10. A 72 lbs + 58 lbs = 130 lbs. Food added = 18lbs + 8 lbs = 26 lbs. New total = 130 + 26 = 156 lbs.

156/130 = 1.20, so there was a 20% increase in food

11. A On the 8x8x8 cube, there are a total of 64x6=384 faces. There are 72 faces painted on only 2 sides.

Fraction of total blocks painted on 2 sides = =

12. D TWELVE = 6!/2! = 720/2 = 360

13. D Sum of interior angles of a triangle = 180o. Let a = smaller angle. Then 2a = larger angle

87 + a + 2a = 180. 3a= 93. a=31. Therefore, larger angle = 2x31= 62o

14. B (1.2)2 =

15. B Put equation into standard y=mx + b form, where m is slope and b is y-intercept: y = 2x + 3

Line B has a slope of 2 and a y-intercept of 3.

Page 3 of 9

2014 SMO 7th/8th GRADE INDIVIDUAL TEST #2 –SOLUTIONS

1. D Volume of a sphere = r3. If r=3, then volume =

x 27 = 36

2. B Average speed = total distance/total time. Total time = 30 + 20 = 50 mins

Road : ( hr x 90 mph) = 45 miles Gravel: (

hr x 60 mph) 20 miles. Total distance = 45+20=65 miles

Avg speed = 65 miles/50 mins x 60 min/hr = 78 miles per hour.

3. B Put equation into standard y=mx + b form, where m is slope and b is y-intercept: y = x – 4

The line intercepts the y axis at (0,-4)

4. A Probability of choosing Reecer’s = # Reecer’s / total # candy = 11/(15+7+11) = 11/33 =1/3

5. C Numbers that satisfy piles of 4, remainder 1 are: 5, 9, 13, 17, 21... Numbers that satisfy piles of 5, remainder 3 are: 7, 12, 17, 22, … Numbers that satisfy piles of 7, remainder 3 are: 10, 17, 24. The smallest number to satisfy all 3 is 17.

6. B To maximize area, make a square: 92/4 = 23 ft per side. Area = 23x23=529 sq. ft.

7. D 15 % off of $24: 24 - .15(24) = 24-3.6 = 20.40. Now take 10% off: 20.40 - .10(20.40) = 20.40-2.04= $18.36

8. B Radius of circle = 9. Constructing a right, isosceles triangle using the radii of the circle as legs, and using Pythagorean theorem, you get the length of one side of the square = 9√ or√ , Perimeter = 4x√

9. B 4(x-2) + 3x = 5(x+7) -11 Use distributive property to multiply out:

4x-8 + 3x = 5x + 35 – 11 Now gather x’s together: 2x = 32. Therefore, x=16

10. C Sequence is of form 2n+1, where n is the previous term. Next term = 2 x 95 + 1 = 191

11. D Use the points to create a right triangle, then use Pythagorean

Theorem to find the length of the diagonal. Horizontal leg = 5- (3) = 8. Vertical leg = 8-2=6. Hypotenuse =√ = 10.

Page 4 of 9

2014 SMO 7th/8th GRADE INDIVIDUAL TEST #2 –SOLUTIONS, con’t.

12. D There are many ways to solve this problem. Trial and error show there must be fewer than 8 adults; 3 @ $34 + 9 @$22 = 102 = 198 = 300.

13. A Volume of a cylinder = r2h. Substitute r=2k and h = h to get V= (2k)2( h) = 2 k2h

14. C Use a venn diagram to show 17 + 12 + 6 = 35. If there are 32 kids in the class, you double counted 35-33 = 3 kids

who like to do both activities 15. B Using similar triangles:

= Cross multiplying give you 8x = 144. Therefore, x=18 feet

6ft

8ft

24 ft

x ft

Page 5 of 9

2014 SMO 7th/8th Mental Math Solutions

Mental Math #1

1. 49 = r2 So, r=7 and d=2r = 14

2. Diagonal forms a right triangle with legs 5 and 12. Length of diagonal = √ = √ = 13

3. x + y = 19, xy = 84. x=7, y=12. The smaller number is 7

Mental Math #2

1. √ x √ + 6 = 3 x 11+ 6 = 33 + 6 = 39

2. Probability (heads) = 1/2. Probability of (sum of 11) = 2/36 = 1/18. Multiply together: 1/2 x 1/18 = 1/36

3. Pie is a circle. Central angle = 360 degrees. 360/9 = 40 degrees per piece.

Page 6 of 9

2014 SMO 7th/8th Team Test #1—Solutions 1. Pipe A can fill pool in 4 hours, or 1/4 pool per hour. Pipe B can fill pool in 6 hours, or 1/6 pool per hour Pipe C can fill pool in 8 hours, or 1/8 pool per hour

All 3 pipes working together = + + =

+ +

=

Inverting, you get

= 1 hours. To get minutes:

= so 13x =660 and x=50.76

Rounding, you get 1 hr, 51 mins. 2. We need a math team of two 7th graders and two 8th Graders. With combinations, “and” means multiply.

Choose two 7th graders = Choose two 8th graders = multiply together: 6 x 10 = 60

3. Distance from D C = 6cm.

If we view line BD as the hypotenuse of right triangle BCD, we can use Pythagorean theorem to find the distance from B D = 6√ (45-45-90 triangle, legs are in the ratio 1:1: √ ).

If we view line AB as the hypotenuse of right triangle BDA, we can use Pythagorean again to find the distance

from A B = √ √ = √ = √

Adding DC + BD + AB = 6 + 6√ + √ = 24.88 cm

4. let x and y be the scores on the next level. Then 56 + 64 + 63 + 59 + x + y = 63 6

So 242 + x + y = 378 and x+y = 136. Because we want the average of x and y, = 68

Page 7 of 9

2014 SMO 7th/8th Team Test #1—Solutions, con’t. 5. The minute hand sweeps 360 degrees every hour. 360 deg/60 min = 6 deg/ min

2:32 pm to 5:56pm is 3 hrs and 24 minutes.

3 hours x

= 1080 degrees

24 mins x

= 144 degrees 1080 + 144 = 1,224 degrees 6. 7 black + 4 brown + 2 yellow = 13 total puppies. Probability that first puppy is brown = 4 /13.

Now there are only 12 puppies left, 3 of which are brown. Probability that second puppy is brown = 3/12 = 1/4

Because we want first and second puppy to be brown, we multiply :

x =

7. Work backwards: 3 cookies were left at the end The last princess took 1/2 the remaining cookies, so there must have been 3 x 2 = 6 cookies The prince before that took 1/3 the remaining cookies, so there must have been 6 x 3/2 = 9 cookies The princess before that took 1/4 of the remaining cookies, so there must have been 9 X 4/3 = 12 cookies The Queen took 1/5 of the remaining cookies, so there must have been 12 X 5/4 = 15 cookies The King took 1/6 of the original cookies, so there must have been 15 x 6/5 = 18 cookies

Page 8 of 9

2014 7th/8th Team Test #2 –Solutions 1. 5 coins totaling 47 cents: must have 2 pennies, 2 dimes, 1 quarter

Probability of drawing a dime then a quarter = x =

or in decimal form 0.1

2. set up 3 equations: # heads = 2L + B + M = 17 # feet = 6L + 4B + 2M = 50 # tails = 2L + 3B + M = 27

We know there are 5 Buxbos, so substituting that into the equations, and solving for the 2 remaining variables gives 6 Moochies (and 3 Lorgats).

3. Refer to diagram at right: Angle x = 180-146 =34 Angle y = angle b = 102 Angle z=180-102 = 78 Angle w = 180-34-78 = 68 Angle c = angle w = 68 degrees 4. make a table, or use the formula n = k x 2(t/d) Where n= number of bacteria after t minutes,

k is number of bacteria at time zero d is the time in minutes that it takes the bacteria to double

For our problem, k=1, t=3hrsx60min/hr = 180 min, and d=15min

So n = 2 (180/15) = 212 = 4,096 5. The dog can roam a ½ circle of radius 10 + ¼ circle of radius 7. Area of ½ circle = ½ 100 = 50 Area of ¼ circle = ¼ 49 = 12.25 Adding together, you get 62.25 = 195.465 which rounds to 195.5 square feet

Page 9 of 9

2014 SMO 7th/8th Team Test #1—Solutions, con’t 6. Make a chart of how many miles after day and night:

Day After Day After night Tues 15 12 Wed 27 24 Thurs 39 36 Fri 51 48 Sat 63

They get to the city during the day on Saturday 7. Volume of box = 16x15x12 = 2880 cm3.

Volume of cylinder = 72x16 =2461.76 cm3. Volume of cone = 102x26 = 2721.33 cm3.

If the price is the same for all three, the best deal for the customer is the biggest one, which is the box

2014 Shoreline Math Olympiad Seventh/Eighth Grade – Mental Math Test #1

Question #1: What is the diameter of a circle with an area of 49 pi? Question #2: What is the length in inches of the diagonal of a rectangle with

side lengths of 5 inches and 12 inches?

Question #3: The sum of two numbers is 19 and their product is 84. What is

the smaller of the two numbers?

2014 Shoreline Math Olympiad Seventh/Eighth Grade – Mental Math Test #2

Question #1: What is the cube root of 27, times the square root of 121, plus 6?

Question #2: A coin is flipped and two six-sided dice are rolled. What is the

probability of getting heads on the coin and a sum of 11 on the die?

Question #3: A circular pie is cut along the radius into 9 separate, equal pieces.

What is the central angle of each piece of pie?

2014 Shoreline Math Olympiad Seventh/Eighth Grade –Individual Test #1

1. Evaluate 3x2 + 4x + 12 for x=5 A. 62 B. 152 C. 87 D. 107

2. Simplify: ( -

) ( -

)

A. 4/21 B. 10/7 C. 7/40 D. 21/30 3. In Superbowl XLVIII, the Seattle Seahawks beat the Denver Broncos 43-8. At the beginning of

the second half, Seattle’s Percy Harvin returned the kickoff for a touchdown, running 87 yards in 12 seconds. What was his average speed, in feet per second?

A. 7.25 B. 21.75 C. 5.53 D. 29.17

4. Rank these numbers from smallest to largest: 0.80, , ,

A. , 0.80, ,

, B.

,

, 0.80, C. , 0.80, ,

D. ,

0.80,

5. Sherlock Holmes is investigating a crime scene and looking for clues. He notices that the two, six-sided dice on

the table add up to 10, and his partner, John Watson notices that the top card on a deck of 52 cards is also 10. What is the probability that the killer drew a 10 and rolled a 10?

A. 25/154 B. 1/25 C. 1/156 D. 5/13 6. What is the prime factorization for the number 540? A. 4x27x5 B. 2x2x2x3x3x5 C. 2x2x3x3x3x5 D. 2x3x5x5 7. Darla is filling her fish tank to bring home her new fish, Nemo. Her fish tank is 30 inches x 12inches, and is 12

inches high. The instructions say to add a one inch layer of rock at the bottom, and leave 2 inches of space at the top of the tank. If her faucet can fill at the rate of 60 cubic inches per minute, how long will it take to fill her tank per the instructions? (assume a solid layer of rock on the bottom)

A. 54 minutes B. 60 minutes C. 66 minutes D. 72 minutes

8. What is the slope of the line that passes through the points (-3,2) and (9,10)?

A. -3/2 B. -2/3 C. 2/3 D. 3/2

But wait, there’s more! (Turn me over for more math fun) (page 1 of 2)

9. Which values of x will make the following equation true? |2x-5| = 3

A. -4, 4 B. 1,8 C. -3, 8 D. 1, 4

10. Robin the sea otter and his friends at the aquarium eat 72 lbs of fish per day and 58 lbs of clams per day. Two new sea otters were brought in, increasing the fish intake by 18 lbs and the clam intake by 8 lbs. What is the percentage increase of food that the sea otters eat per day?

A. 20 B. 25 C. 12 D. 30

11. Maria makes a 8x8x8 cube by gluing together 1x1x1 inch blocks, and paints the outside green. What is the ratio of the number of 1x1x1 cubes with only 2 painted sides to the total number of 1x1 faces showing on her bigger cube?

A. 3/16 B. 2/3 C. 3/32 D. 1/4

12. In how many different ways can the letters in the word TWELVE be arranged? A. 720 B. 120 C. 60 D. 360 13. George has drawn a triangle and labeled the angles A, B, and C. If angle A is 87 degrees and angle B is twice

angle C, what is the measure of angle B, in degrees?

A. 46.5 B. 31 C. 43.5 D. 62

14. The radius of circular disk is increased by 20%. What is the percent increase in the area of the disk?

A. 20 B. 44 C. 40 D. 24

15. On the following graph, which line best represents the equation 2y - 4x = 6?

A. Line A B. Line B C. Line C D. Line D

You are DONE! Great Job! (You may keep this copy for your very own) (page 2 of 2 – 2014 SMO 7th/8th grade individual test #1)

2014 Shoreline Math Olympiad Seventh/Eighth Grade – Individual Test #2

1. What is the volume of a sphere with a radius of 3 cm, in cubic centimeters?

A. 3 3 B. 12 C. 9 2 D. 36 2. The Batmobile can drive 90 miles per hour when driving on roads, but only 60 miles per hour when driving over

gravel. If Batman chased the Joker at top speeds for 30 minutes on roads, and 20 minutes on gravel before he caught the Joker, what was his overall average speed for the entire chase, in miles per hour?

A. 63 B. 78 C. 56 D. 75 3. At what point does the graph of the equation 3x - 5y = 20 cross the y-axis? A. (0, 20) B. (0,-4) C. (4, 0) D. (-4,0) 4. Math coach Patty hands out candy at every math club. She has a bag with 15 Snicklers bars, 7 Herchay’s

chocolate bars, and 11 Reecer’s peanut butter cups. Smartie Suzie answered a question correctly and gets to choose a piece of candy randomly out of the bag. What is the probability that Suzie will choose a Reecer’s?

A. 1/3 B. 15/33 C. 7/22 D. 1/4 5. Chekov has a collection of tribbles. He can make piles of 4 with 1 left over, piles of 5 with 2 left over, or piles of 7

with 3 left over. What is the smallest number of tribbles that Chekov could have?

A. 12 B. 9 C. 17 D. 25 6. Joe needs to build a rectangular pen for his pet snorgleplat. He has 92 ft. of fencing.

What is the largest area of pen that he can make with this fencing, in square feet?

A. 484 B. 529 C. 528 D. 576

7. Lovely Lisa was buying pies to celebrate Pi Day on March 14th. The regular price of the pies she wanted was $24,

but the store had a 15% discount. Lisa also used a coupon that gave her 10% off the discounted price. What was the final price of the pies?

A. $18.00 B. $20.40 C. $24.50 D. $18.36

You know the drill: Flip me over for more test questions (page 1 of 2)

8. A square is inscribed inside a circle with an area of 81 , as shown in the picture. What is the perimeter of the square?

A. 81 √ B. 4 √ C. 162 D. 18

9. Solve for x: 4( 2) + 3x = 5(x + 7) 11

A. 6 B. 16 C. 8 D. 12.

10. Give the next number in the sequence: 11, 23, 47, 95, . . .

A. 139 B. 153 C. 191 D. 127

11. What is the distance between the points (-3,2) and (5,8) ?

A. 14 B. 8 C. 7√ D. 10

12. A group of 12 people are going to see the Macklemore concert at the local thrift shop. Tickets are $22 each for children and $34 each for adults. If the group spent $300 on the concert, how many adults were in the group?

A. 9 B. 5 C. 11 D. 3

13. If a right cylinder with a circular base has a radius k and a height h, which would be an expression of the volume a cylinder with twice the radius, but half the height?

A. 2 k2h B. 4 k2h C. k2h D. ( k2h)/2

14. There are 32 kids in Mr. Grossman’s class. They took a poll of everyone’s favorite after-school activities: 17 kids like to pick their noses, 12 kids like to eat ear wa , and 6 kids don’t like to do either activity. How many kids like to pick their noses and eat ear wax?

A. 6 B. 2 C. 3 D. 4

15. A tree casts a shadow on the ground that is 24 feet long. At the same time, a 6 foot tall flagpole nearby casts a

shadow that is 8 feet long. How tall is the tree?

A. 33 feet B. 18 feet C. 24 feet D. 15 feet

***Another Test Done ! You ROCK! *** (this copy is all yours)

(page 2 of 2 – 2014 SMO 7th/8th grade individual test #2)


7th/8th Grade – Team Test #1

1. Brody is filling his pool for his pet shark, Bruce. One pipe can fill the pool in 4 hours, another pipe can fill the pool in 6 hours, and a third pipe can fill the pool in 8 hours. How long will it take to fill his pool if he uses all three pipes to fill the pool? Give your answer in hours and minutes, rounded to the nearest minute.

2. There are 9 students in a math club. There are four 7th graders and five 8th graders. A four-person math team is being put together for a math contest. In order to compete in the mixed age division, the team must contain two 7th graders and two 8th graders. In how many different ways can the math team be formed?

3. At the flea circus, Frederick Flea is walking along a wire frame cube that is 6 cm on a side. He walks from point A to point B, then from point B to point D, and finally, from point D to point C. What is the total distance that Frederick travels? Round your answer to the nearest hundredth.

4. Evan has been trying to beat his video game, Angry Anteaters. His last game scores were 56, 64, 63, and 59. If he has to average a score of 63 over 6 games to conquer this level, what is the average score he must get on the next 2 games to beat this level?

***More Math Fun on the Flip Side***

(page 1 of 2)

5. Boring Boris painted the walls and ceiling of his room black, then sat back and watched the paint dry. He started waiting at 2:32 pm, and the paint was finished drying later that same day at 5:56 pm. In that time, how many degrees did the minute hand of his analog clock rotate?

6. Heather’s dog had puppies. She had 7 black puppies, 4 brown puppies, and 2 yellow puppies. If she is giving them away randomly, what is the probability that the first two puppies she gives away will be brown? Give your answer as a reduced fraction.

7. Queen Lindsey was celebrating her birthday. The royal kitchen had prepared royal cookies for the Queen’s birthday, and stored them on a plate in the kitchen. That evening, the King couldn’t sleep, so he went downstairs to the kitchen, and finding the delicious cookies, he ate 1/6 of them.

Later that night, Queen Lindsey awoke and was hungry, so she went to the kitchen and ate 1/5 of the remaining cookies, and then returned to her royal bed.

After that, the first royal Princess snuck into the kitchen and ate 1/4 of the remaining cookies.

The smell of the cookies woke up her brother, the royal Prince, who went down and ate 1/3 of the cookies that were left.

Finally, the youngest royal Princess awoke and snuck in to the kitchen and ate 1/2 of the remaining cookies.

When the servants arrived the next morning, looking forward to eating the leftover cookies, they found only 3 cookies left in the bowl.

How many cookies were originally on the plate?

Finished! Great Job, Team! (you can keep this copy if you want)

(page 2 of 2 – 2014 SMO 7th/8th grade team test #1)


7th/8th Grade - Team Test #2

1. Max has 5 coins in his pocket that total 47 cents. What is the probability that he will reach into his pocket and randomly pull out a dime, and then, without replacing it, reach in and randomly pull out a quarter?

2. The Men in Black have captured some aliens and have them in a holding pen for deportation from Earth. There are Lorgats, which have 2 heads, 6 feet, and 2 tails each, Buxbos, which have one head, 4 feet, and 3 tails each, and Moochies, which have one head, 2 feet, and one tail each. If Agent J can see 17 heads, 50 feet, and 27 tails in the pen, and he knows that there are 5 Buxbos in the pen, how many Lorgats are there?

3. In the diagram below, lines M and N are parallel. Angle a is 146 degrees, and angle b is 102 degrees. What is the measure of angle c?

4. A biologist notices that a certain bacterium splits into 2 separate bacteria once every 15 minutes. If there was one bacterium on the slide 3 hours ago, how many are there on the slide now?

*** Don’t forget the problems on the back side ---> (page 1 of 2)

5. A dog is chained to a post at the side of a house, 3 feet from the corner. He is on a 10 foot chain, which can swing freely around the post. How much area does the dog have to roam? Give your answer in square feet, rounded to the nearest 1/10th ft. Use 3.14 for .

6. The Waters family are paddling a raft up a river. They can paddle 15 miles a day. At night, while they are asleep, however, the current pushes the raft 3 miles back downstream. If they set out on Tuesday morning to get to a town 62 miles upstream, on which day will they arrive?

7. Krusty the clown is manager of the concession stands at the circus. He is trying to decide which container to use for popcorn. Krusty has a choice of three different containers: a box, a cylinder, or an inverse cone, each with dimensions given below. If Krusty were to charge $5.75 for each container of popcorn, which one would give the customer the best deal?

End of ALL testing for today!! Excellent Work!

( you know you want to keep this copy and treasure it forever)

(page 2 of 2 – 2014 SMO 7th/8th grade team test #2)

r=7 cm

16 cm

12 cm

16 cm

r=10 cm

House

15 cm

h= 26 cm

Documents

2014 Shoreline Math Olympiad (Answer Key) Fourth Grade Mental Math 1 · PDF file2014 Shoreline Math Olympiad Fourth Grade – Mental Math Test #1 Question #1: What is the largest multiple