2018 Shoreline Math Olympiad Fifth Grade – Mental Math Test #1

Question #1: If Rita divides ALL of 130 cookies evenly among 20 friends, how

many cookies will each friend get?

Question #2: Take 100 and multiply by 200. Now divide by 10. Now multiply by

3,000. Write down the result.

Question #3: There are one and a half times more owl nests than phoenix nests

in the Enchanted Forest. If there are 150 phoenix and owl nests total, how many phoenix nests are in the Enchanted Forest?

2018 Shoreline Math Olympiad Fifth Grade – Mental Math Test #2

Question #1: One side of a rectangle is 8 ft long and its perimeter is 28 ft. What is the rectangle’s area in square feet?

Question #2: Charlie buys 3 goldfish at $1.59 for each fish. How much change

will he get if he pays with a 10 dollar bill? Question #3: Take one-third and multiply by six-eighths. Then subtract one-

sixth. What is the answer in simplest terms?

2018 Shoreline Math Olympiad Fifth Grade – Individual Test #1

1. =

A. 0.20 B. 0.25 C. 0.50 D. 0.75 2. Which of the following numbers is divisible by 3 and 5? A. 425 B. 528 C. 645 D. 710 3. At the pool, Niko bought a water slide wrist band for $1.09, a 10-visit pool pass for $13.99, and a water bottle

for 99 cents. What is Niko’s change from a $20 bill? A. $3.73 B. $3.81 C. $3.93 D. $4.13 4. Zara noticed an invisible ink pen she had wanted to buy that was $2.00. It is now on sale for $1.60. The sale

price is what fractional part of the original price?

A. ` B. C. D.

5.

A. B. C. D.

6. The sum of the measures of 2 interior angles of a trapezoid is 180 degrees. The measure of the 3rd interior angle

is 61 degrees. What is the measure of the 4th interior angle? A. 29 degrees B. 61 degrees C. 119 degrees D. 129 degrees 7. Mischief the dog loves to hide shoes in the backyard. If Mischief originally hid Cody’s shoe in the backyard at a

coordinate plane location of (5 ft, 1ft), and then moved it 3 feet to the north and 2 feet to the west, where can Cody find his shoe? Assume the y-axis value decreases as you travel South.

A. (3, 2) B. (2, 3) C. (4, 3) D. (3, 4)

8. It takes Robin 65 minutes to walk to work and she needs to leave at 7:10 am to be on time. If Robin drives to

work, it takes her of that time. What is the latest time Robin can leave for work if she drives and still be on

time?

A. 7:23 am B. 7:55 am C. 7:58 am D. 8:02 am

4.2

9. What is the largest factor of 690 that is a prime number? A. 13 B. 17 C. 23 D. 29 10. Which of the following is NOT true? A. 485 seconds > 8 minutes > 0.1 hours B. 8000 centimeters > 8 meters > 0.001 kilometers

C. 150 inches > 12 feet > 3.5 yards D. 710 seconds > 12 minutes > 0.1 hours 11. A wand maker has found a 156 inch long branch with a dragon heart-string core. She plans to use every inch of

this precious wood to make wands that are 13 inches long. What is the minimum number of cuts she will need to make to create as many 13 inch wands as possible from the branch?

A. 10 B. 11 C. 12 D. 13 12. Zavier is competing on a new quiz show called “What in the World do Those 3 Letters Mean?” and he needs

your help in the final round. Help Zavier find which of the following statements are true? I. LCM can be useful when adding fractions with unlike denominators. II. GCF is commonly used to find a common denominator. III. LCM is commonly used to simplify fractions. IV. GCF can be used to reduce a fraction A. II. and IV. B. II. and III. C. I. and IV. D. III. only 13. The semi-circle has a diameter of 6.4 ft. The rectangle has a width of 4.2 ft. The largest triangle is an isosceles

triangle. What is the area of the triangle A? A. 12.38 ft2 B. 10.24 ft2 C. 13.44 ft2 D. 26.88 ft2

14. In the Teenage Mutant Ninja Turtle’s bag of Halloween candy there were 6 Skittles, 3 Snickers, 3 M & Ms, 8 Pixie

Sticks, 3 Jolly Ranchers and 1 box of raisins. What is the probability that the Turtle picks a Snickers out of the bag without peeking, assuming all items have an equal chance of being picked?

A. 0.125 B. C. 0.2 D.

15. If J =8, K=4, M=2, P=3, and R=5, what is +

A. 16 B. 23 C. 24 D. 31

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

A

2018 Shoreline Math Olympiad Fifth Grade – Individual Test #2

1. Two whole numbers have a sum of 13 and a product of 36. What is the smaller of the 2 numbers? A. 3 B. 4 C. 5 D. 6 2. A six-sided die is rolled. What is the probability that a prime number is rolled?

A. B. C. D.

3. In the Northwest Banana Slug Race of 2018, 24 banana slugs raced for the grand prize. Alas, the following

banana slugs didn’t make it to the finish line: 1/3 of the banana slugs took a nap, 1/6 went in circles, 1/4 went backwards, and 1/24 crawled into a log along the course. The rest of the banana slugs made it to the finish line. How many banana slugs made it to the finish line?

A. 3 slugs B. 4 slugs C. 5 slugs D. 6 slugs 4. Which of the following is NOT true of an isosceles triangle? A. all three interior angles must be acute B. It has 2 congruent sides

C. a equilateral triangle is an example of an isosceles triangle D. 2 interior angles are the same

5. Which equation describes the relationship between A and B?

A 2 3 4 5

B 5 7 9 11

A. B = 2 x (A +1) B. A= (B 2) - 1 C. A= (2 x B) +1 D. B= (2 x A) +1 6. A game board spinner is divided into 3 sections: A, B, and C. Section A takes up a pie wedge that is 1/2 of the

spinner. Section B takes up 1/3 of the spinner. What is the probability the spinner will land on section C when the spinner is spun?

A. B. C. D.

7. Sloths like to move only when necessary, but if they really need to pick up the pace, they can reach top speeds

of about 3 meters per minute on the ground. If there are about 1,609 meters in a mile, approximately how far can the sloth travel in one day (24 hours) assuming it is able to maintain a constant top speed of 3 meters/min?

A. mile B. 1 miles C. 2 miles D. 3 miles

8. What is 0.0088 divided by 0.022? A. 0.04 B. 0.4 C. 4 D. 2.5 9. What is the total volume of the following 3 cubes combined: a cube with edge of 2 feet, a cube with an edge of

3 feet, a cube with an edge of 4 feet? A. 79 ft3 B. 95 ft3 C. 99 ft3 D. 109 ft3

10. Which of the following fractions has a value of less than ½?

A. B. C. D.

11. There are six identical circles with a radius of 1 foot which fit perfectly edge to edge inside a rectangle. What is

the area of the shaded region? The area of each circle = 3.14.

A. 3.48 ft2 B. 5.16 ft2 C. 7.62 ft 2 D. 20.86 ft2

12. Pirate Pete is keeping his treasure close by putting it under a square shaped tile floor in his kitchen marked with

an “X” using black and white same-sized tiles. If Pirate Pete makes an “x” by making 2 diagonal lines of black tile across the entire square floor with 17 black tiles total forming an “X” and fills in the rest of the floor with white tiles, how many white tiles will he need?

A. 18 B. 64 C. 68 D. 81

13. Adele has a pile of Skittles candies that are the colors red, orange, yellow, and green with no other colors. If of

the Skittles are red, of the Skittles are orange, and of the Skittles are yellow, what is the least number of

green skittles she can have in the pile?

A. 2 B. 3 C. 4 D. 6 14. When a six-sided die is rolled on a table, you can’t see the bottom face of the dice. What is the probability that

the product of the faces that can be seen is divisible by 9?

A. B. C. D.

15. Morrigan must enter the last number in the secret code to unlock the master sorcerer’s box. Solve the secret

code by finding the last number in the sequence: [1, 8, 29, 92, 281, ____]. What number will unlock the box?

A. 664 B. 743 C. 848 D. 912

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

2018 Shoreline Math Olympiad Fifth Grade – Team Test #1

1.

A stack of identical cubes with an edge length of 2.5 feet make up this shape. What is the total surface area in square feet, including the bottom, of the shape above?

2. The secret code to unlock the hidden passageway to Pengo’s time machine is made up of 9 unique single digits

(1-9) labeled A thru I. Use the following clues to discover the secret code. What number is the secret code if you put the digits in order A to I?

A B C D E F G H I

• Digit G is the third largest number

• Digit C is one greater than the smallest composite number

• Digit E is an even prime number

• Digit A is Digit E cubed

• Digit E only hangs out next to multiples of itself

• Digit D > Digit F

• Digit I > Digit G

• Digit H is a prime number 3. How many whole numbers from 90 to 900 inclusive (including 90 and 900) have exactly one zero in them? 4. An ice cream pie is cut into 15 even wedge slices. If Pengo eats 1/3 of the slices and then Pingo eats 1/5 of the

remaining slices, what is the obtuse angle in degrees formed by all the remaining wedge slices put together?

2

3

4

5 6

7

8

9

1 10

5. The tortoise starts in the box position shown in the furthest left grid on the Day 1 and moves clockwise one box

once each day. The hare starts on the outer edge position shown in the furthest left grid on Day 1 and moves counter-clockwise one square edge-length each day. Where will the tortoise and the hare be located on Day 365? Using the Legend Grid (shown furthest right), record one letter (A-F) to indicate the tortoise’s position and one number (1-10) to represent the hare’s position on Day 365. For example, on Day 1 the tortoise and hare positions are [A, 5].

Day 1 Day 2 Day 3 Legend Grid

6. Abby, Brian, and Celeste collect animal erasers. All together they have 275 erasers. If Celeste has 3 times as

many as Abby, Brian has 1/2 as many as Celeste, how many erasers does Brian have? 7. Turner visits the zoo every 24 days and Chris visits the zoo every 90 days. If they both visit the zoo on day 1, in

how many days will they both be at the zoo on the same day again?

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

A B

F C

E D

2018 Shoreline Math Olympiad Fifth Grade – Team Test #2

1. Kaya shoots 40 basketballs and makes of her shots. After she shoots 10 more basketballs, she made of the 50

shots total. How many of the last 10 shots did she make? 2. To create a fractal, you can take a simple pattern and repeat it over and over again. One such fractal,

the Sierpinski Gasket, can be created by repeatedly cutting triangles out of the middle of triangles. If you take a triangle and cut a triangle out of the middle of each white triangle as shown below, how many solid white triangles will there be after the 5th triangle cutout?

Triangle before cutout Triangle after 1st triangle cutout Triangle after 2nd triangle cutout 3. The Curiosity Rover landed on Mars in 2012 and has been exploring Mars for the last 6 years. The Curiosity

rover can travel up to about 200 meters per day on Martian terrain. What is the maximum distance the Curiosity rover could have traveled in miles rounded to the nearest whole mile in 6 years assuming it traveled 200 meters per day? Assume that 3.3 feet = 1 meter, 5,280 feet = 1 mile, and 365 days = 1 year.

4. The order of the following numbers have been rearranged according to these rules:

• The largest and smallest of all the numbers were not first or last.

• The difference between the largest and smallest numbers was not first or last.

• Any numbers that are equal to the sum of all the numbers divided by 8 were not the first or last number.

• The first and last number were not whole numbers.

What is the product of the first and last number, before the order was rearranged, in its most reduced form?

, , , , , , , 1 5. How many different 5 digit numbers can be made by rearranging the digits in the number 12,321?

6. What is the largest factor of 66990 that is a prime number? 7. Minerva is building a pen for her 4 Horntail dragons, and they don’t get along too well in small spaces. If she has

126 feet of dragon-proof fencing and the lengths of her rectangular pen must be integers, what is the area of the largest pen, in square feet, she could make for her dragons?

You do know I can fly, right?

END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

2018 Shoreline Math Olympiad

Answer Sheet 5th Grade Mental Math Test #1

ANSWER KEY NOTE: Don’t need units in these answers; if they are included and wrong, then answer is wrong.

ANSWERS

1) 6.5 or 6 1/2 cookies 130/20 = 6.5

2) 6,000,000 or 6 million 100x200=20,000; 20,000/10=2,000; 2,000x3,000=6,000,000

3) 60 nests or phoenix nests 60 x 2 =120, 120 + (1/2 of 60)= 120 +30=150

(phoenix doesn’t need

to be spelled correctly)

Write clearly!

All computations MUST BE DONE IN YOUR HEAD!

Only ONE answer may be written down on answer sheet.

If scoring room detects any erasures, points earned will be ZERO!

2018 Shoreline Math Olympiad

Answer Sheet 5th Grade Mental Math Test #2

ANSWER KEY NOTE: Don’t need units in these answers; if they are included and wrong, then answer is wrong.

ANSWERS

1) 48 ft2 28- 8(2)=12; 12/2=6; Area = 6x8=48 ft2

2) $5.23 dollars 1.59 x 3 = 4.77; 10.00-4.77 = 5.23

3) 1/12 1/3 x 6/8 = 6/24, 6/24-1/6= 6/24-4/24=2/24=1/12

Write clearly!

All computations MUST BE DONE IN YOUR HEAD!

Only ONE answer may be written down on answer sheet.

If scoring room detects any erasures, points earned will be ZERO!

2018 Shoreline Math Olympiad

5th Grade Individual Test – Answer Keys Individual Test #1

1. B. 0.25 3/8 x 4/6 = ¼=0.25

2. C. 645 A number divisible by 5 when the units digit is a 5 or 0. A number is divisible by

3 when the digits of a number add to a number that is divisible by 3. For 645, 6+4+5= 12,

12 is divisible by 3, so 645 is also divisible by 3.

3. C. $3.93 1.09+13.99+0.99=16.07, 20- 16.07=3.93

4. D. 4/5 160/200=16/20=4/5

5. A. 5/28 All of the numbers cross cancel each other out except 5 in the numerator; and 4 and 7 in

the denominator. 5/ (4x7) = 5/28

6. C. 119 360- (180 +61) = 119

7. D. (3,4)

8. D. 8:02 am 7:10 + 65 minutes = 8:15 =time need to be at work. 65/5 = 13 minutes to drive

8:15 – 13 minutes = 8:02

9. C. 23 Prime factors of 690 are 2, 3, 5, and 23. 23 is largest.

10. D. 710 seconds > 12 minutes > 0.1 hours 12 minutes is 720 seconds. 710 seconds is not greater than 12

minutes.

11. B. 11 156/13 = 12 wands. 11 cuts to make 12 wands.

12. C. I and IV.

13. C. 13.44 ft2 Area of rectangle = 6.4x4.2=26.88, area of 2 small triangles = 4.2x3.2=13.44,

area of triangle A = (area of

rectangle)- (area of 2 small triangles)=26.88-13.44=13.44

14. A. 0.125 3/ (6+3+3+8+3+1) = 3/24 =1/8=0.125

15. B. 23 (8/2) x (4/2) + (3 x 5) = 4 x 2 +15= 8+15=23

Individual Test # 2

1. B. 4 9x4 = 36, 9+4=13, 4<9

2. C. 1/2 2, 3, and 5 are prime numbers, 3 out of 6 number are prime, 3/6= 1/2

3. C. 5 slugs 1/3+1/6+1/4+1/24= 8/24+4/24+6/24+1/24=19/24, 24-19=5

4. A. all three interior angles must be acute

5. D. B= (2xA) +1

6. A. 1/6 1/2 + 1/3 = 3/6+2/6=5/6, 6/6-5/6=1/6

7. C. 2 2/3 miles (3 meters/min)x (60min/hr)x(24hr/day)=4320meters/day; 4320/1609

≈4300/1600=43/16=2.69

8. B. 0.4

9. C. 99 ft3 (2x2x2) + (3x3x3) + (4x4x4) = 8+27+64=99

10. D. 36/74 If a fraction’s value is less than ½, then the numerator X 2 should be equal to less than

the denominator. 13/25 13 x 2 =26 which is > 25, so is greater than one half.

11. B. 5.16ft2 length of rectangle = 6 x radius, width = 4 x radius. Area of rectangle = 6x4=24.

area of 6 circles=6 x 3.14=18.84, area of shaded region=(area of

rectangle) – (area of 6 circles)=24-18.84=5.16

12. B. 64 17 black tiles make an x as below. The resulting square is 9 x 9 = 81 tiles.

17 of the 81 tiles are black. 81-17=64 white tiles.

13. B. 3 Lowest common multiple of 3, 4, and 6 is 12. ¼ of 12 = 3 red skittles, 1/3 of

12= 4 orange skittles,1/6 of 12 = 2 yellow skittles, 12 – 9 = 3 green skittles 14. D. 2/3 If 2,3,4,5,6 visible 6x3 is divisible by 9, so 2x3x4x5x6 is divisible by 9 If 1,3,4,5,6 visible 6x3 is divisible by 9, so 1x3x4x5x6 is divisible by 9 If 1,2,4,5,6 visible not divisible by 9 If 1,2,3,5,6 visible6 x 3 is divisible by 9, so 1x2x3x5x6 is divisible by 9 If 1,2,3,4,6 visible6 x3 is divisible by 9, so 1x2x3x4x6 is divisible by 9 If 1,2,3,4,5 visible not divisible by 9 4 out of 6 are divisible by 9 = 4/6=2/3 15. C. 848 Sequence pattern is take number, multiply by 3, and then add 5, to get next

number in sequence. 281x3 =843, 843+5=848

2018 Shoreline Math Olympiad

Answer Sheet 5th Grade Team Test #1

1) 362.5 ft2 or feet squared 58 faces, 2.5x 2.5 = 6.25 ft2 per face, 58 x 6.25 = 362.5

2) 815624739 or 815,624,739

3) 145 numbers or whole numbers +1 90 +9 101,102,103,104,105,106,107,108,109 +9 110, 120,130,140,150,160,170,189,190 +9 201, 202 … +9 210,220 … +18 301…, 310… +18 401…, 410… +18 501…, 510…. +18 601…, 610… +18 701…,710… +18 801…, 810… (16 x9) +1 = 144+1=145

4) 192 degrees or ° 360°/15 = 24 ° per slice, 15 x 1/3 =5 slices10 slices left 10 x 1/5 = 2 slices, 10-2 = 8 slices left, 8 x 24°=192° 5) [ E, 9] or (9,E) or E9 or 9E or 9,E or E,9 (or similar) 364 moves to get to day 365, tortoise every 6 moves is back at starting point, 364/6= 60 R4 count clockwise 4 moves from starttortoise at position E on day 365. Hare back at starting point every 10 moves, 364/10 = 36R4count counter-clockwise 4 moves from starthare at position 9 on day 365.

6) 75 erasers Can find by trial and error. B=75, C=150, A=50 Or can find by C/3=A, C =2B, A+B+C = 275, 2/3B +B +2B = 275, 3 2/3 B =275

7) 360 days Find lowest common multiple of 24 and 90. Find what the lowest multiple of 90 which is also divisible by 24 which is 360. Or can find prime factors of each number. 24 is 2x2x2x3, 90 is 3x3x2x5 Then multiply the largest number of each of the prime factors together to get the LCM. 2x2x2x3x3x5=360

2018 Shoreline Math Olympiad

Answer Sheet 5th Grade Team Test #2

1) 6 baskets or shots 9/20 x 40 = 18; 24-18=6 2) 243 triangles or white triangles 1st triangle cutout = 3 white triangles, 2nd triangle cutout=9, 3rd =27, pattern is multiply number of white triangles by 3 to find number of white triangles in next cutout. 3x3 = 9, 9x3=27, 27 x 3 = 81, 81x 3 =243. 3) 274 miles 200 x 3.3 =660 ft/day, 660 x 365 = 240900ft/yr, 240900 x6 = 1445400 ft/6 years; 1445400/5280=273.75 miles 274 miles in 6 years

4) largest and smallest are 3/2 and ¼, 3/2 – ¼ = 1 ¼

Sum of all the numbers is 6. 6/8=3/4. Eliminate 8/8 as equal to a whole number. 1/3 x 8/12 = 1/3 x 2/3 = 2/9

5) 30 numbers Number which start with 1: 11223,11232,11323,12132,12123,12213,12231,12321,12312, 13122,13212,13221 = 12 numbers Numbers which start with 2 have same number = 12 numbers Numbers which start with 3: 31122, 31212, 31221,32112,32211,32121 = 6 numbers 12+12+6 = 30 numbers

6) 29 Prime factors = 2,3,5,7,11,29

7) 992 square feet A rectangle with a perimeter of 126 has the sum of adjacent sides of 63 (126/2 = 63); can do guess and check to see that 32 x 31 (closest to a square) will have the largest area; 32 x 31 = 992 ft.2