Sixth Grade Mental Math Test #1

Transcription

1 Sixth Grade Mental Math Test #1 Question #1: What is the product of 0.1 times 0.2 times 0.3 times 0.4 times 0.5? Question #2: Zayn s age is twice Yolanda s age, and Yolanda s age is twice Xander s age. If the sum of all three ages is 35, how old is Yolanda? Question #3: A rectangle has whole number side lengths and a perimeter of 34. What is the largest area the rectangle could have? 2018 Shoreline Math Olympiad Sixth Grade Mental Math Test #2 Question #1: What is 5 divided by one-fifth? Question #2: Start with negative 11. Add 24. Multiply this result by itself. Subtract 23. Now add the digits of that result together. What is the final result? Question #3: What is the mean, of the following set of 5 numbers: {13, 4.5, 6.7, 7.8, and 3}?

2 Sixth Grade Individual Test #1 1. Whenever Georgina the Chicken lays 9 eggs, George the Chicken scrambles 3 of them. If Georgina has laid 882 eggs, what fraction of those eggs has George scrambled? A. B. C. D. 2. What is the range of the set:? A B C D If points,, and lie along a straight line and bisects (cuts in half), what is the measure of? A. 20 B. 40 C. 140 D How many integers between 1000 and 2000 are perfect squares? A. 10 B. 12 C. 13 D An unpopular jewelry collection has ounces of gold, 0.5 ounces of silver, 0.25 ounces of diamonds, and ounces of plutonium. What percent of the total weight are the gold and diamonds combined? A. 12.5% B. 25% C. 30% D. 37.5% 6. What is the mean (average) of the first 100 counting numbers (1 through 100)? A B. 50 C D The theater shows 10 minutes of previews, then Olaf s 20-minute short film, and finally Coco s 2-hour movie at the matinee. How long is Coco s movie, as a percentage of the entire matinee? A. 40% B. 50% C. 75% D. 80%

3 8. A circle and a square share the same center, and the two shapes intersect at 8 points. Which shape s area is greater? A. the circle B. the square C. both shapes have equal areas D. cannot be determined from the information given 9. Arrange the following numbers in order, from least to greatest:, 3,, A. 3, 3.125,, B.,, 3, C.,, 3.125, 3 D., 3, 3.125, 10. Owly the Squirrel is feeling overwhelmed, so Squirrelly the Owl agrees to arrange his acorns for him. Owly had gathered acorns non-stop at a rate of 18 per hour for 2 days. Squirrelly then places as many of those acorns as possible in rows of 11 and then eats the remainder. How many does he eat? A. 0 B. 3 C. 7 D In the equation X =, which value is equivalent to X? A. B. C. D If a math student has a mental block in the shape of a 5 cm x 8 cm x 12 cm rectangular prism, the surface area of the mental block is A. 196 cm 2 B. 272 cm 2 C. 392 cm 2 D. 480 cm What is if? A. 29 B. 38 C. 42 D The area of triangle SMO is A. 12 B. 16 C. 20 D In the puzzle shown, every box is the sum of the two boxes above. For example, 15 is the sum of 7 and whatever number belongs in box. What is the product? A. 0 B. 5 C. 6 D. 8 END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

4 Sixth Grade Individual Test #2 1. If, what is the value of? A. 3 B. 8 C. 16 D If I square my magic number and then subtract my magic number from the result, my final answer is 90. What are the possible values of my magic number? A. 9 and 10 B. -9 and 10 C. 9 and -10 D. -9 and Two toads and three newts cost 64. One toad and two news cost 37. How much would one toad and one newt cost? A. 10 B. 20 C. 27 D What must the product of two numbers be, if their sum is 20 and their difference is 8? A. 84 B. 96 C. 100 D Jack gave 10 of his beans to his mother, then half of his remaining beans to the giant. He used the final 20 beans to purchase a dairy cow. How many beans did he start with? A. 30 B. 40 C. 50 D When Ziggy joined the Iguana Appreciation Society as its 8th member, the average (mean) number of pet iguanas per member increased from 3 to 4. How many pet iguanas does Ziggy own? A. 2 B. 6 C. 8 D Dizzy Dean sits in his spinny chair facing North, then spins 2700 degrees counterclockwise. What direction is he facing now? Stand back! A. North B. South C. East D. West I might be sick. 8. My cocker spaniel was born on March 10, 2010, and my cockatoo was born on March 10, Which of the following expressions relates my cocker spaniel s age, D, to my cockatoo s age, B? A. B. C. D.

5 9. Which of the following expressions most closely describes the relationship between the number of fish in a tank (F) and the number of food pellets they eat every week (P), given the data in the table below? F P You just had to encourage them to take thirds, didn t you A. B. C. D. 10. On Teresa s map, the scale reads 1:1000, and the Funtown Reservoir is drawn as a 3-inch by 4-inch rectangle. How many square inches are in the area of the actual Funtown Reservoir? A. 12 B. 12,000 C. 12,000,000 D. 12,000,000, Peeky and Pokey are cute little inkspots who live on the coordinate plane. Peeky is at (0, 10) and Pokey is at (0, -2). Which of the following points is closer to Pokey than Peeky? A. (1,2) B. (3,4) C. (5,6) D. (7,8) 12. In how many distinct ways can the letters YOYO be arranged? A. 4 B. 6 C. 12 D Julio divided 78 by his favorite counting number, and his calculator showed the result Julio s favorite counting number is A. 26 B. 156 C. 214 D Aaron is buying clown shoes, that for some reason come in sets of three and cost $15 per set of three shoes. He buys 6 sets on Monday, 3 sets on Tuesday, 6 shoes on Wednesday, and 5 sets on Thursday. How much does he spend in all? A. $150 B. $195 C. $240 D. $ Ilia writes 3 different one-digit whole numbers which add up to 23. What is the product of Ilia s numbers? A. 336 B. 432 C. 504 D. more than one product is possible END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

6 Sixth Grade Team Test #1 1. In the addition puzzle, the letters E, S, M, A, and U each represent a different digit. What is the smallest possible value of the 4-digit number? 2. If is written out as a decimal, what is the 1000th digit to the right of the decimal point? (Hint: it s NOT a zero) 3. A perfect number is a number whose factors add up to double the original number. For example, 6 is a perfect number because the sum of its factors is, and. Find a perfect number that is greater than 20 and less than Two canine friends are preparing for dinner. Roux tells Finn, If you give me 2 kibbles, I would have twice as many kibbles as you. Finn tells Roux, If you give me 3 kibbles, I would have the same number of kibbles as you. If neither friend gives the other any kibbles, how many kibbles does Roux have?

7 5. The Duocalc is a special device with only two buttons: an A button that multiplies the current display by 2, and a B button that adds 1 to the current display. Tawana turns on her Duocalc and the display shows 0. What is the minimum number of key presses she needs to make the display show exactly 1000? 6. A square has a diagonal of length 10 meters. In square meters, what is the area of the square? 7. Uh-oh. The gremlins got into the art museum again. They are deciding how to rearrange 4 paintings that were hanging in a line on the wall. How many ways can they arrange the paintings so that at least one painting is in its original location? END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

8 Sixth Grade Team Test #2 1. Mo calculates,,, and. As a simplified mixed number, what is the range of Mo s four results? 2. How many counting numbers less than 61 are not divisible by 2 or 3? 3. What is the surface area of the right square pyramid shown, which has a base side length of 12 and a slant height (from the vertex to the midpoint of every edge of the base) of 10? I ve got my eye on this question 4. Find the sum of the numbers that should be placed in the three blanks to continue the following sequence: 2187, 1458, 972, 648, 432,,,.

9 5. Find the median of the set where A is the number of faces on a cube; B is the number of edges on a cube; C is the number of vertices on a cube; D is the number of faces on a triangular prism; E is the number of edges on a triangular prism; and F is the number of vertices on a triangular prism. Mime in Training 6. Six quiz bowl players are separating into two teams of 3 players each. One player, Malala, is allowed to choose her teammates. How many different ways can she choose her team? (Note: Choosing players A then B is equivalent to choosing B then A.) 7. Eva writes three whole numbers; one of the numbers is the average of the other two. Then she multiplies the three numbers and gets 5,320. If the number that is the average of the other two is the greatest prime factor of 5,320, what is the largest of Eva s original three numbers? END OF TEST! YOU MAY KEEP THIS COPY WHEN FINISHED

10 (Answer Key) Sixth Grade - Individual Test 1 Problem Number Answer Explanation 1 D 3 of 9 eggs scrambled = or of the eggs. 882 eggs is unneeded information. 2 B Range is largest minus smallest number; = A.. 4 C 5 A After trial and error, 1000 is between 961 and 1024 ; 2000 is between 1936 and Thus, there are 31 squares less than 1000 and 44 squares less than 2000;. If we express all weights in thousandths of an ounce (to simplify the arithmetic), the gold and diamonds represent of the total weight. 6 C The counting numbers from 1 to 100 are 50 pairs that add to 101 ( etc.); the sum is. The mean is. 7 D Coco s movie is 120 minutes out of = 150 minutes. 120/150 = 4/5 = 0.8 = 80%. 8 D 9 A The square s corners might barely protrude from the circle (making the circle larger), or the circle might barely protrude from the square s edges (making the square larger). As mixed numbers, the 4 original numbers are,,,. In order from least to greatest, these would be,,, ; or, using the forms in the question:,,,. 10 C 2 1/3 days = 56 hours; 56 x 18 = 1008 acorns; 1008/11 = 91 r7. 11 A. 12 C. 13 B. 14 A B x H/2 = area of triangle; 6 x 4/2 = 6 x 2 = C First, notice that,,, and. Now examine the second and third rows to get and. Add these equations: ; subtract from previous equations to get,.

11 (Answer Key) Sixth Grade - Individual Test 2 Problem Number Answer Explanation 1 D If, then. 2 B 3 C 4 A 5 C 6 D 7 B Test all the values given: for = 81 9 = 72 (no); for (-9) = = 90 (yes); for = = 90 (yes); for (-10) = = 110 (no). Buy 2 toads and 3 newts for 64, then sell back 1 toad and 2 newts for 37. You re left with 1 toad and 1 newt, and you ve paid out. Guess-and-check by adding pairs with difference 8 (. Or, find the two numbers using and. Either way, the numbers are 6 and 14;. After giving 10 to his mother, Jack gave half to the giant and kept the other half (20). Therefore he gave 20 to the giant also.. There were iguanas before Ziggy joined and after Ziggy joined. Therefore, Ziggy contributed iguanas.. So Dizzy Dean spins 7 full rotations and returns to facing North, then another 180 degrees which places him facing the opposite direction, or South. 8 A The cocker spaniel was born 4 years later so its age is 4 years less.. 9 C The ratio of P to F is roughly 30:4 or 7.5:1. Therefore the equation fits best. 10 C The actual dimensions are 3000 in x 4000 in for an area of 12,000,000 square inches. 11 A Any point with will be closer to Pokey than Peeky. The only such point here is (1,2). 12 B With Y 1st: YYOO, YOYO, YOOY (3 places for 2nd Y). Similarly with O 1st: OOYY, OYOY, OYYO (3 places for 2nd O). Total number of distinct arrangements:. 13 D 78 divided by Julio s number is, so his favorite counting number is 14 C 15 B Note that on Wednesday Aaron buys 4 shoes which is 2 pairs. He buys a total of pairs of shoes for. The highest possible sum of 3 different one-digit whole numbers is. To obtain a sum of 23, reduce one of these numbers (addends) by 1 and leave the others the same. The only way to do this is t use..

12 (Answer Key) Sixth Grade - Team Test 1 Problem Number Answer Explanation First, minimize M (first digit of ); M cannot be 0 (leading digit) so set. Now minimize E; E cannot be 0 (leading digit), and 1 is taken (M). So set. Finally, minimize S. because would make which is not allowed. 1 (M) and 2 (E) are taken. So set, which gives. That works. Therefore and. or. The six digits 0, 7, 6, 9, 2, 3 repeat infinitely., so the 1000th digit will be the same as the 4th digit, which is 9. Calculate the sums of factors for 21 through 29: (i.e. for 21 factors are 1,3,7,21; their sum is 32 which is NOT twice 21) The only number whose factors sum to twice the number is 28. There are multiple ways to solve this problem with guess and check being the simplest. If Roux gives Finn 3 then they would have the same number must be a difference of 6; can plug in numbers from there and find R=18 and F=12. The A key increases the display faster than B; use it as much as possible. Going backwards: Tawana will use A before every even number and B before every odd This is a total of 15 key presses. In order from first to last: BABABABABAABAAA. Draw the other diagonal and we have 4 right triangles with legs of length 5 m and 5 m.. If the original order is ABCD, then there are 6 orders with A first (ABCD, ABDC, ADCB, ADBC, ACDB, ACBD), 3 different orders with B first (BACD, BDCA, BCAD), 3 different orders with C first (CABD, CBDA, CBAD), and 3 different orders with D first (DBCA, DBAC, DACB) that qualify (can t have orders where none are in their original spot)..

13 Problem Number 1 Answer 2018 Shoreline Math Olympiad (Answer Key) Sixth Grade - Team Test 2 Explanation ; ; ;. Greatest is and least is. Range is Can eliminate all even numbers (divisible by 2) and run through the remaining numbers to see which are divisible by 3. You are left with 20 numbers. Lateral area (4 triangles):. Base area (square):. Total surface area:. If we subtract successive terms (2nd minus 1st, 3rd minus 2nd, etc.), we may not see a pattern. But if we divide 2nd by 1st, 3rd by 2nd, etc. we see that each term is of the previous one. Therefore, the 3 missing terms are,, and. A B C D E F The values in the set are as shown; in order, they are 5, 6, 6, 8, 9, 12 and the median is 6+8/2=7. For her first choice, Malala chooses from 5 players, and for her second choice, she chooses from the remaining 4. As mentioned in the problem, there are two equivalent ways to choose each pair (eg A then B or B then A) so double-counts the number of possible teams.. Or, call the other players A, B, C, D, E and count the possible teams by only listing each one once, alphabetically: AB, AC, AD, AE, BC, BD, BE, CD, CE, DE. There are 10 of these possible teams. Factoring the product of the three numbers = 5,320 = 2 x 2 x 2 x 5 x 7 x 19; 19 is the largest prime number; can guess and check for the other two numbers that average 19 (i.e. 1&37, 2&36, etc ) or can use the non-prime factors to create the other numbers; in this case 2 x 5 =10 and 2 x 2 x 7 = 28 which is the largest of the original three numbers.

14 (Answer Key) Sixth Grade Mental Math 1 Problem Number Answer Explanation then move decimal point 5 places = Yolanda s age is twice Zander s, so Xavier s age is four times Xander s. The total (35) is times Xander s age, so Xander is 5 and Yolanda is. The half-perimeter,, is the sum of length and width. To maximize area, make length and width close together. so try length 8 and width 9.. Sixth Grade Mental Math 2 Problem Number Answer Explanation This is already a whole number so rounding gives simply Start with ; = As the numbers 13, 4.5, 6.7, 7.8, 3 are read, keep track of the running sum (35) and divide by 5; 35/5 = 7 Could add numbers with decimals first then add to the whole numbers; = 35, then divide by 5 for the mean.