Geometry
Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side AB. What fraction of the regular octagon ABCDEFGH is the the hexagon XOEDCB?
7/16
Each of two boxes contains three chips numbered 1, 2, and 3. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?
5/9
Harry and Terry are each told to calculate 8 - (2 + 5). Harry gets the correct answer. Terry ignores the parentheses and calculates 8 - 2 + 5 . If Harry's answer is H and Terry's answer is T, what is H - T?
-10
Evaluate. Final answer must be in simplest form.
(sin²(pi/6)-sec²x(pi/6)+cos²(pi/6)+csc²(pi/6)+tan²(pi/6)-cot²(pi/6))⁵.
1
Anna had one car. It was blue. However, she wanted to have a gold car, so she went to the store. She saw a red car and bought it. However, her friend wanted a blue car. Since Anna no longer needed her old blue car, she sold it to her friend. Soon after, the blue car exploded, so the friend wanted to get her money back. Thus, Anna refunded her friend the money and took back the blue car. This moment in time is one second after Anna took back the blue car. How many cars does Anna have?
2, the red car and the blue car
What is the smallest whole number larger than the perimeter of any triangle with a side length of 5 and a side length of 19?
48
How many integers between 1000 and 9999 have four distinct digits?
4536
Billy's basketball team scored the following points over the course of the first 11 games of the season: 42, 47, 53, 53 58, 58, 61, 64, 65, 73. If his team scores 40 in the 12th game, which of the following statistics will show an increase?
a) range b) median c) mean d) mode e) mid-range
a) range
Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn't know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements are true."
(1) It is prime
(2) It is even.
(3) It is divisible by 7.
(4) One of its digits is 9.
This information allows Malcolm to determine Isabella's house number. What is its units digit?
8
If February is a month that contains Friday the 13th, what day of the week is January 1st (of the same non-leap year)?
Thursday
Rectangle ABCD and right triangle DCE (right angle at C) have the same area. The length of sides AB and BC is 5 and 6, respectively. What is the length of DE?
13
In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "AMC8"?
1/21,000
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 20 days?
400
If sin(x) = 3cos(x) then what is sin(x) * cos(x)?
3/10
At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save?
30
How many pairs of parallel edges (such as the top front edge and the top back edge) does a cube have?
18
Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?
(A) all 4 are boys
(B) all 4 are girls
(C) 2 are girls and 2 are boys
(D) 3 are of one gender and 1 is of the other gender
(E) all of these outcomes are equally likely
(D) 3 are of one gender and 1 is of the other gender
At Euler Middle School, 198 students voted on two issues in a school referendum with the following results: 149 voted in favor of the first issue and 119 voted in favor of the second issue. If there were exactly 29 students who voted against both issues, how many students voted in favor of both issues?
99
Bridget, Cassie, and Hannah are discussing the results of their last math test. Hannah shows Bridget and Cassie her test, but Bridget and Cassie don't show theirs to anyone. Cassie says, "I didn't get the lowest score in our class,'' and Bridget adds, "I didn't get the highest score.'' What is the ranking of the three girls from highest to lowest?
Cassie, Hannah, Bridget
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?
9
A triangle with vertices as A = (1,3), B = (5,1), and C = (4,4) is plotted on a 6 x 5 grid. What fraction of the grid is covered by the triangle?
1/6
Samantha lives 2 blocks west and 1 block south of the southwest corner of City Park. Her school is 2 blocks east and 2 blocks north of the northeast corner of City Park. On school days she bikes on streets to the southwest corner of City Park, then takes a diagonal path through the park to the northeast corner, and then bikes on streets to school. If her route is as short as possible, how many different routes can she take?
18
Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy?
7
Three members of the Euclid Middle School girls' softball team had the following conversation.
Ashley: I just realized that our uniform numbers are all 2-digit primes.
Bethany: And the sum of your two uniform numbers is the date of my birthday earlier this month.
Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.
Ashley: And the sum of your two uniform numbers is today's date.
What number does Caitlin wear?
11
Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the smallest number of additional cars she must buy in order to be able to arrange all her cars this way?
1