Probability/Combinatorics
You have a bag of marbles with 3 red marbles and 5 blue marbles. You randomly pick a marble from the bag, see that it is red, and return it to the bag. What is the probability that the next randomly drawn marble is also red?
3/8
x = 18
What is the area of a right triangle with a base of 3 units and a hypotenuse of 5 units?
6 square units
The vertex of the parabola y = x² - 2x -3 can be written in the form (a, b). What is the value of a + b?
-3
Underclassmen only!
0!, what is it?
1
You have a standard 52-card deck of playing cards. You randomly draw three cards without replacing them. What is the probability that you draw:
a face card (J, Q, K, A),
then a 7,
then a card with an even number?
32/3315
What line is perpendicular to the line
y = 2x + 5 and crosses the point (-3, 5)
y = -0.5x + 3.5
What shape is both a rhombus and a parallelogram?
How far apart are the points (7, 9, 6) and (-3, 0, 4) on a three-dimensional coordinate plane?
sqrt(185) = 13.601
Solve the following:
6 / (2) * (1+2)
The answer to this problem using modern arithmetic is 9, but past arithmetic would lead to the answer 1.
However, will be accepted here.
You have a standard 52-card deck of playing cards. What is the probability that the top card is the same color (red or black) as the bottom card?
25/51
What are the complex solutions to the equation
3x2 - 5x + 8?
(5/6) + sqrt(11)/6 * i
(5/6) - sqrt(11)/6 * i
The two angles 73 degrees and (3x + 5) degrees are consecutive interior angles. What is x?
x = 34
What is the area of the triangle bounded by the x-axis and the lines y=3x-4 and y=-7x+10
64/105 = 0.61
What are all of the factors of 198?
(There are more than 10!)
1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99 and 198!
Out of 2 Women and 5 Men, a committee of 3 is to be formed. In how many ways can it be formed if at least one woman is to be included?
2C1 × 5C2 + 2C2 × 5C1 = 20 + 5 = 25
Simplify
log(15 * 12) - 2log(641/3) + log(8/9)
1
A triangle has two sides of lengths 8 units and 6 units. The angle between them is 60 degrees. What is the length of the third side?
sqrt(73) or approximately 8.544 units
What is the largest possible area of a triangle inscribed in a circle with center (12, 7) that passes through the point (15, 11)?
75(sqrt(3))/4
What is the value of sin(arcsin(sin(690*)))?
*degrees
0.5 or 1/2
How many different sets of four letters can be formed from the word TRIANGLE if we want at least one vowel?
65
What are the x-coordinates of the points of intersection between the line y = 3x and function x2 + y2 = 3
sqrt(3/10) and -sqrt(3/10)
What is the ratio of the volume of a sphere whose radius is 11 units long to its surface area?
11/3
What is the radius of a circle centered at (1, 9) that is tangent to the circle (x-7)² - (y-1)² = 9?
7
How many squares of any size are contained in a 5x5 grid?
(ex: a square can have any dimension from 1x1 up to 5x5)
55