ALGEBRA
The sum of four numbers is one-half. What is the mean of the four numbers?
1/8
The measures of the three angles of a triangle form an arithmetic sequence. What must be the measure, in degrees, of at least one of its angles?
60
Evaluate the expression log₂(8)
3
Unscramble this calculus word:
VIVID EATER
DERIVATIVE
Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?
5
What number is 17 less than its negative? Express your answer as a decimal to the nearest tenth.
-8.5
Measure of each interior angle of a regular pentagon
108 degrees
Degree angle measure equivalent to 14𝝅/15 radians
168
Second derivative of xln(x)
1/x
On a Tuesday, a magician said, “I made my wife disappear 31 days ago.” What day of the week did he make her disappear?
Saturday
A teacher finds that when she offers candy to her class of 30 students, the mean number of pieces taken by each student is 5. If every student takes some candy, what is the greatest number of pieces one student could have taken?
121
A triangular region is bounded by the two coordinate axes and the line given by the equation 2x + y = 6. What is the area of the region, in square units?
9
Law of sines
a/sinA = b/sinB = c/sinC
Limit of xe-x^2 as x approaches infinity
0
What 5-digit number has the following features:
If we place an extra numeral 1 at the beginning, we get a number three times smaller than if we put that numeral 1 at the end of the number.
42857
We can make an equation:
3(100000 + x) = 10x+1
(Why? Well, adding 100000 puts a 1 at the front of a five-digit number, and multiplying by 10 and adding 1 puts a 1 at the end of a number)
Solving this gives:
10x+1 = 3(100000 + x)
10x+1 = 300000 + 3x
10x = 299999 + 3x
7x = 299999
x = 299999/7 = 42857
The answer is 42857 (142857 is three times smaller than 428571)
The ratio of boys to girls in a room is 6:5. If three boys leave the room, the ratio is 1:1. How many girls are in the room?
15
A domino consists of two congruent squares placed side by side. The perimeter of the domino is 60 units. What is the area of the domino, in square units?
200
Solve the equation: -38 = -(p-30)5/6 - 6
94
Find the derivative:
y = arctan(2x)
d/dx = 2/(4x² + 1)
The greatest multiple of 3 that is less than 500 and is also a multiple of 4
492
A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side?
9
A large rectangular swimming pool is surrounded by a uniform concrete walkway of width x meters. The length of the pool is 10 meters longer than its width. The area of the walkway is equal to the area of the pool. The combined area of the pool and the walkway is 1,000 square meters. Determine the width of the walkway.
4
The range of y= Arctan(x)
-(pi)/2, (pi)/2
The sum of the first N positive odd numbers is 121. What is the value of N?
11