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 log_2(8)
3
Find the area under the curve f(x)=x2 from x=0 to x=3
9
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
What is the measure of each interior angle of a regular pentagon?
108 degrees
What degree angle measure is equivalent to 14𝝅/15 radians?
168
Find the 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
Find the sum of the first 10 terms of the arithmetic sequence where a1=2 and d=3
155
What is the limit of xe-x^2 as x approaches infinity?
0
1 − 3 + 5 − 7 + 9 − ..... − 43 + 45 − 47 + 49
25
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
Evaluate the integral of (1-x2)2 from 0 to 1
8/15
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
How many values of x between 0 and 990 degrees satisfy sin(x)=-0.31?
5
A company manufactures and sells x units of a product. The revenue R(x) in dollars from selling x units is given by the function R(x)=100x−x2. The cost C(x) in dollars to manufacture x units is given by the function C(x)=20x+50. Find the number of units x that maximizes the profit.
40
The sum of the first N positive odd numbers is 121. What is the value of N?
11