Number System
Algebra
Geometry and Trigonometry
Statistics and Probability
Problem Solving
100
Simplify sqrt(16+9)
5
100
Solve for x: 3x-1=8
x=3
100
What is the volume of a rectangular prism with a length of 4 units, width of 2 units, and height of 9 units?
72 units cubed.
100
If there are 3 red marbles, 5 blue marbles, and 8 green marbles, what is the probability of drawing a blue marble? Write your answer as a fraction.
5/16
100
The following equation shows how the total cost of a members-only speaker series is related to the number of events attended. c = 17a The variable a represents the number of events attended, and the variable c represents the total cost. What is the total cost for someone to attend 2 events?
$34
200
Simplify: sqrt(36)
3sqrt(4)
200
Write 4600000 in scientific notation.
4.6*10^6
200
Find the length of one leg of a triangle if the other leg is 6 units long and the hypotenuse of 10 units long.
8 units
200
If there are 3 yellow marbles, 4 purple marbles, and 6 black marbles, what is the probability of drawing a black marble, replacing it, then drawing a yellow marble? Write your answer as a fraction.
18/169
200
Engineering students at Summerfield College last year received, on average, $9,690 in scholarships and grant money. This year, the average is 90% higher. What is the average this year?
$18411
300
Simplify by rationalizing the denominator: (2sqrt(3))/(sqrt(5))
(2sqrt(15))/(5)
300
Find the vertex of a parabola represented by the following function: f(x)=3x^2-12x+7
(2,-5)
300
In right triangle ABC, side AB is 5 units long, side AC is 8 units long, and angle b is 90 degrees. Write an equation that could be used to find angle c.
sin(x)=5/8
300
Given the data set 85, 87, 89, 90, 91, 92, 93, 95, and 209 If the outlier is removed, which measure of CENTER would be the most affected.
Mean
300
A city's population is currently 500,000. If the population doubles every 50 years, what will the population be 200 years from now?
8,000,000 people.
400
Simplify (3+2i)(1-6i)
15-16i
400
Given x=ln(8) Write the equivalent expression using base 10
x=(log(8))/(log(e))
400
What is the equation of a circle that passes through the point (3,-8) and has a diameter of 18? Write your answer in standard form.
(x-3)+(x+8)=81
400
The probability that a student enjoys camping is 0.3, the probability that a student prefers science is 0.6, and the probability that a student enjoys camping and prefers science is 0.1. What is the probability that a randomly chosen student enjoys camping or prefers science? Write your answer as a percent.
80%
400
If one painter can paint the entire house in twelve hours, and the second painter takes eight hours. Exactly what time will the painters finish if they start at 2 pm?
6:48 pm
500
Simplify x^(2/3)=25i
125cis135 125cis315
500
What is the slant asymptote of the following function: f(x)=(2x^2+x-5)/(x+1)
2x+1
500
Prove the identity cot(x) / csc(x) = cos(x)
cot(x)/csc(x) = [cos(x)/sin(x)] / [1/sin(x)] [cos(x)/sin(x)] / [1/sin(x)] = [cos(x)/sin(x)][sin(x)/1] [cos(x)/sin(x)][sin(x)/1] = cos(x)/1 = cos(x) cot(x)/csc(x) = [cos(x)/sin(x)] / [1/sin(x)] = [cos(x)/sin(x)][sin(x)/1] = cos(x)
500
A team of engineers designed a peg machine. To play the game, players drop a ball into the top of a peg-filled, transparent box. The ball bounces off the pegs and eventually settles into one of many holes at the bottom of the box. Only one of the holes is the "winning hole" and the designers claim there is only a 62% chance of the ball landing there. If a student plays the game 2 times, what is the mean of the number of times the player wins the game?
1.24
500
The owners of Leximax bookstore would like to understand the reading habits of their customers. Bookstore employees asked 175 randomly selected customers about the books they read last month. The owners found a 99% confidence interval of (3.5,4.3) for the mean number of books its customers read last month. Why is the following conclusion not valid? There is a 99% chance that the mean number of books Leximax customers read last month is in the interval (3.5,4.3)
The population mean is the average number of books all Leximax customers read last month, not just the ones in the sample. The population mean is a specific number even though you don't know its value. It is not up to chance whether a specific number is inside the confidence interval (3.5,4.3) The number is either in the interval or not.
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