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Rate of change
Linear Equations
Angles and triangles
Volume
Miscellaneous
100
Find the slope of a line passing through the points (-4,4) and (8,-2)
m = -1/2
100
What type of relationship exists between the following two linear equations: y = 7x + 10 and y = -1/7x + 4
They are perpendicular lines
100
A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase?
30 inches
100
The length of square prism is 4 feet. What is the volume?
What is 64 feet ^3
100
Point A is on the coordinate (4, 3). It is reflected over the y-axis. What is its new point?
(-4, 3)
200
Todd had 5 gallons of gasoline in his motorbike before he starting driving. After driving 100 miles, he had 3 gallons left. What is the slope, and what does it mean?
m = -1/50 or .02, which means for every mile, the number of gallons decreases by .02.
200
Two lines are on a graph. One equation is y = 4x + 2, and the other is -4x + 2y = 6. How many solutions exist?
There is one solution. They intersect at one point.
200
Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?
9.4 miles
200
What is the volume of a cone?
1/3 * pi * r ^2 * h
200
Point G is located at point (-2, -5). It is reflected over the x axis, and moved 3 units to the right. What is its new point?
(-2, 8)
300
Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of change? What does it mean?
m = 12.5. For every week, the amount of money in the account increases by $12.50.
300
What is an example of a non-linear equation?
y = x^2, 5 = x/y...etc.
300
Mr. Smith owns a ladder that is 25 feet long. He places the ladder 6 feet away from the wall he is working on. How high up the wall can the ladder reach to the nearest foot?
24 feet
300
What can hold more, a cylindrical fish tank that has a radius of 10 inches and a height of 24 inches, or a spherical fish tank that has a radius of 14 inches?
Sphere (11,488 vs. 5,746)
300
Give the definition of an irrational number. Then, give an example.
A number that never ends and never repeats. Ex: pi
400
You are researching how long babies less than a year old sleep. You find this relationship: y = -2.12t + 15.5, where y = the number of hour of sleep and t = the age of the baby in years. Predict the amount of sleep a 6 month old baby should get.
14.4 hours
400
Solve this system of equations. y = 6x + 11 and -2x - 3y = -7
(2,1)
400
What types of angles are NOT equal? a. Alternate interior angles, b. alternate exterior angles, c. corresponding angles, d. adjacent angles
d. adjacent angles
400
How many times does a cone fill a cylinder of the same radius and height?
3 times
400
You are making scaled models in art class. You are drawing a cylindrical vase. The vase is 16 inches high and 6 inches wide. You decide that in your drawing, the vase will be 2 inches wide. How high will the vase be?
5.3 inches
500
You and a friend are trying to find a relationship between height in inches (y) and age in months (x). You found this relationship: y = 0.6618x + 64.399. Does this equation work for a person who is 20 years old?
No, the person would be 223 inches tall, which is 18 feet.
500
Sam needs to rent a car for a one-week trip to Oregon. He is considering two companies. A+ Auto Rental is $175 plus $0.10 per mile and Zippy Auto Rental is $220 plus $0.05 per mile. Write and solve a system of equations to determine when the rental costs are the same for both companies.
At 900 miles the cost will be the same for both companies.
500
As part of a community service project, the Key Club wants to build a ramp to make the stage in the auditorium wheelchair accessible. The stage is 4 feet above ground level and they want the ramp to start its slope 8 feet from the base of the stage. To insure that the ride is smooth, they want to buy boards that are long enough to cover the entire distance from where the slope begins to the top of the stage. At the lumberyard, they discover that boards come in lengths of 8 feet, 10 feet, 12 feet and 14 feet. What length boards should they buy?
10 feet (c = 8.9, so 8 feet is too short)
500
A beach ball has a radius of 8 inches. Originally, it is blown up to full capacity. Then, overnight, it loses 15% of its air. How much air volume is left inside, to the nearest inch?
Amount left=1,822 in^3; Original: 2143.6, 15%=321.5; 2143.6-321.5
500
Solve for x: −3(x − 1) + 8(x − 3) = 6x + 7 − 5x
x = 7