The Number System
Expressions and Equations
Functions
Geometry
Statistics and Probability
100
Determine if 0.1111111111111... is rational or irrational.
Rational (because it repeats)
100
How many solutions does the equation have?
3(4 + x) = 7x - 2(2x + 3)
0 solutions
100
What is the slope of the line that passes through the points (1, -1) and (-8, -7)? Write your answer in simplest form.
2/3
100
Does the following set of numbers represent the three sides of a triangle? Explain why or why not.
{45, 60, 74}
No, 5625 does not equal 5476
(plug into pythag thm)
100
This scatter plot shows the total amount of money in a bank account at the end of each week for a period of 1212 weeks.
Does the graph show clustered data, a positive linear association, or a negative linear association?
positive linear association
200
What is the product of 840 and 4.6 x 10^2 expressed in scientific notation?
3.864 x 10^5
200
How many solutions does the following equation have?
2(7x + 5) = -2(-7x - 5)
infinitely many solutions
200
Does the following set of points represent a function? Explain why or why not.
(-1, 8), (8, -4), (8, 3), (-5, -6)
No, an x value repeats (8)
200
The image of a point is (1, 2) after it is reflected over the line y = -3. What are the coordinates of the original point?
(-7, 2)
200
A student recorded the high temperature, in degrees Fahrenheit, in his town on each day for the first 10 days in January. This scatter plot shows the data the student recorded.
Based on the scatter plot, on which day does the high temperature seem to be an outlier?
6
300
Convert the following repeating decimal to a fraction in simplest form:
0.0555555555555...
1/18
300
Solve for x:
-10x + 3(3x + 4) + 1 = -3(7x + 3)
-1.1
300
Convert the equation into slope-intercept form, simplifying all fractions.
6x + 15y = -75
y = -2/5x - 5
300
The volume of a right cone is 27π units^3. If its height is 9 units, find its circumference in terms of π.
6π units
300
The coach of a basketball team recorded x, the number of hours the team practiced before each game last season, and y, the number of points the team scored in each game. The coach made a scatter plot and drew a line of best fit for the data, as shown on this coordinate plane.
The equation for the line of best fit is y=4x+28.
Based on the line of best fit, for how many hours would the team need to practice in order to score 70 points?
10.5 hours
400
What is the product of 8.9 x 10^2 and 5.1 x 10^4 expressed in scientific notation?
4.539 x 10^7
400
Solve the system of equations:
-7x + 7y = 7
-4x + 2y = -14
(8, 9)
400
Write an equation of the line that passes through the points (2, -6) and (-2, 4) in slope-intercept form.
y = -5/2x - 1
400
What is the diameter of a hemisphere with a volume of 22778 m^3, to the nearest tenth of a meter?
44.3 meters
400
Ethan asked a random sample of students the two questions below.
- Do you have brothers or sisters?
- Does your family have a dog?
Ethan created this table to display the data he collected.
Based on the table, what is the total number of students that have no brothers or sisters?
40
500
What is the quotient of 1.06 x 10^7 and 2.65 x 10^4 expressed in scientific notation?
4 x 10^2
500
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. The company used 70 liters of real fruit juice to make 3 times as many liters of Drink A as liters of Drink B. Write a system of equations that could be used to determine the number of liters of Drink A made, a, and the number of liters of Drink B made, b.
0.2a + 0.1b = 70
a = 3b
500
This graph shows the costs, in dollars, for different numbers of shirts at a local store.
The shirts are also available online for $4.25 each. There is a $10.50 shipping cost.
Would it be cheaper to buy 20 shirts from the store or online? Explain.
Cheaper online.
Store = $100
Online = $95.50
500
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 21 inches, and the length of the base is 18 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
63.7 inches
500
Ethan asked a random sample of students the two questions below.
- Do you have brothers or sisters?
- Does your family have a dog?
Ethan created this table to display the data he collected.
Ethan believes that students that have no brothers or sidters are more likely to have a dog than students that have brothers or sistes. Does the data support Ethan's belief? Explain why or why not.
He is correct.
Students w/o brother/sister = 62.5% of dog
Students w/ brother/sister = 42.9% have dog