All 8th Grade Math Resources
Example Questions
Example Question #1 : Number Sense
Which of the following answer choices displays a rational number?
Our answer choices consist of two types of numbers: rational numbers and irrational numbers. In order to correctly answer this question, we need to know the difference between the two types of numbers.
Rational numbers are numbers that we use most often, and can be written as a simple fraction.
Irrational numbers cannot be written as fractions, and are numbers that have decimal places that never repeat or end.
In this case, is our only rational number because it can be written as a simple fraction:
Example Question #2 : Number Sense
Solve:
In order to solve this problem, we need to recall our exponent rules:
When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:
Let's apply this rule to our problem
Solve for the exponents
We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:
Solve the problem
Example Question #1 : Algebra
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Example Question #2 : Algebra
Select the equation that best represents a linear function.
In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:
If we are unable to put an equation in this form, then the equation is not linear.
Let's take a look at our answer choices:
Notice that in this equation our value is to the third power, which does not match our slope-intercept form.
Though this equation is not written in form, we can tell straight away that this does not define a linear function because the
value is to the second power.
Again, though this equation is not written in form, we can tell straight away that this does not define a linear function because the
value is to the second power.
For this equation, we can solve for to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.
First, we can subtract from both sides:
Next, we can divide each side by
This equation is in slope-intercept form; thus, is the correct answer.
Example Question #1 : Algebra
Use algebra to solve the following system of linear equations:
There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination.
Substitution can be used by solving one of the equations for either or
, and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the
form, and then set both equations equal to each other.
Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable.
For this problem, substitution makes the most sense because the first equation is already solved for a variable. We can substitute the expression that is equal to , into the
of our second equation:
Next, we need to distribute and combine like terms:
We are solving for the value of , which means we need to isolate the
to one side of the equation. We can subtract
from both sides:
Then divide both sides by to solve for
Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both and
values.
Now that we have the value of , we can plug that value into the
variable in one of our given equations and solve for
Our point of intersection, and the solution to the system of linear equations is .
Example Question #1 : Geometry
The image provided contains a set of parallel lines, and
, and a transversal line,
. If angle
is equal to
, then which of the other angles is equal to
First, we need to define some key terms:
Parallel Lines: Parallel lines are lines that will never intersect with each other.
Transversal Line: A transversal line is a line that crosses two parallel lines.
In the the image provided, lines and
are parallel lines and line
is a transversal line because it crosses the two parallel lines.
It is important to know that transversal lines create angle relationships:
- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent
Let's look at angle in the image provided below to demonstrate our relationships.
Angle and
are vertical angles.
Angle and
are corresponding angles.
Angle and
are exterior angles.
Angle is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs
and
as well as angle
and
.
For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle
and
are vertical angles; thus, both angle
and
are congruent and equal
Example Question #1 : Geometry
Calculate the length of the missing side of the provided triangle. Round the answer to the nearest whole number.
The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or angle. When a triangle includes a right angle, the triangle is said to be a "right triangle."
We can use the Pythagorean Theorem to help us solve this problem.
The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:
We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:
Example Question #1 : Geometry
Calculate the volume of the cone provided. Round the answer to the nearest hundredth.
In order to solve this problem, we need to recall the formula used to calculate the volume of a cone:
Now that we have this formula, we can substitute in the given values and solve:
Example Question #1 : 8th Grade Math
The scatter plot provided displays a group of students' test scores versus the number of missing assignments the students have. Based on plot, select the best answer that describes the direction of the points.
A negative, non linear association
A negative, linear association
A positive, linear association
A positive, nonlinear association
A negative, linear association
The data points in the scatter plot move up the y-axis as the x-axis decreases; thus the data points show a negative association. Also, the data points do not curve, or go up and down, but gradually decreased; thus the scatter plot shows a linear association. We could even draw a "best fit" line:
Example Question #2 : 8th Grade Math
A teacher at a high school conducted a survey of seniors and found that students owned a laptop and
of those students also had a car. There were
students that did not have a laptop, but owned a car. Last, they found that
students did not own a laptop nor a car. Given this information, how many students had a laptop, but did not own a car?
To help answer this question, we can construct a two-way table and fill in our known quantities from the question.
The columns of the table will represent the students who have a laptop or do not have a laptop and the rows will contain the students who have a car or do not have a car. The first bit of information that we were given from the question was that students had a laptop; therefore,
needs to go in the "laptop" column as the row total. Next, we were told that of those students,
owned a car; therefore, we need to put
in the "laptop" column and in the "car" row. Then, we were told that
students do not own a laptop, but own a car, so we need to put
in the "no laptop" column and the "car" row. Finally, we were told that
students do not have a laptop or a car, so
needs to go in the "no laptop" column and "no car" row. If done correctly, you should create a table similar to the following:
Our question asked how many students have a laptop, but do not own have a car. We can take the total number of students that own a lap top, , and subtract the number of students who have a car,
This means that students who have a laptop, don't have a car.
All 8th Grade Math Resources
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