All ACT Math Resources
Example Questions
Example Question #1 : How To Find Excluded Values
Find the excluded values for in the following algebraic fraction.
To find the excluded values, find the -values that make the denominator equal zero.
1) set the denominator equal to zero.
2) solve for .
Example Question #3 : How To Find Excluded Values
Find the excluded values of the following algebraic fraction
The numerator cancels all the binomials in the denomniator so ther are no excluded values.
To find the excluded values of a algebraic fraction you need to find when the denominator is zero. To find when the denominator is zero you need to factor it. This denominator factors into
so this is zero when x=4,7 so our answer is
Example Question #1 : How To Find Excluded Values
Which of the following are answers to the equation below?
I. -3
II. -2
III. 2
II only
II and III
III only
I, II, and III
I only
III only
Given a fractional algebraic equation with variables in the numerator and denominator of one side and the other side equal to zero, we rely on a simple concept. Zero divided by anything equals zero. That means we can focus in on what values make the numerator (the top part of the fraction) zero, or in other words,
The expression is a difference of squares that can be factored as
Solving this for gives either or . That means either of these values will make our numerator equal zero. We might be tempted to conclude that both are valid answers. However, our statement earlier that zero divided by anything is zero has one caveat. We can never divide by zero itself. That means that any values that make our denominator zero must be rejected. Therefore we must also look at the denominator.
The left side factors as follows
This means that if is or , we end up dividing by zero. That means that cannot be a valid solution, leaving as the only valid answer. Therefore only #3 is correct.
Example Question #1 : Matrices
Evaluate:
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Example Question #1061 : Algebra
What is ?
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Then, simplify:
Therefore,
Example Question #1062 : Algebra
If , what is ?
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
and
or
Therefore,
Example Question #1 : How To Find Scalar Interactions With A Matrix
Simplify:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Example Question #1 : Matrices
Simplify the following
When multplying any matrix by a scalar quantity (3 in our case), we simply multiply each term in the matrix by the scalar.
Therefore, every number simply gets multiplied by 3, giving us our answer.
Example Question #5 : Scalar Interactions With Matrices
Define matrix , and let be the 3x3 identity matrix.
If , then evaluate .
The 3x3 identity matrix is
Both scalar multplication of a matrix and matrix addition are performed elementwise, so
is the first element in the third row of , which is 3; similarly, . Therefore,
Example Question #4 : Matrices
Define matrix , and let be the 3x3 identity matrix.
If , then evaluate .
The 3x3 identity matrix is
Both scalar multplication of a matrix and matrix addition are performed elementwise, so
is the first element in the third row of , which is 3; similarly, . Therefore,