All ISEE Upper Level Math Resources
Example Questions
Example Question #81 : Algebraic Concepts
What is ?
can be any real number.
Add the left and right sides of the equations separately:
Divide:
Example Question #82 : Algebraic Concepts
Give the -intercept of the line through points and .
The line has no -intercept.
The slope of this line is
.
Let the -intercept be . Then, using the slope and point , we know that:
Take the reciprocal of both sides:
The -intercept is .
Example Question #81 : Algebraic Concepts
A line through points and has slope . What is ?
Substitute into the slope formula:
Example Question #781 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Give the -intercept of the line through points and .
The line has no -intercept.
The slope of this line is
.
Let the -intercept be . Then, using the slope and point , we know that:
The -intercept is .
Example Question #81 : How To Find The Solution To An Equation
Give the -intercept of the line of the equation:
The line has no -intercept.
Substitute :
The -intercept is .
Example Question #782 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Solve for , giving all real solutions:
The equation has no real solution.
Substitute and, subsequently, .
Factor as , replacing the two question marks with integers whose product is and whose sum is . These integers are , so
.
Break this up into two equations, replacing for in each:
or
Example Question #782 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Give the -intercept of the line through points and .
The line has no -intercept.
The line has no -intercept.
The slope of this line is
.
A line with slope 0 is horizontal, and therefore has no -intercept.
Example Question #82 : How To Find The Solution To An Equation
What is ?
Substitute into the second equation:
Example Question #784 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Solve for , giving all real solutions:
The equation has no real solutions.
Write the equation in standard form:
can be factored out of each term:
Factor the trinomial by writing , replacing the question marks with two integers with product and sum . These integers are , so the above becomes
.
We can disregard the , as it does not contribute a solution. Set each of the other two factors equal to and solve separately:
The solution set is .
Example Question #83 : Algebraic Concepts
For what value of is ?
We need to use logarithms.
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