All ISEE Upper Level Math Resources
Example Questions
Example Question #71 :Algebraic Concepts
John and Tom are farmers. John can produceof an organic product in six months. Tom can produceof the organic product in one year. How many pounds of organic product can they produce in three years together? (Assume that they can work and produce the organic product all year round.)
John can producein six month. Therefore we can set up a proportion:
Tom can producein one year. Then we can set up another proportion:
Example Question #71 :Algebraic Concepts
Solve for.
Example Question #72 :Algebraic Concepts
Solve the set of equations:
Solve the second equation for:
Now substitute this expression into the first equation:
Substitute this new value forinto the first equation:
Example Question #73 :Algebraic Concepts
If, find.
Example Question #74 :Algebraic Concepts
If, find.
Take the square root of both sides:
Example Question #71 :Equations
Solve the set of equations:
Solve the second equation for:
Now substitute this expression into the first equation:
Substitute this new value ofinto the first equation:
Example Question #76 :Algebraic Concepts
Give the slope of the line of the equation:
Rewrite in the slope-intercept form:
The slope is the coefficient of, which is.
Example Question #72 :Algebraic Concepts
Give the slope of the line of the equation:
Rewrite in the slope-intercept form:
The slope is the coefficient of, which is.
Example Question #78 :Algebraic Concepts
Solve for:
The equation has no solution.
The equation has no solution.
,所以我们可以重写这个情商uation as:
Therefore, we set the exponents equal.
This is identically false. This means that the equation has no solution.
Example Question #79 :Algebraic Concepts
Solve for, giving allrealsolutions:
The equation has no solution.
Write the equation in standard form:
Factor out the greatest common factor of:
Factor the trinomial by writing, replacing the question marks with two integers with productand sum. These integers are, so the above becomes
.
Set each of the three factors equal toand solve separately:
The solution set is.