All SSAT Upper Level Math Resources
Example Questions
Example Question #4 :How To Graph Inverse Variation
Give the slope of the line that passes through the- and-intercepts of the graph of the equation.
The line cannot exist as described.
The line cannot exist as described.
The graph ofdoes not have an-intercept. If it did, then it would be the point on the graph with-coordinate 0. If we were to make this substitution, the equation would be
and
This is identically false, so the graph has no-intercept. Therefore, the line cannot exist as described.
Example Question #5 :How To Graph Inverse Variation
Give the-coordinate of a point with a positive-coordinate at which the graphs of the equationsandintersect.
方程的图形不相交。
方程的图形不相交。
Substituteforin the second equation:
The discriminant of this quadratic expression is, where; this is
.
The discriminant being negative, there are no real solutions to this quadratic equation. Consequently, there are no points of intersection of the graphs of the two equations on the coordinate plane.
Example Question #6 :How To Graph Inverse Variation
The graphs of the equationsandintersect in two points; one has a positive协调。和一个有一个负的协调。Give the-coordinate of the point of intersection that has a positive协调。
Substituteforin the second equation:
This quadratic equation can be solved using themethod; the integers with productand sum 5 areand 6, so continue as follows:
Either, in which case, or
, in which case
The desired-coordinate is paired with the positive-coordinate, so we substitute 0.5 forin the first equation:
Example Question #7 :How To Graph Inverse Variation
Give the-coordinate of the point at which the graphs of the equationsandintersect.
方程的图形不相交。
Using the substitution method, set the values ofequal to each other.
Multiply both sides by:
Substitute in either equation:
Example Question #8 :How To Graph Inverse Variation
A line with slope 4 shares its-intercept with that of the graph of the equation. Which of the following is the equation of that line?
This line does not exist, since the graph ofhas no-intercept.
The-intercept of the graph of—the point at which it crosses the-axis—is the point at which, so substitute accordingly and solve for:
The-intercept of this graph, and that of the line, is. Since the slope is 4, the slope-intercept form of the equation of the line is
To put it in standard form:
Example Question #9 :How To Graph Inverse Variation
, whereis a right angle,, and. Which of the following cannot be true?
All of the statements given in the other choices are true.
is a right angle
has perimeter
is a right angle
is a right angle and, so
,
making30-60-90三角形。30-60-90的三角形西奥rem, the length of the short legis half that of hypotenuse:
and the length of long legistimes that of:
Corresponding sides of congruent triangles are congruent, so; since, it follows that.
Also,,, and, so the perimeter ofis the sum of these, or
.
Corresponding angles are congruent, soand. By substitution,and.
The false statement among the choices is thatis a right angle.
Example Question #1 :How To Graph A Quadratic Function
What is the vertex of the function?
The-coordinate of the vertex is, where.
To get the-coordinate, evaluate.
The vertex is.
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