Algebra and Geometry Sample Prob
Algebra and Geometry Sample Problems
Reasoning. State whether the following statement is sometimes, always, or never true and explain
your answer with an example or counterexample. Systems of inequalities made up of parallel lines
have no solutions .
Answer: Sometimes. If the system is 2x + 3y > 5 and 2x + 3y is < 7 the points between the two lines
would be solutions.
Reasoning. Identify the system of equations whose solution is not similar to the other three.
Answer: The third set. This system has no solution. The
lines parallel .
Challenge. Describe the family of functions that define this translation.
Challenge: Use the enlarged internal dilation that begins
with the figure to the right
and your knowledge of dilations to explain that the sum of the
geometric series is true
Answer. Proof Without Words
If your look at teach layer, one of three triangles is shaded which represents 1/3 of the total area.
Writing in Math : Describe the method used to find the equation of a circle if the endpoints of the
diameter are given.
Answer: First you should find the center of the circle which is the midpoint of the diameter. Next
calculate the length of the radius using the distance formula from the radius to one of the points on the
diameter. Finally substitute the values of the center, one endpoint of the diameter, and the length of
the radius into the general equation for the circle (x -h)2 + (y + k)2 = r2.
Writing in Math : Explain if you are graphing a hyperbola from an equation , one of be best ways to
draw a representative sketch is by graphing the asymptotes of a hyperbola.
Answer: The graphs of the asymptotes of a hyperbola provide boundaries for the hyperbola. If the
equation is given, the center, and values of a and b are available . The foci, ± c, can be found using
the Pythagorean Theorem. Graphing the asymptotes gives a frame for the hyperbola.