Learning Packet:
1) Write in words, the inverse, the converse, and the contrapositive of the following conditionals:
a) If today is Friday, then tomorrow is Saturday.
b) If Douglas does well in college, then he will apply to medical school.
c) Arlette will get a role in the play if she auditions.
d) Dorothea will graduate from law school in January if she takes courses this summer.
2)
a) Using the letters given to represent sentences and the proper logic connectives, express each of
the two compound sentences in symbolic form.
b) Prove that the two compound sentences are logically equivalent or give a reason why they are
not equivalent.
Let t represent “Ms. Wu is a teacher.”
Let e represent “Ms. Wu is an engineer.”
Sentences:
If Ms. Wu is a teacher, then she is not an engineer.
If Ms. Wu is not an engineer, then she is a teacher.
3)
Find the geometric mean of 16 and 156.
4) Given triangle ACE, with coordinates A(-6,6), C(-4,2), and E(5,5).
a) Graph and label triangle ACE.
b) Find the coordinates of A’C’E’, the image of ACE after D2.
b) Find the coordinates of A’’C’’E’’, the image of ACE after T -2,-3.
c) Find the coordinates of A’’’C’’’E’’’, the image of ACE after R270.
5) The perpendicular bisectors of ΔLMN intersect at O. If LO = 2x – 4, MO = y – 6, and
NO = 10. Solve for x and y.
6) In ΔABC, medians AD , BE , and CF are concurrent at P. If AP = 8, find the length of AD and
PD .
7) Solve the following quadratic equation:
8) Factor:
x2 = 9x – 20
2x2 + 13x + 21
9) Factor completely:
10x2 – 80x + 150
10) Find the distance, midpoint, and slope of the following set of points:
A(9,-5) & B(-3,7)
11) Given triangle PQO with vertices P(4,10), Q(6,0), and O(0,0).
a) Graph and label triangle PQO.
b) Find the coordinates of R, the midpoint of OP.
c) Find the coordinates of S, the midpoint of QP.
d) Prove RS = ½ OQ.
e) Prove RS is parallel to OQ.
12) Prove that the following is a rhombus. Show all work and write full-sentence explanations!!!!!!!!!!!
A( 2,2)
B(5,-2)
C(9,1)
D(6,5)
13) In parallelogram ABCD, the measure of <ABC = 3x – 12, the measure of <CDA = x + 40. Find each
angle of the parallelogram.
14) ABCD is a square. If the measure of <ABC is 3x + 30, find the measure of x.
15) The measures of two angles that are supplementary are in the ratio 7:2. Find the degree measure of
each angle.
16) The measure of the complement of an angle exceeds the measure of the angle by 24 degrees. Find the
degree measure of the angle.