Download Unit 1: Square Roots

Unit 1: Square Roots
Directions: Simplify the square roots as far as possible.
80
1.
2.
315
3.
1500
Directions: Add/Subtract the following square roots. Be sure to simplify as far as
possible.
4.
3 10  6 10
5.
2 96  216
Directions: Multiply the following square roots. Be sure to simplify as far as possible.
6.
9 5 3 7
7.
4 12  7 6
Directions: Using the FOIL method, multiply the two binomials and simplify as far as
possible.
8.


6  2 24 4  9 2

Mr. S. Cella
Murray Avenue M.S.
Unit 2: Equation of a Line
Directions: Find the equation of a line given the following information.
1.
A line containing point (7 , -3) with a slope of -4.
2.
3
A line containing point (-15 , 12) with a slope of  .
5
3.
A line containing points (-6 , 2) and (3 , 14).
4.
A line which has a y-intercept of -5 and an x-intercept of 7.
5.
A line which is perpendicular to 3 y  2x  15 and goes through the point (6 , 5).
6.
A line containing point (6 , -1) and is parallel to 5x  2 y  42.
7.
Find y so that the line containing (5 , -1) and (3 , y) will have a slope of 2.
8.
Find the intersections for the following lines:
Line 1: 4 x  y  9  0
Line 2: 4x  9 y  47  0
Line 3: 4x  3 y  11  0
Mr. S. Cella
Murray Avenue M.S.
Unit 3: Segments
1. State the Distance Formula:
3.
2. State the Midpoint Formula:
Find the distance and midpoint of AB where A(7 , -2) and B(3 , 10).
Distance AB : ____________
Midpoint AB : ____________
4.
Find endpoint G given endpoint F(-5 , 3) and midpoint H(15 , -9).
5.
Assume that point Y is between points X and Z in XZ . If XY  6w  14,
YZ  9w  1, and XZ  10w  53, find the measure of the three segments.
6.
Assume that W is the midpoint of segment ST . If SW  6m  10 and
ST  16m  4, find the measure of the three segment.
7.
Point B is between points A and C such that AB 
8.
Point W is between points X and Y such that W is
3
AC . If points A and C
5
are located at (-6 , 2) and (4 , -3) respectively, find the location of point B.
2
away from point Y. If
7
point X can be found at (5 , -16) and Y is located at (-16 , -2), find the location
of point W.
Mr. S. Cella
Murray Avenue M.S.
Unit 4a: Angles
1. Find the values for w and m using the following diagram.
2. Find the values for x and y using the following diagram.
3. Assuming that two angles are complementary and one angle is 15 more than two
times the other, find the measure of the two angles.
4. The ratio of two supplementary angles is 7:11. Find the measure of the two
angles.
5. The measure of the supplement of an angle exceeds five times the measure of the
complement of the angle by 10. Find the measure of the original angle.
6. ________________________ are non-adjacent angles formed by the intersection
of two lines.
7. Two _______________________ angles share a common vertex and a common
side, but they don’t share any interior points.
Mr. S. Cella
Murray Avenue M.S.
Unit 4b: Polygons
1. How many sides does a regular polygon have if the sum of the interior angles is
3,060?
2. How many sides does a regular polygon have if the number of diagonals which could
be drawn is 77?
3. How many sides does a regular polygon have if the measure of each exterior angle is
15?
4. How many diagonals does a regular octagon have?
5. What is the sum of the measures of the interior angles of a regular 27-gon?
6. What is the measure of each interior angle of a regular 30-gon?
7. A regular dodecahedron has 12 sides. What is the measure of each central angle?
What is the measure of an exterior angle?
8. Find the value of x in the following diagram:
9. Find the value of x in the following diagram:
Mr. S. Cella
Murray Avenue M.S.
Unit 5: Factoring
Directions: Factor the following expressions completely. You may use the FACTOR
program if necessary.
1.
16x 5  12x 4  4x 3
2.
6x 4  15x 3  9x 2
3.
12x 5  4x 3  x
4.
 18x 7  x 5  4x 3
Directions: Factor and solve the following equations. You may use the FACTOR
program if necessary.
5.
12x 2  x  6  0
6.
6x 2  47x  8  0
7.
56x 2  3x  20  0
8.
120x 2  214x  91  0
9. The perimeter of a rectangular shuffleboard court is 58 meters. It is known that the
length is one meter more than three times the width. Find the dimensions of the
rectangle.
10. A picture frame has two parts: the actual wooden frame and the glass part to insert a
picture. The length of the glass is 8 inches longer than the width of the glass. It is
known that the glass to the outside boarder of the frame is four inches away at all
sides. If the area of the actual frame is 209 squared inches, what is the perimeter of
the glass part of the frame?
Mr. S. Cella
Murray Avenue M.S.
Unit 6: Laws of Logic
Directions: Write the converse, inverse, and contrapositive for the following
conditional. Determine the truth value for each statement.
________ 1. Conditional: If AM  MB , then M is the midpoint of AB.
________
Converse:
________
Inverse:
________
Contrapositive:
2.
Create a truth table for (~p v q) ^ ~r
Q
R
3.
Create a Venn Diagram for the following information:
P
A guidance counselor is planning schedules for 30 students. Sixteen students say they
want to take French, 16 want to take Spanish, and 11 want to take Latin. Five say they
want to take both French and Latin, and of these, three want to take Spanish as well. Five
want only Latin, and 8 want only Spanish. How many students want French only?
Directions: Write the law being applied on the provided lines. If no law is being
applied correctly, write “invalid”.
___________ 4. (1) If you run for five hours a day, you will be in shape.
(2) If you are in shape, then you will participate in tomorrow’s race.
(3) If you run for five hours a day, then you will participate in the race.
___________ 5. (1) If you are 13 years old, you aught to attend middle school.
(2) If you attend middle school, then you should take an algebra class.
(3) If you are 13 years old, then you should take an algebra class.
___________ 6.
(1) If you go to brunch on Sunday, then you will eat a lot of food.
(2) Jimmy ate so much food that he has a belly ache!
(3) Jimmy went to brunch on Sunday.
Mr. S. Cella
Murray Avenue M.S.