entering geometry summer packet 2013 summer packet/geometry... · | g–5 x x x x x x algebra 1...
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Name: _____________________ Period: ____
Math Summer Packet For
Students Entering Geometry
Doral Academy Prep School
Math Department
Dear Parents and Students,
This Summer Packet has been designed to provide the students entering Geometry with an
appropriate review of basic skills and concepts they have already been exposed to on previous math courses.
It is intended to ease the transition into a new math discipline. It is not intended to be worked on one sitting.
This packet will be collected and graded. It will be the first grade you will receive; make it count.
What is geometry?
The word Geometry literally means “measuring of the earth.” Geometry the oldest math discipline and
it developed from the need to measure and delimit what surrounds us. It is the least computational of the
mathematical disciplines, but the one with the largest amount of vocabulary and terminology.
In this course you will not be required to perform calculations as you are accustomed. While there will
be calculations and applications of what you have learned in Algebra, you will be required to apply vocabulary
and concepts in a logical and systematic manner. Learning the vocabulary is not an option, and it is mostly
how you will work, and what you will be assessed and graded on. If you do not know the vocabulary and
concepts, your calculations will be wrong.
Familiarize yourself with the Geometry – Algebra 1 EOC Reference sheet. While you will be provided
with it in class, and you will be allowed to use it during the End Of Course Test, you must know how to use it to
your advantage. That includes knowing the meaning of each term included in it.
Your partners in education,
Doral Academy’s Math Department Team
orV bwh = V Bh =
S A . . = S A. . =
orbh bw hw + +2 2 2 Ph B+ 2
orV r h = � 2
= S A. . = S A. . =
rh r+2 2 2� �
rh B+2 2�
or
= 1 3
1 2
orV r h =
=
1 3 1 3
� 2 S A. . = r B( ) +1 2
2�
=
slant height of base
a apothem S.A. surface area
b base A area h height B area of base w width C circumference d diameter V volume r radius P perimeter
−180
−180 2( )n n
2( )n
Algebra 1 End-of-Course and Geometry End-of-Course Assessments Reference Sheet
Sum of the measures of the interior angles of a polygon =
=Measure of an interior angle of a regular polygon
where: n represents the number of sides
Florida Department of Education
| G–5
x x
x
x x
x
Algebra 1 End-of-Course and Geometry End-of-Course Assessments Reference Sheet
y2 y1
x2 x1
x1 y1 x2 y2
Slope formula
− −(x2 x1)2 + (y2 y1)
2
Midpoint between two points
( (
x1
x1
y1
y1
Quadratic formula
- −
Trigonometric Ratios opposite
opposite
hypotenuse
hypotenuse adjacent
adjacent
sin A°
tan A°
cos A°A°
Distance between two points
Slope-intercept form of a linear equation
Point-slope form of a linear equation
Special Right Triangles
Florida Department of Education
Vocabulary
• Use the Word bank to label the parts of each illustration, then
• Use the Key on the provided Reference Sheet to state what each variable on their related formula(s) stand for:
Word bank Label each part Formula breakdown:
Name of figure:
_________________
• Base
• Height
A = bh
b-___________________________
h-___________________________
Name of figure:
_________________
• Base
• Height
A = 1 2� bh
b-___________________________
h-___________________________
Name of figure:
_________________
• Base 1
• Base 2
• Height
A = 1 2� h(b1 + b2)
h- ___________________________
b1- ___________________________
b2- ___________________________
Name of figure:
_________________
• Radius
• Diameter
A= πr2
π-___________________________
r-___________________________
Name of figure:
_________________
• Side
• Apothem
A = 1 2� aP
a-___________________________
P-___________________________
• Use the Word bank to label the parts of each illustration, then
• Use the Key on the provided Reference Sheet to state what each variable on their related formula(s) stand for:
Word bank Label each part Formula breakdown:
Name of figure:
_________________
• Base
• Width
• Height
V = bwh
b-___________________________
w-___________________________
h-___________________________
SA = Ph + 2B
P-___________________________
h-___________________________
B-___________________________
Name of figure:
_________________
• Base
• Height
• Radius
V = Bh
B- ___________________________
h-___________________________
SA = 2πrh + 2B
π-___________________________
r-___________________________
h-___________________________
B-___________________________
What formula is used to calculate the
area of the Base? ________________
Name of figure:
_________________
• Base
• Height
• Slant height
• Vertex
• Lateral face
• Lateral edge
V = 1 3� Bh
B-___________________________
h-___________________________
SA = 1 2� Pllll + B
P-___________________________
llll----___________________________
B-___________________________
• Use the Word bank to label the parts of each illustration, then
• Use the Key on the provided Reference Sheet to state what each variable on their related formula(s) stand for:
Word bank Label each part of the figure Formula breakdown:
Name of figure:
_________________
• Base
• Height
• Radius
V = 1 3� πr2h
π-___________________________
r2-___________________________
SA = 1 2� (2 πr)llll + B
π-___________________________
r-___________________________
llll----___________________________
B-___________________________
Name of figure:
_________________
• Diameter
• Radius
• Center
• Great circle
• Hemisphere
V = 4 3� πr3
π-___________________________
r3-___________________________
SA = 4πr2
π-___________________________
r2-___________________________
Solve for x on the equations below. SHOW ALL YOUR WORK.
1) -2x - 2 = 9x + 75
2) -3x + 2 = -7x - 26
3) -4x + 8 = 8x - 64
4) 18x - 7 = 11x - 56
5) -13x + 3 = -5x - 85
6) -9x + 12 = -11x + 14
7) -20x - 11 = -9x + 99
18) -11x + 11 = -4x - 45
9) -x - 9 = -7x - 45
10) 3x + 7 = 9x + 1
Show your
work!
Solve for the indicated variable in the parenthesis.
1) P = IRT (T) 2) A = 2(L + W) (W)
3) y = 5x - 6 (x) 4) 2x - 3y = 8 (y)
5) x + y = 5 (x) 6) y = mx + b (b)
3
7) ax + by = c (y) 8) A = 1/2h(b + c) (b)
9) V = LWH (L) 10) A = 4πr2 (r2)
11) V = πr2h (h) 12) 7x - y = 14 (x)
13) A = x + y (y) 14) R = E (I)
2 I
15) x = yz (z) 16) A = r (L)
6 2L
17) A = a + b + c (b) 18) 12x – 4y = 20 (y)
3
Show your
work!
Problem Solving: Solve, if possible.
(1) During the month of June, a store manager recorded the expenses and receipts shown at the right. At the end of the month, what was the net income or loss?
Income Expenses
$665.44 $3766.58
$1378.90 $986.50
$2254.22 —
(2) A map distance of 1.25 inches represents 225 actual miles. What distance is represented by a 2 inch map
distance? (3) Margaret can pour 125 cubic feet of water per minute to fill a pool. How long will it take her to fill a pool
that is 20 feet wide and 75 feet long?
Numeric and Algebraic Expressions: Add, subtract, multiply, or divide.
(1) (-2)(7)(6)
(2) -14.3 + (-3.5) (3) - 61 - 14 (4) 21 - 63
(5) -36 ÷ (-6)
(6) -(3 • 12) (7) −8�� (8) −7813
Evaluate the expression.
(1) (3 - 5)2 - 14 ÷ 2
(2) 3−8
2−5•3 (3) -9 + 33 - 2
(4) 38 • 32 − 22 + 1
(5) 5(8 – 3)2
(6) 2.3(5.1 + 0.9)
(7) 3.6 ÷ (0.3 • 1.2) (8) [3 – (-6 – 1)2] ÷ 2
Evaluate the expression when x = 6 and y = – 5. Show all your work.
(1) � �
�
(2) 5y - � (3) (x ÷ 2)(3 + y)
(4) x2 – y + 9
Evaluate the expression when x = - 3 and y = 2. Show all your work.
(1) 3xy (2) (x2)(y2) (3) (x + y)(x – y)
(4) �+3�−3
Use the distributive property to rewrite the expression without parentheses. Show all your work.
(1) 2x(4x – 11y) (2) − �� (6� + 15)
(3) − �� �(2� + 6� − 4) (4) (–d)( –2d – 7e + 4)
Find the reciprocal of the number.
(1) 0.61
(2) −0.25 (3) − � (4) -242
Simplify the ratio.
(1) ����� !�" #
(2) $%�&'& (3)
�()�� !*()�+ (4)
�,-'%%-
(5) .$%&/
�/
(6) '012+!�" # (7)
'3)12#!�-144(�! (8)
�&���%%"#
Find the ratio of part-time employees to full-time employees, given the number of part-time employees and the total number of employees.
(1) 11 part-time employees, 30 employees (2) 28 part-time employees, 34 employees
(3) 6 part-time employees, 16 employees (4) 14 part-time employees, 21 employees
Solve the equation. Show all your work.
(1) 49 = 7n
(2) 3.11a = 31.1 (3) 0.3s = 9 (4) 12 = –20 + h
(5) 16 = 6s − 9 –s
(6) 4(6n + 2) = 7n − 3(3n −8) (7) 14k + (–11 + 2k) = 21 (8) � (61 − 36) = 25
Solve the inequality. Show all your work.
(1) 2r – 5 > 4r – 2
(2) k – 7k > 2k + 9 (3) 9p + 6 < 3p (4) s + 11.2 <25.6
Check whether the given number is a solution of the inequality. Show all your work.
(1) 4(x + 3) > 20; 2 (2) Name three solutions of (3a – 4) + (a – 2) > a + 11. Is a = 5a solution? Explain.
(3) Name three solutions of 41 + 8x < x – 15 Is x = -9.5 a solution? Explain.
Use the correct notation and give the coordinates of each of the following points: A: _____ D: _____ F: _____ N: _____ C: _____
Plot each point in the provided coordinate plane.
A(-2, 1) B(2, -2) C(0, -4) D(2, 5)
E�� , 0�
Write an equation in slope-intercept form of the line that passes through the given point and has the given slope. Show all your work.
(1) (2, -7), m = 1
(2) �� , −���, m = 6
(3) (-3, 1), m = ��
(4) (-8, 8), m = 3
Write an equation in slope-intercept form of the line that passes through the given points. Show all your work.
(1) (2, -1), (1, 3)
(2) (0, 2), (-5, 1)
(3) (3, 0), (2, 9)
(4) (0, -7), (-8, 0)
Find all square roots of the number or write no square roots. Check the results by squaring each root.
(1) 125
(2) -49 (3) 256 (4) 0.16
Simplify the expression. Give the exact value in simplified form.
(1) �√� (2) √4 • √7
(3) ;(−3)� +8� (4) $
√�$
Vocabulary
• These are the mathematical terms all students entering Geometry should know. More will be learned throughout the course.
• Instructions: Use the Mathematics Glossary for Algebra 1 EOC and Geometry EOC to define each vocabulary term; provide an illustration.
Term Definition Illustration
1. Acute Angle
2. Altitude
3. Angle
4. Bisector
5. Circle
6. Complementary Angles
7. Congruent Angles
Term Definition Illustration
8. Congruent Segments
9. Congruent Triangles
10. Line
11. Line Segment
12. Median
13. Midpoint
14. Obtuse Angle
15. Parallel Lines
16. Perpendicular Lines
Term Definition Illustration
17. Perpendicular Bisector
18. Plane
19. Point
20. Ray
21. Right Angle
22. Similar Triangles
23. Supplementary Angles
24. Straight Angle
25. Vertex