entering geometry summer packet 2012 geometry... · familiarize yourself with the geometry –...
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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
Label each illustration and state what each variable on each formula stand for:
Name Label each part Formula breakdown:
A = 1 2� bh
b-
h-
A = 1 2� bh
b-
h-
A = 1 2� h(b1 + b2)
h-
b1-
b2-
A= π2r
A = 1 2� aP
a-
P-
Label each illustration and state what each variable on each formula stand for:
Name Label each part Formula breakdown:
V = bwh
b-
w-
h-
SA = Ph + 2B
P-
h-
B-
V = Bh
B-
h-
SA = 2πrh + 2B
π-
r-
h-
B-
What formula is used to calculate the
area of the Base?
V = 1 3� Bh
B-
h-
SA = 1 2� Pllll + B
P-
llll----
B
Name Label each part Formula breakdown:
V = 1 3� πr2
π-
r2-
SA = 1 2� (2 πr)llll + B
π-
r-
llll----
B-
V = 4 3� πr3
π-
r3-
SA = 4πr2
π-
r2-
Perform the indicated operation. Show all your work and DO NOT USE DECIMALS.
1) 65/6 ÷ 61/11 =
_____
11) 55/12 ÷ 16/7 =
_____
2) 27/9 ÷ 21/2 =
_____
12) 81/3 ÷ 31/8 =
_____
3) 32/4 ÷ 25/10 =
_____
13) 61/9 ÷ 21/5 =
_____
4) 41/5 ÷ 91/3 =
_____
14) 51/6 ÷ 11/4 =
_____
5) 89/10 ÷ 66/11 =
_____
15) 41/8 ÷ 22/12 =
_____
6) 71/7 ÷ 51/2 =
_____
16) 31/4 ÷ 92/6 =
_____
7) 83/12 ÷ 81/2 =
_____
17) 31/11 ÷ 41/8 =
_____
8) 18/9 ÷ 75/7 =
_____
18) 57/10 ÷ 43/5 =
_____
9) 91/2 ÷ 31/3 =
_____
19) 92/9 ÷ 93/8 =
_____
10) 41/3 ÷ 51/7 =
_____
20) 31/6 ÷ 86/11 =
_____
Show your
work!
Simplify the radicals. State your answer in radical form. DO NOT USE DECIMALS.
1) 5√20 + 4√125 =
11) 2√12 =
2) 22√2 / √11 =
12) 2√75 =
3) 34√27 - 5√192 =
13) 3√432 * 2√27 =
4) 2√32 * 2√8 =
14) 4√72 + 3√18 =
5) 2√12 * 4√12 =
15) 4√48 + 4√75 =
6) 28√27 - 4√48 =
16) 4√48 * 5√27 =
7) 4√18 + 5√50 =
17) 4√12 + 2√75 =
8) 3√50 * 2√32 =
18) 4√32 * 3√8 =
9) 5√75 =
19) 4√108 * 5√27 =
10) 5√27 * 4√75 =
20) 4√192 + 4√12 =
Show your
work!
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!
11) -12x + 3 = -5x - 60
12) 15x - 7 = 10x + 38
13) -7x + 3 = -5x + 5
14) 5x - 2 = 3x
15) -6x + 9 = 5x + 75
16) 3x - 7 = -3x - 49
17) -7x + 4 = -4x - 20
18) -x + 2 = -10x - 70
19) -x - 9 = -3x - 31
20) -15x + 10 = -7x + 74
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 = 4r2 (r2)
11) V = r2h (h) 12) 7x - y = 14 (x)
13) A = x + y (y) 14) R = E (I)
2 l
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!
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
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