entering geometry summer packet 2013 summer packet/geometry... · | g–5 x x x x x x algebra 1...

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