Math Summer Packet For

Students Entering Geometry

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

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

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