P;re-AP Geometry "Summer Assignment

At ECHS, the Pre-AP program is designed for motivated students and inci~pC=ndfnt thinkers who will be also taking various college classes. At this level, you will be reqUfr'~'étt'o work ·, · independently and collaboratively through various tasks and activities, This summer

. . . . ! . '

assignment will give you the opportunity to review expected skills so that you are as well prepared as possible for Geometry this fall.

Assignment Specifications: • ' Due the 1st df( o,f_ class-quiz gra,qf . . . • Completed neatly and.legibly with your answers bqxed--=-iflq~:n-n-9trffar.ht~·-1w1tl-not· -- -- ------ ---

grade it!;,· ,. ''·'· ,.-,. • SHOW ALL WORK! • If you need extra room, use notebook paper and staple to the back of thepacket. ¡',

• Any work on notebook paper must be neatly labeled.

Additionally, an assessment (major grade) will be given within the first two weeks to evaluate basic understanding and skill mastery of the topics. This formal, in-class assessment will occur after students have beeh provided with reasonable opportunity to ask qrrestions, ,A "" representative sample of problems will be selected for the assessment, modeled after those

( from the assignment. Both the assignment grade (quiz) and the assessment grade (major) will bepa-rf"ofthel5thir\eW~'ek'sgrade. , "''. ,¡, L,; •· . '

You can find assistance on the following websites: • purplemath.com • math.com • algebra.com • khanacademy.com - • schooltube.corn

I '· ~ ' • ,

- . - If you have any questions regarding the Summer Assignment au ring the summer break, I can hie .

1

reached through email: kimberly.buchmeyer@gpisd.org

Have a fantastic summer break! I look forward to meeting you in August!

Sincerelv,

L¡d,¡..,' <

f/l/0fr Mrs. Buchmeyer ECHS@ SGPHS

ORDER OF OPERA TIO NS REMEMBER: PLEASE EXCUSE MY DEAR AUNT SALLY

P-Perform all operations that occu,rwi!~in grouping symbols such as ( ), {},or []. E -..:i. Évaluate e'i<pÓnen+s (pci'wers and roots)

M & D - Perform muttiplicction-cnd &yis,ion, operations from left to right A & S - Perform addition and subtraction operations from left to right.

Simplify the following expressions.

1] (-4 + 2)(-2 + 5)2 • 2] 5 - 12 + 3 - 7 3J a·+co-2)+5 4] 11x622-3

LINEAR EQUATIONS Helpful hints:

• When solving a linear equation the go.al is to is~late the variable. • To move a tJrm across the equál sign, you must use inverse opercftóns. "' '

· To keep the equation balanced, you must perform the operation on both sides of the equation.

Find the value ofthe variable.

4 1] - a= - 20 5

X 2] -- = 5

.3 3]2p+5=13 4] 12 + 2b = 2 + 5b

'' \

5] 4x+ 5 + 5x+40 = 1'80 · 6,] 2(4X+ 4)= X+ J 7] 2(x+ 5) = 3 (x- 2) 8] 180 - x= 3 (90 -x)

1 ·; 1 · • · 'l '', 9] -(6 + 4x) - -(8x- 12) = - (2x- 4)

2 4 2

1 :"'

10] 5x- [7 - (2x-1)] = 3 (x- 5) + 4(x,+ 3)

FRACTIONS Examples: Simplify the fraction.

a] Bw Bw 5x- 10 5x-10 5 (x- 2) x-2 x+6 x+6 x+6 b] --- c] --- -· -=4w - 36 - x2 36 - >f- (6 - x)(6 + x) (6 -.~ 2 2 15 15 15 3

Simplify the fraction.· ' 1] 14 2] 75 3] 18 a 41 3x ,5] 5 be

-·-'· 10 15 36 X 10b2

6

x+2

9] 3x+ 6 5a+ 5b -8y3

6] 10y2

- 18r 3 t 6a+ 12 7]

12 rt 8] 10] ·'

a 2 - b'2'

b 2 - 25 11] ----

b 2 - 12b+ 35

a 2 +Ba+ 16 12]----

a 2- 16

3x 2 - 6x- 24 13]

3x2 + 2x- 8

THE COORDINATE PLANE

--- ---- Name the coordinates of each point. í ' I \

1. M 2. N 3. K 4. R M R

T N u p

s 1K ~ . V z Q

w

J

5. S 6. T 7. U 8. V

9. W 10.Q

11. Name all the points shown that lie on thex-axis.

12. Name all the points shown on the y-axis.

13. What is thex-coordinate of every point that lies on a vertical line through P?

14. Which of the following points lie on a horizontal line through W? (-2, 1) (2, 3) (1, -3) (-2, O) (O, -3) (2, O)

· Name all the points shown that lie in the quadrant indicated. (A point on an axis is not in any quadrant.) 15. Quadrant I 16. Quadrant II 17. Quadrant Ill 18. Quadrant IV

Plot each point on the graph shown to the right. y

~- -+-- --~ : -- --+- [ __ L_"_--:-~---

19.A (2, 1) 20. B (5, O)

21.C (O, 3) 22. D (-3, 1) ;

l

l 'l 3 ' ~ I X

23. E (-2, -1) 24. F (1, -2) -2

~----1-- --i----- ---- -::3 __ _,_-I--- ----- ----1----

25. G (4, -2) 26. H (-4, -3)

--··---- ------.- ----·-- ----·--------- ·- _71-i-- --- --·-- .. !..---

\_j Find the coordinates of the midpoint of AB.

27. A (O, 1),8 (4, 1) 28. A (-3, 4), B (-3, -4)

GRAPHS AND EQUATIONS OF LINES

SLOPE-INTERCEPT FORM

y= m x + b, where m = slope and b = y-intercept Graphing Equations in Slope-Intercept Form 1. Write the equation in slope-intercept by solving for y 2. Find the y-intercept and use it to plot the point where the line crosses the y-axis. 3. Find the slope and use it to plot a second point on the line. 4. Draw a line through the two points.

WRITING EQUATIONS OF LINES

To write the equation of a line in slope-intercept form you must have the slope and the y-intercept.

Given a Graph

Identify the y-intercept and the slope from the graph and plug those values into the point-slope

equation y - Y1 = m(x - x-).

Given the Slope and a Point

Example: Write an equation of the line that passes through (1, 3) and has a slope of -5.

Step 1: Substitute -5 form, 1 for x1, and 3 for y¡. Step 2: Distribute -5(x - 1 ). Step 3: Solve for y by adding 3 to each side.

Given Two Points

Step 1 : Find the slope of the line using the two points and the formula m = Yf ~1 Step 2: Choose either point and follow the steps above.

2 1

y - 3 = -5(x - 1) y- 3 = -5x + 5 y= -sx + 8

PROBLEMS:

Write an equation of the line that passes through the given point and has the given slope. 1. (O, 4), m = 2 2. (1, O), m = 3 3. (9, 3), m = -23

Write an equation of the line that passes through the given points. 4. (8, 5), (11, 14) 5. (-5, 9), (4, 7) 6. (-8, 8), (O, 1)

Write an equation of the line. 7. I

I ... J -

I ~. - -- - I I •

I I .,

J - ,...._.

- - - _7

8. t-- - -- -

... - -6 ." ·- -- --- - - - -, - --

" •

" -2 -- 1--. " " .. .

I

\.J

SYSTEMS OF LINEAR EQUATIONS

REVIEW: SUBSTITUTION

/--, METHOD

' ) Solve: Y =5-2x 5X-6Y=21

Solution: Substitute 5 - 2x for y. sx - 6(5 - 2X) = 21 Sx - 30 + 12X = 21

17X-30 = 21 17X=51

x = 3 Then substitute 3 for x. y= 5 - 2(3) y= -1

CÁNSWER: (3, -1D Solve each system using substitution. 1. y= 2x + 5 2. Bx + 3y = 26

3x - y = 4 2x = y - 4 3.x -7y=13

3x- Sy= 23 4. 3x +y= 19

2x-5y=-10

REVIEW:

ELIMINATION METHOD Example 1 - Solve: 3x + 4Y = -10

5X-2Y= 18 Solution: 3X + 4Y = -10 3x + 4y =

2(5X-2Y= 18)~10 10X-4Y 13.x: 36 = 26

x = 2 Then substitute 2 for x. 3(2)+4y=-10

4Y = -16 Y=

~ Example 2 - 5x- 2y = -19

2x+3y=O Solution: 3(5x - 2y = -19)

2(2x + 3y = O) 15x -6y = -57 4x + 6v= o

19x = -57 X = -3 Then substitute -3 for x.

2(-3) + 3y = O -6 + 3y = O

3y=6 =2

Solve each system using elimination. 1. 3x + 4y = 9 2. 5x + 3y = 30

-3x- 2y = -3 3x + 3y = 18 3. 3x +y= -3

X+ 4y = 10 4. 4x-6y=-26

-2x+3y=13

5. 2x-8y = 24 3x +Sy= 2

6. 5x-9y=47 6x + 2y = 18

RADICAL EXPRESSIONS

Simplify.

1. -../56 Solution: .J's6= ,/4 · 14 = 2v'I4 ../7

2. -./3 Solution: {z = ,/7 · ,/3 =fil= fil - ~ 3 ,/3 ,/3 ,/9 3

3. (3F7}2 Solution: (3../7)2 = (3.ff. 3~ = 3(3)( ff.~= 9(7) = 63

Simplify the following.

2 . .Jsf 3 . ../24

[Bo 7.~25

.s 8. J3

2../[3 9. $2

2 14. (3./8) 15. (9·tif

4. J§a

{265' 10. ~48

16. 5"18

5 . .J300 6. ~

11. 032 2 12. (%!)

17. 4./27 18. 6../24

Solve for x. 1. 22 + X 2 = 42

Solution: 4 + x 2 = 16 x2 =12 X =,fu X = 2,/3

2. x2 + (3,/2/= 92

Solution: x 2 + (9)(2) = 81 x2+18=81 x2 = 63 x= -163 x=~ x= 3,/7

Solve for x. Assumex represents a positive number. 1. 32+42= x2 2. x2+42= 52

5. 42 + 72 = x2

7. !2+x2= 32

6. x2 + 52 = 102

9. x2+ (7J3)2 = (2x)2

EXPONENTS

REVIEW: Exponent Rules

a O= 1 Example: 5° = 1 am º an = am+ n Example: X 2 º X 4 = X 2 + 4 = X 6

am .a 7-3 4 an=am-n Example: \3=b =b (amt= a rrun) Example: (y 3)4 = y 3(4l = y 12

a·m = ;i;i Example: 6 ·2 = t = ;6

Simplify.

1. (-6)3 2. (-5)4 3. 3·2 4. 2"3 5. (-4)"3

8. 15º 9. (-1)20 10. (-1)99

Simplify. Use only positive exponents in your answers. [9

13.r5·r8 14.x·1·x·2 15. 4 r

m3 16.

ms 17. a • a ·1

24. (-2ab 5)(-4ab ·3)

FACTORING

Examples: Factor. 1. 24X 3

- 32x 2 Hint: Bx 2 is the greatest = Bx 2(3X - 4) common factor between

the two terms.

2. x2-12x - 28 (x -14)(x + 2)

Factor the trinomial. if the trinomial cannot be factored, say so. 1. X 2 + 5X + 4 2. X 2 - BX+ 12 3. 5x2+5x-10

4. 3x2+ 54x+ 243 5. -X2+ 2X-1

I j' ~---

QUADRATIC EQUATIONS

Example: 3x2+14x+8=0 Solution: (3x + 2)(x + 4) = O 3x + 2 = O or x + 4 = O

Solve each equation by factoring. (Hint: You may need the Quadratic Formula, from Algebra l. If you are not familiar with the Quadratic Formula, please do some research on the web. If this doesn't help, please email me and I will help.)

1 . X 2 + 5X - 6 = Ü 2.x2-7x-18=0 3. X 2 = 20X- 36

4. x 2 +Bx= 20 5. 4.x2 + 15 = 17x 6. 3x 2- 13x - 10 = O

PROPORTIONS

Example: 1. I=L 2 22

3(22) = 2y 66=2y 33=y

2. X+4 X-2 --=--

5 3 3(x + 4) = 5(x - 2) 3x + 12 = 5x - 1 O

22 = 2x 11 =X

Solve the following proportions using the format used in the examples.

1 7 = y 2 7 =~ . 2 3 . 3 X

10 6 4. ----- 6x+7 2x+9

4 6 5. --=-- x-3 x+3

3x-5 X-15 6' -2-=-4-

2-4X 6X-8 7. --=--

-6 10 x+2 4

B. -5-= x+l 2 x-2 9. --=--

x-3 6

Solve the formula for the indicated variable. 10, Perimeter of a parallelogram:

P= 2(a +b). Solve for b 11. Area of a rectangle:

A=lw. Solve for l

l L Area of a regular polygon: 1 A= -aP. Solve for a 2

13. Volume of a pyramid I V =-Bh. Solve for B 3