2010 assessment review_homework_1-4-done

Assessment Review Homework

• Homework #1• Homework #2• Homework #3• Homework #4• Homework #5

Assessment ReviewHomework #1

Assessment Review HW #1

1) What equation represents the relationship between x and y ?

A)y = 2xB)y = 4xC)y = x + 6D)y = 2x + 2

Check each equation with two points:

a) (2,8) y = x + 6

8 = 2 + 6 8 = 8 YES

(x , y)a) (6,12)

y = x + 6 12 = 6 + 6 12 = 12 YES

(x , y)

22

my

x= =VV

xV yV

y = mx + b

y = 1x + ?

2

21=

2) Complete the function table below with the missing values for y. Based on the function table, write a function rule that shows the relationship between x and y.

Answer ___________

y = mx + b

19

23

41

y = 4x + ?

my

x= VV

xV yV0 b

y = 4x + -1

y = 4x + -1

-1

44

1= =

Bring x back to 0.

3) The table below shows a relationship between x and y.

Which equation shows the relationship between x and y ?A) y = 3xB) x = 3yC) y = x + 4D) x = y + 4

y = mx + b

3

y = 1x + ?

my

x= VV

xV

yV

3

b

y = 1x + 4

13

3= =

3

-1

1

1

5

1

4

0

Bring x back to 0.

4) Plot the ordered pairs from the table onto the graph paper below. Then draw a line segment connecting the points.

160180

Time (min)

Wat

er (

gal)

180160140120100 80 60 40 20

00 1 2 3 4 5 6 7 8

Line Segment: No Arrows

Need to Label Graph

Pool Being Filled

5) Graph the line with equation y = 2x – 3.

a) Slope:m = 2

b) y-intercept:b = -3

6) Given the linear equation, y = -2x + 3, identify the slope and y-intercept.

m = ________ b = ________

Coordinates of y-intercept: _______

What does the slope tell you?

_____________________________

What does the y-intercept tell you?

Down 2 to the Right 1

-2 3

(0,3)

Point where line crosses y-axis

A) 2 - 6 hB) 2h - 6C) 6 - 2hD) 6h - 2

7) This month, Drew worked six hours less than twice the number of hours, h , he worked last month.What expression represents the number of hours Drew worked this month?

6 -

2h

LESS THAN REVERSE ORDER6 - 2h

8) Luisa works in her grandfather’s jewelry shop. She deposits her earnings in a savings account. Her savings account balances for five of the last six weeks are shown in the function table below.

Part A: According to the data in the function table, write a function rule that shows how much money Luisa saves each week.Rule ______________

y = mx + b

y = 110x + ?

my

x= VV

y = 110x + 400

1

110110= =

b = 110w + 400

1101xV yV

b

x y

Don’t forget to change equation using b and w!!!

Week (w) Savings Balance(b)

1 $510

2 $620

3 $730

4 $840

5 ?

6 $1,060

0 400

8) Part BBased on the table, how much money is in Luisa’s savings

account in week 5?Show Work

Answer $__________

950

b = 110w + 400Plug in w =5

b = 110(5)+ 400b = 550 + 400b = 950

950

Week (w)

Savings Balance

(b)1 $510

2 $620

3 $730

4 $840

5 ?

6 $1,060

840+110 950

9) Find the greatest common factor (GCF) of 12x and (4x2 + 8x).

GCF: 4: 1, 4 12: 1, 2, 3, 4, 6, 12 8: 1,2,4,8

GCF: x: x x2: x x x: x

GCF: 4x

10) Steve drew figure ABCD. He plans to create figure A'B'C'D' by reflecting it over the x-axis. Label the new figure A'B'C'D‘.

What are the coordinates of A’?

________

D’

A’ B’

C’

(-9,-7)

Add Multiply2 6 8x x+ + Multiply to +8

(1)(8)(2)(4)

(-1)(-8)(-2)(-4)

Which pair adds up to +6?

11) Factor into two binomials

Step #1

Step #2

Step #3

(x+4)(x+2) or

(x+2)(x+4)

12) In the diagram below, line f and line h are parallel, and line n is a transversal.

a) Name two angles that are vertical angles.

b) Name two angles that are corresponding angles.

c) Name two angles that are alternate interior angles.

c 5 and 5 8 6 and 6 7

2 and 2 6 4 and 4 8

4 and 4 5 3 and 3 6

13) Graph a line with the given values.

x -4 -2 0 4y 0 1 2 4

Assessment Review Homework #2

1) Which figure below shows a reflection?

Rotation

Translation Translation

Reflection

2) Gary drew a triangle on the coordinate grid shown below. If Gary reflects the triangle in the y-axis, what will be the new coordinates of the vertices of the triangle? Which figure below shows a reflection?

A) (-1, -1), (4, -3), (-5, 1)B) (-1, -1), (-4, -3), (-5, -1)C) (-1, 1), (-4, 3), (5, -1)D) (1, 1), (4, 3), (5, 1)

3) Triangle ABC and triangle A’ B’C’ are plotted on the coordinate plane below.What is the name of the transformation applied to triangle ABC that resulted in triangle A’B’C’?

∆A’B’C is a reflection over

the y-axis.

4) Which property does the equation below demonstrate?

7(x - 4) = 7x - 28

A) Associative B) Commutative C) DistributiveD) Identity

7(x) 7(-4)+

5) Ana drew two figures on the coordinate grid shown below.Which transformation did Ana apply to Figure A to get Figure B ?

6 5 4 3 2 1

This is a SLIDE!!!A) Rotated by 90o B)Dilated by 6C)Reflected in the y-axisD) Translated 6 units to the left

A) 4k + 5B) 5k - 4C) 5k + 4D) 5k(k + 4)

6) Cindy has four more than five times as many cousins as Kathy, k. Which expression represents how many cousins Cindy has compared with Kathy?

4 + 5x

4 + 5kor

5k + 4

7) Which verbal expression is the same as

A) two more than half of sixB) six more than half of a numberC) the sum of a number and two plus sixD) six more than the product of a number and two

62

n +

2 +1/2(6)

6 + 1/2nn + 2 + 6

6 + 2n

8) Melissa drew the shape on the grid shown below. Draw the reflection of this shape in the x-axis. Label the coordinates of each point on the new figure.

Explain how you determined the reflection of the shape.

(4,-2)

(6,-6)

(4,-8)

(2,-6)

2 boxes to x-axis

2 boxes away from x-axis

6 boxes to x-axis

6 boxes away from x-axis

I counted how many boxes each point was away from the x-axis. I then counted that many boxes on the other side of the x-axis. I plotted the new point.

ORI kept the same x-coordinate andnegated the y-coordinate for each point.

9) A translation has the rule (x- 2, y+1). If the point R at (7,-4) is put through the translation, what are the coordinates of its image location at R’?

(x – 2, y + 1)

R’(7 – 2, -4 + 1)

R’(5, -3

10) Shawn drew figure ABCD. He plans to create figure A'B'C'D' by translating figure ABCD 6 units down and 4 units to the right. On the coordinate plane below, draw and label Shawn's figure A'B'C'D'. (MARCH 2009)

D’

A’ B’

C’

Next Shawn plans to create a figure A”B”C”D” by translating figure A’B’C’D’ 2 units up and 8 units to the right. What will be the coordinates of point A’’?

A’’(3,3)

A’’(3,3)

11) Simplify.(3x2y3)(-4xy-4)

(3)(-4)= -12x2•x= x3

y3•y-4=y-1-12x3y-1

Explain using the laws of exponents how you arrived at your answer.

I multiplied 3 & -4 and got -12. I multiplied powers by keeping base and adding the exponents.

Add Multiply2 1 12x x− − Multiply to -12

(1)(-12)(2)(-6) (3)(-4)(-1)(12)(-2)(6) (-3)(4)

Which pair adds up to -1?

12) Factor into two binomials

Step #1

Step #2

Step #3

(x+3)(x-4) or

(x-4)(x+3)

13) Find the product of the two binomials (x – 6) and (3x + 7)

3x2 -18x +7x - 42

3x

x

+7

-6

3x2

3x2 - 11x - 42

+7x -18x -42

Multiply

(x - 6)(3x + 7)

A) 2 + d – 3B) 3 + d – 2C) 2d – 3D) 3 – 2d

14) Janine’s dog weighs three pounds less than twice the weight of Wanda’s dog, d.

Which expression represents the weight of Janine’s dog?

3 -

2d

LESS THAN REVERSE ORDER3 - 2d

15) Erika is assigned to graph the line of the equation y = 2x+1. Use Erika’s equation to complete the table below

for the given values of x.

Using the information from the table, graph the line of the equation y =2x+1 on the coordinate plane below. Be sure to plot all points from the table and draw a line connecting the points.

x y

-2 -3

-1 -1

0 1

2 5

4 9

y=2x

+1

• What is the product of (2a2b3c6) and (4ab4c2)?

(2a2b3c6) (4ab4c2)

MULTIPLY

2∙4∙a2∙a∙b3∙b4∙c6∙c2

8a3b7c8

MULTIPLY Powers Multiply Coefficients. Keep Base & Add Exponents

“I multiplied 2(4) to get 8. I multiplied powers by keeping the base and added the exponents.”

2) What is the quotient of ?

• 3x2y2z2

• 3x2y4z5

• 12x2y2z2

• 12x2y4z5

DIVIDE

Dividing Powers Divide Coefficients. Keep Base & Subtract Exponents

“I divided 18 by 6 to get 3. I divided powers with same base by keeping the base and subtracted the exponents.”

4 8 10

2 4 5

18

6

x y z

x y z

2 4 53x y z

3) Solve for x in the equation below.2(x + 6) = 8x - 42

Show your work.

Answer __________

USE CALCULATOR!!

6 6

x = 9

2x +12 = 8x - 42

2(x + 6) = 8x - 42

x + 6

2 2x +12Distribute

+12 = 6x - 42

54 = 6x

Multiply

Cancel 2x

x = 9

-2x -2x

+42 +42Cancel -42

4) Simplify the expression below.

DIVIDE

Dividing Powers Keep Base & Subtract Exponents

“I divided 36 by 12 to get 3. I divided powers with same base by keeping the base and subtract the exponents.”

2

3

36

12

xy

x y• 24x4y3

• 3x4yC)

D)

2

3y

x2

2

24x

y

3xyy

xxxy

2

3y

x

5) Multiply the two binomials below.(2x – 3)(2x + 3)

A) 4x2 +9B) 4x2 – 9C) 4x2 – 6x – 9D) 4x2 –12x + 9

4x2+ 6x -6x -9

2x

2x

+3

-3

4x2

4x2- 9

+6x -6x -9

Multiply

6) What is the product of the expression below?(3x – 7)(3x + 2)

A) 9x2 -15x -14B) 9x2 +15x+14C) 9x2 -15x +14D) 9x2 +15x -14

9x2-21x+ 6x -14

3x

3x

+2

-7

9x2

9x2- 15x-14

+6x -21x -14

Multiply

Always smallest exponent

GCF: 6 (Biggest)

Second: List factors of x3 and x4

x3: x x x x4: x x x x

GCF: 6x3

7) What is the greatest common factor of 18x3

and 24x4?

GCF: x3

First: List factors of 18 and 24

18: 1, 2, 3, 6, 9, 18

24: 1, 2, 3, 4, 6, 8,12, 24

Add Multiply2 3 18x x+ −

Multiply to -18

(1)(-18)(2)(-9)(3)(-6)(-1)(18)(-2)(9)(-3)(6)

Which pair adds up to 3?

8) Factor x2 + 3x – 18 into two binomials.A) (x + 9)(x - 2)B) (x – 9)(x + 2)C) (x + 6)(x – 3)D) (x – 6)(x + 3)

(x -3)(x+6)or(x +6)(x- 3)

Step #1Step #2

Step #3

9) Simplify the expression below.2-3

A) -6B) 1/6C) 1/8D) -8

3

1

2

1

8=

Flip Base & Make Exponent POSITIVE

NEGATIVE Exponents

10) Katie converts the outside temperature from degrees Fahrenheit, F, to degrees Celsius, C. She uses the formula below to convert the temperature.

If the outside temperature is 50 degrees Fahrenheit, what is the outside temperature in degrees Celsius?

A) 2B) 5C) 9D) 10

( ) 532

9F C− =

18 5

1 9C• =

( ) 532

950 C− =

90

9C=

Plug F = 50

11) Factor the expression below using the greatest common factor (GCF).

18n6 – 12n4+ 6n

A) 6n(3n5 -2n3 + 1) B) 6n(3n5 -2n3 + n)C) 6n(12n6 -6n3 + 1) D) 6n(12n6 -6n3 + n)

GCF:18:1, 2, 3, 6, 9, 1812: 1, 2, 3, 4 ,6, 12 6: 1, 2, 2, 3, 6

GCF:n6: n ,n , n , n ,n ,nn4: n ,n ,n ,nn: n

6 418 12 6

6 6 6

n n n

n n n− +

5 33 2 1n n− +

You can check by multplying answer out

GCF: 6n

3n( ? ) =18n6 -12n4 +3n

12) Simplify the expression

2 2(3 5 11) (11 2 12)a a a a+ − − + −

3a2 + 5a-11 – 11a2 + 2a – 12

+1-8a2 +3a

Rewrite without

Parenthesis

+-– 3a2 +5a - 11 - 11a2 -2a +123a2 - 11a2+5a -2a- 11 +12

13) Solve, graph, and check

-8x – 8 < -3x + 12 Variables on Different SidesCancel Smaller+3x +3x

-5x - 8 < 12

+8 +8-5x < 20-5 -5

x > 4

4 5 6

Check

-8x – 8 < -3x + 12-8(5) – 8 < -3(5) + 12

– 48 < -3

Divide by NegativeFlip Inequality Directio

14) Complete the table of values given the line below.

x y

-2

0

1

3

8

(-2,-1)

-1

0

2

(0,0)

(2,1) (6,3)

6

4

(8,4)

15) In the diagram below, line f and line h are parallel, and line n is a transversal.

a) Name two angles that are vertical angles.

b) Name two angles that are corresponding angles.

c) Name two angles that are alternate interior angles.

c 5 and 5 8 6 and 6 7

2 and 2 6 4 and 4 8

4 and 4 5 3 and 3 6

1) What is 18a11b7 divided by 3a3b?


“I divided 18 by 3 to get 6. When dividing powers with same base you keep the base and subtract the exponents.”

11 7

3

18

3

a b

a b

8 66a b


• 4x2y2 • 4xy2

•

E)


“I divided 12 by 3 to get 4. When dividing powers with same base you keep the base and subtract the exponents.”

2 312

3

x y

xy

24xy2

4

xy

2

4x

y

3) Which expression is equivalent (14a - 4a) + (5a -3a)?

Combine Like Terms

10a + 2a

(14a- 4a) + (5a – 3a)

12a


2(3 4 3) (2 1)x x x+ − − −

3x2 +4x - 3 + -2x + 1

-23x2 +2x

Rewrite without

Parenthesis

3x2 4x-2x

-3+1

Need to show how signs change!

5) Simplify the expression.

(x3y2)(xy4)

x4y6

MULTIPLY Powers Keep Base & Add Exponents


5752

59

MULTIPLY Powers Keep Base & Add Exponents


Dividing Powers Divide Coefficients. Keep Base & Subtract Exponents

“I divided 3 by 6 to get ½ . When dividing powers with same base you keep the base and subtract the exponents.”

3 9

5 3

3

6

d k

d k6 2 6

2

1 1

2 2

k d kor

d

−


A) 9a2bB) 9a4b2 C) 18a2bD) 18a4b2

Combine Like Terms

3a2b + 6a2b

9a2b


2 2(3 7) (9 3 4)a a a a+ − − + −

3a2 + a – 7 + 9a2 + 3a – 4

-3-6a2 - 2a

Rewrite without

Parenthesis

+– – 3a2 +a – 7 - 9a2 -3a +43a2 -9a2+a -3a - 7 +4

Add Multiply2 4 12x x+ −

Multiply to -12

(1)(-12)(2)(-6)(3)(-4)(-1)(12)(-2)(6)(-3)(4)

Which pair adds up to 4?

10) Factor x2 + 4x – 12 into two binomials.A) (x + 4)(x - 3)B) (x – 3)(x + 3)C) (x + 6)(x – 2)D) (x – 6)(x + 2)

Step #1Step #2

Step #3

(x )(x ) or(x +6)(x- 2)

-2 + 6

11) On the coordinate plane below, draw the image of polygon ABCDE translated 8 units to the right and 4 units up. Label the image A'B'C'D'E'. (MARCH 2008)

SLIDE!!!A’

B’E’ D’

C’

12) Write an equation that represents the table below.

Answer ___________

y = mx + b

+3+2

my

x= VV

xV yV2

3= x y

-2 -5

0 -2

2 1

4 4

22

3y x= −

Why is “y” on top?

13) Using the slope formula, , find slope of the line given two points A(3,4) and B(-3,-2).

Show Work

Slope: ____

Describe the slope:

4 2

3 3m = − −

− −

Why is “y” on top?

1 2

1 2

y

x xx

yy −=−

VV

16

6= =

1

Up 1 to the right 1

14) Given the linear equation, y + 2x = 7, identify the slope and y-intercept.

m = ________ b = ________

Coordinates of y-intercept: _______

What does the slope tell you?

_____________________________

What does the y-intercept tell you?

Down 2 to the Right 1

-2 7

(0,7)

Point where line crosses y-axis

-2x -2xy = -2x + 7

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