Math 7 Pinto Final Review 2019

1

Name:________________________

REVIEW MATH 7

Sets Of Numbers

Counting Numbers

- are the Natural Numbers (1, 2, 3, 4 …)

Whole Numbers

- all the Counting Numbers AND zero

(0, 1, 2, 3, 4, …)

Integers

- all the Whole Numbers AND their opposites

(…,-4, -3, -2, -1, 0, 1, 2, 3, 4, …)

Opposite numbers are the same distance from zero on a number line in

opposite directions.

For example 5 and -5 are opposites.

Comparing Integers :

>

and

<

The number

farther right

on the number line is the

larger

number.

1) 15 _____

-

15 2) 92 _____63

3) 0 _____ 12

4)

-

5 _____ 0 5)

-

5 _____

-

18

Ordering Integers:

6) Order from least to greatest:

6,

-

5, 3,

-

9, 0,

-

3

______________________________________

**The three questions most often missed.

7)

Name a number that is not an integer? __________

2

Absolute Value measures the distance a number is from zero on the number

line. The symbol for absolute value is “| |.”

|4| “What is the absolute value of 4?” |4| = _______

|

-

4| “What is the absolute value of

-

4?” |

-

4| = _______

**Absolute value bars are evaluated like parentheses. Do whatever is inside

the bars first, and then find the absolute value.

Example

:

|-

4

|

+

|

5

|

|-

4 + 5

|

4 + 5

|

1

|

9

1

10)

|

102

|

-

|-

2

|

11)

|

102

--

2

|

12) |102| - |-2|

13) |102 -

-

2|

14) -|10| - |-2|

15) -(|102| - |2|)

3

Simplify the expression. (Start from the inside and work it out)

17)

-

(

-

4) _____

18)

-

(

-

(

-

4)) _____

19)

-

[

-

(

-

(

-

4))]

20) -(-(-36 – 4))

21) -(3

2

)

22) -3

2

ADDING INTEGERS

SAME SIGNS, ADD the numbers and KEEP the sign. DIFFERENT signs IGNORE the signs and SUBTRACT numbers. Keep the sign of whatever you have more of. Subtract the absolute values. Keep the sign of the number with the largest absolute value.

Examples:

-

14 +

-

3 =

-

17

12 +

-

8 = 4

-

37 + 16 = 21

1) 12 + 20 = _______

2)

-

12 +

-

20 = _____

3)

-

12 + 20 = ______

4) 12 +

-

20 = ______

5) 20 +

-

10 + 5 = ____

6)

-

15 + 7 + 8 = ____

SUBTRACTING INTEGERS

FOLLOW the RULES for ADDING INTEGERS but BEWARE OF DOUBLE NEGATIVES!!!! Remember (-) means opposite AND the sign in front of the number goes with the number.

Ex: 7 – 4

-7 – 4

8 - -4

8 + -4

3

-11

8 + 4

8 - 4

12

4

4

11)

-

5

-

3

12)

-

6

-

-

8

13) 7

-

13

14)

-

13

-

-

1

MULTIPLYING

and

DIVIDING

INTEGERS

:

TWO

SAME

SIGNS

your answer will be

POSITIVE

.

Ex:

5(4) = 20

-

5(

-

4) = 20

18

÷

3 = 6

-

18

÷

-

3 = 6

TWO

DIFFERENT

SIGNS

your answer will be

NEGATIVE.

Ex:

-

9(2) =

-

18

9(

-

2) =

-

18

-

18

÷

9 =

-

2

18

÷

-

9 =

-

2

15) (100)(

-

7)

16) (

-

6)(13)

17)

-

9(

-

11)

18) (

-

15)(7)

19)

-

144

÷

12

20) 62

÷

2

21)

30

150



22)

-

90

÷

-

15

23)

5 40

5

Name:________________________

REVIEW MATH 7

Write a number sentence and evaluate.

1) A dolphin swam to a depth of 110 feet below sea level. Then, it rose 85 feet. What was the dolphin’s final depth?

2) The temperature outside was 22˚F. The wind chill made it feel like -8˚F. Find the difference between the real temperature and the apparent temperature.

3) The temperature one morning in was –16o_{F. By the afternoon, the temperature had risen}

9o_{F. What was the temperature in the afternoon?}

FRACTIONS 4) Write

5

17 _{as a mixed number. _______ 5) Write} 6

20 _{as a mixed number. _______}

Write each mixed number as a fraction. 6) 2

31 _______ 7) -594 _______

Write each ratio as a FRACTION in SIMPLEST FORM.

8) _{12 ________} 3 9) 20 to 5 ________ 10) 30 : 18 _______

11) A bag contains 6 peaches, 4 plums, and 3 bananas. What is the ratio of plums to peaches? A)

3

2 _B)

2

1 _C)

4

3 _D)

2 3

12) A bag contains 5 red marbles, 7 blue marbles, and 3 green marbles. What is the ratio of blue marbles to the number of marbles in the bag?

A) 12

7 _B)

7

15 _C) 15

7 _D)

6

Adding and Subtracting Fractions

-Remember to use your integer rules.

-Find the Least Common Denominator (LCD) if the denominators are different. -Add or subtract the numerator and keep the denominator the same.

13) 4₈

+

3₈ 14)

−

11₁₈

+

₁₈4 15)

−

5

13

+ (−

3

13

)

16) 2 9

− (−

3

9

)

17)

3 5 +

2

15 18) −

2

5 + (− 5 6)

Multiplying Fractions

-Use your integer rules to determine whether your answer is going to be positive or negative. -Change any mixed numbers to improper fractions (if necessary).

-Multiply the numerators and multiply the denominators. Look to simplify before you multiply. -State your final answer in simplest form (fraction or mixed number).

1) −₁₀9

•

2

3 2) −

5

6

•

−1

4

5 3) 2 1

2

•

1

2 5

Dividing

Fractions & Mixed Numbers

-To divide fractions, multiply the first fraction by the multiplicative inverse (reciprocal) of the second fraction. You can use the key words “keep, change, flip” to help you remember the steps of this process.

4) −2₃

÷

5

6 5)

4

5

÷

−6

6) 7 1

2

÷

2

1 10

Find the multiplicative inverse (reciprocal) of each fraction.

7

)

4

7

8)

7

Decimals

Round each of the following to the specified place.

1) 58.6857 Nearest Whole: _________ 2) 4.0999 Nearest Whole: _________ 58.6857 Tenths: __________ 4.0999 Tenths: __________

58.6857 Hundredths:__________ 4.0999 Hundredths:__________ 58.6857 Thousandths:__________ 4.0999 Thousandths:__________ Using ,  or =, compare the following.

3) 0.0604_____0.062 4) -2.0______-2.8 5) 3.3______3.25

Change into a decimal. 6)

8

1_{________ 7) 5} 3

2 _{_________ 8) 3} 4

1 _{_________}

Change into fraction or mixed number. 9) 0.5 _________ 10) 4.6 ________

Adding and Subtracting Decimals

-Always line up decimals, add zeroes to help line things up.

-Add and subtract but remember to carry over or borrow if necessary. -Bring decimal straight down in your answers.

1) 3.72

-

0.55 2)

-

2.34

-

0.4

3)

-

5.44 + 12.2 4) 0.34 + 3.27

Multiplying Decimals

-Multiply the number like you would whole numbers, carry over when necessary. -Count the number of decimal spaces for the original two factors.

-The decimal places in the product is the sum of decimal places in the factors. 5)

-

2.4 ⦁ (

-

2.3) 6) 0.4 ⦁ (

-

1.6)

8

Dividing Decimals

-Move the decimal right in the dividend the same amount it’s moved in the divisor -Rewrite the problem as two integers

-Bring the decimal point up on top of quotient

quotient

-Do normal division add zeroes if needed

divisor dividend

9)

-

5.4 ÷ 9 10) 3.96 ÷ 0.6

11)

-

4.8 ÷ (

-

2.2) 12) 0.96 ÷ 0.02

13) List the following numbers in order from least to greatest: 66 , 6.75, 6.07, 6.7 .

________________________________________________________________

Evaluate each expression when a = 2, b =

-

3, and c = 4

14) 4a + c _{15) 2b}

-

_3c

Evaluate each expression when x = 1.4 and y =

-

0.6

16) x

–

y 17) 3x + 2y

Evaluate using the correct order of operations.

Translate each verbal phrase or sentence into an algebraic expression. 1) 12 more than a number n ________________________

2) A number, n , increased by seven _____________________ 3) The product of 15 and x _________________

4) Twice y decreased by 20 _____________________

5) Seven more than the quotient of x and

-

2. ______________________ 6) The difference of twice n and three _______________________ 7) Three times the sum of 12 and x _______________________

Simplify Expressions

-Get rid of parentheses by using the Distributive Property

-Combine like terms if they have the same variable raised to the same power

-Look at the coefficient and use you integer rules or just combine the constant terms

List the terms, like terms, coefficient(s), and constant(s) for the following expressions. A)

5x + 2y – x + 3y – 7

B)

-4a – 10b + 8 – 2a + 7

Terms: ____, ____, ____, ____, ____ Terms: ____, ____, ____, ____, ____

Like Terms: ____ and ____; ____ and ____ Like Terms: ____ and ____; ____ and ____

Coefficient(s): ____, ____, ____, ____ Coefficient(s): ____, ____, ____

DISTRIBUTIVE PROPERTY

!!!

a(b + c) = ab + ac

Make sure you multiply every number in the group (parentheses) by that number.

Ex.

-

2(3 + x) = (

-

2)(3) + (

-

2)(x)

If distributing a negative value, all the signs on the inside become opposite. Rewrite using the Distributive property.

1. 5(2x + 6) 2. -5(2x + 6) 3. 5(2x – 6)

4. -5(2x – 6) 5. x(y + z) 6. x(-y + z)

Solving Multi-Step Equations

1) Get rid of any parentheses

How? Use the DISTRIBUTIVE PROPERTY!!! a(b + c) = ab + ac

Make sure you multiply every number in the group (parentheses) by that number. Ex. -2(3 + x) = (-2)(3) + (-2)(x)

2) Combine Like-Terms on the Same side of = sign. (Same Side Use Same Operation)

Ex. -5x + 2x + 12 = -10x +16 + 17 -3x +12 = -10x + 33

3) Get All Variables on One Side & Constants on the Other Side (Opposite Sides Use Opposite Operations)

Ex. -3x + 12 = -10x + 33 + 10x = + 10x 7x + 12 = 33 - 12 = -12 7x = 21 4) Solve for the Variable

11 Solve and check each equation algebraically. Show all work!

1) 4c

–

6 = 2 CHECK:

2)

–

4 = 2x

–

2 CHECK:

Solve each equation algebraically.

3)

-

1 = 4

-

5x 4) 12

-

3x = 6

5)

-

3(2x + 7) = 3 ₆₎

4

5

4

3

2

1





m

12

INEQUALITIES

Use an Open Circle Use a Closed Circle

 “is greater than”  “is greater than or equal to”

 “is less than”  “is less than or equal to”

 “is not equal to”

True or False

4  4 False 4 is not greater than 4

4  4 True 4 is not greater than 4, however, 4 is equal to 4.

GRAPHING INEQUALITIES

You can only graph an inequality on a number line if the VARIABLE is BY ITSELF.

You solve inequalities the same way you solve equations. Remember, whatever you do to one side of the inequality you must do the same thing to the other side.

Graph each solution to the following inequalities on a number line.

(Hint: If the variable is on the left side of the inequality symbol shade the direction the symbol points to.

)

1) x  12 2) x  12 -12 0 12 -12 0 12

3) x  12 4) x  12 -12 0 12 -12 0 12

5) x + 9



-

20



(

You cannot graph this

6)

-

2x

+

7



25

-

9

-

9 inequality until you get x by itself!)

-

7

-

7 x 

-

29 (Now you can graph this inequality

-

2x



18

because x is by itself.)

-

2

-

2



FLIP SIGN x



-

9

13 Graph each inequality on a number line.

1) x  5 2) x  2 3) x -2

Solve and graph on a number line.

4) x + 12  9 ₅₎

-

_{2x + 7}  17 6)

-

15 + x  19

9) Write the inequality represented by the graph below.

| | | | | | | | |

-4 -3 -2 -1 0 1 2 3 4 _______________

Write yes or no if the inequality symbol needs to FLIP? (Look for a negative coefficient or a negative denominator)

1) 8(y + 5)  80 2)

-

4y + 11  9 3) y + 12  54 4) 9 y

 

-

3

14 When translating phrases into mathematical INEQUALITIES:

● Identify key words or phrases

● Translated in the exact order they are read

● Place parentheses around sums and differences

● Inequalities will contain one or more operations and one of the four inequality symbols (, ,  or ).

Translate the following into an algebraic inequality to represent each of the following. 1) Four more than a number, n, is no more than thirteen. _____________________ 2) The difference of a number, n, and

-

6 is less than 9. _____________________ 3) A number, n, decreased by 11 is no less than 17. _____________________

4) Nine more than 4 times a number is at least 30. ___________________ 5) Three times a number divided by 4 is no more than 5. ___________________ 6) The sum of twice a number, n, and 9 is less than 37. ___________________

7) Six times the difference of a number, x and 3 ismore than 24. ___________________ 8) Four times a number, x plus nine is at most 30. ___________________

15

PROPORTIONS

We use proportions to solve for missing information, to solve word problems, conversion problems, scale problems and so much more. The key to using proportions correctly is to

BE CONSISTENT

!!!!

Once you set up a proportion just cross multiply and solve algebraically.

12) _{16 =} 6 ₂₄ x 13) 7 = _{8 40}x

14) A microscope slide shows 37 red blood cells out of 60 blood cells. How many red blood cells would be expected in a sample of the same blood that has 900 blood cells?

Let x = __________________________ Proportion:

Sentence: ________________________________________________________________

15) The distance from the roller coaster to the food court on the map is 3.5 centimeters. If the scale on the map is 1 cm = 10 m then find the actual distance to the food court.

Let x = __________________________ Proportion:

16 16) On a scale drawing of a house, the dimensions of the living room are 4 inches by 3 inches. If the scale of the drawing is 1 in = 6 ft, find the actual length and width of the living room. (You will need two separate proportions)

Let x = The length of the living room Proportion:

Sentence:

___________________________________________ _____________________

Let x = The width of the living room Proportion:

Sentence:

___________________________________________ _____________________

17) If it rained 6 inches in 3 weeks how many inches did it rain per week?

Let x = _________________________________ Proportion:

Sentence: ________________________________________________________________

18) Kelsey babysat for 4 hours and earned $25. How much did Kelsey earn per hour?

19) Lee packed 2 sweatshirts and 6 T-shirts in her suitcase. Which ratio does not represent the number of sweatshirts to the number of T-shirts in Lee’s suitcase?

17 20) One mechanic can repair 4 cars a day. Which proportion shows how to find the number of mechanics needed to repair 20 cars in a day if they all work at the same rate?

A) _{4 =} 1 20_n B) _{4 =} 1 ₂₀ n C) _{20 =} 1 ₄ n D) n_{1 = 20} 4

21) Which two ratios could form a proportion?

A) 3 2 _and

12

8 _B) 8 1 _and

16

3 _C) 5 10 _and

7

12 _D)

4 7 _and

7 4

22) Tell which is the better buy. Show all work and explain your answer.

20 pounds of pet food for $14.99

OR

50 pounds of pet food for $37.99

(Hint: divide cost/unit to get a denominator of 1) (FIND THE UNIT RATE OF EACH) 20 pounds of pet food for $14.99 50 pounds of pet food for $37.99

23) Tell which is the better buy. Show all work and explain your answer. (FIND THE UNIT RATE OF EACH)

2 compact discs for $26.50

OR

3 compact discs for $40.00

18 1) Given the equation, C = 5T, what is the constant of proportionality? ____________

19 0

5 10 15 20

1 2 3 4

4 8 12 16

0 2 4 6 8

3)

4)

5) Find the constant of proportionality (in simplest form) for graphs A and B.

A) B)

C.O.P. = _____ C.O.P. =____

20 Use the table above to answer the following questions.

a) Fill in the missing values in the table above:

b) Find the constant of proportionality: _________

c) Write an equation showing the relationship between total cost, c, and the number of gallons, g: _________

d) Use your equation to calculate the cost of 20 gallons: _____________

e) Use the same equation to find how many gallons you can buy for $126: ____________ f) Graph the data on the grid below:

Title: ________________________

*Label x and y axis *Number each axis

Cost

Cost (c) 6 9 12 15

21

Percent Proportion

Solve each of the following word problems using the percent proportion. Remember to define a variable using a let statement.

of is ₌

100 % _or

whole part ₌

100 %

1) Find 12% of 95?

Let x = ________________________

Sentence:

2) 15 is 60% of what number?

Let x = ________________________

Sentence: 3) 23 is what percent of 115?

Let x = ________________________

Sentence:

4) 35% of what number is 52.5?

Let x = ________________________

Sentence:

5) The cost of developing film is $5.49 per roll. There is also 6% sales tax charged. What would be the cost of developing 1 roll of film after tax?

Let x = __________________________________ (Remember to add tax)

$5.49 + ___________ = ___________ (total cost of developing the film after tax) (tax)

22 6) Mary sold $192 worth of greeting cards. If she received 25% commission on her sales, how much commission did she earn?

Let x = __________________________________

Sentence:

7) Jenny bought a pair of boots priced at $85. If the boots were on sale for 15% off the regular price, how much did Jenny pay for the boots?

Let x = __________________________________ (Remember to subtract sale amount)

$85 - ___________ = ___________ (total cost of boots) (sale)

Sentence:

8) There are 350 people at a luncheon. If 12% of the people will win a door prize, how many door people will win a door prize?

Let x = __________________________________

Sentence:

9) If Robert got 42 questions correct out of 60 questions on a test, what percent of the questions on the test did Robert get correct?

Let x = __________________________________

23 10) Jen’s bill at a restaurant before tax and tip is $22. If tax is 5.25% and she wants to leave 15% of the bill before the tax for a tip, how much will she spend in total?

Let x = amount of tax Let y = amount of tip

________ + __________ + _________ = total bill (bill) (tax) (tip)

Sentence:

11) A $300 mountain bike is discounted by 30%, and there is a 8% sales tax. Find the final cost of the mountain bike.

Let x = amount of discount Let y = amount of tax

*Subtract discount from cost to calculate tax*

$300 - ___________ = ___________

________ - __________ + _________ = total cost (bill) (discount) (tax)

24 Rectangle: A=lw

Note: These are all

Square: A=s2 _{parallelograms. So A = bh}

will work for all of these. Parallelogram: A=bh

**Height – Can never be slanted. Height must be PERPENDICULAR () with the base.

Triangle: A=bh2 or A=12 bh Trapezoid:

2 h ) b + b ( =

A 1 2 _{or A=}

2 1_(b

1 + b2)h

**Note: A trapezoid has 2 bases. The bases are the 2 parallel sides. Circle : Area = r2 _{AND Circumference = d or 2r}

Rectangular Prism: V= lwh Triangular prism: V bhh

      2 1

Cube:

V



b

3 Pyramid: V Bh 3 1

 , where B is the area of the shape’s base

Rectangular Prism:

SA



2

wl



2

lh



2

wh

Triangular Prism: SA bhlwlwlw

      2 1 2

Cube:

 

2

6

b

SA



Cylinder:

SA



2



r

2



2



rh

Square Pyramid: ) 2 1 ( 4 2 bs b

SA 

Rectangular Pyramid:

SA



lw



2

(

ls

)



2

(

ws

)

Find the area of each figure.

1) 2) 3) 2.3 cm 5’ 5”

1.3 cm

8’ 11.2” 1.6 cm

4) Find the EXACT area AND circumference of the following circle. (leave in terms of π) d = ______ r = ______

Area = r2 _{Circumference = d} 20 mm

Exact Area = __________ Exact Circumference: _________mm

25 1) Find the EXACT CIRCUMFERENCE of a circle whose diameter is 10 m.

Circumference = d

2) Find the EXACT AREA of a circle with a diameter of 12 in. r = ________ Area = r2

3) If the circumference of a circle is 12



m, find its diameter. Circumference = d

12

 =

d

4) If the area of a circle is 36



in2_{, find its diameter.}

Area = r2 36



=

r2

r = _______ d = _______

5) A circle has a circumference of 24



,

find the diameter AND radius of the circle. Circumference = d

r = _______ d = _______

6) Find the surface area AND volume of the rectangular prism below.

SA = 2lw + 2lh + 2wh Volume = lwh

10 m

5 m 15 m

l = _____

w = _____

26

TRIANGLES:

The sum of the angles of a triangle is 180

QUADRILATERALS

: The sum of the angles of a quadrilateral is 360.

1) In a triangle the measure of one angle is 68, the measure of the second angle is 38. Find the measure of the third angle, x.

2) Given quadrilateral WXYZ. If mX = 45, mY = 110, mZ = 65 find the mW.

3) Given quadrilateral ABCD, if mA = x, mB = x + 5, mC = x + 15, and mD = 2x find the measure of each angle.

PROBABILITY

Probability is the study of chance. What is the “chance” that something is going to happen.

Probability is a ratio, a comparison of 2 numbers. NUMBER OF POSSIBLE OUTCOMES_{NUMBER OF TOTAL OUTCOMES}

First you have to find the total number of outcomes, than you make your comparisons. Example:

You have 5 blue pens, 7 black pens, 3 red pens, and 1 green pen.

(Before you can answer any probability questions using the above info, you need to find the total number of pens!!)

5 + 7 + 3 + 1 = 16 pens

1) P(black) means “What is the probability the pen you choose will be black?”

27 2) P(black or red) = ₁₆ 7 + ₁₆ 3 = 10₁₆ = 5₈ Remember: OR  ADD (1 event)

3) P(black and red) = ₁₆ 7  ₁₆ 3 = ₂₅₆ 21 Remember: AND  MULTIPLY (2 or more events)

EXAMPLES:

1) P( red and green) with replacement = ₁₆ 3 ₁₆ 1 =₂₅₆ 3 (Notice the denominator stayed the same)

2) P( red and green) without replacement = ₁₆ 3  ₁₅ 1 = ₈₀ 1 (Notice the denominator changed)

To find the total number of outcomes with more than one event you can multiply the

outcomes of each event. Example:

1) There are 4 different shorts (plaid, striped, and solid), 3 different shirts (white, blue, and black), and 2 different belts (brown and blue).

How many different outfits can you make? 4  3  2 = 24 different outfits 2) You flip 3 coins. How many possible outcomes will there be?

2  2  2 = 8 possible outcomes.

If you forget the Basic Counting Principle you could draw a Tree Diagram. Just remember when you use a Tree Diagram only possible outcomes can be in the diagram.

1) There are 4 different shorts (plaid, striped, solid, and dots), 3 different shirts (yellow, blue, and black). There are 12 possible outfits.

yellow yellow Plaid blue Solid blue black black

yellow yellow Striped blue Dots blue black black

28 3) Whitney has a choice of a floral, plaid, or striped blouse to wear with a choice of tan,

black, navy, or white skirt. How many different outfits can she make? Use the Basic Counting Principal

_______  ________ = _________ possible outfits

A box contains 5 green pens, 3 blue pens, 8 black pens, and 4 red pens. A pen is picked at random. Answer the following questions.

4) What is the probability the pen is green? ________ 5) P(blue or red) __________

6) P(gold) __________ 7) P(blue and gold) _______________

8) P(green and red) with replacement _________________

9) P(green and red) without replacement _________________

10) Use the information given to make a frequency table. Results of people’s favorite movie:

comedy, action, comedy, romance, horror, comedy, comedy, romance, romance

romance, action, action, action, horror, comedy, foreign, action, action, romance, horror

Type of Movie Tally Frequency comedy

foreign action romance horror

29 12) Find the MEAN, MEDIAN, MODE, and RANGE of the following set of data: Show all work 15, 12, 21, 18, 25, 11, 17, 19, 20

Remember to put the data in order from least to greatest first!

MEAN MEDIAN

MODE RANGE

Given the line plot chart about the heights of plants, answer the following information.

17 18 19 20 21 22 23 24 25 26 27

1) What are the extremes of the data?_____ and _____ 2) What is the median? ______

3) What is the mean?________ 4) What is the mode? ________ 5) range:_______

6) Create a Box and Whisker diagram, 15, 21, 22, 22, 23, 24, 27.

a) What are the extremes of the data?______ and ______

b) What is the median? ________

c) What is the lower quartile? ________ d) What is the upper quartile? ________

e) Interquartile Range: ________ f) Range:_________

X

X

X

X

X

X

X

X

X

30 7) Which of these is NOT a random sample that would be valid to determine the favorite

food of students in your school? (Which would you not use.) A) five students at a Chinese restaurant

B) every 8th _{student on the school roster}

C) every 10th _{student entering school in the morning} D) three students from each table in the lunchroom

8) The double box and whisker plot shows the number of miles cycled by Dave and by Scott while they were training for a summer race.

Based on the Box and Whisker Plots above, on average, who cycles the higher number of miles?

A) Dave B) Scott C) They have the same average

Find the area of the irregular shapes. (see formulas on p. 24)

Hint: separate this shape into two shapes and find the area of each. Then add them together.

1)

3ft 4ft

2 ft

31 Each of the following pairs of triangles is similar. Find the missing side.

Hint: Set up a proportion

1) 2)

ANGLES

Complementary angles – Two angles are complementary if the sum of their angle measures is 90

Supplementary angles – Two angles are supplementary if the sum of their angle measures is 180

Vertical Angles – congruent angles formed by 2 intersecting lines. They are opposite each other

3) Find the complement of a 40 angle. _____ 4) Find the supplement of a 55 angle. _______

5) Solve for x ALGEGBRAICALLY and then find the measure of each angle.

a) b)

x

x + 15

32 Use the given formulas to calculate the volume of the figures below.

1) What is the volume of the pyramid: ___________

Rectangular Pyramid: V Bh 3 1

 -OR-

h lw

V ( )

3 1



12in

7in 5 in

2) Estimate the volume triangular prism: ___________

8.2ft 15.3ft 11.7ft

Triangular prism: V bhh

     

2 1