2019 spring review answer key - manghammath.com answers/2019 spring review answer key.pdf ·...

Created by Lance Mangham, 6th grade math, Carroll ISD

Accelerated Mathematics Formula Chart Name:

Linear Equations

Slope-intercept form y mx b= + Direct Variation y kx= (8th grade)

Constant of proportionality y

kx

= Slope of a line 2 1

2 1

y ym

x x

−=

− (8th grade)

Circumference Circle 2C rπ= or C dπ=

Area

Rectangle A bh= Trapezoid 1 2

1( )

2A b b h= +

Parallelogram A bh= Circle 2A rπ=

Triangle 2

bhA = or

1

2A bh=

Surface Area (8th grade) Lateral Total

Prism S Ph= 2S Ph B= +

Cylinder 2S rhπ= 22 2S rh rπ π= +

Volume

Triangular prism V Bh= Cylinder 2 or V Bh V r hπ= = (8th grade)

Rectangular prism V Bh= Cone 21 1 or V=

3 3V Bh r hπ= (8th gr.)

Pyramid 1

3V Bh= Sphere 34

3V rπ= (8th grade)

Pi 22

3.14 or 7

π π≈ ≈

Distance d rt= Compound Interest (1 )tA P r= +

Simple Interest I prt= Pythagorean Theorem 2 2 2a b c+ = (8th grade)

Customary – Length 1 mile = 1760 yards

1 yard = 3 feet 1 foot = 12 inches

Customary – Volume/Capacity 1 pint = 2 cups

1 cup = 8 fluid ounces 1 quart = 2 pints

1 gallon = 4 quarts

Customary – Mass/Weight 1 ton = 2,000 pounds 1 pound = 16 ounces

Metric – Length 1 kilometer = 1000 meters 1 meter = 100 centimeters

1 centimeter = 10 millimeters

Metric – Volume/Capacity 1 liter = 1000 milliliters

Metric – Mass/Weight 1 kilogram = 1000 grams 1 gram = 1000 milligrams


Accelerated Spring Exam Review Name:

STEPS FOR FULL CREDIT 1. Complete 2. Check 3. Correct

Part of your review should be looking at old reviews and test. Show all work on a separate sheet of paper. Write all geometry formulas and steps.

On the exam calculators will not be allowed so it is suggested you do not use one on the review.

PROPORTIONS & PERCENTAGES

1.

The scale of a map is 1

2inch:25 miles. If the map distance from Southlake to

Hillsboro is 1

14

inches, how far is it to Hillsboro from Southlake?

62.5 mi

2. The sales tax in Grapevine is 8.25%. If you spend $120.00 at Academy on sporting goods, how much tax will you have to pay, and how much is the total amount?

$9.90 $129.90

3. Mr. Mangham sells Duke basketballs for $25 each. If there is a 15% shipping charge added to the original price and 6% sales tax added to the original price, what is the total price for 4 basketballs?

$121.00

4. A radio tower casts a shadow 40 meters long at the same time that a tall tree casts a shadow 12 meters long. If the tree is 28 meters tall, how tall is the radio tower?

93.3 m

5. 66 feet were painted in 6 minutes. How long will it take to paint 2750 feet? 250 min

6. The results of a random survey showed that 30 out of 80 people plan to vote for Mr. Jones for city council. Find the total number of votes he will receive if 10,000 people vote.

3750 votes

7. Sam saved $47 when he purchased a jacket at a clearance sale. If the sale price was 20% off the regular price, what was the regular price of the jacket?

$235

8. The cost of gasoline rose from $2.50 to $3.25. What was the percent increase in the price of gasoline?

30%

9. The number of tarantulas in Mr. Mangham’s room dropped from 40 to 8. What was the percent decrease in the number of tarantulas?

80%

10.

What value would complete the table below to make the relationship between the two quantities proportional?

x y

2 11.2

3 ?

4 22.4

5 28.0

7 39.2

16.8


LINEAR EQUATIONS

11.

Which line above shows direct variation with an equation of 2.5y x= ?

B

12.

How many of the lines above demonstrate direct variation?

0

13. Katniss earns $40 an hour shooting apples with her bow and arrow. List 4 ordered pairs one would find when graphing this relationship.

(1,40), (2,80), (3,120), (4,160)

14. Ria creates a graph of how many cups of lemonade she sold (x) and much money she earned selling lemonade (y) last summer. Her graph contains the points (5, 6.25) and (8, 10). How much did Ria charge per cup of lemonade?

$1.25

15.

Kim starts with $500 and spends $15 per week for a total of 20 weeks. An equation shows this relationship, where x is the number of weeks and y is the amount of money she has. What is the slope and y-intercept of the equation showing this relationship?

15

500

m

b

= −

=

16.

Which of the following represents a non-proportional relationship? A Making $5 a day selling cookies B Paying $8 a month to subscribe to Netflix C Starting with 50 Legos and adding 6 each month D Having Mrs. Arnold give you 2 homework passes each month

C

17.

Which of the following represents a proportional relationship?

A 5 8y x= − + C 3y x=

B 10 2y x= − D 7.6y x=

D

18. A pizzeria charges $8 for a large cheese pizza, plus $2 per topping. Write an equation in the form of y mx b= + to demonstrate the total cost of a pizza.

2 8y x= +


19.

The graph below shows the distance Chris travels over a number of hours. John travels 180 miles in 4 hours. Who travels faster and by how much?

Chris

5 mph

20.

This graph shows a bicyclist moving at a constant rate.

This table shows another bicyclist.

Bicycle Rider B

Time (h) 3 5 8

Distance (km) 72 120 192

How much faster is the unit rate of bicyclist A than bicyclist B?

6 km/hr

21.

List all the items below which are functions. A 6 3y x= + B (2,2), (3,1), ( 2, 2)− − , (4,1), (3,0)

C D

Input 3 6 9 3

Output 1 8 2 4

E

A

C


22.

Which graph shows a function?

4

23.

The scatter plot above shows the hours studied for a science test and the resulting test scores. Write an equation for the trend line on the scatter plot. What does the y-intercept represent? What does the slope represent?

6 35y x= +

Slope = grade increase per

hour of studying

y-int = 35 if you did not study at all

24.

Mr. Mangham’s Guinea Pig-Walking Business

Time (hr) 2 5 8 13

Charge ($) 36 90 144 234

Mr. Mangham charges a constant unit rate for walking people’s guinea pigs. Using the table in the question above, what is the constant of proportionality for the data?

18k =

25.

Write an equation, y mx b= + , to represent the relationship shown in the table.

x y

8 1

12 3

18 6

20 7

0.5 3y x= + −


26.

Which graph above represents a proportional relationship? For the correct one, what is the constant of proportionality?

Left graph 20k =

27.

The Seasick Sailboat Rental Company charges an hourly rate to rent sailboats. The costs are shown in the table below.

Number of Hours

(t) 2 4 6 8

Cost

(C) $7.70 $15.40 $23.10 $30.80

The Starboard Sailboat Rental Company charges hourly based on the equation,

3.95C t= . Which company has a lower unit rate? How much cheaper will a sailboat rental be for 12 hours?

Seasick

$1.20

28.

Write an equation, y mx b= + , to represent the relationship shown in the table.

x 0 1 3

y 5 7 11

2 5y x= +

29.

Use the data in the table. Which equation shows the number of trees planted per day? Use a 5-day workweek.

Time (weeks) 2 5 10

Trees Planted 130 325 650

A 13y x= B 65y x= C 130y x= D 325y x=

A

30. Find the slope of a line that passes through ( 2,6)− and (4, 5)− . 11

6m = −

31. Find the slope of a line that passes through ( 3, 5)− − and (1,7) . 3m =

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7

Acc

ou

nt

Ba

lan

ce (

4)

Weeks


32.

Write an equation, y mx b= + , of the graph below.

2 5y x= − +

33.

Write an equation, y mx b= + , of the graph below.

14

3y x= +

34.

Use the two points on the graph above to determine the slope of the line.

1

3m =

35. Using the two points on the graph above to determine the y-intercept of the line. 5

3b =


MEASUREMENT & STATISTICS

36. { 6, 12, 8, 6, 4, 18}− − − − − −

What is the mean of the set of data above? Median? Mode? Range?

9, 7, 6,14− − −

37. {2, 4, 8, 10, 10, 12, 14, 16}

Which number would you change to make the mode change? 10

38. How many two-quart containers can be made from 24 gallons of water? 48

39. Mr. Mangham can jump 1.5 meters. On which jump will he cross the 2 kilometer mark?

1,334

40.

The box plot below compares the average daily temperature in three cities.

A Which city has the highest median? B Which city has the greatest range? C Which city has the greatest interquartile range? D Which city has the lowest 3rd quartile?

A: Tucson

B: Boston

C: Boston

D: Seattle

41.

Favorite Sport

The graph above shows the results of a survey of 400 students at a local elementary school. A How many students chose swimming? B How many more students chose track than gymnastics?

108

36

42. Kevin’s mother made 385 pints of salsa. How many liters of salsa does she have? [1 pt = 0.473 L]

182.105 L

43. The sailboat was 13.5 meters long. What is the length of the sailboat in yards? [1 m = 1.094 yd]

14.769 yd


44.

The dot plots above show the score of two different classes on a recent science test. Using the data to answer the following questions. A Which class has a higher median? B Which class has a higher MAD? C Which class has a higher interquartile range? D Which class has a higher mode?

A, B, C, D:

They are all Class 2.

45. The cup held 56 fluid ounces of milk. How many milliliters of milk is there? [1 fl oz = 29.58 mL]

1656.48 mL

46. The truck weighed 4,836 kilograms. How many pounds did it weigh? [1 kg = 2.205 lb]

10,663.38 lb

47.

What percent of the people above live in the two least populous cities?

Find the mean.

37.7%

45,000


GEOMETRIC RELATIONSHIPS

48.

Are the two quadrilaterals above similar? If so, state why. If not, state why not.

Yes, all corresponding

angles are congruent.

49.

Are the two triangles above congruent? If so, state why. If not, state why not.

No. While corresponding

angles are congruent,

corresponding sides are not congruent.

50.

Find all the missing angles in the figure below.

27, 45, 65

51.

Find the measure of all three angles in the triangle above.

40, 45, 95

52.

Name all angles that are supplementary to angle 5.

2, 3, 6, 7

70 4x+5 2x+15

x+12


53.

Write and solve a proportion to find x. Write and solve a proportion to find y.

12

18 28

57

7

x

x

=

=

20 20

18 28

111

9

y

y

+=

=

54.

Find the values of angles 1, 2, 3, and 4.

1: 88 degrees 2: 57 degrees 3: 35 degrees

4: 145 degrees

55. How many degrees are in a triangle? quadrilateral? 180, 360

56. If one angle of a triangle measures 38 degrees, another measures 74 degrees, how much is the third angle?

68 degrees

57. If two angles are supplementary, and the measure of one of them is 2 12x + , and

the other is 2 8x − , how much is x and what is the measure of each angle?

44x = 80, 100 degrees

58. If two angles are complementary, and one of them measures 37 degrees, how much is the other one?

53 degrees

59. In triangle DEF, m D∠ = 25o, m E∠ = 37o, find the measure of m F∠ . 118 degrees

60. What is a regular polygon? all sides congruent, all

angles congruent

61.

Figure B′ is the image of figure B under what transformation? Write your

answer is symbolic form [ ( , )x y → ….]

( , )

( , )

x y

x y

→

−


62.

The figure on the left is a transformation of the figure on the right. Describe the

transformation in symbolic form [ ( , )x y → ….]

( , )

( 5, 3)

x y

x y

→

− +

63.

A rectangle is plotted on a coordinate grid. The rectangle is then transformed

using the following: ( , ) ( 3, 6)x y x y→ − + Describe in words the movement

of the rectangle.

left 3, up 6

64.

The triangle on the left was dilated to create the triangle on the right.

What is the sum of the two missing side lengths?

27

AREA & CIRCLES

65. Find the area of a trapezoid with bases of 7cm and 11cm and a height of 8cm. 272 cm

66. Find the height of a trapezoid with bases of 7 and 3 and an area of 45. 9 units

67. The moat around King Arthur’s castle was 2 miles from the center of Camelot, where his castle was located. How far did his knights have to walk around the moat?

12.56 mi

68. A serving platter that matches the china has a diameter of 18 inches. What is the area of the platter?

2254.34 in

69. If the radius of a bicycle tire is 14 inches, what distance will the bike travel in one revolution?

87.92 in

70. The circumference of a circle is 54 inches. What is the radius to the nearest tenth?

8.6 in

71. If a clock has an area of 34 square inches, write an equation that could be used to find the diameter of the clock.

342d

π=

72. A rectangle has a perimeter of 24 inches. What length and width measurements will give the greatest area?

6 in


73. A square has a side length of

22

3 yards. If tape is to be placed around the

entire square, how many rolls of 15-foot tape are needed?

3 rolls

74.

What is the distance x?

48

75. The floor of a square room has an area of 2,500 ft.2. How long is each side of the floor?

50 ft

76.

Mr. Mangham is looking for a new window for his living room. He finds an interesting one at Home Depot with the shape below. What is the area of the window?

243.065 ft

77.

The figure below represents the first floor plan of a new museum. What is the area of the museum’s first floor on the floor plan?

2586.17 cm

78. A circle has a radius of

1

6 cm. Using pi as a fraction, solve to determine the

circumference and area of the circle. 2

22 cm

21

11A= cm

126

C =

DIMENSIONAL GEOMETRY

79. Find the volume of a rectangular prism if l=8m, w=6m, h=5m? 3240 in

80. Find the volume of a square pyramid with a base side length of 6cm, and a height of 9cm.

3108 cm

81. Mrs. Oliver has a beaker with a radius of 8cm and a height of 20cm. She needs another one with the same radius but half the volume. How tall should the new one be?

10 cm

82. Find the surface area of a cylinder with a radius of 8cm and a height of 20cm. 21406.72 cm

x

3 ft

12 ft


83. Find the volume of a triangular prism with a base of 10 units, a base height of 5 units and a figure height of 20 units.

3500 un

84. A company wants to fence in a rectangular car-testing site with the largest possible area using 60 miles of fencing. What should the length and width of the fenced site be?

15 mi

85.

Connie fills three of the cylinders below to bring her food for lunch to school. What is the volume of her entire lunch?

3103,393.92 cm

86. Find the volume of the cone to the nearest whole number. h = 10ft, r = 3ft

394 ft

87. A figure has a rectangular base. Which of the following figures can it not be?

cylinder, cube, rectangular prism, square pyramid cylinder

88.

Find the volume and surface area of the figure to the nearest tenth.

3

2

5240.0 cm

2969.2 cm

V

S

=

=

89.

Find the volume and surface area of the figure to the nearest tenth.

3

2

324.8 in

402.6 in

V

S

=

=

90. The side length of cube A is one-fourth of the side length of cube B. How many times larger is the surface area of cube B?

16

91. In the problem above, how many times larger is the volume of cube B? 64

92. A square pyramid has a base side length of 20 ft and a height of 10 ft. What is the volume of the pyramid?

31333.3 ft

93. A triangular pyramid has a base area of 250 in2 and a volume of 750 in3. What is the height of the pyramid?

9 in

28 cm.

14 cm.

19.7 cm.

4.3 cm.

11.1 in

2.2 in 13.3 in.


94.

What is the total surface area of the rectangular prism whose net is shown?

1078 m2

95.

Find the lateral surface area of the prism’s net shown.

375 m3

96.

Find the lateral and the total surface area of the cylinder below.

LSA = 1884 cm2

TSA =

2512 cm2

PROBABILITY

97. When rolling a die, what is the theoretical probability of a rolling a prime number?

1

2

98. If you have a spinner divided into 8 equal parts and containing the numerals 1 though 8, find the probability of spinning a 7 then a 5.

1

64

99. There is a bag with 6 blue, 4 red, 2 green and 8 yellow marbles. What is the theoretical probability of drawing a blue marble, and then without replacing it, drawing another blue marble?

3

38

100. What is the theoretical probability of rolling an even number if you roll a die? 1

2

101. Lauren has 7 pairs of shorts, 8 shirts, and 3 pairs of sandals on her trip to the beach. How many different outfits can she wear while she is there?

168

102. If you flip three coins at the same time, what is the P(H,H,H)? 1

8

103. There are 12 colored cubes in a bag, 5 yellow, 6 red, and 1 blue. What is the theoretical probability that Kenneth can draw a yellow, then another yellow, without replacement?

5

33

5 m

25 m


104. A taco stand sells both corn and flour tortillas, with a choice of three fillings, and two different toppings. If you are allowed only one selection from each category, how many different tacos can you choose?

12

105.

Mrs. Arnold asked students if they should be given more homework. Their answers were: yes, yes, no, yes, yes, yes, no, no, yes, yes What is the experimental probability that the next student will answer no?

3

10

106.

Mr. Mangham put colored marbles into a hat. The table below shows how many times he randomly chose each color (replacing after each draw).

Pink Purple Green Red

Draws 18 12 7 13

What is the experimental probability that the next draw will not be green?

43

50

107. A True-False test has ten questions. What is the probability of getting all 10 right if you are having to guess at all the answers?

1

1024

108. The numbers 0-9 are all placed in a hat. If you replace the number after each draw, what is the probability after three draws that you have not chosen the number 8?

729

1000

109. A bag contains 15 red marbles, 12 blue marbles, and 13 green marbles. One marble is drawn at random and then replaced. After 160 drawings, how many times would you expect a red marble to be selected?

60

110. The experimental probability of Holly winning Survivor is 8%. Out of 60 times playing Survivor, about how many times will Holly win?

5 (4.8)

PYTHAGOREAN THEOREM

111. The sides of a square are 30 inches long. How long is a diagonal that cuts the square into two triangles? 30 2

112. If the area of a square is 49 square inches, how long is a diagonal that cuts it into two triangles? 7 2

113. How far is ( 3, 6)− − from (6, 10)− ? 97

114. Find the distance between the points (2, 5)− and (6, 10)− to the nearest tenth. 41 6.4≈

115. Use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if the legs are 12 and 15 inches respectively. 3 41

116. If a hunting eagle flies 5 miles north, then 4 miles east, then 4 more miles north of his nest, then is going to fly back directly to his nest, how many total miles does he have to fly?

13 97+ mi

117. Jack walks 5 blocks south and 12 blocks west. How far is Jack from where he started?

13 blocks


FINANCIAL LITERACY

118.

The circle graph above is the monthly budget for the Delacruz family. If their total monthly budget is $3000, how much does the family spend each year on food?

$6,480

119. Using the Delacruz budget in the problem above, how much more does the family spend each month on housing than on clothing?

$780

120.

Quinn lives in a house with a value of $200,000. She has a mortgage of $150,000. She owes $6,000 on her car, which is valued at $18,000. She has a credit card balance of $800. Quinn also has $1,200 in a bank account. What is Quinn’s net worth?

A $50,800 B $74,100 C $62,400 D $80,100

C

121.

The table shows Kenny’s net worth. Assets are shown as positive numbers, and liabilities are shown as negative numbers.

Net Worth

House (current value) $87,900

Checking account $1,250

Credit-card debt $2,850−

Automobile (current value) $10,500

Student loans $7,000−

Investments

Personal loans $1,800−

Savings account $2,400

Kenny’s net worth is $100,800. Based on the information in the table, what is the amount of money Kenny has in his investments?

$10,400

122. Samuel put $5,000 in a savings account that pays 5% compounded interest compounded annually. What is the value of the account after 2 years?

$5,512.50


123. Sally puts her $500 savings from her summer job in the bank. The bank will pay her 4% simple interest for 3 years. Write an equation that could be solved to determine the amount of interest Sally will have at the end of 3 years.

500(0.04)(3)I =

124.

Johnny puts his $1200 savings from his summer job in the bank. The bank will pay him 2% compounded interest for 2 years. Write an equation that could be solved to determine the total amount Johnny will have in the bank at the end of 2 years.

21200(1.02)A =

125. SpongeBob deposits $300 into a savings account that earns simple interest at a rate of 5%. How much total interest has SpongeBob earned after 4 years?

$60

Optional Extra Problems

1.

The experimental probability that Ming will win a game of chance is 2

5. The

experimental probability that Tyrell will win the same game is 5

8 . If Ming and

Tyrell each play 200 games, how many more games can Tyrell expect to win? A 16 B 24 C 25 D 45

D

2. The results of a random survey showed that 42 out of 80 people prefer chocolate ice cream to any other flavor ice cream. How many people will prefer chocolate ice cream if 2000 people are surveyed?

1050

3.

Rene is in charge of making props for a school play. She needs to make a large circular wooden clock that measures about 6 feet in circumference. Which equation can she use to find r, the radius of the clock?

A 6

rπ

= B 12

rπ

= C 6

2r

π= D

12

2r

π=

C

4.

An airplane flight has 228 seats. The probability that a person who buys a ticket actually goes on that flight is about 95%. If the airline wants to fill all the seats on the flight, how many tickets should it sell? A 217 tickets C 345 tickets B 2400 tickets D 240 tickets

D


5.

Latisha spins both spinners. How many outcomes are in the sample space? A 9 outcomes C 18 outcomes B 20 outcomes D 6 outcomes

B

6.

Use the Pythagorean theorem to find the missing side.

8 km

7.

The graph shows the relationship between the number of members in a club and the number of years after the club began. Based on the trend shown in this data, predict the year in which the club will have no members. A 1 year B 3 years C 6 years D 8 years

D

8.

John creates cones for fun on the weekends. Each cone has a circular top. The cones are 10 inches in diameter and 12 inches high. The lateral/slant height (going up the side) of the cone is 13 inches. Find the volume of the cone to the nearest tenth.

314 in3

9.

Which set of ordered pairs represents a function? A (2, 5), (1, 6), (0, 5), (1, 10) C (2, 1), (3, 1), (5, 1), (5, 4) B (0, 0), (1, 1), (2, 0), (3, 3) D (5, 4), (4, 5), (1, 2), (1, 4)

B

10.

What are the slope and y-intercept of the relationship in the table below?

Months 1 2 3

Savings $225 $300 $375

75

150

m

b

=

=

15 km.

17 km.


11. A map scale is 1 cm:50 km. Two cities are 3.8 cm apart. How many kilometers is it from one city to the other?

190 km

12. A CD player is on sale at a 20% discount. If it normally sells for $49.95, what is the sale price?

$39.96

13. 20% of 30 is… 6

14.

The enrollment at Clifford Junior High from 1997 to 2001 is shown below.

If the enrollment trend shown in the table continued, which is the best prediction of the enrollment at Clifford Junior High in 2004? A Fewer than 1,100 C Between 1,200 and 1,300 B Between 1,400 and 1,500 D More than 1,500

C

15.

Mary has two different types of boxes. Both are cubes and the larger has a side length that is twice the smaller. How many of the small boxes can fit in one large box?

8

Enrollment at Clifford Junior High

900

1000

1100

1200

1997 1998 1999 2000 2001

Year

En

roll

men

t

4 ft. 2 ft

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