2011 HSPA Summer Packet

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3.

6.

4.

5.

1

2.

During the 6 th game of the 1999 playoffs between the Knicks and the Pacers, the Knicks made 5 times as many two point shots as they did three point shots and twice as many foul shots (one point shots) as three point shots. They scored 90 points. Which equation below can be used to find out the number of points scored by making the three point shots? a. c.

3x + 2x + 1x = 90

2x + 10x + 3x = 90 b. d.

2x + 5x + x = 90

5(3x) + 2(2x) + 1(1x) = 90

Which of these equations is satisfied by the pairs of numbers in the table? x

0

2

6

10 y

6

12

24

36 a. c. y = x + 6 y = 6 – x b. d. y = 3x – 6 y = 3x + 6

Solve the equation for y: ay = by + 6 a. c.

6a + 6b a

 b

6

What is the next term in the sequence below?

1, 8, 27, 64, …. a. 5 b. 25 b. d. c.

6 a

 b

6

 b a

96 d. 125

Which of the following would yield a repeating decimal pattern? a.

1

6 b.

1

4 c.

3

16 d.

1

25

If the volume of a cube is a function of the length of length of an edge, which of the following equations represents the situation? a. c.

V = 3e

V = e + 3 b. d.

V = e 3

V =

3 e

8.

7. Find the equation of the line containing the points (−1, −3) and (0, 5) a. c. y = 8x y = 8x + 5 b. d. y = −8x + 5

1 y =

8 x + 5

Mrs. Anderson had her 30 students vote for their favorite lunch as shown:

Lunch Item

Tacos

Pizza

Number of Votes

7

9

Hot Dogs

Hamburgers

Spaghetti

3

6

5

She then told them to show the data in a circle graph. How many degrees in the central angle of the sector of that circle would represent the number of votes for pizza? a. 72 b. 84 c. 96 d. 108

11.

9.

10.

Mrs. Holiday’s math class got the following scores on one of her exams: 81, 87, 84, 83, 82 and

90. What was the mean exam score? a. 83.5 b. 84 c. 84.5 d. 85

A number is chosen at random from the first 25 counting numbers. What is the probability that the selected number will be a prime number? a.

2

5 b.

9

25 c.

8

25 d.

7

25

What is the probability of drawing 2 blue marbles from a bag containing 5 blue and 7 green marbles? a.

5

12 b.

2

5 c.

5

7 d.

5

33

12. Wildwood Bookstore and North Wildwood Bookstore plan to merge. Their final inventories are represented by the matrices below, with row 1 indicating hardcover books and row 2 indicating paperbacks. The three columns represent non-fiction, fiction, and reference books, respectively.

A=

6270 1670 1890

B=

5340 4220 1780

2940 2810 2080 3050 3100 2810

What would be the total inventory of reference books for the new company formed by the merger? a. 3,970 b. 8,560 c. 16,790 d. 37,960

13. A local man has a property that is 600 feet wide and 200 feet long. His house is 50 feet wide by

30 feet long. He is away on vacation but his neighbor just called to tell him that lightening struck his property, but he does not know where. What is the probability that lightening struck his home?

(Assume that lightening is equally likely to strike anywhere on the property.) a.

1

10 b.

1

80 c.

5

6 d.

15

12

14. For which of the following situations would you expect the scatter plot to show a negative correlation? a. b. c. d.

The number of students in a high school and the average temperature of the city

The age of the car and the resale value

The price of an item and the amount of tax on the item

The speed of a car and the distance traveled in a fixed time

16.

15. A steel rod is 4.25 feet long. If you cut the rod into 10 equal pieces, how many inches long will each piece be? a. c.

0.425 inches

4.8 inches b. d.

4.2 inches

5.1 inches

What is the perimeter of a polygon whose coordinates are (1, 6), (4, 6), (1, -2) and (4, -2)? a. 11 b. 12 c. 22 d. 24

18.

19.

20.

17. A jar contains x pennies and y nickels. Liam removed a nickel from the jar and replaced it with a penny that he had in his pocket. Following Liam’s actions, what fraction of the coins in the jar are nickels? a. c. x y

1

 x y

 y y b. d. x y

1 y

1 x y

 y

1

A cubic foot will hold 7.5 gallons of water. If Lisa’s waterbed measures 8 feet by 5 feet by 4 inches, approximately how many gallons of water will she need to fill the mattress? a. c.

105 gallons

95 gallons b. d.

100 gallons

90 gallons

A sphere has a surface area of 1256 square meters. What is the radius of the sphere? a. 10 m b. 20 m c. 100 m d. 200 m

In the diagram below, ABC @ DEF. What transformation will map ABC onto DEF?

21. a. Reflection over the x-axis and translation 2 spaces to the right. b. Reflection over the x-axis followed by a reflection over the y-axis. c. Reflection over the y-axis and translation 5 spaces down. d. Reflection over the y-axis followed by a reflection over the x-axis.

If the volume of a cube is 64 cubic feet, what is its surface area? a. c.

16 square feet

96 square feet b. d.

64 square feet

384 square feet

22.

23.

The hypotenuse of a right triangle has a length of 20 centimeters. The shortest leg has a length of

10 centimeters. What is the length of the other leg, rounded to the nearest centimeter? a. 10 b. 15 c. 17 d. 18

24.

A gardener wishes to decorate a garden which is 576 square feet in area, and he must decide how to apportion each section of the garden with specific plants. He has decided to set aside 20% of the garden with roses and an additional 32.9 square feet for a tomato patch. How much of the garden is set aside for the roses and tomatoes? a. c.

52.9 square feet

523.1 square feet b. d.

148.1 square feet

569.42 square feet

25.

27.

26.

28.

A rectangle has a perimeter of 34 inches and an area of 72 square inches. What are the lengths of the sides of the rectangle? a. c.

2 in and 36 in

8 in and 9 in b. d.

4 in and 18 in

10 in and 7 in

A rectangular sheet of paper is 14 inches long. Its area (in square inches) is twice its perimeter (in inches). How wide is the sheet of paper? a. 5.6 b. 10 c. 7 d. 14

A figure undergoes a transformation. The pre-image and the image are not congruent. What type of transformation took place? a. c.

Dilation

Rotation b. d.

Reflection

Translation

If ∆ABC with vertices A(−2, 0), B(−2, −2), C(−4, −2) is reflected over the x-axis and then the image is reflected over the y-axis, which coordinates would represent the final image of point A? a. (−2, 0) b. (2, 0) c. (0, 2) d. (0, −2)

A rectangle located in the first quadrant has two vertices at (0, 0) and (0, 6). Where would the other two vertices be if the area of the rectangle is 30 square units? a. b.

(0, 5) and (6,5)

(5, 0) and (5, 6) b. d.

(5,0), and (6, 5)

(9, 0) and (9, 6)

31.

32.

33.

29.

30.

34.

35.

A rectangle has dimensions 5 cm by 12 cm. How many centimeters long is a diagonal of the rectangle? a. 12 b. 13 c.

Which of the following results in a negative number? a. c.

(-3) + 4

3 x (-4) b. d.

17

(-3) x (-4)

3 x 4

Which of the following types of numbers would solve the equation x 2 = 15? a. c.

Whole number

Terminating decimal b. d.

Fraction

Irrational number d.

A catalog advertises a sweater available in the following styles, sizes and colors:

Style

Long Sleeve

Sleeveless

Size

S

M

L

XL

Color

Black

Navy

Red

White

Green

How many variations of this sweater are there? a. 11 b. 20 c. 40 d.

30

60

The price of a pair of sneakers was reduced 20%. The amount by which the price was reduced was $12. What was the original price of the sneakers? a. $36 b. $48 c. $60 d. $72

Which of the following equals 0.0503? a. c.

5.03 x 10 2

5.03 x 10 -2 b. d.

5.03 x10

5.03 x 10 -3

36.

A softball player’s batting average is the ratio of the number of times she gets a hit to the total number of times at bat. Jackie got 15 hits during a season and had a batting average for the season of .250. What was her total number of times at bat? a. 375 b.

Which number sentence is true? a. c.

0.43 < 0.043

0.00043 > 0.043

60 c. b. d.

50

0.0043 > 0.43

0.043 > 0.0043 d. 25

39.

37.

38.

Which of the following numbers is irrational? a. 0 b. ¾ c. 36

Ralph simplified the expression

1

15(

3

2

+

5

) to (5 + 6)

Which of the following properties of the real numbers did Ralph use? a. b. c. d. associative property of multiplication commutative property of multiplication distributive property multiplicative identity property d. 2

43.

42.

40.

41. a. b. c. d.

A local jewelry store is offering a Valentine’s Day special of 35% off on selected watches. After the sale, the dealer raises the price of the watch by 35% of its sale price. The price of the watch is then:

Less than the original price

The same as the original price

More than the original price

There is not enough information to compare the two prices

If 30% of a number equals 27, what is 60% of that same number? a. 90 b. 74 c. 54 d. 18

The towns of Arepa and Jansen are 176 miles apart. The scale on the map reads:

1 inch = 25 miles. How far apart are Arepa and Jansen on the map? (rounded to nearest inch) a. 5 b. 6 c. 7 d. 8

Allana saves 20% on a $125 bowling ball, but must pay 6% sales tax. What is the total amount that she must pay? a. c.

$94.00

$106.00 b. d.

$100.00

$107.50

Richard earns $10 per hour, and Mark earns $8 per hour. How long must Mark work in order to earn the same amount of money as Richard earns in five hours? a. c.

5 hours, 45 minutes

6 hours, 15 minutes b. d.

6 hours

6 hours, 25 minutes

44.

45.

(−3 x 10 25 ) x (4 x 10 7 ) = a. c.

−1.2 x 10 32

−12 x 10 18 b. d.

−12 x 10

−1.2 x 10

31

33

The general partners in a small company, Miranda, Cohen, and Brown, share its profits in the ratio of: 3:2:5, respectively. If that company’s profits amount to $24,300 this year, what is Mr.

Miranda’s hare? a. $2,430 b. $7,290 c. $8,100 d. $14,580

46.

47.

48.

A diagram of a rectangle with dimensions 6 inches by 8 inches is placed in a copy machine which is set to enlarge all dimensions by 10 percent. Will the resulting figure fit on an 8.5” x 11” sheet of paper? a. b. c. d.

Yes, it will fit with room to spare.

Yes, it will fit with no room to spare.

No, one dimension will fit, but not the other.

No, both dimensions are too large.

In a class of 25 students, there are 13 boys. What is the ratio of girls to boys? a. 12:13 b. 12:25 c. 13:12 d. 13:25

Laura bought a softball glove at 40% off the original price. This discount saved her $14.40. What was the original price of the glove? a. $5.76 b. $20.16 c. $36 d. $50.40

1.

The data provided shows test scores for twelve students and the number of hours they studied for the test during the three days prior to taking it.

Hours

Studied

Test

Score

1.0

60

1.25

70

1.5

68

3.0

1.75

85

2.0

90

2.25

98

Hours

Studied

Test

Score

2.5

85

2.75

92 91

3.25

87

3.5

85

3.75

72

Make a scatter plot of this data.

Does there appear to be a relationship between a student's test score and the time spent studying?

Use the scatter plot to support your answer.

Do any of the points appear to be outliers? Explain.

2 . The length of the rectangular playroom in Sheila's basement is 1½ times its width. The room has no windows and has a height of 8 feet. Sheila has decided to wallpaper the entire room and put a border over the wallpaper at the top around the room. To determine how much wallpaper is needed, she has to add together the area of each wall to get the total surface area of the room. The door to this room measures 2.5 feet wide by 6.5 feet high and will not need wallpaper.

C)

A)

B)

Let x be the width of the room. Write and simplify an equation in terms of x to determine the total surface area (S) of the playroom's walls.

The playroom is 12 feet wide. Each roll of wallpaper will cover approximately 56 square feet. The wallpaper has no pattern; therefore, it is not necessary to allow for matching patterns when calculating the amount of wallpaper to purchase. What is the least number of rolls Sheila will need to paper her room? Show your work.

Sheila plans to spend no more than $350.00 (ignore tax) on the wallpaper and border. The border costs $19.97 per 10-yard roll. The border will be pasted onto the wallpaper at the top of each wall with no overlap. Explain how to determine the most expensive wallpaper Sheila can buy while staying within her budget.

3. The fine for speeding on the highways of most states is a function of the speed of the car. The fine for speeding on the New Jersey Turnpike, for example, can generally be determined by the formula:

F = 2(S – 55) + 46

Where F is the fine in dollars and S is the speed your car was going in miles per hour.

What would your speeding fine be if you were caught traveling 85 mph?

Suppose you received a speeding ticket for $126. How fast were you going? Explain how you arrived at your answer.

Why is it unlikely for someone to receive a $40 speeding fine in New Jersey?

Use the information you arrived at above and construct a line graph that shows the fine and the car’s speed for all speeds from 55 to 100 mph.

4. Assume that the following table continues forever, to the nth row.

A)

B)

C)

D)

Row 1

Row 2

Row 3

Row 4

Row 5

...

Row 100

Row n

Column A

1

1/2

1/3

?

1/5

...

?

?

Column B

6

5 1/2

5 1/3

5 1/4

?

...

?

?

Column C

-2

-2 1/2

-2 2/3

-2 3/4

?

...

?

?

Complete rows 4 and 5 in the duplicate chart provided.

What numbers belong in row 100? Write your answers in the chart provided.

Write expressions to determine the values of the nth row, for columns A, B, and C.

What number do the values of column A approach? What number do the values of column C approach? Explain your answers or show what the values approach on a number line to support your answer.

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