PA Grade 4-8 Core Assessment: Math (5155)

The weekly revenue from shirt sales at Store X was the same for two weeks. In the first week at Store X, 140 shirts were sold at $5 each. If Store X increased shirt prices in the second week to $7 each, how many shirts were sold in the second week?

A) 70

B) 80

C) 90

D) 100

D

The boxplots shown summarize the prices, in dollars, of 20 low-mileage used minivans and the prices, in dollars, of 20 low-mileage hatchbacks as listed on the auto dealer’s website. Each of the 40 vehicles has a different price. Which of the following statements is the best comparison of the minimum price of the minivans to the prices of the hatchbacks?

A) The minimum price of the minivans is less than the prices of 75% of the hatchbacks.

B) The minimum price of the minivans is less than the prices of 100% of the hatchbacks.

C) The minimum price of the minivans is greater than the prices of 50% of the hatchbacks.

D) The minimum price of the minivans is greater than the prices of 75% of the hatchbacks.

C

Which of the following pairs of fractions are equivalent? Select all that apply.

A) 3/5 and 9/25

B) 5/6 and 11/12

C) 4/7 and 24/42

D) 5/8 and 13/20

E) 8/12 and 14/21

C, E

A cup of whole milk has 30 more calories than a cup of orange juice. If j represents the number of calories in a cup of orange juice, which of the following represents the number of calories in a cup of whole milk, in terms of j?

A) j + 30

B) j - 30

C) 30j

D) j / 30

A

A 224-mile trip requires 6 gallons of gasoline. At this rate, how many gallons of gasoline would be required for a 168-mile trip?

A) 4

B) 4.5

C) 8

D) 8.5

B

The table shows the distances, in miles, between selected cities. Juniata will travel directly from Boston to Seattle. Gary will travel from Boston to Denver and then from Denver to Seattle. How many more miles will Gary travel than Juanita?

A) 323

B) 657

C) 1,018

D) 1,341

A

In the figure above, each circle is tangent to the other two circles. The points X, Y, and Z are the centers of the circles. If the circles have radii of 3, 4, and 5 respectively, what is the perimeter of the triangle XYZ?

A) 12

B) 19

C) 20

D) 24

D

Marta has $88 in a jar. If she adds $6 each week to the money already in the jar without withdrawing any money, in how many weeks will she have a total of $142 in the jar?

A) 7

B) 8

C) 9

D) 10

C

During a two-week period, a library reported that 6,590 people used the library/ The table above shows the numbers of people in various categories of library use for that two-week period. Approximately what percent of the total number of people who used the library used it during the afternoon?

A) 15%

B) 20%

C) 25%

D) 30%

B

Put the following in order of shapes with the least number of lines of symmetry to the greatest number of lines of symmetry.

A) An equilateral triangle

B) A square

C) A regular hexagon

D) An isosceles triangle

E) A rectangle that is not a square

D, E, A, B, C

Sean’s bookshelf contains science fiction, mystery, fantasy, and non-fiction books. There are an equal number of science fiction books and mystery books, there are ½ as many fantasy books as there are mystery books, and there are 5 times as many nonfiction books as there are fantasy books. If Sean chooses a book at random from the bookshelf, what is the probability that Sean will choose a science fiction book?

A) ½

B) ¼

C) 1/5

D) 1/10

C

Bob’s checking-account balance was $982. He then deposited a check for x dollars and withdrew $35 out of the account. His new balance is $1,104. What is the value of x?

A) 33

B) 87

C) 122

D) 157

D

Sandra purchased the following items at the local grocery store: 6 cans of peas at $0.99 per 3 cans, 2 packages of frozen vegetables at $2.49 per package, and 5 bunches of celery at $1.19 per bunch. Excluding sales tax, which of the following is the closest approximation of the total cost of her purchase?

A) $11.00

B) $13.00

C) $16.00

D) $17.00

B

p = 3 ( w + 5 ) + 7

If the value of w in the equation is increased by 1, how will the value of p change?

A) It will increase by 1.

B) It will increase by 3.

C) It will increase by 5.

D) It will increase by 7.

B

The figure above represents a kitchen floor that is to be covered with square tiles the length of 6 inches on a side. If the tiles cost $0.75 each, what will be the cost of the tiles to cover the floor?

A) $75

B) $200

C) $240

D) $300

D

7 less than 3 times a number is equal to half of the square of the number

If x represents the unknown number, which of the following equations is the translation of the sentence above?

A) 7 - 3x = ½ x²

B) 3x - 7 = ½ x²

C) 7 - 3x = ( x / 2 )²

D) 3x - 7 = ( x / 2)²

B

Point P has integer coordinates and is shown in the xy-plane. What are the coordinates of point P?

5,3

Based on the information in the right triangle shown, which of the following expressions is equivalent to x?

A) w - 4

B) w + 4

C) √w² - 16

D) √w² + 16

C

3, 3, 6, 9, 15, 24, …

The first two terms in the sequence above are 3. Each term after the first two is equal to the sum of the two preceding terms. How much greater is the tenth term of the sequence than the seventh term of the sequence?

A) 39

B) 63

C) 102

D) 126

D

The population of Country X is 0.36 billion persons, and the population of County Z is 12 million persons. The population of Country X is how many times that of Country Z?

A) 300

B) 30

C) 0.3

D) 0.03

B

A plumber charges a flat fee of $36 per hour for work on the weekdays and $48 per hour for work on Saturdays and Sundays. The plumber worked on a job for 4 hours last Friday, finished the job last Saturday, and charges a total of $288. How many hours did the plumber work on the job last Saturday?

A) 3

B) 4

C) 6

D) 8

A

A scale drawing of an automobile is being created in which a length of 1/3 inch on the drawing is equivalent to an actual length of 1 foot. If the actual length of the car is 14 feet, which of the following is closest to the length, in inches, of the car in the drawing?

A) 4.3

B) 4.7

C) 5.3

D) 9.4

B

An English teacher surveyed 48 tenth-grade students and found out that 18 had read Hamlet, 20 had read Macbeth, and 21 had read neither play. How many of the students surveyed had read both plays?

A) 11

B) 18

C) 23

D) 25

A

A light display for a festival consists of a string of 1,000 bulbs in the colors red, yellow, green, and blue repeated consecutively in that order for the entire display. The 543rd lightbulb needs to be replaced. If the first bulb is red, what is the color of the lightbulb that needs to be replaced?

A) red

B) yellow

C) green

D) blue

C

Isosceles triangle DEF is congruent to isosceles triangle XYZ, as shown in the figure. Based on the information given, which of the following is equivalent to b?

A) 90+ a

B) 180 - a

C) 180 - 2a

D) 2a

C

Which of the following graphs could represent the distance of an object from a given point as time passes?

A, B, C

The amount of money that Lindsey had in her checking account at the beginning of last summer is 15% of the amount of money she had in her checking account at the end of last summer. If Lindsey had $540 in her checking account at the beginning of last summer, what was the amount of money, in dollars, that she had in her checking account at the end of last summer?

A) 81

B) 810

C) 3,600

D) 4,140

C

Elizabeth owns x books. Kierra owns 5 more books than Elizabeth and 8 fewer than Ana. Which of the following represents the total number of books the three girls own?

A) 3x - 3

B) 3x + 3

C) 3x + 13

D) 3x + 18

D

The sides of a square are each 8 centimeters long. If two of the opposite sides are reduced by 3 centimeters each and the other two sides are increased by 3 centimeters each to form a rectangle, which of the following statements is true?

A) The areas of the rectangle and the square are the same, and the perimeters of the rectangle and the square are the same.

B) The area of the rectangle is 9 square centimeters less than the area of the square, and the perimeters of the rectangle and square are the same.

C) The area of the rectangle is 9 square centimeters less than the area of the square, and the perimeter of the rectangle is 6 centimeters greater than the perimeter of the square.

D) The area of the rectangle is 9 square centimeters greater than the area of the square, and the perimeter of the rectangle is 6 centimeters less than the perimeter of the square.

B

In a certain store, pencils can be bought only in packs of 5 or in packs of 8. Annie plans to buy a total of 100 pencils, and she needs to buy at least one pack of 8 pencils. Of the following, how many packs of 8 pencils could she buy?

A) 5

B) 6

C) 7

D) 8

A

Ben bicycled a distance of 6 miles from his home to the mall, then he returned home after spending time at the mall. The line graph above shows Ben’s distance from home, in miles, versus the time away from home, in minutes, for his bike trip. Which of the following statements about Ben’s trip are supported by the graph? Select ALL that apply.

A) Ben spent 150 minutes at the mall.

B) Ben traveled at an average speed of 8 miles per hour on the way to the mall.

C) Ben stopped for 15 minutes on the way home from the mall.

D) Ben spent 90 minutes riding his bike during the bike trip.

B, C, D

The average (arithmetic mean) of 40, 80, and m is 50. The average of 40, 80, m, and v is 60. What is the value of v?

A) 30

B) 50

C) 90

D) 100

C

The sum of three consecutive integers is 19 less than four times the smallest integer. What is the value of the middle integer?

58

Line segment JK is shown in the xy-plane. Line segment JK will be reflected over the x-axis to form line segment J’K’. What will be the coordinates of point K’?

A) ( -5 , 4 )

B) ( -4 , 5 )

C) ( 4 , -5 )

D) ( 5 , -4 )

D

A quarter-mile-long fence is divided into 100 equally sized nonoverlapping sections. What is the total length, in feet, of the first 10 sections of the fence? (1 mile = 5,280 feet)

A) 132

B) 264

C) 528

D) 1,320

A

If f(x) = -x² - 2x + 4 , what is the value of f(-2)?

A) -4

B) -2

C) 4

D) 12

C

7.5

The function h is defined by h(x) = -2x - 17 for all real numbers x. Which of the following is a partial table of the values for h(x)?

A

Company F charges a one-time fee of $85.00 to rent a truck plus $0.06 for every mile driven.

Company G charges a one-time fee of $61.00 to rent a truck plus $0.09 for every mile driven.

For what number of miles is the cost to rent a truck the same at both companies?

80

Melinda has a spool with 3 meters of ribbon on it. Which of the following values is closest to the number of inches of ribbon Melinda will have left on the spool if she cuts 15 inches off the spool to use for a craft? (1 meter = 3.28 feet)

A) 103.1

B) 118.1

C) 132.6

D) 147.6

A