December 1 — 1:45 pm, 2015

Can you solve these 6th-grade math questions?

The following multiple-choice questions are from a selection of sample test items provided by the Pennsylvania Department of Education for the 6th-grade PSSA exam in math. Calculator use is permitted. The exam also includes open-ended questions where students are expected to explain their answers.

 

1. Emily is making bows using ribbon. She has two pieces of ribbon to use. One is 23 yards long. The other is 4 1/4 yards long. She needs 1 5/6 yards of ribbon to make each bow. What is the greatest number of bows Emily can make?

A. 12

B. 14

C. 15

D. 19

 

2. Gracie is rewriting the expression (24 + 40) as an integer times the sum of two integers. By factoring out a 2, she knows she can rewrite the expression as 2 times the sum of two integers. What are all the other numbers greater than 2 that Gracie can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers?

A. 4, 8

B. 4, 6, 8

C. 3, 5, 6, 10, 12, 20

D. 3, 4, 5, 6, 8, 10, 12, 20

 

3. Quincy and Ray keep track of their scores in a game. The person with the greater score is winning the game. Quincy has a score of –70, and Ray has a score of –60. Which statement best explains who is winning and how many points away from 0 that person is?

A. Ray is winning and needs to lose 60 points to get to 0.

B. Ray is winning and needs to gain 60 points to get to 0.

C. Quincy is winning and needs to lose 70 points to get to 0.

D. Quincy is winning and needs to gain 70 points to get to 0.

 

4. At a factory, a machine tests 1 out of every 75 items produced for quality. The machine requires a safety check after testing 450 items. The factory produces 303,750 items each month. How many safety checks does the machine require each month?

A. 6

B. 9

C. 50

D. 54

 

5. When a farmer harvests chicken eggs, he expects 2% of the eggs to be cracked. How many eggs would the farmer expect to be cracked when harvesting 350 eggs?

A. 3

B. 7

C. 18

D. 70

 

6. Alex and Payton each have a favorite pancake recipe.

• Alex’s recipe uses 7 1/2 cups of flour for 5 batches.

• Payton’s recipe uses 3/4 cup of flour more per batch than Alex’s recipe uses per batch.

Which expression can be used to determine the number of cups of flour used to make x batches of Payton’s pancake recipe?

A. 2 1/4 x

B. 8 1/4 x

C. 1 1/2 x + 3/4

D. 7 1/2 x + 3/4  

 

7. This soccer season, Gavin scored 9 fewer than 3 times the number of goals that Rico scored. Rico scored 12 goals. The value of which expression is equivalent to the number of goals Gavin scored this soccer season?

A. 3(4 – 3)

B. 3(12 – 9)

C. 9(4 – 1)

D. 9(36 – 1)

 

8. Which expression uses exactly three terms and is equivalent to 6(2 + x + x + y)?

A. 8 + 8x + 7y

B. 12 + 12x + 6y

C. 8 + 6x + 6x + 6y

D. 12 + 6x + 6x + 6y

 

9. Michael has $68. Craig has $24 less than Michael has. Michael spends $20 on a new hat. The solution of which equation represents the amount of money (x), in dollars, Craig has after Michael buys the hat?

 

A. x + 4 = 48

B. x + 4 = 68

C. x + 20 = 44

D. x + 24 = 48

 

10. The heights, rounded to the nearest foot, of the trees in a park are listed below.

23 13 8 52 26 42 48 52

What is the median of the tree heights?

A. 33 feet

B. 34 feet

C. 39 feet

D. 44 feet

 

Answers:

 

1. B;  2. A;  3. B;  4. B;  5. B;  6. A;  7. C;  8. B;  9. A;  10. B

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