New York State Math Test Grade-7 With Solution

Session-1

TIPS FOR TAKING THE TEST

Here are some ideas to help you do your best:

• Read each question carefully. Take your time.

• You have a ruler, a protractor, a reference sheet, and a calculator that you can use on the test if they help you answer the question.

1. A store sells packages of butter. The table below shows the cost, in dollars, for different numbers of packages of butter.

Cost of Butter

Number of Packages -        3             4                 7                    11

Cost ( dollars)                    9.75        13.00           22.75           35.75

What is the cost, per package, of the butter?

    4.  A farmer plants 4 rows of seedlings. The first 3 rows are equal in length. The length of the fourth row is 19 yards. The total length of the 4 rows is 61 yards. What is the length, in yards, of each of the first 3 rows the farmer plants?

5.  On average, ocean temperatures around the world range from -2० C to 32०C. What is the difference between the two ocean temperatures?

32०C - (-2०C)

= 34०C

Q. 10. Victoria has a movie subscription. She pays an annual membership fee of $24.00 and also a fee of $4.00 for each movie she watches. Which inequality can be used to determine the total number of movies, m, Victoria can watch if she wants to spend less than $100.00 per year?

Solution:

     4m + 24 < 100

Q.11. The regular price of a shirt is n dollars. During a sale, the shirt is discounted by 15%. Which pair of expressions includes two correct ways to represent the price, in dollars, of the shirt after the discount?

Solution:

     n - 0.15 n                                                                 15% = 0.15

  = 0.85

Q.13. Which expression is equivalent to 3.6(x - 5) + 2.5( X + 4) ?

Solution:

 3.6 X - 18 + 2.5X. + 10

= 6.1X - 8

17. There were two movies shown at a theater. A total of 150 tickets were sold for the first movie, and 40% more tickets were sold for the second movie than for the first movie. If each ticket sold for $13.50, what was the total amount of ticket sales, in dollars, for both movies?

Solution:      1st movie

                     150

150 X 40/100  = 60

2nd movie

150 + 60 = 210

Total

150 + 210 = 360

360 X $13.60 = $4860

21. The table shown below represents a proportional relationship between x and y.

x           y

9             2.25

13          3.25

17          4.25

21         5.25

Which equation represents this proportional relationship?

Solution:

y = kx

2.25  = k . 9

k = 1/4

y = 1/4 x

26. Pat uses 2 ⁵/8 cups of sugar for 3 1/₂ batches of cookies. She uses the same amount of sugar for each batch of cookies bakes. How much sugar, in cups per batch, does Pat use to bake cookies?

Solution:

2 ⁵/8  ➗ 3 1/₂ 

3/4

29. A seventh grade class sells gift cards as a fundraiser for the school library. Each gift card sells for $15.00. The library gets 35% of the money earned for each gift card sold. How much money does the library get if the class sells 500 gift cards?

Solution: 

500  X   15 = $7500

 

7500  X 35/100 = $2625

Session-2

33. Which situation results in a final value of zero?

Solution:

The total number of cookies Tiffany has if she bought 4 batches of cookies and sold the 4 batches of cookies.

34. Cheryl earns $23.75 babysitting for 2 1/2 hours. At that rate, how much does Cheryl earn when babysitting for 5 3/4 hours?

Solution:

$23.75/2.5h.    =   X/ 5.75h

2.4 X. = 136.56

X = $54.63

39. Marty types at an average rate of 25 words per minute. Write an equation that could be used to determine the average number of words, w, Marty types in t minutes.

Solution: 

w = 25 t

40. What is the value of the expression -2(-3)(4) ?

Solution:         6(4)

                   = 24

41. Kenneth bought a shirt that was originally priced at $55.00. After a discount, he paid $38.50. What was the percent discount of the original price of the shirt?

Solution:

$55.00 - $38.50 = $16.50

16.50/55.00 = 0.3

0.3/100 = 30%

44. A map has a scale of 1 cm = 50 miles. The actual distance between New York City and Washington, D.C. is 225 miles. What is the distance, in cm, between the two cities on  the map?

Solution:

225/50

= 4.5 cm

45. During lunch, a sandwich shop owner sold 2 types of sandwiches: turkey and roast beef. Each sandwich cost $4.99 and the total sales from all of the sandwiches sold was $219.56. There were 25 turkey sandwiches sold. How many roast beef sandwiches were sold?

Solution:

4.99 X = $219.56

X = 44

Roast Beef sandwiches were sold = ( 44- 25) = 19

46. Write the expression -8(4 - X) +20 as the sum of two unlike terms. Be sure to show the use of the properties of operations in your answer.

Solution:

- 8(4 - X) + 20

= - 32 + 8X + 20

= 8x - 12

47. Jonah received a gift card to a movie theater. The gift card allows him to choose one type of movie, one snack, and one drink. His options are shown in the list below.

Movies: drama, action, comedy

Snacks: popcorn, chips, candy

Drinks: water, juice

He chooses one movie, one snack, and one drink at random. What is the probability that Jonah chooses a comedy, chips, and juice? Write your answer as a fraction.

Solution:

3 X 3 X 2 = 18

1/18

Q.48. A furniture store is advertising a 20% discount on the price of sofas. Scott chooses a sofa with a discounted price of $460.00. He must also pay an 8% sales tax. How  much money will Scott save on the discounted sofa, including tax, compared to the originally priced sofa, including tax?

Solution:

20% discount

80% on

80/100 = 0.80

0.8 X = $460.00

8% tax

= 0.08

=1.08

X = $575 x 1.08

   = $ 621.00

$460 x 1.08 = $496.80

$621.00 - $496.80= $124.20 

New York State Mathematics Test -2023

Grade-7

Session-1

Q.2. Maria and two friends are at a movie theater. They have $52.00 and spend $34.50 of it on movie tickets. They also buy 3 drinks that each cost the same amount. After buying the movie tickets and drinks, they have $4.00 remaining. How much did each drink cost?

$52.00 - $34.00 = $17.50

                 $17.50 - $  4.00

= $13.50

$13.50 / 3

= $4.50

Q.4. Megan reads the same number of pages in a book each day. The table below represents the total number of pages read at the end of the given number of days.

Number of Pages Read

Number of Days............Total Number of Pages

2 ............32

4. ..............64

5 ................80

7................112

How many pages does Megan read in a day?

Ans: 16

32/2= 16

Q.5. Which expression is equivalent to the one shown below?

- 1.5 +  2/5 + (-7) + 2.6

Solution:

Simplify

Ans: ( - 8.5 + 2.6) + 2/3

Q.8. Joel has three buckets which contain different amounts of liquid. The amount of liquid in each bucket is listed below.

7 1/2 liters

3 3/4  liters

6 3/4  liters

Joel mixes all the liquid together. Then he pours all the liquid equally into 5 containers. How many liters of liquid does Joel pour into each container?

Ans: 4

Solution :

Add all the amount of liquid 

Then Divide by 5 because he pours all the liquid equally into 5 containers.

Joel pours 4 liters of liquid into each container.

Q.9. A student's science scores are shown below.

76,82,65,82,93,63,45,82,90,74

What is the mode and how does it compare to the median?

Ans: The mode is 82 and it is higher than the median

Q.13. The table below shows the amount of money, in dollars, that Kathy earns babysitting for a given number of hours worked.

BABYSITTING EARNINGS

Number of Hours, h...........Earnings, of (dollars)

4 ............$50.00

5................$62.50

6...............$75.00

9................$112.50

Based on  the table, which statement is true about the relationship between the number of hours, h she works and the amount of money, d, she earns?

Ans: It is proportional because the ratios between the values of d and h are the same for each pair.

Q.21. A store sells blue hats and green hats. Each hat is priced at $8.00. The expression 8b + 8g can be used to determine the total price when a customer buys any number of blue hats, b, and any number of green hats, g. Which equivalent expression could also be used to determine the total price, in dollars, of the hats?

Ans: 8(b + g)

Q. 23. A store manager collects information about the number of people who visit his store each week. The information, collected over a 3-week period, is listed below.

# The number of people that visited the store in week 1 was 3,200.

# The number of people that visited the store in week 2 was 10% more than week 1.

# The number of people that visited the store in week 3 was 15% more than week 2.

How many people visited   the store in week 3?

Ans: 4,048

1: 3200

2:3200 

10%  = 10/100

= 0.10

3 : 3520

15%

100 + 15

1.15

= 4048

Q.25. Joseph has a part-time job. The graph below represents 

the amount Joseph earns, in dollars, for the number of hours he works.

Based on the graph, which equation can be used to determine the earnings, 

in dollars, for every hour he works?

Solution: 

                    Y = KX

                 30/2       = k.2/2

             y = 15X

X = 6

y = 15( 6 )

     = 90

Ans: y = 15 x

Q.32. The bill for a dinner at a restaurant is $58.20, before sales tax and tip. Sales tax is 5% of the dinner bill. Tip is 20% of the dinner bill. How much is the total bill including tax and tip?

5% tax = 0.05

20% tip = 0.20

58.20 + 58.20(0.05) + 58.20(0.20)

= $72.75

34. At a deli, customers buying a sandwich can choose one type of bread, one type of meat, and one type of cheese. The options for each sandwich are listed below.

bread: white or wheat

meat: turkey or beef

cheese: American, Swiss, or cheddar

Assuming each choice is equally likely, what is the probability a customer will choose a sandwich with white bread, turkey, and Swiss cheese?

Ans:    2 x 2 x 3

           1/12

35. Frank is riding in a taxi to get to work. The cost of riding in a taxi includes a one-time fee of $2.75 and $2.60 per mile. If Frank rides in a taxi for 4 miles and pays a $2.00 tip, how much money will he have left over if he pays with a $20.00 bill?

Solution:  $2.75 + ( 2.60 x 4) + 2

               = $2.75 + 10.40 + 2

               = 15.15

$20.00 - $15.15 = 4.85

Ans:   $4.85

Q.36. The sum of two numbers is zero. If one of the numbers is 5, what is  the other number?

Solution:

       5 + (-5)

    = 0

Ans: -5

Q. 37. Ms. Jacobs has $15.00 to spend on coffee and donuts. She buys 1 coffee for $2.59. The cost of each donut is $1.09. Which inequality could be used to determine the greatest number of donuts, d that Ms. Jacobs can buy?

Solution: 1.09d + 2.59 ≤ 15

Q.38. Maggie owns a dog grooming business. The prices for two services are listed below

# $31.50 for a dog wash

# $17.00 for a nail trim

A customer receives an 18% discount when paying for both a dog wash and a nail trim. What is the total price the customer will pay for a dog wash and a nail trim with the discount?

18% off

100- 18

= 82% on

$31.50 + $17.00 = $48.50 

$48.50 x 0.82

= $39.77

Q.43. This question is worth 2 credits.

Diane is planning a party at a trampoline park. It will cost $55.00 to rent the park, plus an additional $8.00 per guest. She wants to spend less than $100.00 on the party. Write and solve an inequality to determine the maximum number of guests, g, that can be invited when spending less than a total of $100.00.

Show your work.

Total bill

8g + 55 < 100

     - 55    - 55

= 5 guest Ans.

Q.44. This question is worth 2 credits.

A student tosses a fair coin with heads (H) on one side and tails (T) on the other, and rolls a fair number cube with faces numbered 1 through 6. How many different outcomes are possible? Be sure to provide the sample space for all possible combinations to support your answer.

Explain your answer.

Ans: By the Multiplication Principle, there are 2 x 6 = 12 possible outcomes for the student tossing the fair coin and rolling the fair number cube.

2 x 6 = 12

Q.45. This question is worth 2 credits.

A scale drawing of the floor of a rectangular-shaped classroom is shown in the diagram below. The drawing has a scale of 1 inch to 14 feet.