STAAR Grade 7 Math

1. Question 1 · Number and Operations

   Maya's math class at school drew the Venn diagram shown to describe how whole numbers, integers, and rational numbers are related. Based on the Venn diagram, which statement is true?
   • A.All rational numbers are integers.
   • B.Every whole number is also an integer and a rational number.
   • C.Some integers are not rational numbers.
   • D.The number −6 is a whole number but not an integer.
   Show answer and explanation

   Answer: B. Every whole number is also an integer and a rational number.

   The whole numbers circle sits completely inside the integers circle, which sits completely inside the rational numbers circle, so every whole number is also an integer and a rational number. The statement that all rational numbers are integers reverses the diagram: a number such as 1/2 is rational but lies outside the integers circle. The number −6 is an integer, but it is not a whole number because whole numbers are never negative.

2. Question 2 · Proportionality

   Pounds of Tomatoes (x)	Total Cost (y)
   3	$5.25
   5	$8.75
   8	$14.00

   At the community garden stand, the cost of tomatoes is proportional to the number of pounds bought, as shown in the table. Which equation represents the relationship between x, the number of pounds, and y, the total cost in dollars?
   • A.y = 1.75x
   • B.y = 0.57x
   • C.y = x + 2.25
   • D.y = 5.25x
   Show answer and explanation

   Answer: A. y = 1.75x

   The constant of proportionality is y ÷ x: 5.25 ÷ 3 = 1.75, 8.75 ÷ 5 = 1.75, and 14.00 ÷ 8 = 1.75. So the equation is y = 1.75x. The equation y = 5.25x uses the cost of 3 pounds as if it were the cost of 1 pound.

3. Question 3 · Expressions, Equations, and Relationships

   Hours (x)	1	2	3	4
   Total Cost, y ($)	14	20	26	32

   The table shows the total cost y, in dollars, to rent a bike from a bike shop for x hours. The cost includes a fixed fee plus an hourly charge. Which equation represents the relationship shown in the table?
   • A.y = 14x
   • B.y = 8x + 6
   • C.y = 6x + 14
   • D.y = 6x + 8
   Show answer and explanation

   Answer: D. y = 6x + 8

   The cost increases by $6 for each additional hour, so the rate of change is 6. Working back from 1 hour, 14 − 6 = 8 is the cost for 0 hours, so y = 6x + 8. The equation y = 6x + 14 uses the cost for 1 hour as the starting value instead of the cost for 0 hours.

4. Question 4 · Measurement and Data

   Grace wants to put a fence around a circular community garden bed with a diameter of 14 feet. Use 22/7 for π. How many feet of fencing does Grace need to go around the bed exactly once?
   • A.22 ft
   • B.88 ft
   • C.44 ft
   • D.154 ft
   Show answer and explanation

   Answer: C. 44 ft

   The circumference is C = πd = 22/7 × 14 = 44 feet. The value 154 is the area of the bed in square feet, 22/7 × 7², not the distance around it.

5. Question 5 · Measurement and Data

   Simulation Results

   Trials 1–5	Trials 6–10	Trials 11–15	Trials 16–20
   504	796	370	038
   382	035	915	794
   917	621	246	521
   263	889	683	960
   148	452	157	413

   A soccer league player makes 60% of her penalty kicks. To simulate 3 kicks, Jamal uses random digits: 0 through 5 mean a made kick, and 6 through 9 mean a missed kick. The table shows 20 trials. Based on the simulation, what is the probability that she makes at least 2 of 3 kicks?
   • A.1/4
   • B.9/20
   • C.7/10
   • D.3/10
   Show answer and explanation

   Answer: C. 7/10

   Count the digits 0 through 5 in each trial. Nine trials have exactly 2 made kicks and 5 trials have 3 made kicks, so 9 + 5 = 14 trials have at least 2 made kicks. The probability is 14/20 = 7/10; the value 9/20 counts only the trials with exactly 2 made kicks.

6. Question 6 · Number and Operations

   The Venn diagram shows how the sets of whole numbers, integers, and rational numbers are related. During a robotics club test run, members recorded the numbers 14, 3/5, 0, and −8. Which of these numbers belongs in the set of integers but NOT in the set of whole numbers?
   • A.14
   • B.3/5
   • C.0
   • D.−8
   Show answer and explanation

   Answer: D. −8

   Whole numbers are 0, 1, 2, 3, and so on, and the integers are the whole numbers together with their opposites. The number −8 is the opposite of 8, so it is an integer, but it is not a whole number because it is negative. The number 0 is tempting, but 0 is a whole number, so it belongs in the innermost oval. The number 3/5 is rational but not an integer.

7. Question 7 · Proportionality

   Table	Ordered Pairs (x, y)
   Table 1	(2, 5), (4, 9), (6, 13)
   Table 2	(3, 6), (5, 10), (8, 15)
   Table 3	(1, 4), (2, 8), (4, 12)
   Table 4	(3, 7.5), (6, 15), (10, 25)

   The robotics club recorded four relationships between the number of robots built, x, and the number of a certain part used, y. Each table lists three ordered pairs (x, y). Which table shows a proportional relationship between x and y?
   • A.Table 1
   • B.Table 2
   • C.Table 3
   • D.Table 4
   Show answer and explanation

   Answer: D. Table 4

   A relationship is proportional when y ÷ x is the same for every pair. In Table 4, 7.5 ÷ 3 = 15 ÷ 6 = 25 ÷ 10 = 2.5, so it is proportional. Table 2 is tempting because 6 ÷ 3 = 10 ÷ 5 = 2, but 15 ÷ 8 is not 2.

8. Question 8 · Expressions, Equations, and Relationships

   Ride Tickets, x	Total Cost, y
   2	$32.00
   4	$49.00
   6	$66.00
   8	$83.00

   The table shows the total cost, y, of Olivia's visit to a theme park when she buys x ride tickets. The total cost includes a parking fee plus the same price for each ticket. Which equation represents this relationship?
   • A.y = 16x
   • B.y = 15x + 8.50
   • C.y = 8.50x + 15
   • D.y = 8.50x + 32
   Show answer and explanation

   Answer: C. y = 8.50x + 15

   The rate of change is (49 − 32) ÷ (4 − 2) = 17 ÷ 2 = 8.50 dollars per ticket. The starting value is 32 − 2 × 8.50 = 15, so y = 8.50x + 15. The equation y = 16x fits the first row, 2 × 16 = 32, but gives 64 for 4 tickets instead of 49.

9. Question 9 · Measurement and Data

   A Ferris wheel at a theme park has a diameter of 42 meters. Camila rides the Ferris wheel, and her seat goes around 3 complete times. Use 22/7 for π. How far does Camila's seat travel during the ride?
   • A.132 meters
   • B.198 meters
   • C.396 meters
   • D.792 meters
   Show answer and explanation

   Answer: C. 396 meters

   One trip around is the circumference: C = πd = 22/7 × 42 = 132 meters. Three times around is 3 × 132 = 396 meters. The value 198 meters comes from using the radius, 21 meters, in place of the diameter in C = πd.

10. Question 10 · Measurement and Data

    Trial	Random Digits
    1	5 8 2 0
    2	3 9 1 7
    3	0 2 1 4
    4	7 6 8 5
    5	4 1 2 9
    6	9 0 3 6
    7	2 7 5 0
    8	6 8 4 3
    9	1 1 8 2
    10	5 3 7 6

    A food truck owner knows that 30% of customers order a drink. To simulate the next 4 customers, Mia generates 4 random digits from 0 to 9, where the digits 0, 1, and 2 represent a customer who orders a drink. The table shows 10 trials. Based on the simulation, what is the experimental probability that at least 2 of the next 4 customers order a drink?
    • A.1/5
    • B.3/10
    • C.1/2
    • D.7/10
    Show answer and explanation

    Answer: C. 1/2

    Count the digits 0, 1, and 2 in each trial: the counts are 2, 1, 3, 0, 2, 1, 2, 0, 3, and 0. Five trials (1, 3, 5, 7, and 9) have at least 2 such digits, so the probability is 5/10 = 1/2. The value 3/10 counts only the trials with exactly 2 drinks.

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