FAST - Florida State Assessment Readiness Mathematical: Algebraic Reasoning Questions and Answers — Questions and Answers
Question 1: Maya is buying tickets for a carnival. The admission fee is a flat $10, and each ride ticket costs $1.50. Which expression represents the total cost for Maya to enter the carnival and buy *r* ride tickets?
- 10 + 1.50r (Correct answer)
- 10r + 1.50
- 11.50r
- 10 - 1.50r
Correct answer: 10 + 1.50r
The total cost is calculated by starting with the fixed admission fee ($10) and adding the variable cost of the ride tickets. The cost of the tickets is $1.50 multiplied by the number of rides (r), which is 1.50r. Therefore, the correct expression is 10 + 1.50r.
Question 2: A function machine follows a specific rule, as shown in the input-output table below. | Input (x) | Output (y) | |---|---| | 2 | 7 | | 4 | 11 | | 6 | 15 | | 8 | 19 | Which equation describes the rule for the function machine?
- y = x + 5
- y = 3x + 1
- y = 2x + 3 (Correct answer)
- y = 4x - 1
Correct answer: y = 2x + 3
To find the correct rule, substitute the input (x) values from the table into each equation to see if the result matches the output (y) value. For the correct equation, y = 2x + 3: when x=2, y = 2(2)+3 = 7; when x=4, y = 2(4)+3 = 11; when x=6, y = 2(6)+3 = 15. This rule works for all pairs in the table.
Question 3: A roller coaster has a sign that reads, 'Riders must be at least 48 inches tall.' Which of the following inequalities correctly represents the height, *h*, in inches, that a person must be to ride?
- h < 48
- h > 48
- h ≤ 48
- h ≥ 48 (Correct answer)
Correct answer: h ≥ 48
The phrase 'at least 48 inches' means that a height of exactly 48 inches is allowed, as well as any height greater than 48 inches. The mathematical symbol for 'greater than or equal to' is ≥. Therefore, the inequality h ≥ 48 correctly represents the height requirement.
Question 4: Which equation correctly demonstrates the distributive property of multiplication over addition?
- 5 + (8 + 2) = (5 + 8) + 2
- 7(x + 3) = 7x + 21 (Correct answer)
- 4 × 9 = 9 × 4
- 12y × 1 = 12y
Correct answer: 7(x + 3) = 7x + 21
The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the products. In option B, the 7 is 'distributed' to both the x and the 3 through multiplication, resulting in 7x + 21. Option A shows the associative property, C shows the commutative property, and D shows the identity property.
Question 5: Which algebraic expression correctly translates the verbal phrase '8 less than the product of a number, n, and 3'?
- 8 - 3n
- 3n - 8 (Correct answer)
- 8 < 3n
- 3(n - 8)
Correct answer: 3n - 8
First, identify 'the product of a number, n, and 3,' which translates to 3n. The key phrase 'less than' indicates subtraction, but it reverses the order of the terms. So, '8 less than' means you subtract 8 from the previously identified product. This results in the expression 3n - 8.
Question 6: Leo sold boxes of cookies for a fundraiser, earning $2.50 for each box he sold. By the end of the fundraiser, he had raised a total of $112.50. If *b* represents the number of boxes Leo sold, which equation correctly models this situation?
- b / 2.50 = 112.50
- 2.50 + b = 112.50
- 112.50 - b = 2.50
- 2.50b = 112.50 (Correct answer)
Correct answer: 2.50b = 112.50
The total amount raised ($112.50) is the result of multiplying the earnings per box ($2.50) by the number of boxes sold (b). Therefore, the situation is correctly modeled by the equation 2.50b = 112.50.
FAST - Florida State Assessment Readiness Mathematical: Algebraic Reasoning Questions and Answers
Maya is buying tickets for a carnival.
The admission fee is a flat $10, and each ride ticket costs $1.50.
Which expression represents the total cost for Maya to enter the carnival and buy *r* ride tickets?