i-Ready Diagnostic Algebra and Algebraic Thinking Questions and Answers 1 — Questions and Answers
Question 1: A baker starts the day with 48 muffins. After selling some muffins, there are 15 left. If 'm' represents the number of muffins sold, which equation correctly represents this situation?
- m - 15 = 48
- 48 + m = 15
- 48 - m = 15 (Correct answer)
- 15m = 48
Correct answer: 48 - m = 15
The initial amount (48) minus the amount sold (m) equals the remaining amount (15). Therefore, the correct equation is 48 - m = 15. This shows the starting total being reduced by the number sold to find the final amount.
Question 2: Which of the following equations demonstrates the associative property of addition?
- 7 + 5 = 5 + 7
- (3 + 8) + 4 = 3 + (8 + 4) (Correct answer)
- 6 × (2 + 3) = (6 × 2) + (6 × 3)
- 9 + 0 = 9
Correct answer: (3 + 8) + 4 = 3 + (8 + 4)
The associative property of addition states that how numbers are grouped in an addition problem does not change the sum. Choice B shows that grouping (3 + 8) first is the same as grouping (8 + 4) first, which is the definition of this property.
Question 3: A numerical pattern starts with the number 3. The rule for the pattern is 'multiply by 2, then add 1.' What is the fourth number in this pattern?
- 15
- 29
- 7
- 31 (Correct answer)
Correct answer: 31
To find the fourth number, apply the rule sequentially: 1st number: 3. 2nd number: (3 × 2) + 1 = 7. 3rd number: (7 × 2) + 1 = 15. 4th number: (15 × 2) + 1 = 31.
Question 4: A student is saving money for a new video game that costs $60. They already have $22 saved. Which inequality represents 'm', the amount of money the student still needs to save to have *at least* enough for the game?
- 22 + m ≥ 60 (Correct answer)
- 22 + m < 60
- 22 + m > 60
- 22 + m ≤ 60
Correct answer: 22 + m ≥ 60
The phrase 'at least' means the total amount saved must be greater than or equal to $60. The amount they have ($22) plus the amount they still need (m) must be greater than or equal to (≥) the cost of the game ($60).
Question 5: A school is planning a field trip. The total cost is represented by the expression 5b + 150, where 'b' is the number of students attending. What does the term '150' most likely represent in this context?
- The number of buses needed.
- A fixed fee, such as the bus rental cost. (Correct answer)
- The cost per student.
- The total number of students on the trip.
Correct answer: A fixed fee, such as the bus rental cost.
In the expression 5b + 150, the term '5b' changes depending on the number of students ('b'), suggesting 5 is a per-student cost. The term '150' is a constant that is added regardless of the number of students, making it a fixed fee, like the cost to rent the bus for the day.
Question 6: The equation y = x + 4 describes a relationship between two variables, x and y. Which of the following scenarios could be represented by this equation?
- The total cost, y, of buying x books that cost $4 each.
- The number of miles left to run, y, in a 4-mile race after running x miles.
- The age of Sam, y, who is 4 years older than his brother, whose age is x. (Correct answer)
- The number of pencils, y, remaining in a box of pencils after x pencils are given away from a starting total of 4.
Correct answer: The age of Sam, y, who is 4 years older than his brother, whose age is x.
The equation y = x + 4 means that the value of y is always 4 more than the value of x. This matches the scenario where Sam's age (y) is 4 years more than his brother's age (x).
i-Ready Diagnostic Algebra and Algebraic Thinking Questions and Answers 1
A baker starts the day with 48 muffins.
After selling some muffins, there are 15 left.
If 'm' represents the number of muffins sold, which equation correctly represents this situation?