NJSLA Mathematical Reasoning and Modeling 3 โ Questions and Answers
Question 1: Which situation can best be modeled by a linear function?
- A bacteria population that doubles every hour
- A savings account earning compound interest
- The distance traveled by a car moving at a constant speed (Correct answer)
- The height of a ball thrown upward
Correct answer: The distance traveled by a car moving at a constant speed
Constant speed means equal distance is covered each hour, producing a linear relationship between time and distance.
Question 2: The table shows: x = 1,2,3,4 and y = 5,8,11,14. What is the equation of the linear function?
- y = 2x + 3
- y = 3x + 2 (Correct answer)
- y = 3x โ 2
- y = 4x + 1
Correct answer: y = 3x + 2
The rate of change is (8โ5)/(2โ1) = 3, and using the point (1,5): 5 = 3(1) + b gives b = 2, so y = 3x + 2.
Question 3: A scale model of a building uses a ratio of 1:200. If the model is 15 cm tall, how tall is the actual building in meters?
- 30 m (Correct answer)
- 3,000 m
- 30 cm
- 300 m
Correct answer: 30 m
15 cm ร 200 = 3,000 cm = 30 meters.
Question 4: A quadratic equation has roots at x = โ3 and x = 5. Which equation represents this?
- (x + 3)(x โ 5) = 0 (Correct answer)
- (x โ 3)(x + 5) = 0
- (x + 3)(x + 5) = 0
- (x โ 3)(x โ 5) = 0
Correct answer: (x + 3)(x โ 5) = 0
Roots at x = โ3 and x = 5 come from factors (x + 3) = 0 and (x โ 5) = 0.
Question 5: Maria earns $15 per hour and works h hours. Her rent is $900 per month. Which inequality models how many hours she must work to afford rent?
- 15h > 900
- 15h โฅ 900 (Correct answer)
- 900h โฅ 15
- h + 15 โฅ 900
Correct answer: 15h โฅ 900
She needs her earnings (15h) to be at least $900, so 15h โฅ 900.
Question 6: A graph of y = f(x) passes through (0, 3) and has a slope of โ2. What is f(5)?
- โ7 (Correct answer)
- 7
- 13
- โ13
Correct answer: โ7
Using y = โ2x + 3: f(5) = โ2(5) + 3 = โ10 + 3 = โ7.
Question 7: The volume of a sphere is given by V = (4/3)ฯrยณ. If the radius is doubled, by what factor does the volume increase?
- 2
- 4
- 6
- 8 (Correct answer)
Correct answer: 8
Replacing r with 2r gives V = (4/3)ฯ(2r)ยณ = (4/3)ฯยท8rยณ, which is 8 times the original volume.
NJSLA Mathematical Reasoning and Modeling 3
Which situation can best be modeled by a linear function?