NJSLA Mathematical Reasoning and Modeling 2 — Questions and Answers
Question 1: A town's population grows according to the model P(t) = 12,000 · (1.03)^t, where t is years. What does the value 1.03 represent?
- The initial population
- A 3% annual growth rate (Correct answer)
- The number of years to double
- A 3% annual decay rate
Correct answer: A 3% annual growth rate
In an exponential growth model P = P₀ · b^t, the base b = 1.03 means the population increases by 3% each year.
Question 2: A rectangle has a perimeter of 54 cm and a length that is twice its width. Which equation correctly models this situation?
- 2w + 2(2w) = 54 (Correct answer)
- w · 2w = 54
- w + 2w = 54
- 2(w + 2w) = 27
Correct answer: 2w + 2(2w) = 54
Perimeter = 2(length + width) = 2(2w + w) = 6w = 54, so the equation 2w + 2(2w) = 54 correctly models the perimeter.
Question 3: On a number line, which value is closest to √50?
- 6
- 7 (Correct answer)
- 8
- 25
Correct answer: 7
Since 7² = 49 and 8² = 64, √50 ≈ 7.07, making 7 the closest whole number.
Question 4: A car rental company charges $40 per day plus $0.15 per mile. Which inequality represents renting for 3 days and staying under $200?
- 40 + 0.15m < 200
- 120 + 0.15m < 200
- 3(40 + 0.15m) ≤ 200
- 120 + 0.15m ≤ 200 (Correct answer)
Correct answer: 120 + 0.15m ≤ 200
The cost for 3 days is 3 × $40 = $120 plus $0.15 per mile, giving 120 + 0.15m ≤ 200 for staying within budget.
Question 5: A function is defined as f(x) = 3x² − 12. For which value of x does f(x) = 0?
- x = 2 only
- x = ±2 (Correct answer)
- x = ±4
- x = 4 only
Correct answer: x = ±2
Setting 3x² − 12 = 0 gives x² = 4, so x = ±2.
Question 6: Two hikers start at the same point. One walks north at 4 mph and the other walks east at 3 mph. After 2 hours, how far apart are they?
- 5 miles
- 10 miles (Correct answer)
- 14 miles
- 7 miles
Correct answer: 10 miles
After 2 hours, one hiker traveled 8 miles north and the other 6 miles east; by the Pythagorean theorem, distance = √(8² + 6²) = √100 = 10 miles.
Question 7: A store sells notebooks for $2.50 each and pens for $1.00 each. Jake buys 4 notebooks and some pens, spending exactly $14. How many pens did he buy?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
4 notebooks cost $10, leaving $4 for pens; at $1.00 each, Jake bought 4 ÷ 1 = 4 pens — wait, $14 − $10 = $4, so 4 pens; correct answer is 4.
NJSLA Mathematical Reasoning and Modeling 2
A town's population grows according to the model P(t) = 12,000 · (1.03)^t, where t is years.
What does the value 1.03 represent?