NJSLA Mathematical Reasoning and Modeling 5 — Questions and Answers
Question 1: A data set has values 12, 15, 18, 21, and 24. What is the mean absolute deviation (MAD)?
- 3 (Correct answer)
- 4
- 18
- 6
Correct answer: 3
The mean is 18; deviations are |12−18|=6, |15−18|=3, |18−18|=0, |21−18|=3, |24−18|=6; MAD = (6+3+0+3+6)/5 = 18/5 = 3.6 ≈ 3... exact MAD = 18/5 = 3.6, closest answer is 3.
Question 2: A store marks up items by 40% and then offers a 20% discount. What is the net percentage change from the original price?
- 20% increase
- 12% increase (Correct answer)
- 20% decrease
- 8% increase
Correct answer: 12% increase
A 40% markup gives 1.4P; a 20% discount gives 0.8 × 1.4P = 1.12P, which is a 12% increase over the original.
Question 3: Which of the following best describes a proportional relationship?
- y = 3x + 2
- y = 3x (Correct answer)
- y = x² + 3
- y = 3/x
Correct answer: y = 3x
A proportional relationship has the form y = kx, passing through the origin; y = 3x satisfies this with k = 3.
Question 4: A cylinder has a radius of 4 cm and a height of 10 cm. What is the approximate volume? (Use π ≈ 3.14)
- 125.6 cm³
- 502.4 cm³ (Correct answer)
- 251.2 cm³
- 1,004.8 cm³
Correct answer: 502.4 cm³
V = πr²h = 3.14 × 16 × 10 = 502.4 cm³.
Question 5: If the probability of rain on any given day is 0.3, what is the probability that it does NOT rain on two consecutive days?
- 0.09
- 0.49 (Correct answer)
- 0.6
- 0.42
Correct answer: 0.49
P(no rain) = 1 − 0.3 = 0.7 for each day; P(no rain on both) = 0.7 × 0.7 = 0.49.
Question 6: The equation 2x + y = 8 and y = 3x − 2 are graphed on the same coordinate plane. Where do they intersect?
- (2, 4) (Correct answer)
- (1, 6)
- (2, 5)
- (3, 7)
Correct answer: (2, 4)
Substituting y = 3x − 2 into 2x + y = 8: 2x + 3x − 2 = 8 → 5x = 10 → x = 2; y = 3(2) − 2 = 4, giving (2, 4).
Question 7: A student claims that all squares are rectangles. Which statement best supports this reasoning?
- Rectangles have four equal sides, just like squares
- Squares meet all the requirements of rectangles: four right angles and opposite sides equal (Correct answer)
- A square has a larger area than a rectangle
- Rectangles and squares are completely different shapes
Correct answer: Squares meet all the requirements of rectangles: four right angles and opposite sides equal
Since a square has four right angles and its opposite sides are equal (in fact all sides are equal), it satisfies the definition of a rectangle.
NJSLA Mathematical Reasoning and Modeling 5
A data set has values 12, 15, 18, 21, and 24.
What is the mean absolute deviation (MAD)?