NYSTCE NYSTCE Mathematics (004) 5 — Questions and Answers
Question 1: A teacher uses algebra tiles to model 2x² + 3x − 2. What is one factored form students might discover?
- (2x − 1)(x + 2) (Correct answer)
- (2x + 1)(x − 2)
- (x + 2)(x − 1)
- (2x − 2)(x + 1)
Correct answer: (2x − 1)(x + 2)
Expanding (2x−1)(x+2) gives 2x²+4x−x−2 = 2x²+3x−2, confirming the factorization.
Question 2: What is the sum of the interior angles of a convex polygon with 7 sides?
- 720°
- 900° (Correct answer)
- 1080°
- 540°
Correct answer: 900°
The sum of interior angles of an n-gon is (n−2)×180°; for n=7: 5×180°=900°.
Question 3: Which property justifies the step: If 3x = 12, then x = 4?
- Additive inverse property
- Multiplicative identity property
- Division property of equality (Correct answer)
- Distributive property
Correct answer: Division property of equality
Dividing both sides of an equation by the same nonzero number preserves equality (division property).
Question 4: Which representation best models a proportional relationship?
- y = 2x + 3
- y = x²
- y = 4x (Correct answer)
- y = 3/x
Correct answer: y = 4x
A proportional relationship has the form y = kx (passes through the origin with constant ratio), so y = 4x qualifies.
Question 5: A student measures a cylinder's radius as 5 cm (±0.1 cm) and height as 10 cm (±0.2 cm). Which concept applies when considering measurement error in the volume calculation?
- Significant figures
- Relative error propagation (Correct answer)
- Absolute value
- Scientific notation
Correct answer: Relative error propagation
When computing V=πr²h from measured values, errors in r and h combine through relative error propagation.
Question 6: Which of the following sets is closed under subtraction?
- Natural numbers (ℕ)
- Whole numbers (𝕎)
- Integers (ℤ) (Correct answer)
- Positive integers only
Correct answer: Integers (ℤ)
The integers are closed under subtraction because subtracting any two integers always yields another integer.
Question 7: A scatter plot shows a strong negative correlation between study time and quiz errors. What does this suggest?
- More study time causes fewer errors
- As study time increases, errors tend to decrease (Correct answer)
- Study time and errors are unrelated
- Fewer errors always lead to more study time
Correct answer: As study time increases, errors tend to decrease
A negative correlation means that as one variable increases the other tends to decrease, but correlation does not imply causation.
NYSTCE NYSTCE Mathematics (004) 5
A teacher uses algebra tiles to model 2x² + 3x − 2.
What is one factored form students might discover?