AS Associate Of Science In Mathematics 2 — Questions and Answers
Question 1: What is the integral of f(x) = 4x³?
- 12x²
- x⁴ + C (Correct answer)
- x⁴
- 4x⁴ + C
Correct answer: x⁴ + C
Using the power rule for integration: ∫4x³ dx = 4 · (x⁴/4) + C = x⁴ + C.
Question 2: Which property states that a(b + c) = ab + ac?
- Commutative property
- Associative property
- Distributive property (Correct answer)
- Identity property
Correct answer: Distributive property
The distributive property states that multiplying a number by a sum is the same as multiplying it by each addend and then adding the products.
Question 3: What is the standard form of the equation of a circle with center (h, k) and radius r?
- (x − h)² + (y − k)² = r
- (x + h)² + (y + k)² = r²
- (x − h)² + (y − k)² = r² (Correct answer)
- (x − h) + (y − k) = r²
Correct answer: (x − h)² + (y − k)² = r²
The standard form equation of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.
Question 4: If a data set has values 4, 7, 7, 9, 13, what is the median?
- 7 (Correct answer)
- 8
- 9
- 6
Correct answer: 7
The median is the middle value of an ordered data set; with 5 values, the middle (3rd) value is 7.
Question 5: What does a negative discriminant (b² − 4ac < 0) indicate about a quadratic equation?
- Two distinct real roots
- One repeated real root
- Two complex (non-real) roots (Correct answer)
- No roots
Correct answer: Two complex (non-real) roots
A negative discriminant means the quadratic has no real roots; instead, it has two complex conjugate roots.
Question 6: Which trigonometric identity states that sin²θ + cos²θ = 1?
- Double angle identity
- Sum-to-product identity
- Pythagorean identity (Correct answer)
- Reciprocal identity
Correct answer: Pythagorean identity
The equation sin²θ + cos²θ = 1 is known as the fundamental Pythagorean identity and is derived from the Pythagorean theorem applied to the unit circle.
AS Associate Of Science In Mathematics 2
What is the integral of f(x) = 4x³?