B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 5 — Questions and Answers
Question 1: What does the Fundamental Theorem of Calculus state?
- Every polynomial has a real root
- Differentiation and integration are inverse operations (Correct answer)
- Every continuous function has a maximum
- The derivative of a constant is zero
Correct answer: Differentiation and integration are inverse operations
The Fundamental Theorem of Calculus establishes that differentiation and integration are inverse processes.
Question 2: In which number base does 101 + 11 = 1000?
- Base 4
- Base 8
- Base 2 (Correct answer)
- Base 10
Correct answer: Base 2
In binary (base 2): 101₂ = 5 and 11₂ = 3; 5+3=8 = 1000₂.
Question 3: Which of the following correctly describes a geometric sequence?
- Each term increases by a constant difference
- Each term is the square of its position
- Each term is found by multiplying the previous term by a constant ratio (Correct answer)
- The sequence alternates between positive and negative values
Correct answer: Each term is found by multiplying the previous term by a constant ratio
A geometric sequence is defined by a constant ratio between consecutive terms.
Question 4: What is the matrix product of [[1,2],[3,4]] × [[0,1],[1,0]]?
- [[2,1],[4,3]] (Correct answer)
- [[0,2],[3,4]]
- [[1,0],[0,1]]
- [[2,3],[4,1]]
Correct answer: [[2,1],[4,3]]
Row 1: [1·0+2·1, 1·1+2·0]=[2,1]; Row 2: [3·0+4·1, 3·1+4·0]=[4,3].
Question 5: If the standard deviation of a data set is 0, what does this tell you?
- The mean is zero
- All values in the data set are identical (Correct answer)
- The data set has only one value
- The data set contains negative numbers
Correct answer: All values in the data set are identical
A standard deviation of 0 means there is no spread, so every data point equals the mean.
Question 6: What is the contrapositive of the statement 'If it rains, then the ground is wet'?
- If the ground is wet, then it rains
- If it does not rain, then the ground is not wet
- If the ground is not wet, then it does not rain (Correct answer)
- It rains if and only if the ground is wet
Correct answer: If the ground is not wet, then it does not rain
The contrapositive of 'If P then Q' is 'If not Q then not P', which is logically equivalent.
Question 7: Which conic section is represented by x²/16 + y²/9 = 1?
- Circle
- Parabola
- Ellipse (Correct answer)
- Hyperbola
Correct answer: Ellipse
The equation x²/a² + y²/b² = 1 with a ≠ b represents an ellipse.
B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 5
What does the Fundamental Theorem of Calculus state?