B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 5

Question 1

What does the Fundamental Theorem of Calculus state?

Accepted Answer

Differentiation and integration are inverse operations

Answer

The Fundamental Theorem of Calculus establishes that differentiation and integration are inverse processes.

Question 2

In which number base does 101 + 11 = 1000?

Accepted Answer

Base 2

Answer

In binary (base 2): 101₂ = 5 and 11₂ = 3; 5+3=8 = 1000₂.

Question 3

Which of the following correctly describes a geometric sequence?

Accepted Answer

Each term is found by multiplying the previous term by a constant ratio

Answer

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]]?

Accepted Answer

[[2,1],[4,3]]

Answer

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?

Accepted Answer

All values in the data set are identical

Answer

A standard deviation of 0 means there is no spread, so every data point equals the mean.

B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Practice Test