Free Bachelor of Mathematics: Concepts and Theories Questions and Answers

Question 1

Which steps are included in Polya's Four Step Process for Problem Solving?

Accepted Answer

Understand the problem, Select a strategy, Carry out the strategy, Looking back

Answer

George Polya's Four-Step Process for Problem Solving is a widely recognized heuristic. The four distinct steps are: 1) Understand the problem, 2) Devise a plan (or Select a strategy), 3) Carry out the plan (or Carry out the strategy), and 4) Look back (or Review/Reflect). This systematic approach helps in tackling various mathematical and real-world problems effectively.

Question 2

Which one of the options listed below is not considered a method for solving problems?

Accepted Answer

Carry out the strategy

Answer

While 'Carry out the strategy' is a crucial step in Polya's problem-solving process, it is not a problem-solving *method* itself. Methods refer to specific techniques or heuristics used to devise a strategy, such as making a table, looking for a pattern, or examining a related problem. Carrying out the strategy is the execution phase of a chosen method.

Question 3

What type of sequence involves each term being obtained from the previous term by adding or subtracting a fixed number?

Accepted Answer

Arithmetic Sequence

Answer

An arithmetic sequence is defined by a constant difference between consecutive terms. Each term is obtained from the previous term by adding or subtracting a fixed number, known as the common difference. This consistent additive or subtractive relationship is its defining characteristic.

Question 4

Which sequence involves each term being obtained from the previous term by multiplying by a fixed number?

Accepted Answer

Geometric Sequence

Answer

A geometric sequence is characterized by a constant ratio between consecutive terms. Each term is obtained from the previous term by multiplying by a fixed, non-zero number, known as the common ratio. This consistent multiplicative relationship distinguishes it from other types of sequences.

Question 5

What kind of sequence involves using the preceding term(s) to determine each successive term?

Accepted Answer

Recursive Sequence

Answer

A recursive sequence is one where each term is defined by one or more preceding terms. This means that to find a term, you need to know the value of the term(s) before it, often along with an initial term or terms to start the sequence. The Fibonacci sequence is a classic example of a recursive sequence.

BMath Bachelor of Mathematics Practice Test

BMath Bachelor of Mathematics Practice Test

Free Bachelor of Mathematics: Concepts and Theories Questions and Answers