Tag: maths

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Multiple choice maths axioms, postulates and theorems conditional statements and converse euclid's postulates introduction to euclid's geometry euclid's fifth postulate

A proof is required for :

  1. Postulate

  2. Axiom

  3. Theorem

  4. Definition
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Axiom/Postulate — a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved. 


Theorem — a mathematical statement that is proved using rigorous mathematical reasoning.  In a mathematical paper, the term theorem is often reserved for the most important results.
  
So, the correct option is $C$ as a theorem needs a proof.

Multiple choice maths axioms, postulates and theorems conditional statements and converse euclid's postulates introduction to euclid's geometry euclid's fifth postulate

A theorem is:

  1. an assumption

  2. always true

  3. always false

  4. sometimes true and sometimes false
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A theorem is a Statement (logic) that has been proved on the basis of previously established statements, such as other theorems, and generally accepted statements.
A theorem is based on assumption that theorem is true.


Example: In a Euclidean space, the sum of measures of the three angles of any triangles is invariably equal to the straight angle, also as $180^o$

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Convert the following fraction into simple decimal recurring form.

$\displaystyle \frac{1}{6}$= ?

  1. $0.1\bar 9$
  2. $0.1\bar 6$
  3. $0.1\bar 4$
  4. $0.1\bar 3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
    Pure recurring decimal is a decimal fraction in which all the figures after the decimal point are repeated.
    $\displaystyle \frac { 1 }{ 6 }= 0.6666666666..$ is $ 0.\overset { \ _ \ _  }{ 6 } $.
Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Find whether it is a terminating or a non-terminating decimal.

$2.4 \div 0.072$.

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.

$2.4\div 0.072=33.3333333333....$.
The division gives recurring factor.
Hence, it is a non-terminating decimal.

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Find whether it is a terminating or a non-terminating decimal.

$3.2 \div 2.24$.

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.

$3.2\div 2.24= 1.428571429....$.
The division does not gives end result.
Hence, it is a non-terminating decimal.

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Find whether it is a terminating or a non-terminating decimal.

$0.3 \div 0.09$.

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.

$0.3\div 0.09= 3.33333333333333...$. 
The division results in recurring factor.
Hence it is a non terminating decimal.

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

The rational number which can be expressed as a terminating decimal is

  1. $\displaystyle \frac{1}{6}$
  2. $\displaystyle \frac{1}{12}$
  3. $\displaystyle \frac{1}{15}$
  4. $\displaystyle \frac{1}{20}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits. 
$\displaystyle \frac {1}{20}= 0.05$ 

In the other options, the decimal does not end with a finite number of digits.