Maths facts

 A baseball diamond is a perfect rhombus. A rhombus is a parallelogram with opposite equal acute angles, opposite equal obtuse angles and four equal sides.. If you’re planning a road trip, Texas is the place to be! Texas is the state with the most roads in the United States, with 679,917 total miles of lanes to get lost on. 

Exercise 41

 

15. Very often, the number 1 is confused as a prime number but by dividing 1 by 1, you get 1. Nothing has been divided.

16. The power of exponential growth is shocking. You can actually reach the moon by folding a paper of 0.01mm 45 times.

Exercise 40

 

13. 9 is also known as the magic number. This is because if you multiply a number by 9 and add all the digits of the new number together, the sum will always add up to 9. For example: 8 x 9 = 72 or, 7 + 2 = 9

Exercise 38

 Leonardo Fibonacci from Pisa, in the 13th century, discovered the Fibonacci sequence. Starting at 0 and 1, this sequence is created as the sum of the two preceding numbers, For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

Exercise 39

 

9. We follow the decimal system number which has 10 digits from 0 to 9. It is also known as the Hindu Arabic numeral system. It was discovered more than 1000 years ago.

10. Pi is also known as the ratio of circumference to the diameter of a circle. It is a special number that is irrational. There is a designated day, called Pi day, that we celebrate on March 14.

Exercise 37

 If you take any number multiplied by three and sum the digits in the answer, then the answer you receive after adding the digits will always be divisible by three. For example: 3 x 4 = 12 or, 1 + 2 = 3 or, 3 / 3 = 1

Exercise 36

 Mathematically, an even number is a number that can be divided into two smaller numbers which are actually whole numbersh

hereis only one number in the entire Hindu Arabic number system which can be spelled with the same number of letters as itself. That number is four.

Exercise 35

 man numerals only have seven different letters which form the entire number system:  I, V, X, L, C, D, and M.

Exercise 34

 Romans didn't consider 0 to be a number at all. Therefore, there are in total zero zeros in Roman numerals.

Theidea of zero was invented by an Indian astronomer and mathematician Brahmagupta in around 600 A.D. He contributed a lot to mathematics and astronomy and is known for explaining how to find the cube and cube-root of an integer

Exercise 33

2. 2. We all have heard about the Pythagoras theorem. But there is also something which is known as Pythagoras constant. The square root of 2 i.e. 1.41 was the first rational number to be discovered which is known as the Pythagoras constant.

   

Exercise 32

 

1. There are types of interesting numbers in mathematics. One such number is hundred. The number 100 does not actually mean 100. It is derived from the Old Norse word "hundredth," which actually means 120.

Exercise 31

  If you shuffle a deck of cards properly, it’s more than likely that the exact order of the cards you get has never been seen before in the whole history of the universe.

Exercise 30

 . -40 °C is equal to -40 °F.

.In France, a pie chart is sometimes referred to as a “camembert”.

. The symbol for division (i.e.÷) is called an obelus.

. 2 and 5 are the only prime numbers that end in 2 or 5.

Exercise 28

 Zero is not represented in Roman numerals.

14. The word “mathematics” only appears in one Shakespearean play, “The Taming of the Shrew”.

Exercise 29

 

Assessment started: undefined.

Item 1

You arrive at a fork in the road and need to choose the correct path that leads to your destination.

There are two people standing at the fork, and you know that one must be a knight and the other must be a knave.

A knight will always tell the truth whereas a knave will always lie.

What single question could you ask one of the people to determine the correct path, A$A$ or B$B$?

• Which is the correct path?
• What path would the other person tell me to choose?
Solution

If you ask the questions “Which is the correct path?”, “Shall I choose path A$A$” or “Shall I choose path B$B$” , then the knight and knave would give opposite answers. For example: If A$A$ is the correct path, the knight will tell you to choose A$A$ and the knave will tell you to choose B$B$. You won’t be able to make any deductions from the question asked.
But, if you ask the remaining question, the knave will say that the other person will tell you to select path B$B$ and the knight will tell the truth and say that the other person will tell you to choose path B$B$. Hence, you’ll get to know that the correct path is A$A$.

Exercise 27

 

Assessment started: undefined.

Item 1

If the circle with centre O$O$ has area 9π$9𝜋$, What is the area of the equilateral triangle ABC$ABC$?

• 153√$15\sqrt{3}$
• 123√$12\sqrt{3}$
• 63√$6\sqrt{3}$
• 103√
• Solution

  Given the area of the circle is 9π$9𝜋$. 

  Then, the radius of the circle will be 3$3$. 

  Therefore, AD=6$AD=6$  (diameter of the circle.)

  AD$AD$ is the height of an equilateral triangle.

  12×a ×6 = 3√4×a2$\frac{1}{2}\times a\times 6=\frac{\sqrt{3}}{4}\times a^2$

  a =123√$a=\frac{12}{\sqrt{3}}$

  The area of the equilateral triangle =12 ×123√×6 =363√=(12×3)3√=(12×(3√)2)3√=123√