6th Class Mathematics Mental Ability

Mental Ability

Category : 6th Class

MENTAL ABILITY

FUNDAMENTALS

Mental Ability: The power to learn or retain knowledge, in law, the ability to understand the fact and significance of your behavior.

•                      Mental ability develop logical thinking among students.
•                      Mental ability is based on some concepts.

Series completion

•                      Number series
•                     Alphabet series

•                Number Series: The three or more numbers having a sequence of pattern is given. The numbers follow a certain rule which relates the consecutive terms. Students should be able to recognize the rule or pattern. This will be help them to find the next term or number.

Look at the example given below

1.            Series of odd number

1, 3, 5, 7, 9, ___________

Ans.:    Next number is 11.

2.            Series of even number.

12, 14, 16, 18, ____________

Ans.:    Next number is 20.

3.            Series of prime number.

2, 3, 5, 7, 11, 13, 17, __________   .

Ans.:    Next number is 19.

4.            Series of squares of consecutive odd numbers

1, 9, 25, 49, 81, __________

${{1}^{2}},\,\,{{3}^{2}},\,\,{{5}^{2}},\,\,{{7}^{2}},\,\,{{9}^{2}}$

Ans.:    Next number is ${{11}^{2}}=121.$

5.            Series of square of consecutive even numbers

4, 16, 36, 64, 100, ______

${{2}^{2}},\,\,{{4}^{2}},\,\,{{6}^{2}},\,\,{{8}^{2}},\,\,{{10}^{2}}$

Ans.:    Next number is 122 = 144.

6.            Series of cube of consecutive even numbers

8, 64, 216, 512, ___________

${{2}^{3}},\,\,{{4}^{3}},\,\,{{6}^{3}},\,\,{{8}^{3}},$

Ans.:    Next number is${{10}^{3}}=1000$

7.            Series of cube of consecutive odd number

1, 27, 125, 343, _________

Ans.:    Next number is${{9}^{3}}=729.$

8.            Series of each term is multiplied by a fixed number or certain pattern to get the next number.

Ans.:    Next number is$80\times 2=160$

9.            Series of each term is divided by a fixed number or certain pattern to get the next number.

Ans.:    Next number is$30\div 2=15.$

Note:    Students first remember the square up to 20 and cube up to 20.

Squares:

 ${{1}^{2}}=1,$ ${{2}^{2}}=4,$ ${{3}^{2}}=9,$c ${{4}^{2}}=16,$ ${{5}^{2}}=25$ ${{6}^{2}}=36,$ ${{7}^{2}}=49,$ ${{8}^{2}}=64,$ ${{9}^{2}}=81,$ ${{10}^{2}}=100$ ${{11}^{2}}=121,$ ${{12}^{2}}=144,$ ${{13}^{2}}=169,$ ${{14}^{2}}=196,$ ${{15}^{2}}=225$ ${{16}^{2}}=256,$ ${{17}^{2}}=289,$ ${{18}^{2}}=324,$ ${{19}^{2}}=361,$ ${{20}^{2}}=400$

Cubes:

 ${{1}^{3}}=1,$ ${{2}^{3}}=8,$ ${{3}^{3}}=27,$ ${{4}^{3}}=64,$ ${{5}^{3}}=125,$ ${{6}^{3}}=216,$ ${{7}^{3}}=343,$ ${{8}^{3}}=512,$ ${{9}^{3}}=729,$ ${{10}^{3}}=1000$ ${{11}^{3}}=1331$ ${{12}^{3}}=1728,$ ${{13}^{3}}=2197$ ${{14}^{3}}=2744$ ${{15}^{3}}=3375$ ${{16}^{3}}=4096$ ${{17}^{3}}=4913$ ${{18}^{3}}=5832$ ${{19}^{3}}=6859,$ ${{20}^{3}}=8000$

Series:

An arrangement of letters which follows a particular rule / pattern is called alphabet series.

Note: Students first remember this alphabetical order.

•                     Given below alphabets are opposite alphabets to each other.
 $1\leftarrow A-Z\to 26$ $2\leftarrow B-Y\to 25$ $3\leftarrow C-X\to 24$ $4\leftarrow D-W\to 23$ $5\leftarrow E-V\to 22$ $6\leftarrow F-U\to 21$ $7\leftarrow G-T\to 20$ $8\leftarrow H-S\to 19$ $9\leftarrow I-R\to 18$ $10\leftarrow J-Q\to 17$ $11\leftarrow K-P\to 16$ $12\leftarrow L-O\to 15$ $13\leftarrow M-N\to 14$

Look at the examples given below

•                    Complete the series

1.            A, B, C, D,_________

Ans.:    Next series is E.

2.            AB, CD, EF,__________

Ans.:    Next series is GH.

3.            ABC, EFG, IJK,__________

Ans.:    Next series is MNO.

4.            AZ, BY, CX,__________

Ans.:    Next series is DW

5.            7 A 8, 10 B 11, 13 C 14,_________

Ans.:    Next series is 15 D 16.

Analogy;

•                  Analogy means similar relationship.
•                  Students are required to establish the relationship between the given set of numbers, letters and words.
•                  Let us see some examples.

(i)         Safe: Secure:: Protect: __________

(a) Conserve                   (b) Sure                         (c) Guard                       (d) Look

Ans.:    (c) Guard: Because, 'safe is synonym of 'secure', similarly, 'protect is synonym of 'Guard'.

(ii)         MA: PD : : WA : _____________

(a) YQ                           (b) YD                           (c) NA                           (d) ZD

Solution: The pattern is as follows:

Ans.:    ZD

(iii)        __________

(a) 1331            (b) 1024                        (c) 1565                         (d) 243

Solution:          The pattern is as follows:

Similarly,

•                   Ranking test:  In this test, the ranks of a person both from top and from the bottom are given and the student is asked to find the total number of persons.

Sometimes the questions based on ranking test are puzzle type.

•                   Let us see the examples given below.

1.            In a row of students, Santosh is 9th from the either end of the row. Find the number of students in a row.

(a) 10                            (b) 18                            (c) 17                                        (d) 19

Solution: Clearly, the number of students in row are x = Top rank + Bottom rank { total no. of students}

Note: Students let us remember rule

(i)

(ii)

(iii)

2.            Rohit ranks eighteenth in a class of 47 students. What is his rank from the last?

(a) 30                            (b) 40                            (c) 50                            (d) 36

Solution: Rohit's rank from the start or front =18th

So, Rohit's rank from the last

•                   Direction sense test:
•             There are four main directions:

(i)  North (N)                  (ii) South (S)

(iii) East (E)                    (iv) West (W)

•             Four cardinal directions:

(i) North East (NE)

(ii) North West (NW)

(iii) South East (SE)

(iv) South West (SW)

•           Students checking the sense of direction use this diagram.

Interesting Note: Students for solving the problem of direction, first learn about right angled triangles.

ABC is a right angled triangle in which

•                   Use Pythagoras theorem

(a) or

(b) or

(c) or

Let us see the example

Example: 1 Rohit starts walking from his home southward a distance of 20 metres. He then took a half turn torwards right. In which direction is he walking now?

(a) East                               (b) West                         (c) South west                (d) North East

Solution: Draw the direction diagram.

Rohit starts from x towards south and reach y after covering a distance of 20 m. He then takes half right turn and now his position is toward.

Ans.    South - west

Example: 2 One day, Rahul left home and cycled 10 kms southwards, turned right and cycled 5 kms and turned right and cycled 10 kms and turned left and cycled 10 kms. How many kilometers will he have to cycle to reach his home staright?

(a) 10 kms                     (b) 15 kms                     (c) 20 kms                                  (d) 25 kms

Solution. Draw direction diagram.

A is the starting point goes to B. Then moves to C, then to D and finally he is at E. So, he has to go back a distance EA which is equal to  i.e. 15 km.

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