Module II
Number system, HCF 7 LCM, Ratio and Proportion, Averages, Ages, Percentages, Partnerships, Time, Speed and Distance, Profit and Loss, Data Interpretation, Problems based on simple interest, Compound interest, Clocks, and Calendars.
A Series is a sequence numbers/alphabetical letters or both which follow a
particular rule. Each element of series is called ‘term’. We have to analyse
the pattern and find the missing term or nest term to continue the pattern.
Ascending series (1,2,3,4,5,6,7,8,9/1 < 2 < 3 < 4 < 5 <
6 < 7 < 8 < 9)
Descending series (9,8,7,6,5,4,3,2,1/9>8>7>6>5>4>3>2>1)
Oscillating series
An oscillating series has a sum that wavers between one
number and another. For example, the series 1 + 1 – 1 + 1, 1… wavers between 2
and 1. More formally, we would say that the limit oscillates between 2 and 1.
Number series, Relationship Between the Terms of Number
Series
Consecutive even number
A set of even numbers
that follow each other in order, with a difference of 2 between each number and
each number is divisible by 2.
Examples
2, 4, 6, 8, 10, 12, 14, and so on are consecutive even
numbers.
Consecutive odd number
odd numbers that follow each other in ascending order with a
difference of 2 between them and number that is not divisible by 2 is called an
odd number. In the case of an odd number, the remainder is always 1.
Consecutive prime number
For of all, prime numbers are positive integers greater than
1, and every prime number is evenly divisible, i.e., a zero remainder, by
exactly two positive integers: itself and 1. For
example, 5 and 7 are prime numbers because each is a positive integer greater
than 1, and each is evenly divisible by only two positive integers:
itself and 1, i.e., 5/5 = 1 & 5/1 = 5 and 7/7 = 1 & 7/1 = 7.
Square of numbers
When a number or integer (not a fraction) is
multiplied by itself, the resultant is called a ‘Square Number’. For example,
3 multiplied by 3 is equal to 3-squared or 3 x 3 = 32.
Square numbers are always positive. If negative sign is
multiplied by itself, it results in positive sign (+). For example, (-4)2 =
16. So, we can say here 16 is a positive square number, whose square root is an
integer again, i.e.√16 = 4.
The square root of a
number is the value of power 1/2 of that number. It is the number whose
product by itself gives the original number123. The square root of a number is
represented using the symbol '√ '. Finding the square root of a number is
the opposite of squaring a number. The square root of a number is a number
that, when multiplied by itself, equals the desired value. For example,
the square root of 49 is 7 (7x7=49)
Squares of 1 to 50
|
Numbers |
Squares |
Numbers |
Squares |
Numbers |
Squares |
Numbers |
Squares |
Numbers |
Squares |
|
1 |
1 |
11 |
121 |
21 |
441 |
31 |
961 |
41 |
1681 |
|
2 |
4 |
12 |
144 |
22 |
484 |
32 |
1024 |
42 |
1764 |
|
3 |
9 |
13 |
169 |
23 |
529 |
33 |
1089 |
43 |
1849 |
|
4 |
16 |
14 |
196 |
24 |
576 |
34 |
1156 |
44 |
1936 |
|
5 |
25 |
15 |
225 |
25 |
625 |
35 |
1225 |
45 |
2025 |
|
6 |
36 |
16 |
256 |
26 |
676 |
36 |
1296 |
46 |
2116 |
|
7 |
49 |
17 |
289 |
27 |
729 |
37 |
1369 |
47 |
2209 |
|
8 |
64 |
18 |
324 |
28 |
784 |
38 |
1444 |
48 |
2304 |
|
9 |
81 |
19 |
361 |
29 |
841 |
39 |
1521 |
49 |
2401 |
|
10 |
100 |
20 |
400 |
30 |
900 |
40 |
1600 |
50 |
2500 |
A cube number is found when we multiply a number by
itself and then itself again. The symbol for cubed is 3. Example of a
Third Space Learning Lesson slide exploring cube numbers. For example, 8 is a
cube number because it's 2 x 2 x 2; this is also written as 23.
Cubes are the values that are obtained when a number is
multiplied by itself three times.
Cubes 1 to 25 Table
The cubes of natural numbers 1 to 50 are available here in
tabular form.
|
Number (x) |
Multiplied Three times
by itself |
Cubes (x3) |
|
1 |
1× 1× 1 |
1 |
|
2 |
2× 2× 2 |
8 |
|
3 |
3× 3× 3 |
27 |
|
4 |
4× 4× 4 |
64 |
|
5 |
5× 5× 5 |
125 |
|
6 |
6× 6× 6 |
216 |
|
7 |
7× 7× 7 |
343 |
|
8 |
8× 8× 8 |
512 |
|
9 |
9× 9× 9 |
729 |
|
10 |
10× 10× 10 |
1000 |
|
11 |
11× 11× 11 |
1331 |
|
12 |
12× 12× 12 |
1728 |
|
13 |
13× 13× 13 |
2197 |
|
14 |
14× 14× 14 |
2744 |
|
15 |
15× 15× 15 |
3375 |
|
16 |
16× 16× 16 |
4096 |
|
17 |
17× 17× 17 |
4913 |
|
18 |
18× 18× 18 |
5832 |
|
19 |
19× 19× 19 |
6859 |
|
20 |
20× 20× 20 |
8000 |
|
21 |
21× 21× 21 |
9261 |
|
22 |
22× 22× 22 |
10648 |
|
23 |
23× 23× 23 |
12167 |
|
24 |
24× 24× 24 |
13824 |
|
25 |
25× 25× 25 |
15625 |
Square root 1 to 100: Square root of a number is a
value, which on multiplication by itself, gives the original number. If p is a positive
integer, then the square root of p is represented by √p, such that √p
= q.
List of Square Roots from 1 to 25
Below is the table carrying the list of numbers from 1 to 25,
along with their squares and square roots. Memorising these values of square
roots will help to solve many mathematical problems.
|
Number (N) |
Square (N2) |
Square root (√N) |
|
1 |
1 |
1.000 |
|
2 |
4 |
1.414 |
|
3 |
9 |
1.732 |
|
4 |
16 |
2.000 |
|
5 |
25 |
2.236 |
|
6 |
36 |
2.449 |
|
7 |
49 |
2.646 |
|
8 |
64 |
2.828 |
|
9 |
81 |
3.000 |
|
10 |
100 |
3.162 |
|
11 |
121 |
3.317 |
|
12 |
144 |
3.464 |
|
13 |
169 |
3.606 |
|
14 |
196 |
3.742 |
|
15 |
225 |
3.873 |
|
16 |
256 |
4.000 |
|
17 |
289 |
4.123 |
|
18 |
324 |
4.243 |
|
19 |
361 |
4.359 |
|
20 |
400 |
4.472 |
|
21 |
441 |
4.583 |
|
22 |
484 |
4.690 |
|
23 |
529 |
4.796 |
|
24 |
576 |
4.899 |
|
25 |
625 |
5.000 |
Omission of certain number of letters in any consecutive
order
Addition/Subtraction/Multiplication/Division by some number
(for example: A.P & G.P/Arithmetic Progression, Geometric Progression) or
any other relation.
Types of series are explained in the following chart
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