Math Guide

Monday, January 28, 2013

Percentage to Grade Conversion

The percentage of the number is a method of showing the number with the denominator 100 as fraction. The percentage of the number is represented by the symbol “%” or “pct”. Percentage shows the relation of the two quantities, the first quantity is associated with the second quantity. So, first quantity should be larger than zero

Grades are the measurements which are standardized for understanding the academic level of the students. Percentage and its grades are listed below.

Percentage to Grade Conversion Table

Percent to grade point table
Percent	Grade points	Letter grade
0.1	0	F
0.25	0	F
0.26	0	F
0.27	0	F
0.28	0	F
0.29	0	F
0.3	0	F
0.31	0	F
0.32	0	F
0.33	0	F
0.34	0	F
0.35	0	F
0.36	0	F
0.37	0	F
0.38	0	F
0.39	0	F
0.4	0	F
0.41	0	F
0.42	0	F
0.43	0	F
0.44	0.1	F
0.45	0.2	F
0.46	0.3	F
0.47	0.4	F
0.48	0.5	F
0.49	0.6	F
0.5	0.7	D-
0.51	0.8	D-
0.52	0.9	D
0.53	1	D
0.54	1.1	D
0.55	1.2	D+
0.56	1.3	D+
0.57	1.4	D+
0.58	1.5	C-
0.59	1.6	C-
0.6	1.7	C-
0.61	1.8	C-
0.62	1.9	C
0.63	2	C
0.64	2.1	C
0.65	2.2	C+
0.66	2.3	C+
0.67	2.3	C+
0.68	2.4	C+
0.69	2.4	C+
0.7	2.5	B-
0.71	2.5	B-
0.72	2.6	B-
0.73	2.6	B-
0.74	2.7	B-
0.75	2.7	B-
0.76	2.8	B-
0.77	2.8	B-
0.78	2.9	B
0.79	2.9	B
0.8	3	B
0.81	3	B
0.82	3.1	B
0.83	3.1	B
0.84	3.2	B+
0.85	3.2	B+
0.86	3.3	B+
0.87	3.3	B+
0.88	3.4	B+
0.89	3.4	B+
0.9	3.5	A-
0.91	3.5	A-
0.92	3.6	A-
0.93	3.6	A-
0.94	3.7	A-
0.95	3.7	A-
0.96	3.8	A-
0.97	3.8	A-
0.98	3.9	A
0.99	3.9	A
1	4	A

Example to Percentage to Grade Conversion:

Example 1:

John scored the marks in five subjects 87, 90, 88, 76 and 65. The test is conducted for 100 marks in each subject. Find the grade of the john.

Solution:

Total marks of the test = 5 `xx ` 100 = 500

Total marks of the john = 87 + 90 + 88 + 76 + 65 = 406

Percentage of the marks scored by john = `406/500` `xx` 100 = 81.2% or `81.2/100` = .812

Therefore john got B grade

Example 2:

Martin scored the marks in five subjects 85, 95, 65, 75 and 55. The test is conducted for 100 marks in each subject. Find the grade of the Martin.

Solution:

Total marks of the test = 5 `xx` 100 = 500

Total marks of the Martin = 85 + 95 + 65 + 75 + 55 = 375

Percentage of the marks scored by Martin = `375/500` `xx` 100 = 75% or `75/100` = .75

Therefore Martin got B- grade

Practice Problems to Percentage to Grade Conversion:

Problem 1:

Paul scored the marks in five subjects 85, 98, 58, 67 and 94. The test is conducted for 100 marks in each subject. Find the grade of the Paul.

Solution is, Paul got B grade

Problem 2:

Steve scored the marks in five subjects 76, 86, 96, 66 and 56. The test is conducted for 100 marks in each subject. Find the grade of the Steve.

Solution is, Steve got B- grade

Friday, January 25, 2013

Inverse Cosine Graph

Inverse cosine is one of the essential inverse trigonometric function . Its principal values and range is
cos^-1 : {(y,x)l y = cos x , x `in [ 0, pi]` , y `in` [-1,1]}

In this we deals with determining inverse tangent graphs.

Function	Domain	Principal Value (Range)
y =cos ^-1 x	R	[ 0, `pi`]

The graph of cos^-1x is as follows :

. inverse cosine graph1

Inverse Cosine Graph : Examples

Example 1 : Draw the inverse cosine graph for the function

y = cos^-1 ( x + 4 )

Solution : As it is given y= cos ^-1 ( x + 4 ) so, there is a horizontal shift in the graph of y = cos^-1 x by 4 units leftwards

Graph as shown :

Example 2 : Draw the inverse cosine graph for the function

y = cos^-1 ( x ) - 3

Solution : As it is given y = cos^-1 ( x ) - 3

It can also be wirtten as y + 3 = cos^-1 ( x ) so , there is a vertical shift in the graph of y =cos ^-1 x by 3 unit downwards

Graph as shown :

Example 3 : Draw the inverse cosine graph for the function

y = cos^-1 ( x + 2 ) and y = cos^-1 ( x - 1 ) on the same graph

Solution : As it is given y = cos^-1 ( x + 2 ) so, there is a horizontal shift in the graph of y = cos^-1 x by 2 units leftwards and

for y = cos ^-1 ( x - 1 ) there is a horizontal shift in the graph of y = cos^-1 x by 1 unit rightwards

Graph as shown :

Inverse Cosine Graph : Practice Problems

Problem 1  : Draw the inverse cosine graph for the function
                                        y = cos^-1 ( x + 5 )
Problem 2 :  Draw the inverse cosine graph for the function
                       y = cos^-1 ( x ) + 6
Problem 3  : Draw the inverse cosine graph for the function
                                        y = cos^-1 ( x + 1) and   y = cos^-1 ( x - 7 ) on the same graph

Thursday, January 24, 2013

Number Line Estimation

In mathematics, a line with points marked on it is termed as number line. Every point represents a number in number line. This number line is mainly used for representing the numbers. From online, we have a clear description of number line estimation. This article gives the explanation of number line estimation and some example problems using number line.

Explanation to Number Line Estimation:

The facts of number line is as follows.

A straight horizontal line with points that are evenly spaced.
A number o is at center and positive numbers are at right side of 0 while the negative numbers are at left side of 0.
The number line makes easy the arithmetic operations addition and subtraction.

A number line with points is as follows.