Math links

SAT college Test

know all these formulas

 http://www.mcelroytutoring.com/blog-post.php?id=281

http://www.allmathtricks.com/percentage-formulas/

Type 1 : General Percent formulas.

Find X is what percent on Y ?

http://www.allmathtricks.com/wp-content/uploads/2017/10/X-what-percent-on-Y-4-50x15.png 50w" alt="percentage formulas | percentage calculation with examples | Quantitative mathematics " width="165" height="50" style="box-sizing: inherit; border-style: initial; vertical-align: middle; max-width: 100%; height: auto; display: inline; float: left; margin-right: 1.5em; margin-top: 5px; margin-bottom: 5px;">

X is what percent greater than Yhttp://www.w3.org/1998/Math/MathML">y" style="box-sizing: inherit;"> ?

http://www.allmathtricks.com/wp-content/uploads/2017/10/x-is-what-percent-greater-than-y-2-50x14.png 50w" alt="percentage formulas | percentage calculation with examples | Quantitative mathematics " width="165" height="45" style="box-sizing: inherit; border-style: initial; vertical-align: middle; max-width: 100%; height: auto; display: inline; float: left; margin-right: 1.5em; margin-top: 5px; margin-bottom: 5px;">

http://www.w3.org/1998/Math/MathML">x" style="box-sizing: inherit;">is what percent lesser than Yhttp://www.w3.org/1998/Math/MathML">y" style="box-sizing: inherit;"> ?

http://www.allmathtricks.com/wp-content/uploads/2017/10/x-is-what-percent-lesser-than-y-1-50x14.png 50w" alt="percentage formulas | percentage calculation with examples | Quantitative mathematics " width="165" height="46" style="box-sizing: inherit; border-style: initial; vertical-align: middle; max-width: 100%; height: auto; display: inline; float: left; margin-right: 1.5em; margin-top: 5px; margin-bottom: 5px;">

 

Type 3 : Net percent change in area of circle or square

http://www.w3.org/1998/Math/MathML">(x2100+2x)%" style="box-sizing: inherit;">If radius of a circle is increased by http://www.w3.org/1998/Math/MathML">x%" style="box-sizing: inherit;">, then its area is increased by

http://www.allmathtricks.com/wp-content/uploads/2017/10/increased-by-X-and-then-again-decreased-by-Y.-3-300x85.png 300w" alt="percentage formulas | percentage calculation with examples |Net percent change in area of circle or square " width="160" height="46" style="box-sizing: inherit; border-style: initial; vertical-align: middle; max-width: 100%; height: auto; display: inline; float: left; margin-right: 1.5em; margin-top: 5px; margin-bottom: 5px;">

If radius of a circle is decreased by http://www.w3.org/1998/Math/MathML">x%" style="box-sizing: inherit;">, then its area is decreased by

http://www.allmathtricks.com/wp-content/uploads/2017/10/radius-of-a-circle-is-decreased-by-x-then-its-area-is-decreased-by-300x91.png 300w" alt="percentage formulas | percentage calculation with examples | Net percent change in area of circle or square" width="160" height="49" style="box-sizing: inherit; border-style: initial; vertical-align: middle; max-width: 100%; height: auto; display: inline; float: left; margin-right: 1.5em; margin-top: 5px; margin-bottom: 5px;">

Examples for the above percentage formulas

Ex.1 : Find the net change in area of a circle ,  If radius of the circle decreases by http://www.w3.org/1998/Math/MathML">x%" style="box-sizing: inherit;"> and again its radius increases by 10http://www.w3.org/1998/Math/MathML">y%" style="box-sizing: inherit;">

Solution :   – 20 + 10 – [(20 x 10) / 100)]  = -10 – 2 = -12% ( i.e radius decreased by 12% so change in radius 1- 0.12 = 0.88)

Area =    π x r2  = π x (0.88 r)2  =  0.7744 x  π x r2

So Area of the circle decreased by 100- 77.44 = 22.56%

Ex.2 : Find the net change in area of a circle ,  If radius of the circle increases by http://www.w3.org/1998/Math/MathML">x%" style="box-sizing: inherit;"> and again decreases by 10http://www.w3.org/1998/Math/MathML">y%" style="box-sizing: inherit;">

Solution :   30 – 10 – [(30 x 10) / 100)]  = 20 – 3 = -17% ( i.e radius increased by 17% so change in radius 1+0.17 = 1.17)

Area =    π x r2  = π x (1.17 r)2  = 1.3689 x  π x r2

So Area of the circle increased by 136.89 – 100 = 36.89%

Ex.3 : Find the net change in area of a square ,  If side of the square increases by http://www.w3.org/1998/Math/MathML">x%" style="box-sizing: inherit;">.http://www.w3.org/1998/Math/MathML">y%" style="box-sizing: inherit;">

Solution :  (2 x 30) + (30 x 30 /100) = 60 + 9 = 69%

So Area of the square increased by 69%

Ex.4 : Find the net change in area of a circle ,  If radius of the circle decreases by http://www.w3.org/1998/Math/MathML">x%" style="box-sizing: inherit;">.http://www.w3.org/1998/Math/MathML">y%" style="box-sizing: inherit;">

Solution :  – (2 x 18) + (18 x 18 /100) = – 36 +3.24 = – 32.73%.

So Area of the circle increased by 32.73%.