Chapter 3 Mathematica Commands

1. Express Fractional Power indices to Surd Form

(("Enter Base number here")^("Enter Exponential Fraction here"))//TraditionalForm

(6^(1/4))//TraditionalForm

2. Evaluate surd Expressions

Evaluate["Enter Surd Expression here"]

Evaluate[5(Sqrt[5])+(Sqrt[180])]

Evaluate[5/(Sqrt[5])+1/(Sqrt[180])]

Evaluate[((5^3)^(1/4))]

3. Binomial Expand

Expand["Enter Expression here"]

Expand[((Sqrt[11])+10)((Sqrt[3])-9)]

4. Rationalise Surds

r=(("Enter Numerator Here")/("Enter Denominator Here"));
Rationalize[((Expand[Numerator[r]*Denominator[r]])/(Denominator[r]*Denominator[r]))]

r=((-20(Sqrt[5])+7(Sqrt[11]))/(Sqrt[6]));
Rationalize[((Expand[Numerator[r]*Denominator[r]])/(Denominator[r]*Denominator[r]))]

r=(6/(Sqrt[3]))+(3/(Sqrt[6]));
Rationalize[((Expand[Numerator[r]*Denominator[r]])/(Denominator[r]*Denominator[r]))]

5. Scientific Notation

ScientificForm[{"Enter Expression Here"},"How many Sig. Figs."]

ScientificForm[{12345.0},4]

ScientificForm[{123450000.0,0.000012345,123.45},3]

6. Solve Exponential Equations/Index laws

Solve["Enter Equation here with ==","the thing you are looking for",Reals]//N

Solve[5^(2x+1)==125^x,x,Reals]//N

7. Graph Exponential Equations

Plot one graph

Plot["Enter Equation here",,{x,"Minimum value for x","Maximum value for x"},PlotLabels->"Expressions"]

Plot three graphs

Plot[{"Enter first equation here","Enter second equation here","Enter third equation here"},{x,"Minimum value for x","Maximum value for x"},PlotLabels->"Expressions"]

Plot[{y=7^x,y=-7^x,y=7^(-x)},{x,-3,3},PlotLabels->"Expressions"]

Tables Completing of Equations

TableForm[Table[{x,"Enter equation here"},{x,"Minimum value for x","Maximum value for x"}],TableHeadings->{None,{"x","y"}},TableDirections->Row]

TableForm[Table[{x,y=2^x,y=-2^x,y=2^(-x)},{x,-3,3}],TableHeadings->{None,{"x","y=2^x","y=-2^x","y=2^(-x)"}},TableDirections->Row]

8. Simple Interest

Solve["interest in $"==(("principal"*"interest rate"*"period")/100),"the thing you are looking for"]

Solve["interest in $"==((2000*4*3)/100),"interest in $"]

9. Compound Interest

The total amount in investment:

Solve[amount in investment=="principal"×(((1+(("interest rate")/100)))^("period")),"the thing you are looking for"]

The interest earned:

Solve[earned interest=="principal"×(((1+(("interest rate")/100)))^("period"))-"principal","the thing you are looking for"]

TableForm[Table[{"period","principal"×(((1+(("interest rate")/100)))^("period"))-"principal","principal"×(((1+(("interest rate")/100)))^("period"))}, {"period", starting year, ending year}],TableHeadings->{None,{"Year","Interest earned","Investment"}}]

TableForm[Table[{n,12000 (((1.03))^n)-12000,12000 (((1.03))^n)}, {n, 0, 10}],TableHeadings->{None,{"Year","Interest earned","Investment"}}]

Compound interest and Simple Interest Comparing

Plot[{"principal"×(((1+(("interest rate")/100)))^("period")),"principal"+((("principal"*"interest rate"*"period")/100))},{"period",starting year,ending year}]

Plot[{1000×(((1+(7/100)))^T),1000+(((1000*10*T)/100))},{T,0,40}]

TableForm[Table[{"principal"×(((1+(("interest rate")/100)))^("period")),"principal"+((("principal"*"interest rate"*"period")/100))},{"period",starting year,ending year}],TableHeadings->{None,{"Compound","Simple"}}]

TableForm[Table[{1000.0×(((1+(7/100)))^T),1000.0+(((1000*10*T)/100))},{T,0,10}],TableHeadings->{None,{"Compound","Simple"}}]