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Educational Level

Secondary school, High school and College 
Program Purpose

Provide step by step solutions of your problems using online calculators (online solvers)

Problem Source

Your textbook, etc 
1.
Algebra Calculators

1. Addition, subtraction, multiplication, division of two polynomials
eg.`(X^34X^2+4X8)` `xx` `(X2)`
2. Factoring Polynomials
eg. (1) `25x^236`, (2) `4x^2+12xy+9y^2`, (3) `x^33x^26x+8`, (4) `a^2(bc)+b^2(ca)+c^2(ab)`
3. Expand and simplify polynomial
eg. (1) `(X+2)(X+3)`, (2) `(2X+3Y)^2`, (3) `(2X+3Y+4Z)^2`, (4) `102^2`, (5) `102 xx 106` (Expand using the identity)
4. Complete square, Is perfect square, Find missing term
1. Completing the square for quadratic equation
eg. `9x^2+6x+1= 9( x+1/3 )^2`
2. Determining if the polynomial is a perfect square
eg. (1) `x^24xy+4y^2`, (2) `3x^2+5x+2`
3. Find the missing term in a perfect square trinomial
eg. (1) `9x^2`  __ + 16, (2) __ + `12x^2` + 9, (3) `49x^2` + 56 xy + __
5. HCF(GCD)LCM of Polynomials
eg. Find GCD, LCM of `(2X^24X), (3X^412X^2), (2X^52X^44X^3)`
6. Rational Expression of Polynomials
1. Reduced terms of rational expressions
eg. `(4X^225)/(8X^3125)`
2. Adding, subtracting, multiplying, dividing of rational expressions polynomials
eg. `(X3)/(X+1)(X6)/(X)`
7. Simplifying Algebraic Expressions
eg. (1) `(4x+1)/(3x2)=3/2`, (2) `(2x1)/(3x+1)+(4x1)/(6x)=0`
8. Quadratic Equation
1.1 Solving quadratic equations by factoring,
eg. (1) `25x^230x+9=0`, (2) `x^2+10x56=0`
1.2 Solving quadratic equations by Completing the Square,
eg. (1) `25x^230x+9=0`, (2) `x^2+10x56=0`
1.3 Discriminant & Nature of Roots
eg. (1) `25x^230x+9=0`, (2) `x^2+10x56=0`
2. Find the quadratic equation whose roots are alpha and beta
eg. (1) `alpha=3, beta=4`, (2) `alpha=1+3sqrt(2), beta=13sqrt(2)`
3. Roots for nonzero denominator
eg. (1) `(5x18)/(x+2)=(2x6)/(x1)`, (2) `(x)/(x+1)+(x+1)/(x)=5/2`,
(3) `4((4x+1)/(4x1))^(2)+(4x+1)/(4x1)=3`, (4) `(4x+1)/(4x1)+(4x1)/(4x+1)=3`
4. Roots of nonquadratic equation
eg. (1) `6(x^2+1/x^2)25(x1/x)+12=0`, (2) `(x^2+1/x^2)8(x+1/x)+14=0`
9. Solve linear equation in two variables by (eg. Solve `7y+2x11=0` and `3xy5=0` using Substitution method)
1. Substitution method
2. Elimination method
3. Cross multiplication method
4. AdditionSubtraction method
5. Inverse matrix method
6. Cramer's Rule method
7. Graphical method
10. Solve linear equation of any number of variables (simultaneous equations) using
1. Inverse Matrix method
2. Cramer's Rule method
3. Gauss Elimination (Jordan) method
4. Gauss Elimination (Back Substitution) method
5. Gauss Seidel method
6. Gauss Jacobi method
11. Variation Equations
1. Find value of variation using given value
(1) x `prop` y and x=6 when y=3. Find y=? when x=18,
(2) x `prop` `y/z`. x=8 when y=4 and z=3. Find x=? when y=6 and z=4.
2. Prove results for given variation
(1) If x `prop` y then prove that `x^3+y^3 prop x^2yxy^2`,
(2) If 3x5y `prop` 5x+6y then prove that x `prop` y.
12. If `X+1/X=2` then find `X1/X, X^21/X^2, X^3+1/X^3`
1. If `x1/x=6` then find
(1) `x^2+1/x^2` (2) `x+1/x` (3) `x^21/x^2`
2. If `x+y=5` and `xy=6` then find `x^2+y^2`
3. If `x^2+y^2+z^2=29` and `xy+yz+zx=14` then find `x+y+z`
13. Interval notation and set builder notation
eg. (1) `3 <= x <=7`, x is odd. (2) `x^32 <= 25`, x in Z. (3) `x in[2,8)`
14. Set Theory
eg. `A={x<=5; x in N}, B={2<=x<=8; x in N}, C={x^33x^24x=0},` Find
1. Union
eg. `A uu (B uu C)=(A uu B) uu C`
2. Intersection
eg. `A nn (B uu C)=(A nn B) uu (A nn C)`
3. Complement
eg. `(A uu B)'=A' nn B'`
4. Power set(Proper Subset)
eg. `P(A)`
5. Difference
eg. (1)`AB`, (2) `A(B uu C)=(AB) nn (AC)`
6. Symmetric difference
eg. (1)`A Delta B`, (2) `B Delta C`, (3) `A Delta C`
7. Cross Product
eg. `A xx B`
8. Prove that any two expression is equal or not
eg. `A(B uu C)=(AB) nn (AC)`
9. Cardinality of a set
eg. `n(A)`
10. is Belongs To a set
eg. `2inB` ?
11. is Subset Of a set
eg. `AsubB` ?
12. is two set Equal or not
eg. `A=B` ?
15. Functions
1. Find Range of `f:A>B`
eg. 1. `f(x)=5x+2` where `A={1<=x<5}`, 2. `f(x)=sqrt(x)` where `A={1,4,16,36}`
2. Composite functions and Evaluating functions
eg. `f(x)=2x+1`, `g(x)=x+5`. Find `fog(x)`, `gof(x)`, `fog(2)`, `f(3)`, `g(4)`
3. Find value
eg. 1. `f(x)=x(x+1)(2x+1)`. Find `f(x)f(x1)`, 2. `f(x)=x^22^x`. Find `f(2)f(0)`
16. Descartes' rule of signs
eg. `x^5x^4+3x^3+9x^2x+5`
17. Mathematical Logic, truth tables, logical equivalence
eg. Prepare the truth table `p^^(qvvr)=(p^^q)vv(p^^r)`
18. Boolean Algebra
eg. `D_(6)`, `D_(9)` is a boolean algebra ?







4.
Statistical Methods Calculators


1.1 Ungrouped data

85,96,76,108,85,80,100,85,70,95

1. Mean, Median and Mode for ungrouped data
2. Quartiles, Deciles and Percentiles for ungrouped data
3. Population Variance, Standard deviation and coefficient of variation for ungrouped data
4. Sample Variance, Standard deviation and coefficient of variation for ungrouped data

1.2 Grouped data

Class  5055  4550  4045  3540  3035  3530  2025  f  25  30  40  45  80  110  170 

1. Mean, Median and Mode for grouped data
2. Quartiles, Deciles and Percentiles for grouped data
3. Population Variance, Standard deviation and coefficient of variation for grouped data
4. Sample Variance, Standard deviation and coefficient of variation for grouped data

1.3 Mixed data

Class  1  2  5  610  1020  2030  3050  5070  70100  f  3  4  10  23  20  20  15  3  2 

1. Mean, Median and Mode for mixed data
2. Population Variance, Standard deviation and coefficient of variation for mixed data
3. Sample Variance, Standard deviation and coefficient of variation for mixed data

2. Missing frequency for

1. Ungrouped data

The Mean of the observations `18,14,15,19,15,a,12,15,16` is `16`. Find missing frequency `a`

2. Grouped data

The mean of a frequency distribution of 40 persons is 16.5. Find the missing frequencies.
Class  0  5  5  10  10  15  15  20  20  25  25  30  30  35  f  1  7  11  ?  ?  4  2 

3. Statistics Word Problem

The mean of 10 observations is 35 . While calculating the mean two observations were by mistake taken as 35 instead of 25 and 30 instead of 45 . Find the correct mean.

5. Arithmetic Mean, Geometric Mean, Harmonic Mean

1. Find Arithmetic mean, Geometric mean, Harmonic mean

Find Arithmetic mean, Geometric mean, Harmonic mean for ungrouped data like 2,3,4,5,6

2. Find X from Arithmetic mean, Geometric mean, Harmonic mean

Find X where Arithmetic mean=3.5 for ungrouped data 2,3,X,5

3. Find Mean or Median or Mode from other two's

Find Mode when Mean=3 and Median=4

7. Mean deviation about mean for

1. Ungrouped data

85,96,76,108,85,80,100,85,70,95

2. Grouped data

Calculate mean deviation about mean for the following distribution.
Marks  010  1020  2030  3040  4050  5060  6070  No. of student  6  5  8  15  7  6  3 

8. Pearson's Correlation Coefficient

1. for X & Y or ClassX & Y

Calculate correlation coefficient for following weights fathers X and their sons Y
X  65  66  67  67  68  69  70  72  Y  67  68  65  68  72  72  69  71 

2. for bivariate grouped data

Calculate the correlation coefficient
ClassY ClassX  90100  100110  110120  120130  5055  4  7  5  2  5560  6  10  7  4  6065  6  12  10  7  6570  3  8  6  3 


9. Spearman's Rank Correlation Coefficient (RHO)

1. Ten participants in a contest are ranked by two judges as follows
2. Obtain the rank correlation coefficient for the following data.
X  68  64  75  50  64  80  75  40  55  64  Y  62  58  68  45  81  60  68  48  50  70 










8.
Geometry Calculators

1. Coordinate Geometry Calculators
2. Graphs
1. Graphs  Plotting of mathematical functions f(x) or f(y)
2. Graph  Using Points and Slope
2.1 Points : (3,5),(5,3)
2.2 Points on Xaxis : 3,5,12,7,0
2.3 Points on Yaxis : 3,5,12,7,0
2.4 Lines : x=3y+5; 2x+y=1; x+2y<=5; x+y>=15
2.5 Line using Slope & point : Slope=7 and Point=(4,6)
2.6 Line using Slope & YIntercept : Slope=2 and YIntercept=4
2.7 Line passing through two points : Point1=(3,5) and Point2=(5,3)
3. Circle
4. Ellipse
5. Parabola
6. Hyperbola
7. Polar Graph
8. Statistics Graph
8.1 Histogram
8.2 Frequency Polygon
8.3 Frequency Curve
8.4 Less than type cumulative frequency curve
8.5 More than type cumulative frequency curve
3. Area
1. Circle
2. SemiCircle
3. RegularHexagon
4. Square
5. Rectangle
6. Parallelogram
7. Rhombus
8. Trapezium
9. Scalene Triangle
10. Right angle Triangle
11. Equilateral Triangle
12. Isosceles Triangle
13. Sector Segment
4. Volume
1. Cuboid
2. Cube
3. Cylinder
4. Cone
5. Sphere
6. HemiSphere
5. Pythagorean Theorem



9.
PreAlgebra Calculators

1. Addition, Subtraction, Multiplication, Division of two numbers
2. Pronounce a number
3. Factors of a number (Prime factors, All factors)
4. HCF and LCM of numbers
5. Prime Numbers
6. Simplifying Numerical Expressions
7. Decimal number
1. Decimal to Fraction conversion
2. Fraction to Decimal conversion
3. Round off decimal number
4. Decimal number To Scientific notation
5. Scientific notation To Decimal number
8. Fraction
1.1 Reduced Terms
1.2 Improper Fraction To Mixed Number
1.3 Fraction to Decimal
2. Mixed Number To Improper Fraction
3. Compare Two Fraction
4. Addition, Subtraction, Multiplication and Division of Fraction Numbers
9.1 Powers
1. Square of a number
2. Cube of a number
3. N^{th} Power of a number
9.2 Radicals
4. Square root of a number using prime factorization method
5. Cube root of a number using prime factorization method
6. N^{th} root of a number using prime factorization method
7. Square root of a number using long division method
8. Cube root of a number using long division method
9. Find the smallest number which must be Added to 180 to make it perfect Square
10. Find Least number of 4 digits which is a perfect Square
10. Divisibility test by 2,4,8, 3,9, 5,10, 7,11,13,17,19,23,29,31,37,41,43
11. Find the next term in the number series (1. 3, 6, 18, 72, ___ 2. 20, 19, 17, 14, 10, ___)
12. Unit Conversion
1. Angle to Degree Conversion
2. Degree Conversion
3. Length Conversion
4. Mass Conversion
5. Money Conversion
6. Power Conversion
7. Speed Conversion
8. Temperature Conversion
9. Time Conversion
10. Volume Conversion
13. One Base to Other Base Conversion
1. Decimal to Binary
2. Decimal to Octal
3. Decimal to Hexadecimal
4. Binary to Decimal
5. Binary to Octal
6. Binary to Hexadecimal
7. Octal to Decimal
8. Octal to Binary
9. Octal to Hexadecimal
10. Hexadecimal to Decimal
11. Hexadecimal to Binary
12. Hexadecimal to Octal
13. Decimal to Other
14. Other to Decimal
15. Other to Other
14. Tables
1. Addition table / Chart
2. Multiplication table / Chart
3. Roman table
4. Factorial table
5. Number system conversion table
6. Square table
7. Cube table
8. Power table
9. Sin table
10. Cos table
11. Tan table
12. Sin, Cos, Tan table
13. Area formula
14. Volume formula
15. Factors of an equation formula
15. Place Value
16. Leap Year



10.
College Algebra Calculators (For BCA, MCA Students)

1. Addition, Subtraction, Multiplication, Division of two numbers
1. Addition, Subtraction, Multiplication, Division of two numbers in Decimal
2. Addition, Subtraction, Multiplication, Division of two numbers in Binary
3. Addition, Subtraction, Multiplication, Division of two numbers in Octal
4. Addition, Subtraction, Multiplication, Division of two numbers in HexaDecimal
5. Addition, Subtraction, Multiplication, Division of two numbers in Other (Eg: Base=6)
2. Number System Conversion
3. 1's, 2's, 7's, 8's, 9's, 10's, 15's, 16's complement subtraction method
1. 1's complement subtraction method
2. 2's complement subtraction method
3. 7's complement subtraction method
4. 8's complement subtraction method
5. 9's complement subtraction method
6. 10's complement subtraction method
7. 15's complement subtraction method
8. 16's complement subtraction method
4. Matrix Algebra
5. Numerical Methods
6. Statistical Methods
7. Operation Research (OR)
8. Mathematical Logic, truth tables, logical equivalence
9. Boolean Algebra










