 ## Math Formula Sheet | Worksheet Problems and Solutions

In this section there are wide range of Math Formula Sheets, thousands of mathematics problems, examples and questions with solutions and detailed explanations are included to help you explore and gain deep understanding of math, pre-algebra, algebra, pre-calculus, calculus, functions, quadratic equations, logarithms, exponents, trigonometry and geometry etc.
Topic wise Free pdf Downloads of Math Formula Sheet, Examples, Problems and Worksheets in Mathematics.

1. Sets Theory and Relations
Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations.

2. Logarithm and Exponent Rules

3. Complex Numbers and its application
Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality.

Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficient, nature of roots, formation of quadratic equations with given roots.

5. Sequence and Series (Progression)
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: Sn, Sn2, Sn3. Arithmetico – Geometric progression.

6.Permutations and Combinations
Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

7.Binomial Theorem and Mathematical Induction
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications. Mathematical Induction, Principle of Mathematical Induction and its simple applications.

8. Probability
Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

9.Trigonometry-1
Trigonometrical identities and equations. Trigonometrical functions.

10.Trigonometry-2
Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

11. Co-ordinate Geometry and Straight lines
Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.

12. Pair of Straight lines

13. Circles
Standard form of equation of a circle, general form of the equation of a circle, its radius and center, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the center at the origin and condition for a line to be tangent to a circle, equation of the tangent.

14. Conic Sections (Parabola, Ellipse and Hyperbola)
Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

15. Statistics and Measures of Dispersion
Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

16. Matrices and Determinants
Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

17. Inverse Trigonometry
Inverse trigonometrical functions and their properties.

18. Differential Calculus-1 (Function, Limit, Continuity and Differentiability)
Functions: one-one, into and onto functions, composition of functions. Real – valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability.

19. Differential Calculus-2 (Derivatives and Application of Derivatives)
Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

20. Indefinite Integration (Integral Calculus-1)
Integral as an anti – derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.

21. Definite Integral and Area Under Curves (Integral Calculus-2)
Evaluation of simple integrals of the type
Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

22. Differential Equations
Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of different types.

23. Vector Algebra
Vectors and scalars, addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product.

24. 3D Geometry
Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, co-planar lines.

25. Mathematical Reasoning
Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.

Basic Math Algebra, Pre-Algebra

Arithmetic, Roots and Powers, Factorization, Natural numbers, Integers, Rational expressions, Rules of evaluation of expressions, variable manipulation, Surds and Indices, Basic algebra formulas.

Topics of Pre-Calculus

1. The formal rules of algebra

2. Rational and irrational numbers, what is a rational number? Which numbers have rational square roots? The decimal representation of irrationals. What is a real number?

3. Functions, what is a function? The domain and the range. Functional notation. The argument. A function of a function.

4. Introduction to graphs, The graph of a function. Coordinate pairs of a function. The height of the curve at x.

5. Basic graphs, The constant function. The identity function. The absolute value function. The parabola. The square root function. The cubic function. The reciprocal function.

6. The vocabulary of polynomial functions Variables versus constants. Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial.

7. The roots, or zeros, of a polynomial. A polynomial equation. The roots of a polynomial. The x- and y-intercepts of a graph. The relationship between the roots and the x-intercepts.

8. The slope of a straight line. Definition of the slope. Positive and negative slope. A straight line has only one slope. “Same slope” and “parallel.” Perpendicular lines. The slope and one point specify a straight line.

9. Linear functions: The equation of a straight line. The equation of the first degree. The graph of a first-degree equation: a straight line. The slope-intercept form, and its proof.

10. Quadratics: Polynomials of the second degree. Quadratic equation: Solution by factoring. A double root. Quadratic inequalities. The sum and product of the roots.

11. Completing the square. Solving a quadratic equation by completing the square. The quadratic formula.

12. Synthetic division by x – a. The remainder theorem.

13. Roots of polynomials of degree greater than 2. The factor theorem. The fundamental theorem of algebra. The integer root theorem. Conjugate pairs.

14. Multiple roots. Point of inflection. Concave upward, concave downward.

15. Reflections of a graph. Reflection about the x-axis. Reflection about the y-axis. Reflection through the origin.

16. Symmetry of a graph. Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry. Odd and even functions.

17. Translations of a graph. Definition of a translation. The equation of a circle. The vertex of a parabola. Vertical stretches and shrinks.

18. Rational functions. Singularities. The reciprocal function. Horizontal and vertical asymptotes.

19. Inverse functions. Definition of inverses. Constructing the inverse. The graph of an inverse function.

20. Logarithms. The system of common logarithms. The system of natural logarithms. The three laws of logarithms. Change of base.

21. Logarithmic and exponential functions. Inverse relations. Exponential and logarithmic equations. Creating one logarithm from a sum.

22. Sigma notation for sums

23. Factorials

24. Permutations and Combinations. The Fundamental Principle of Counting. Factorial representations.

25. The binomial theorem. Pascal’s triangle. Multiplication of sums. A proof of the binomial theorem.

26. Mathematical induction

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