AIM Academics & AIM4A Tutoring/Test Prep

High School Mathematics
Curriculum Outline

Topic 1. Algebra Basics

1Converting Sentences into Mathematical Form
2Algebraic Expressions
3Mathematical Statement
4Algebraic Equations
5Algebraic Equations and Expressions
6Story Problem for Equation
7Equations and Expressions
8Solving an Equation by Guess Method
9Solving Equations - 2
10Solving Equations - 3
11Applications of Simple Equations
12Solving Equations
13Basic Operations With Variables - I
14Basic Operations With Variables - II
15Translating Verbal Statements into Algebraic Expressions
16Linear and Non-Linear Equations
17Linear Equations
18Linear Equations - 2
19Linear Equations - One Variable
20Linear Equations - Two Variables
21Linear Equations in Two Variables- Solving by the Method of Substitution
22Linear Equations in Two Variables- Solving by the Method of Elimination
23Linear Equation - Three Variables
24Solve the Equations Using Graphs - I
25Solve the Equations Using Graphs - II
26Review I

Topic 2. Arithmetic - Irrational Numbers

1Arithmetic - Irrational Numbers Review - II
2Square Root (Division Method) - II
3Square Root (Division Method) - I
4Problems on Square Root - III
5Problems on Square Roots - II
6Problems on Square Roots - I
7Square Root (Factorization Method)
8Radicals Review - IV
9Radicals Review - III
10Radicals Review - II
11Radicals Review - I
12Important Points in Radicals
13Rationalize the Denominator - IV
14Rationalize the Numerator
15Rationalize the Denominator - III
16Rationalize the Denominator - II
17Rationalize the Denominator - I
18Finding Square Roots of Decimal Fractions - I
19Finding Square Roots of Decimal Fractions - II
20Arithmetic - Irrational Numbers Review - I
21Square Roots of Real Numbers Review - IV
22Square Roots of Real Numbers Review - III
23Square Roots of Real Numbers Review - II
24Square Roots of Real Numbers Review - I
25Important Points in Extraction of Square Roots of Real Numbers
26Application of Square Root - IV
27Application of Square Root - III
28Application of Square Root - II
29Application of Square Root - I
30Finding Square Roots (Historical Method)
31Square Roots Table
32Finding Square Root of Common Fraction
33Finding Square Roots of Numbers Which are not Perfect Square Numbers - II
34Finding Square Roots of Numbers Which are not Perfect Square Numbers - I
35Finding Square Roots of Decimal Fractions - III
36Problems on Radicals - III
37Problems on Radicals - II
38Problems on Radicals - I
39Subtraction of Radicals - II
40Subtraction of Radicals - I
41Addition of Radicals - III
42Addition of Radicals - II
43Addition of Radicals - I
44Radicals - Descending Order
45Radicals - Ascending Order
46Comparing Radicals
47Mixed Radicals or Surds
48Pure Radicals or Surds
49Simplifying Radicals
50Laws of Radicals - Radicals and Exponents Combined
51Laws of Radicals - Radical of a Radical
52Laws of Radicals - Division of Radicals
53Laws of Radicals - Multiplication of Radicals
54Types of Radicals
55Multiplication of Radicals - I
56Multiplication of Radicals - II
57Rationalizing Radicals Using its Conjugate
58Conjugate Radical
59Rationalization of Binomial Radicals - III
60Rationalization of Binomial Radicals - II
61Rationalization of Binomial Radicals - I
62Rationalization of Monomial Radicals - IV
63Rationalization of Monomial Radicals - III
64Rationalization of Monomial Radicals - II
65Rationalization of Monomial Radicals - I
66Division of Radicals - I
67Division of Radicals - II
68Distributive Law
69Problems on Radicals Using Formulas - I
70Problems on Radicals Using Formulas - II
71Problems on Radicals Using Formulas - III
72Multiplication of Radicals - III
74Review - Radicals

Topic 3. Introduction to Logarithms

1Logarithmic Form
2Problems on Logarithms - VI
3Problems on Logarithms - VII
4Problems on Logarithms - VIII
5Problems on Logarithms - IX
6Characteristic and Mantissa of a Logarithm
7Finding Number of Digits
8Problems on Logarithms - X
9Important Points in Logarithms
10Logarithms Review - I
11Logarithms Review - II
12Logarithms Review - III
13Problems on Logarithms - V
14Prove the Statements
15Simplifying the Logarithms - II
16Exponential Function
17Unity in Logarithms
18Logarithm of a Product
19Logarithm of a Quotient
20Logarithm of a Power
21Problems on Logarithms - I
22Problems on Logarithms - II
23Problems on Logarithms - III
24Change of base of a Logarithm
25Problems on Logarithms - IV
26Simplifying the Logarithms - I
27Logarithms Review - IV

Topic 4. Solid Geometry - Surface Area and Volumes of Solids

1Geometry Formulas Summary
2Formulas - Volumes of Three Dimensional Shapes
3Formulas - Surface and Lateral Surface Areas of Solids
4Lateral Surface Area of a Cube
5Total Surface Area of a Cube
6Lateral Surface Area of a Cuboid
7Total Surface Area of a Cuboid
8Volume of Cuboid
9Word Problems on Sphere - I
10Volume of The Sphere
11Surface Area of a Sphere - III
12Surface Area of a Sphere - II
13Surface Area of a Sphere - I
14Cone Review - II
15Word Problems on Cone - I
16Cone Review - I
17Important Points on Cone
18Word Problems on Cone - III
19Word Problems on Cone - II
20Word Problems on Sphere - II
21Important Points in Sphere
22Word Problems on Sphere - III
23Solid Geometry Final Review - IV
24Solid Geometry Final Review - III
25Solid Geometry Final Review - II
26Solid Geometry Final Review - I
27Solid Geometry - Review
28Total Surface Area of Hemisphere
29Surface Area of Hemisphere
30Review on Sphere - II
31Review on Sphere - I
32Volume of The Cone
33Curved Surface Area of Cone
34Area of Base of Cone
35Word Problems on Cylinder - I
36Lateral Surface Area of a Cylinder
37Prism Review - III
38Prism Review - II
39Prism Review - I
40Important Points in Prism
41Length of the Edges of Triangular Prism
42Volume of the Prism - IV (Hexagonal Prism)
43Volume of The Prism - III
44Volume of The Prism - II (Right Angled Isosceles Triangle Prism)
45Volume of the Prism - I (Triangular Prism)
46Total Surface Area of a Triangular Prism
47Word Problems on Cylinder - II
48Curved Surface Area of a Cylinder
49Slant Height of a Cone
50Total Surface Area of a Cone
51Cylinder Review - II
52Cylinder Review - I
53Important Points in Cylinder
54Total Surface Area of a Cylinder - I
55Curved Surface Area of a Cylinder - I
56Radius of The Cylinder
57Volume of the Cylinder - III
58Volume of the Cylinder - II
59Volume of the Cylinder - I
60Total Surface Area of a Cylinder
61Lateral Surface Area of a Triangular Prism

Topic 5. Revision of Exponents and Algebraic Expressions

1Revision of Algebraic Expressions - I
2Revision of Algebraic Expressions - II
3Revision of Algebraic Expressions - III
4Revision of Algebraic Expressions - IV
5Revision of Algebraic Expressions - V
6Revision of Algebraic Expressions - VI
7Important Points

Topic 6. Quadratic Expressions - Square Roots of Algebraic Expressions

1Square Root of Monomials - Perfect Squares
2Reciprocal Equation
3Solving Quadratic Equation by Using Quadratic Formula
4Relation Between Roots and Coefficients of a Quadratic Equation
5Forming a Quadratic Equation Using Its Roots
6Nature of the Roots of a Quadratic Equation
7Problems on Roots
8Square Roots and Algebraic Expressions Review
9Square Roots of Algebraic Expressions Review - I
10Solving Equations Reducible to Quadratic Form
11Solving Quadratic Equations by Method of Factorization
12Method of Finding Square Roots - Inspection Method
13Finding Square Root by Division Method
14Finding Square Root of The Method of Undetermined Coefficient
15Problems on Square Root - I
16Problems on Square Roots - II
17Problems on Square Roots - III
18Homogeneous Expressions
19Symmetric and Cyclic Expressions
20Square Roots of Algebraic Expressions Review - II

Topic 7. Sets

1Union of Sets
2Intersection of Sets
3Problems on Sets
4Prove The Given Statements
5Difference of Two Sets
6Complement of Sets
7Problems on Sets Using Diagrams - I
8Problems on Sets Using Diagrams - II
9Important Points in Sets

Topic 8. Relations

1Cartesian Product of Sets
2Relations and Functions
3Types of Relations - Reflexive, Symmetric, Anti-Symmetric, Transitive, and Equivalance
4Types of Relations - One-to-One, One-to-Many, Many-to-One and Many-to-Many
5Inverse Relation or Inverse Functions
6Domain and Range of a Relation using Diagrams
7Domain and Range of a Relation
8Problems on Relations
9Cartesian Product With Diagrams
10Important Points in Relations

Topic 9. Coordinate Geometry

1General Concepts - Coordinate Geometry or Cartesian C or Analytical Geometry
2Coordinate Plane - Quadrants
3Problems: Find the value of x and y
4Slope - I
5Slope - II
6Slope - III
7Parallel Line - Slope
8Distance Between Two Points
9Mid Point of the Segment Joining Two Points
10The Point Slope Form of a Line
11Intercept Form of a Line
12The Two Points Form of A Line
13Parallel Lines & Perpendicular Lines - Slope
14The Slope - Intercept Form of a Line
15Problems on Slope
16Coordinate Geometry - Review

Topic 10. Linear Equations and Inequations

1Finding The Value of X
2Solve Absolute Value Inequalities
3Solve Absolute Value Equations
4Linear equations and inequation Review - II
5Linear Equations and inequation Review - I
6Solving Inequations Using Graphical Method
7Solving Inequations
8Representing Inequation on Number Line
9Solving Equations Using Graphical Method
10Solving Equations
11Absolute Value Inequalities - 2

Topic 11. Matrices

1Matrix and Order of a Matrix
2Subtraction of Matrices
3Distributive Law in Matrices (Addition)
4Multiplication of Matrices - I
5Multiplication of Matrices - II
6Multiplication of Matrices - III
7Properties of Matrices in Multiplication
8Multiplication Distributes Over Addition
9Important Points in Matrices
10Scalar Product of Matrix
11Symmetric Matrix and Skew Symmetric Matrix
12Square Matrix and Rectangular Matrix
13Row Matrix, Column Matrix and Null Matrix
14Principal Diagonal of a Square Matrix, Scalar Matrix and Identity Matrix
15Transpose of a Matrix
16Equality of Two Matrices
17Matrices Addition - I (Commutative)
18Matrices Addition - II (Associative)
19Identity Matrix in Addition and Additive Inverse
20Matrices Review

Topic 12. Geometry

1Final Review - II
2Construction Review - I
3Brahma Guptha's Theorem
4Review - VII
5Review - VI
6Review - V
7Important Points in Circles
8Theorem - XXVI
9Theorem - XXV
10Theorem - XXIV
11Theorems - XX_XXI_XXII_XXIII
12Theorem - XIX
13Theorem - XVIII
14Theorem - XVII
15Construction of Triangle - I
16Construction of Triangle - II
17Final Review - I
18Construction Review - II
19Solve The Problems Using Theorems - VI
20Construction of Triangle - XII
21Construction of Triangle - XI
22Construction of Triangle - X
23Construction of Triangle - IX
24Construction of Triangle - VIII
25Construction of Triangle - VII
26Construction of Triangle - VI
27Construction of Triangle - V
28Construction of Triangle - IV
29Construction of Triangle - III
30Theorem - XVI
31Theorem - XV - Circles
32Review - IV
33Concurrency Theorems
34Theorem - V
35Theorem - IV
36Introduction to Locus
37Review - III
38Review - II
39Review - I
40Solve The Problems Using Theorems - II
41Theorem - III
42Theorem - II
43Theorem - I
44Solve The Problems Using Theorems - I
45Problem Using Picture
46Important Points - Locus
47Solve The Problems Using Theorems - III
48Important Points - Areas
49Solve The Problems Using Theorems - IV
50Find The Area of The Given Figure
51Theorem - XIV
52Theorem - XIII
53Theorem - XII
54Theorem - XI
55Theorem - X
56Theorem - IX
57Theorem - VIII
58Theorem - VII
59Theorem - VI
60Areas Introduction
61Quadrilaterals - Review

Topic 13. Trasformation Geometry

1Reflection Mapping, Finding the Reflection Image of a Point in a Line
2Fixed Lines, Reflection Images of Parallel Lines, Collinearity and Betweenness
7Trasformations Review - Reflection, Rotation, Translation and Dilation
8Transformations Review - II

Topic 14. Statistics

1Range of a Data
2Introduction to Statistics
3Preparation of Frequency Table
4Types of Variates - Discrete
5Types of Variates - Continuous
6Inclusive and Exclusive Class Intervals
7Less Than Cumulative Frequency
8Greater Than Cumulative Frequency
9Classes, Tally Marks, Frequencies, Cumulative Frequencies
10Cumulative Frequency
11Forming a Frequency Table from a Cumulative Frequency Distribution
12Finding out Unknown Entries from the Frequency Table
13Graphical Representation of Statistical Data - Bar Graphs
14Graphical Representation of Statistical Data - Histograms
16Frequency Polygon
17Frequency Polygon - 2
18Frequency Polygon without Histograms
19Measures of Location or Measures of Central Tendency
20Arithmetic Mean of Discrete Values
21Properties of Arithmetic Mean
22Median of Discrete Values
23Partition Values for Discrete Variables (Percentiles, Quartiles and Interquartile Range)

Topic 15. Review Tests

1Final Review - I
2Final Review - II
3Final Review - III
4Final Review - IV
5Final Review - V
6Final Review - VI