AIM Academics & AIM4A Tutoring/Test Prep

High School Mathematics
Curriculum Outline

Topic 1. Algebra Basics

#ChapterDateNotes
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

#ChapterDateNotes
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
   
                                  
73Radicals
   
                                  
74Review - Radicals
   
                                  

Topic 3. Introduction to Logarithms

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
1Reflection Mapping, Finding the Reflection Image of a Point in a Line
   
                                  
2Fixed Lines, Reflection Images of Parallel Lines, Collinearity and Betweenness
   
                                  
3Reflections
   
                                  
4Translation
   
                                  
5Rotation
   
                                  
6Dilation
   
                                  
7Trasformations Review - Reflection, Rotation, Translation and Dilation
   
                                  
8Transformations Review - II
   
                                  

Topic 14. Statistics

#ChapterDateNotes
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
   
                                  
15Histogram
   
                                  
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)
   
                                  
24Mode
   
                                  

Topic 15. Review Tests

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