AIM Academics & AIM4A Tutoring/Test Prep

Middle/High School Algebra, Geometry, and Statistics (AGS)
Curriculum Outline

Topic 1. Linear Equations

1Find the Value of x - I
2Graph for Straight Line y = x
3Graph of y = x, y = 2x, y = (1/2)x and y = (1/3)x
4Graph of y = -x, y = -2x, y = -(1/2)x and y = -(1/3)x
5Y - Intercept (Using graph)
6Y - Intercept (Problems)
7Slope - I
8Slope - II
9Proof for Slope (X - axis and Y - axis)
10Writting Equations in Y - intercept Form
11Solve the Equations Using Graphs - I
12Solve the Equations Using Graphs - II
13Graphs for the Staright Lines y = 0 and x = 0
14Graphs for Constant Coordinates
15Plotting of Points
16Find the Value of x - II
17Solution Set - I
18Solution Set - II
19Solving Equations - Elimination Method 1
20Solving Equations - Elimination Method II
21Solving Equations - Substitution Method I
22Solving Equations - Substitution Method II
23Dependent Equations
24Inconsistent Equations
25Solving Equations - V
27Linear Equations Review Test

Topic 2. Linear Inequations

1True Statement
2Graph for y x + 3
3Graph for y > 5
4Graph for x > 2
5Graph for y -2
6Graph for x 3
7Solving Inequations - VI
8Solving Inequations - V
9Solving Inequations - IV
10Solving Inequations - III
11Solving Inequations - I
12Solving Inequations - II
13Representing Inequations on Number Line - II
14Representing Inequations on Number Line - I
15Graph for y < 2x+1
16Linear Inequalities: Solutions Using Graphing
17Inequation Review Test

Topic 3. Factorization

1Important Formulas
2Factorization: a3 - b3
3Factorization: c(a3 + b3)
4Factorization: a3 + b3
5Factorization: (a-b)3
6Factorization: (a+b)3
7Factorization: Completing the Square
8Factorization: (2a+b)2 - c2
9Factorization: a2 - b2
10Factorization: (a-b)2
11Factorization: (a+b)2 with Binomial Factors
12Factorization: c(a+b)2
13Factorization: (a+b)2
14Factorization Review Test

Topic 4. Quadratic Equations

1Quadratic Equations - I
2Quadratic Equations - II
3Factorization of any Quadratic Polynomial - I
4Factorization of any Quadratic Polynomial - II
5Factoring Quadratics with One Variable
6Factoring Quadratic Equations with Two Variables
7Quadratic Equations Review Test

Topic 5. Straight Lines

1Basic Geometrical Concepts - Points and Lines
2Basic Geometrical Concepts - Parallel Lines, Collinear Points and Plane
3Basic Geometrical Concepts - Coplanar Points, Coplanar Lines, Concurrent Lines and Space
4Parallel Rays
5Parallel Lines and Transversal
6Parallel Lines - Interior Angles are Supplementary - II
7Parallel Lines - Corresponding Angles
8Parallel Lines - Interior Angles are Supplementary - I
9Parallel Lines - Corresponding and Alternative Angles
10Theorem: Distinct Lines
11Stages in The Structure of a Theorem
12Important Points

Topic 6. Triangles And Polygons

1Problems on Interior Angles of a Regular Polygon - II
2Theorem - 12
3Problems on Exterior Angles of a Regular Polygon - II
4Problems on Interior and Exterior Angles of a Regular Polygon
5Congruent Triangles
6Properties of Parallelogram (Geometrical Proof)
7Theorem 9 - Isosceles Triangles (Angles)
8Theorem 10 - Isosceles Triangles (Sides)
9Problems on Triangles - IV
10Problems on Exterior Angles of a Regular Polygon - I
11Problems on Interior Angles of a Regular Polygon - I
12Triangle Theorem - 13
The Sum of Any Two Sides of a Triangle is Greater Than The Third Side
13Theorem: Triangle Sum Theorem
14Find the Angles of Triangle
15Theorem: Exterior Angle Theorem of a Triangle
16Problems on Triangles
17Theorem: Sum of the Exterior Angles of a Convex Polygon
18Theorem: Sum of the Interior Angles of a Convex Polygon
19Sum of the Interior Angles of a Polygon
20Triangle Theorem 11
Angle Opposite Longer Side is Greater Than Angle Opposite Shorter Side
21Theorem - 14 (Perpendicular Theorem)
22Triangles And Polygons Review
23Triangles and Polygons Review Test

Topic 7. Circles and Concurrent Lines in Triangles

1Theorem 15
Perpendicular Bisector of a Chord of Circle
2Construction - 4 (Incircle)
3Construction - 5 (Excircle)
4Construction - 6
Collinearity of G, S, O, I in an Isosceles Triangle
5Construction - 7
Coincidence of G, S, O, I in an Equilateral Triangle
6Construction - 8
Construction of a Triangle When Two sides and Median are given
7Construction - 9
Construct a Triangle When One side and Two Medians are given
8Construction - 10
Construct a Triangle When The Medians are Given
9Circles and Concurrent Lines in Triangles Review Test
10Theorem 23 - Angle Bisectors of a Triangle
11Construction - 3 (Orthocenter)
12Theorem 22
Altitudes of a Triangle
13Theorem 16
Diameter Which is Perpendicular to a Chord of a Circle
14Theorem 17
One and only One Circle Through Three non Colliner Points
15Theorem 18
Two Chords are equal in a Circle
16Theorem 19
Two Chords of a Circle are Equidistant
17Theorem 20
Medians of a Triangle
18Construction - I (Triangle)
19Theorem 21: Perpendicular Bisector
20Construction 2 - (Circumcircle)
21Circles and Concurrent Lines in Triangles - Review

Topic 8. Symmetry

1Line Symmetry
2Point Symmetry
3Symmetry Important Points
4Symmetry Review - I
5Symmetry Review - II
6Finding the Image of a Point or Line Segment

Topic 9. Statistics

1Introduction to Statistics
2Range of a Data
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)
25Box and Whisker Plots
26Measure of Variation: Standard Deviation and Variance
27Standard Deviation - Ungrouped Data
28Normal or Gaussian Distributions
29Normal and Skewed Distributions
30Exponential Distributions
31Binomial Distributions

Topic 10. Review Tests

1Final Review Test