AIM Academics & AIM4A Tutoring/Test Prep

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

Topic 1. Linear Equations

#ChapterDateNotes
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
   
                                  
26Quadrants
   
                                  
27Linear Equations Review Test
   
                                  

Topic 2. Linear Inequations

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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

#ChapterDateNotes
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
   
                                  
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
   
                                  
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

#ChapterDateNotes
1Final Review Test