SAT Math (Synthetic and Analytic Geometry)

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SAT Math (Synthetic and Analytic Geometry)

SAT Score Range

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11 sessions

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About

Geometry, both in its synthetic and analytic flavors, contains some of the easiest and yet most of the hardest parts of the test. 
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In this series, we will learn about a plethora of common and uncommon laws on geometry and trigonometry. Note that analytic geometry also contains a good bit of algebra to work with points and curves in the cartesian plane.
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 Due to the nature of the material, I recommend this course for both beginner and intermediate learners (About 200-700). I have also divided this course into a basic and advanced variant.  The course will also be adaptive; I will adjust the material as needed from the initial pre-test and learners' input.

Tutored by

Nathanael Dean J 🇮🇩

Certified in 5 topics

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Greetings, I am a senior high school student in Indonesia. I hope I can help you with your SAT prep and help myself develop communication skills. I love to write lyrics and play shoot-em-ups.

Sessions

Upcoming

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✋ ATTENDANCE POLICY

Your attendance policy will depend on your score for the pre-test.

If your pre-test score is less than 70% and your last score for SAT math is less than 500 (if you have one), please attend every session labeled "basic". Failure to do so without sufficient reason given at most a day before the session will result in your discontinuance. You may take the advanced sessions, but I will assume you have understood the materials of the basic sessions as written on the prerequisites of the session.

Otherwise, basic sessions are optional, but I highly advise you to join them if you feel that you are not fully cognizant of the material. For the advanced sessions, all of them are mandatory. You must give your reason a day before the session at the latest. Again, if you fail to do so, you will be withdrawn.

Finally, the enrichment session is there for learners who want to learn uncommon theorems for the SAT. These theorems and concepts are rare, but they might unexpectedly appear, especially in module 2. Attendance is optional, but highly encouraged for those who want to break 700.

SESSION 1

11

Oct

SESSION 1

SAT Math

Sat 9:45 AM - 11:15 AM UTCOct 11, 9:45 AM - 11:15 AM UTC

Introductions and the Pre-Test. 
The pre-test will include the following : 
1. Synthetic Geometry
- Similarity and congruency
- Basic trigonometry
- The pythagorean theorem
- Solid geometry
- Area, perimeter and volume
- Circles and polygons
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2. Analytic Geometry
- Lines, quadratics (parabolae), and circles
- Midpoint and distance
- Area in coordinate systems.
- Deductive graph reading (multiple choice)
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Preparation for the Pre-Test is optional.

SESSION 2

12

Oct

SESSION 2

SAT Math

Sun 6:45 AM - 8:15 AM UTCOct 12, 6:45 AM - 8:15 AM UTC

Synthetic Geometry (Basic)
1. Similarity and congruency
- Concept of similarity
- Corresponding angles and sides
2. Angles
- Common theorems about angles
-Angles on paralel lines
3. Trigonometry
- Introduction  to sin, cos, and tan
-Reflexive identities
-Pythagorean Theorem

SESSION 3

12

Oct

SESSION 3

SAT Math

Sun 9:45 AM - 11:15 AM UTCOct 12, 9:45 AM - 11:15 AM UTC

Prerequisites : trigonometry and similarity
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Synthetic Geometry (Advanced)
1. Similarity and congruency
-Thales's intercept theorem
-Geometric Mean Theorem
2. Angles
- Angles in a polygon
-Angles on a cyclic quarilateral
-Angles on a circle
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SESSION 4

18

Oct

SESSION 4

SAT Math

Sat 6:45 AM - 8:15 AM UTCOct 18, 6:45 AM - 8:15 AM UTC

Synthetic Geometry (Basic)
1. Areas
- Similarity for areas
- Area of a triangle and rectangle
- Area of a trapezoid and a parallelogram
-Area of a kite.
-Area of a circle
2. Perimeter
- Perimeter of a triangle and quadrilaterals
- Perimeter of a circle

SESSION 5

18

Oct

SESSION 5

SAT Math

Sat 9:45 AM - 11:15 AM UTCOct 18, 9:45 AM - 11:15 AM UTC

Prerequisites : Basic area and Pythagoras in two dimensions
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Synthetic Geometry (Advanced)
1. Areas of the triangle 
-Heron's rule
-Area from sine
-Area from circumradius and inradius
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2. Solid geometry
- Distance in three dimensions
- Pythagorean theorem/Euclidean distance in three dimensions

SESSION 6

19

Oct

SESSION 6

SAT Math

Sun 6:45 AM - 8:15 AM UTCOct 19, 6:45 AM - 8:15 AM UTC

Synthetic Geometry (Basic)
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1. Volume
-Volume of prisms and pyramids
-Similarity for volume
-Volume of spheres
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2. Surface area
-Surface area of prisms and pyramids
-Surface area of a sphere
-Surface area of a cone

SESSION 7

19

Oct

SESSION 7

SAT Math

Sun 9:45 AM - 10:45 AM UTCOct 19, 9:45 AM - 10:45 AM UTC

Analytic geometry (Basic)
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1. Points and distances
- What is the Cartesian coordinate system?
- Euclidean distance
- Midpoint formula
2. Applications of synthetic geometry in coordinate systems.
3. How to read graphs in general
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SESSION 8

25

Oct

SESSION 8

SAT Math

Sat 6:45 AM - 8:15 AM UTCOct 25, 6:45 AM - 8:15 AM UTC

Analytic geometry (Basic)
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1. Lines
- Equation for a line 
- Gradient of a line
- A line through two points
- A line through one point with a known gradient
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2.Quadratics
- Equation for a quadratic
- Finding the root of a quadratic
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3. Circles
- General Form
- Radius

SESSION 9

25

Oct

SESSION 9

SAT Math

Sat 9:45 AM - 11:15 AM UTCOct 25, 9:45 AM - 11:15 AM UTC

Analytic geometry (Advanced)
Prerequisites : Basic notions of lines, quadratics, and circles
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1. Lines
- Systems of Two Variables
- Linear Programming
- Absolute value
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2. Quadratics
-Determinant
- Maxima and minima
- Vieta's theorem
-Vertex form
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3. Circles
- Tangent lines
- Power of a point

SESSION 10

26

Oct

SESSION 10

SAT Math

Sun 6:45 AM - 8:15 AM UTCOct 26, 6:45 AM - 8:15 AM UTC

Enrichment 
(This is an optional session for learners who want to learn rare concepts which may be needed in the SAT)
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It is highly advised that you have mastered the previous advanced sessions.
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- Intersection of quadratics
- Trigonometric Graphs
- Exponential Graphs
- Similarity on a trapezoid
- Asymptotics
- The annulus

SESSION 11

26

Oct

SESSION 11

SAT Math

Sun 9:45 AM - 11:15 AM UTCOct 26, 9:45 AM - 11:15 AM UTC

Post Test
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This test will be slightly harder than the pre test, but you will be soundly equipped for it from the sessions you have learned.
There will be two different versions depending on your level.

Public Discussion

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Oct 11 - Oct 26

3 weeks

60 - 90 mins

/ session

Next session on October 11, 2025

SCHEDULE

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9:45AM

Sundays

6:45AM

Sundays

9:45AM

Saturdays

6:45AM