Math 9a, 2023-24

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Room: HUM3015
Time: Sunday 9:15AM - 10:50AM
Grades: 9-10
Prerequisites: Math 8 or placement test
Material fee: $0.00

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Description: This is the tenth (10) year in the sequence of mathematical courses offered by SchoolNova. Math 9. Algebra: Mathematical induction and elements of mathematical logic. Elements of set theory. Infinite sets. Cardinality and dimensionality. Number sets. Functions. Algebraic equations and inequalities. Trigonometry. Complex numbers. Geometry: Advanced planimetry. Similarity. Point masses. Inscribed and circumscribed triangles and quadrilaterals. Method of coordinates. Curves of the second degree. Inversive geometry. Vectors and vector algebra. Approaching weekly homework is vital, and participating actively in class is crucial for progressing to the next level.

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Homeworks

These homeworks are copyrighted material, posted here for use by SchoolNova students and parents. Everyone else is welcome to print a copy of these materials for their personal use; any redistribution or commercial use is prohibited

• Assigned on 09/17: Algebra classwork: Baseline review  |  Geometry classwork: Baseline review  |  
  Solve the unsolved problems from the baseline review test and past years' placement tests.
  
• Assigned on 09/24: Algebra classwork: Elements of mathematical logic. Notations.  |  Geometry classwork: Commensurate segments. Euclidean algorithm.  |  Homework: Assignment for Oct 1  |  
  
• Assigned on 10/1: Algebra classwork: Mathematical logic. Predicates. Quantifiers.  |  Geometry classwork: Thales intercept theorem. Similarity.  |  Homework: Assignment for Oct. 15  |  
  
• Assigned on 10/15: Algebra classwork: Mathematical induction. Homework review.  |  Homework: Assignment for Oct 22  |  
  
• Assigned on 10/22: Algebra classwork: Mathematical induction (contd). Homework review.  |  Geometry classwork: Direct and inverse Ceva theorem. Homework review.  |  Homework: Assignment for Oct. 29  |  
  
• Assigned on 10/29: Algebra classwork: Arithmetic-Geometric mean inequality.  |  Geometry classwork: Similarity, homothety, central symmetry.  |  Homework: Assignment for Nov 5  |  
  
• Assigned on 11/5: Geometry classwork: The center of mass and method of mass points  |  Homework: Assignment for Nov 12  |  
  
• Assigned on 11/12: Algebra classwork: Recap: Elements of number theory.  |  Geometry classwork: The Inscribed Angle Theorem. Rowland circle.  |  Homework: Assignment for Nov 19  |  
  
• Assigned on 11/19: Algebra classwork: Euclid's algorithm and continued fractions  |  Geometry classwork: Point masses. Extended Ceva and Menelaus theorems  |  Homework: Assignment for Dec 3  |  
  
• Assigned on 12/3: Algebra classwork: Introduction to set theory  |  Geometry classwork: Mass points problems. Pappus theorem.  |  Homework: Assignment for Dec 10  |  
  
• Assigned on 12/10: Algebra classwork: Set counting: inclusion exclusion principle  |  Geometry classwork: Euclid's theorems. Euler's theorem.  |  Homework: Assignment for Dec 17  |  
  You do not need to solve problems on material not covered in class yet, eg Ptolemy's theorem.
  
• Assigned on 12/17: Geometry classwork: Ptolemy theorem. The nine point circle problem.  |  Homework: Assignment for January 7  |  
  
• Assigned on 01/7: Algebra classwork: Cartesian product of sets. Homework review.  |  Geometry classwork: Method of coordinates. Apollonius problem.  |  Homework: Assignment for Jan 14  |  
  Since we did not have time to consider new topics - please look through the problems and try solving where you can using your previous knowledge
  
• Assigned on 01/14: Algebra classwork: Maps. Functions. Injections, surjections, bijectio  |  Homework: Assignment for Jan 21  |  
  
• Assigned on 01/21: Algebra classwork: Equivalence relations on sets. Partitions.  |  Geometry classwork: Method of coordinates: curves of the second degree  |  Homework: Assignment for Jan 21  |  
  
• Assigned on 01/28: Algebra classwork: Comparing finite and infinite sets. Cardinality  |  Geometry classwork: Ellipse, hyperbola, parabola (contd)  |  Homework: Assignment for Feb 4  |  
  
• Assigned on 02/4: Algebra classwork: Number sets. Real numbers.  |  Geometry classwork: Optical properties of the curves of the 2nd degree  |  Homework: Assignment for Feb 11  |  
  
• Assigned on 02/11: Algebra classwork: Powers and roots. Homework review  |  Geometry classwork: Sine and cosine theorems. Trigonometry.  |  Homework: Assignment for Feb 25  |  
  
• Assigned on 02/25: Algebra classwork: Polynomials and factorization. Vieta theorem.  |  Geometry classwork: Trigonometric formulas and equations  |  Homework: Assignment for March 3  |  
  
• Assigned on 03/3: Algebra classwork: Functions and graphs. Exponent and Logarithm.  |  Geometry classwork: Trigonometry homework review.  |  Homework: Assignment for March 10  |  
  
• Assigned on 03/10: Algebra classwork: Trigonometric series. Homework review.  |  Geometry classwork: Vectors. Dot product.  |  Homework: Assignment for March 17  |  
  
• Assigned on 03/17: Algebra classwork: Complex numbers  |  Geometry classwork: Solving vector problems  |  Homework: Assignment for March 24  |  
  
• Assigned on 03/24: Algebra classwork: Complex numbers. de Moivre formula. n-th root  |  Homework: Assignment for Apr 7  |  
  
• Assigned on 04/7: Geometry classwork: Inversive Geometry (part 1)  |  Homework: Assignment for Apr 14  |  
  Solve problems 3-6 from the previous complex numbers homework. From the new homework on inversive geometry, solve problems 1-2. If you have time, try solving other problems, primarily complete the previous homeworks on complex numbers.
  
• Assigned on 04/14: Homework: Assignment for April 21  |  
  Continue studying the inversive geometry handout from April 7. Solve the unsolved problems from the last homework and try completing the problems in the present homework.
  
• Assigned on 04/21: Geometry classwork: Inversive Geometry (part 2)  |  Homework: Assignment for May 5  |