Module 1: Quadratic Equations in One Variable
Core Concept: Extending from linear to quadratic equations, mastering the solutions for the general form
ax² + bx + c = 0.Key Content:
Definition and standard form of a quadratic equation.
Solving by Factoring (using methods from Grade 8).
Solving by Completing the Square.
Deriving and applying the Quadratic Formula.
Understanding the Discriminant (Δ = b² – 4ac) and its role in determining the nature of roots (real/distinct, real/equal, no real roots).
Applications: word problems involving area, growth, and projectile motion.
Module 2: Introduction to Quadratic Functions
Core Concept: Transitioning from linear to non-linear relationships, understanding the parabola as the graph of
y = ax² + bx + c.Key Content:
Definition of a quadratic function. Graph: the parabola.
Key features: Vertex, Axis of Symmetry, Direction of Opening (up/down based on
a), y-intercept, x-intercepts (roots).Standard Form (
y = a(x - h)² + k) and Vertex identification.Connecting roots of quadratic equations to x-intercepts of the function.
Simple transformations: vertical/horizontal shifts, stretching/compressing.
Module 3: Deep Dive into Quadratic Functions & Modeling
Core Concept: Analyzing and applying quadratic functions to model real-world phenomena and solve optimization problems.
Key Content:
Finding maximum/minimum values (vertex) in applied contexts (e.g., maximum profit, minimum cost, maximum height).
Graphical solutions to quadratic inequalities.
Systems involving linear and quadratic equations (graphical and algebraic solutions).
Project-based learning: modeling a real scenario with a quadratic function (e.g., trajectory of a ball, arch of a bridge).
Module 4: Geometric Transformations: Rotation
Core Concept: Understanding rotation as a rigid transformation and its properties.
Key Content:
Definition of rotation: center, angle, and direction.
Properties of rotated figures: corresponding segments and angles are equal; figures are congruent.
Rotating points and simple shapes on the coordinate plane.
Identifying rotational symmetry in figures.
Concept of a Center of Rotation.
Module 5: The Geometry of the Circle (Part 1)
Core Concept: Exploring the fundamental elements and properties of the circle.
Key Content:
Basic terminology: radius, diameter, chord, arc (minor/major), sector, segment.
Relationships among chords, arcs, and central angles.
Theorem: The perpendicular from the center to a chord bisects the chord and its arc.
Inscribed angles and their measure theorem (
∠ = ½ * intercepted arc).Angles formed by chords, secants, and tangents within and outside a circle.
Module 6: The Geometry of the Circle (Part 2) & Synthesis
Core Concept: Investigating lines relative to circles and solving complex geometric problems involving circles.
Key Content:
Tangents to a circle: definition, property (radius ⟂ tangent at point of contact), length of tangents from an external point.
Cyclic quadrilaterals and their property (opposite angles are supplementary).
Circumference and area formulas (review and application).
Comprehensive problem-solving: integrating circle theorems with triangle properties (e.g., isosceles triangles formed by radii).
Module 7: Introduction to Probability
Core Concept: Moving from descriptive statistics to predictive likelihood.
Key Content:
Review of basic probability (concepts from earlier grades).
Classical probability:
P(A) = (Favorable Outcomes) / (Total Possible Outcomes).Calculating probabilities involving simple and compound events.
Using tree diagrams and two-way tables to list outcomes.
Experimental vs. theoretical probability.
Module 8: Proportionality and Similarity
Core Concept: Extending the idea of congruence to shapes that have the same form but different size (scale).
Key Content:
Ratios and proportions (review and extension).
Definition of similar polygons: corresponding angles equal, corresponding sides proportional.
Similarity Theorems for Triangles: AA (Angle-Angle), SAS (Side-Angle-Side), SSS (Side-Side-Side).
Properties of similar triangles: ratio of perimeters, areas (
area ratio = (scale factor)²).Applications: indirect measurement (e.g., finding heights using shadows).
Module 9: Inverse Proportion and Its Function
Core Concept: Modeling relationships where one quantity increases as another decreases, represented by
xy = k.Key Content:
The concept of inverse variation.
The inverse proportional function:
y = k/x (k ≠ 0).Graph of the inverse proportional function: the hyperbola, its branches and asymptotes.
Properties: no graph at x=0, symmetry.
Real-world applications (e.g., speed vs. time for a fixed distance, number of workers vs. time to complete a job).
Module 10: Right Triangle Trigonometry
Core Concept: Defining the trigonometric ratios as functions of an acute angle in a right triangle, linking angles to side ratios.
Key Content:
Sine (sin), Cosine (cos), Tangent (tan) as ratios of sides in a right triangle: SOH-CAH-TOA.
Using a calculator to find trigonometric values and angles.
Solving right triangles: finding missing sides and angles.
Simple applications: angle of elevation/depression problems.
Module 11: Projections, Views, and Spatial Reasoning
Core Concept: Developing 3D visualization skills by interpreting and creating 2D representations of 3D objects.
Key Content:
Parallel projection and central projection concepts.
The Three Standard Views: front, top, and side views of simple solids (cubes, prisms, cylinders, cones).
Interpreting and constructing simple three-view drawings.
Relating 2D views to 3D models. This module bridges geometry to technical drawing and design.
Module 12: Year-End Grand Synthesis and Capstone Project
Core Concept: Integrating algebraic, geometric, and functional knowledge to solve complex, multi-step problems.
Key Content:
Cross-topic review and advanced problem-solving sessions.
Problems combining algebra (quadratic equations/functions) and geometry (circle theorems, similarity, trigonometry).
Capstone Project Example: Design a Sustainable Garden Plot
Use a quadratic function to model an optimal parabolic sprinkler range.
Apply circle geometry to design circular planting beds.
Use trigonometry to calculate the angle of sunlight.
Use similarity to create a scale drawing (projection/view).
Preview of key concepts in senior high school mathematics (e.g., functions in greater depth, coordinate geometry, introductory calculus concepts).
Instructional Strategy & Assessment:
Spiral Synthesis: Concepts like functions evolve from linear (Gr.8) to quadratic and inverse (Gr.9). Geometry proofs integrate triangle, quadrilateral, and circle knowledge.
Modeling Focus: Heavy emphasis on translating real-world situations into quadratic, inverse, or trigonometric models.
Assessment: Balanced between procedural fluency (solving equations, applying theorems) and conceptual understanding/modeling (projects, open-ended problems). The final module project serves as a key performance task.
