STEM QUIZ

1. Number Systems

• Real Numbers: The collection of all rational numbers (terminating or repeating decimals) and irrational numbers (non-terminating, non-repeating).
• Classification: Decimal expansions are used to distinguish between rational and irrational numbers.

2. Introduction to Euclid’s Geometry

• Fundamentals: Defines basic entities like points (0D), lines (1D), and surfaces (2D).
• Principles: Distinguishes between axioms (general truths) and postulates (geometric assumptions), including rules about parallel lines and right angles.

3. Coordinate Geometry

• The Cartesian Plane: Uses perpendicular axes (x and y) to divide the plane into four quadrants.
• Location: Points are located using coordinates: abscissa (x-distance) and ordinate (y-distance), originating from the intersection point (0,0).

4. Linear Equations in Two Variables

• Characteristics: These equations have infinitely many solutions, and their graphical representation always forms a straight line.

5. Lines, Angles, and Triangles

• Angle Relations: Linear pairs sum to 180°, and vertically opposite angles are equal.
• Triangle Properties: The interior angles sum to 180°. Congruence is established using specific criteria (SAS, ASA, SSS, RHS), implying that corresponding parts (CPCT) are equal.

6. Quadrilaterals

• Parallelograms: Opposite sides and angles are equal, and diagonals bisect each other.
• Mid-Point Theorem: A line segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.

7. Circles

• Key Properties: Equal chords are equidistant from the center. Angles in the same segment are equal, and the angle at the center is double the angle at the circumference.
• Cyclic Quadrilaterals: A four-sided figure with vertices on a circle, where opposite angles sum to 180°.

8. Mensuration

• Area: Using Heron’s formula to find the area of a triangle given its three sides.
• Solids: Calculating surface area and volume for right circular cones, spheres, and hemispheres.