【People's Education Press】Junior High School Mathematics Grade 8, Lower Term

This course covers the core content of the eighth-grade lower secondary mathematics curriculum, focusing on quadratic radicals, the Pythagorean theorem, parallelograms, linear functions, and data analysis. Through theoretical exploration and mathematical activities, it aims to develop students’ logical reasoning and problem-solving abilities.

Deepen mathematical thinking, master the core mysteries of algebra and geometry.

Author: Middle School Mathematics Curriculum Research and Development Center, Curriculum and Textbook Research Institute, People's Education Press

Acknowledgments: This book is developed according to the "Compulsory Education Mathematics Curriculum Standards (2011 Edition)" issued by the Ministry of Education.

1. Understand and apply the multiplication rule for quadratic radicals (\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}) and division rule (\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}) for computation and simplification.
2. Identify and simplify radicands into "simplest quadratic radicals," mastering two core criteria for simplification.
3. Master the addition and subtraction rules for quadratic radicals, able to combine like radicals by analogy with combining like terms in polynomial operations.
4. Understand and master multiple proof methods of the Pythagorean theorem (e.g., Zhao Shuang’s string diagram), and apply the theorem to represent irrational numbers on the number line.
5. Understand the concepts of original and converse propositions, and be able to prove and apply the converse of the Pythagorean theorem to determine right triangles.
6. Gain preliminary understanding of the derivation and application of Heron-Qin Jiushao’s formula, and have basic awareness of mathematical history such as Fermat’s Last Theorem.
7. Understand and master the properties (sides, angles, diagonals) and determination theorems of parallelograms, rhombuses, and squares.
8. Grasp the concept of distance between two parallel lines and its application in geometric proofs.
9. Master the properties of the midline of a triangle and apply them to solve problems involving position and length relationships of segments.
10. Master the graphical method: Accurately draw function graphs using the plotting method (listing, plotting points, connecting lines), and extract information from the graph.