{ "meta": { "title": "HK EDB Junior Secondary Mathematics — S1-S3 Learning Objectives", "grades": ["S1", "S2", "S3"], "language": "bilingual", "version": "2024" }, "strands": [ { "id": "NA", "name_en": "Number and Algebra", "name_zh": "數與代數", "objectives": [ { "code": "MATH.S1.INT.BASIC", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Integers", "name_en": "Integers and Basic Operations", "name_zh": "整數與基本運算", "description_en": "Understand integers, their ordering on the number line, and perform addition, subtraction, multiplication and division of integers including negative numbers.", "description_zh": "理解整數及其在數線上的排列，能對整數（包括負數）進行加、減、乘、除運算。", "difficulty_range": [1, 2] }, { "code": "MATH.S1.FRACTION.BASIC", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Fractions", "name_en": "Fractions — Concepts and Equivalence", "name_zh": "分數概念與等值分數", "description_en": "Understand proper/improper fractions and mixed numbers. Simplify fractions and find equivalent fractions.", "description_zh": "理解真分數、假分數及帶分數的概念，能化簡分數及求等值分數。", "difficulty_range": [1, 2] }, { "code": "MATH.S1.FRACTION.ADD", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Fractions", "name_en": "Addition and Subtraction of Fractions", "name_zh": "分數的加法與減法", "description_en": "Add and subtract fractions and mixed numbers with unlike denominators using LCM.", "description_zh": "能利用最小公倍數對不同分母的分數及帶分數進行加減運算。", "difficulty_range": [2, 3] }, { "code": "MATH.S1.FRACTION.MULT", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Fractions", "name_en": "Multiplication and Division of Fractions", "name_zh": "分數的乘法與除法", "description_en": "Multiply and divide fractions and mixed numbers; understand the reciprocal concept.", "description_zh": "能對分數及帶分數進行乘除運算，理解倒數概念。", "difficulty_range": [2, 3] }, { "code": "MATH.S1.DECIMAL.OPS", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Decimals", "name_en": "Operations on Decimals", "name_zh": "小數的運算", "description_en": "Perform addition, subtraction, multiplication and division of decimals; convert between fractions and decimals.", "description_zh": "能對小數進行加減乘除運算，並能在分數與小數之間互相換算。", "difficulty_range": [1, 3] }, { "code": "MATH.S1.PERCENT.BASIC", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Percentages", "name_en": "Percentages — Concepts and Applications", "name_zh": "百分數概念與應用", "description_en": "Convert between percentages, fractions, and decimals. Solve problems involving percentage change, profit, loss, and discount.", "description_zh": "能在百分數、分數及小數之間互換。解決涉及百分比變化、利潤、虧損及折扣的問題。", "difficulty_range": [2, 4] }, { "code": "MATH.S1.RATIO.BASIC", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Ratio and Rate", "name_en": "Ratio and Rate", "name_zh": "比率與速率", "description_en": "Understand ratio and rate. Simplify ratios, divide quantities in a given ratio, and solve speed/distance/time problems.", "description_zh": "理解比率與速率的概念，能化簡比率、按比例分配數量，並解決速度/距離/時間問題。", "difficulty_range": [2, 4] }, { "code": "MATH.S1.ALGEBRA.INTRO", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Introduction to Algebra", "name_en": "Introduction to Algebra", "name_zh": "代數入門", "description_en": "Use letters to represent unknowns. Write, read, and simplify algebraic expressions. Evaluate expressions by substitution.", "description_zh": "能以字母代表未知數，撰寫、閱讀及化簡代數式，並以代入法求代數式的值。", "difficulty_range": [1, 3] }, { "code": "MATH.S1.ALGEBRA.EQUATION1", "grade": "S1", "topic": "Number and Algebra", "subtopic": "Linear Equations", "name_en": "Linear Equations in One Unknown", "name_zh": "一元一次方程", "description_en": "Solve linear equations in one unknown using inverse operations. Formulate and solve equations from word problems.", "description_zh": "能用逆運算解一元一次方程，並能從文字題中建立及求解方程。", "difficulty_range": [2, 4] }, { "code": "MATH.S2.ALGEBRA.POLY", "grade": "S2", "topic": "Number and Algebra", "subtopic": "Polynomials", "name_en": "Polynomials — Expansion and Factorisation", "name_zh": "多項式的展開與因式分解", "description_en": "Expand products of polynomials, factorise using common factors and identities (difference of squares, perfect squares).", "description_zh": "能展開多項式的乘積，以公因式及恆等式（平方差、完全平方式）進行因式分解。", "difficulty_range": [2, 5] }, { "code": "MATH.S2.ALGEBRA.EQUATION2", "grade": "S2", "topic": "Number and Algebra", "subtopic": "Linear Equations", "name_en": "Simultaneous Linear Equations", "name_zh": "聯立一次方程", "description_en": "Solve simultaneous linear equations in two unknowns by substitution and elimination. Apply to real-world problems.", "description_zh": "能以代入法及消元法解二元一次聯立方程，並應用於實際問題。", "difficulty_range": [3, 5] }, { "code": "MATH.S2.INEQUAL.BASIC", "grade": "S2", "topic": "Number and Algebra", "subtopic": "Inequalities", "name_en": "Linear Inequalities in One Unknown", "name_zh": "一元一次不等式", "description_en": "Understand inequality symbols. Solve linear inequalities in one unknown and represent solutions on a number line.", "description_zh": "理解不等號，解一元一次不等式，並在數線上表示解集。", "difficulty_range": [2, 4] }, { "code": "MATH.S3.NUMBER.RATIONAL", "grade": "S3", "topic": "Number and Algebra", "subtopic": "Rational and Irrational Numbers", "name_en": "Rational and Irrational Numbers", "name_zh": "有理數與無理數", "description_en": "Distinguish between rational and irrational numbers. Understand surds; simplify and operate on surds. Approximate irrational numbers using a calculator.", "description_zh": "區分有理數與無理數，理解根式，能化簡及運算根式，並用計算器近似無理數。", "difficulty_range": [2, 4] }, { "code": "MATH.S3.ALGEBRA.QUADRATIC", "grade": "S3", "topic": "Number and Algebra", "subtopic": "Quadratic Equations", "name_en": "Quadratic Equations in One Unknown", "name_zh": "一元二次方程", "description_en": "Solve quadratic equations by factorisation, completing the square, and the quadratic formula. Determine the nature of roots using the discriminant. Formulate equations from word problems.", "description_zh": "以因式分解、配方法及求根公式解一元二次方程，利用判別式判斷根的性質，並由文字題建立方程。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.ALGEBRA.FUNCTIONS", "grade": "S3", "topic": "Number and Algebra", "subtopic": "Functions and Graphs", "name_en": "Functions and their Graphs", "name_zh": "函數及其圖形", "description_en": "Understand the concept of a function, domain, co-domain, and range. Sketch graphs of linear and quadratic functions; identify key features (vertex, axis of symmetry, intercepts).", "description_zh": "理解函數的概念，包括定義域、值域。繪製一次及二次函數的圖形，識別頂點、對稱軸及截距等特徵。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.ALGEBRA.FRACTIONS", "grade": "S3", "topic": "Number and Algebra", "subtopic": "Algebraic Fractions", "name_en": "Algebraic Fractions and Equations", "name_zh": "代數分式與方程", "description_en": "Simplify algebraic fractions. Add, subtract, multiply, and divide algebraic fractions. Solve fractional equations and check for extraneous solutions.", "description_zh": "化簡代數分式，對代數分式進行加減乘除，解分式方程並檢驗外來根。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.PERCENT.ADVANCED", "grade": "S3", "topic": "Number and Algebra", "subtopic": "Percentages", "name_en": "Compound Interest and Financial Mathematics", "name_zh": "複利息與金融數學", "description_en": "Apply compound interest formula A = P(1 + r)^n. Solve problems involving hire purchase, taxation, and foreign exchange.", "description_zh": "應用複利息公式 A = P(1 + r)^n，解決分期付款、稅務及外幣兌換等問題。", "difficulty_range": [3, 5] } ] }, { "id": "MG", "name_en": "Measures, Shape and Space", "name_zh": "度量、圖形與空間", "objectives": [ { "code": "MATH.S1.MEASURE.PERIMETER", "grade": "S1", "topic": "Measures, Shape and Space", "subtopic": "Perimeter and Area", "name_en": "Perimeter and Area of Plane Figures", "name_zh": "平面圖形的周界與面積", "description_en": "Find perimeter and area of triangles, quadrilaterals, and composite figures. Use appropriate units.", "description_zh": "能求三角形、四邊形及複合圖形的周界與面積，並使用適當的單位。", "difficulty_range": [1, 3] }, { "code": "MATH.S1.MEASURE.CIRCLE", "grade": "S1", "topic": "Measures, Shape and Space", "subtopic": "Circles", "name_en": "Circumference and Area of a Circle", "name_zh": "圓的周長與面積", "description_en": "Understand pi. Calculate circumference and area of circles and sectors. Solve problems involving circular shapes.", "description_zh": "理解圓周率π，計算圓和扇形的周長與面積，解決涉及圓形的問題。", "difficulty_range": [2, 3] }, { "code": "MATH.S1.GEOM.ANGLES", "grade": "S1", "topic": "Measures, Shape and Space", "subtopic": "Angles and Lines", "name_en": "Angles and Parallel Lines", "name_zh": "角與平行線", "description_en": "Identify types of angles. Understand properties of parallel lines: corresponding, alternate, and co-interior angles.", "description_zh": "識別各種角的類型，理解平行線的性質：同位角、交錯角及同旁內角。", "difficulty_range": [2, 3] }, { "code": "MATH.S1.GEOM.TRIANGLE", "grade": "S1", "topic": "Measures, Shape and Space", "subtopic": "Triangles", "name_en": "Properties of Triangles", "name_zh": "三角形的性質", "description_en": "Identify types of triangles. Apply angle sum and exterior angle theorem. Understand congruence and similarity criteria.", "description_zh": "識別各類三角形，應用角和定理及外角定理，理解全等與相似的判別條件。", "difficulty_range": [2, 4] }, { "code": "MATH.S2.GEOM.QUADRILATERAL", "grade": "S2", "topic": "Measures, Shape and Space", "subtopic": "Quadrilaterals", "name_en": "Properties of Quadrilaterals", "name_zh": "四邊形的性質", "description_en": "Identify and apply properties of parallelograms, rectangles, rhombuses, squares, and trapezoids.", "description_zh": "識別並應用平行四邊形、長方形、菱形、正方形及梯形的性質。", "difficulty_range": [2, 4] }, { "code": "MATH.S2.GEOM.3D", "grade": "S2", "topic": "Measures, Shape and Space", "subtopic": "3D Figures", "name_en": "Volume and Surface Area of 3D Figures", "name_zh": "立體圖形的體積與表面積", "description_en": "Calculate volume and surface area of prisms, cylinders, pyramids, cones, and spheres.", "description_zh": "計算棱柱、圓柱、棱錐、圓錐及球的體積與表面積。", "difficulty_range": [3, 5] }, { "code": "MATH.S2.COORD.BASIC", "grade": "S2", "topic": "Measures, Shape and Space", "subtopic": "Coordinate Geometry", "name_en": "Introduction to Coordinate Geometry", "name_zh": "坐標幾何入門", "description_en": "Plot points in the Cartesian plane. Find distance and midpoint between two points. Understand slope of a line.", "description_zh": "在笛卡兒坐標平面上描點，求兩點間的距離與中點，理解直線的斜率。", "difficulty_range": [2, 4] }, { "code": "MATH.S3.GEOM.PYTHAGORAS", "grade": "S3", "topic": "Measures, Shape and Space", "subtopic": "Pythagoras' Theorem", "name_en": "Pythagoras' Theorem", "name_zh": "畢氏定理", "description_en": "Understand and apply Pythagoras' theorem to find unknown sides in right-angled triangles. Identify Pythagorean triples. Apply to 2D and 3D problems.", "description_zh": "理解並應用畢氏定理求直角三角形的未知邊長，識別畢氏數，應用於二維及三維問題。", "difficulty_range": [2, 4] }, { "code": "MATH.S3.TRIG.BASIC", "grade": "S3", "topic": "Measures, Shape and Space", "subtopic": "Trigonometry", "name_en": "Trigonometric Ratios", "name_zh": "三角比", "description_en": "Define sine, cosine, and tangent (SOH-CAH-TOA). Find trigonometric ratios for special angles (30°, 45°, 60°). Solve right-angled triangle problems using trig ratios.", "description_zh": "定義正弦、餘弦和正切（SOH-CAH-TOA），求特殊角（30°、45°、60°）的三角比，用三角比解直角三角形問題。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.TRIG.APPLICATIONS", "grade": "S3", "topic": "Measures, Shape and Space", "subtopic": "Trigonometry", "name_en": "Applications of Trigonometry", "name_zh": "三角學的應用", "description_en": "Apply trigonometry to solve problems involving angles of elevation and depression. Solve bearings and 3D trigonometry problems.", "description_zh": "應用三角學解仰角與俯角的問題，解方位角及三維三角學問題。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.GEOM.CIRCLES", "grade": "S3", "topic": "Measures, Shape and Space", "subtopic": "Circles", "name_en": "Properties of Circles", "name_zh": "圓的性質", "description_en": "Apply circle theorems: angle at centre, angle in semicircle, angles in the same segment, cyclic quadrilaterals. Understand tangent properties.", "description_zh": "應用圓的定理：圓心角、半圓上的圓周角、同弓形上的圓周角、圓內接四邊形，理解切線的性質。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.COORD.LINES", "grade": "S3", "topic": "Measures, Shape and Space", "subtopic": "Coordinate Geometry", "name_en": "Equations of Straight Lines", "name_zh": "直線方程", "description_en": "Write equations of straight lines in slope-intercept (y = mx + c) and general form. Find intersections of lines. Understand parallel and perpendicular line conditions.", "description_zh": "以斜截式（y = mx + c）及一般式表達直線方程，求直線的交點，理解平行線及垂直線的條件。", "difficulty_range": [3, 5] } ] }, { "id": "DS", "name_en": "Data Handling", "name_zh": "數據處理", "objectives": [ { "code": "MATH.S1.DATA.BASIC", "grade": "S1", "topic": "Data Handling", "subtopic": "Statistical Diagrams", "name_en": "Statistical Diagrams and Tables", "name_zh": "統計圖表", "description_en": "Construct and interpret bar charts, pie charts, broken-line graphs, and frequency tables.", "description_zh": "能繪製及詮釋棒形圖、餅圖、折線圖及頻數分佈表。", "difficulty_range": [1, 3] }, { "code": "MATH.S1.DATA.AVERAGE", "grade": "S1", "topic": "Data Handling", "subtopic": "Averages", "name_en": "Measures of Central Tendency", "name_zh": "集中趨勢的量度", "description_en": "Calculate and interpret mean, median, and mode. Understand when each measure is appropriate.", "description_zh": "計算及詮釋平均數、中位數和眾數，並理解各量度的適用情況。", "difficulty_range": [1, 3] }, { "code": "MATH.S2.PROB.BASIC", "grade": "S2", "topic": "Data Handling", "subtopic": "Probability", "name_en": "Introduction to Probability", "name_zh": "概率入門", "description_en": "Understand probability as a measure of likelihood (0 to 1). List sample spaces, calculate simple and complementary probabilities.", "description_zh": "理解概率作為可能性的量度（0至1），列出樣本空間，計算簡單及互補概率。", "difficulty_range": [2, 4] }, { "code": "MATH.S3.DATA.DISPERSION", "grade": "S3", "topic": "Data Handling", "subtopic": "Measures of Dispersion", "name_en": "Measures of Dispersion", "name_zh": "離差的量度", "description_en": "Calculate range, inter-quartile range, and standard deviation. Interpret and compare variability of data sets using box-and-whisker plots.", "description_zh": "計算全距、四分位距及標準差，用箱線圖詮釋及比較數據集的分散程度。", "difficulty_range": [3, 5] }, { "code": "MATH.S3.PROB.ADVANCED", "grade": "S3", "topic": "Data Handling", "subtopic": "Probability", "name_en": "Advanced Probability", "name_zh": "進階概率", "description_en": "Calculate probabilities of mutually exclusive and independent events using addition and multiplication laws. Understand conditional probability. Use tree diagrams and tables.", "description_zh": "用加法和乘法定律計算互斥及獨立事件的概率，理解條件概率，運用樹形圖及列表法。", "difficulty_range": [3, 5] } ] } ], "demo_questions": [ { "id": "demo-q1", "stem_en": "Evaluate: \\( \\frac{3}{4} + \\frac{5}{6} \\)", "stem_zh": "計算：\\( \\frac{3}{4} + \\frac{5}{6} \\)", "option_a_en": "\\( \\frac{8}{10} \\)", "option_b_en": "\\( \\frac{8}{12} \\)", "option_c_en": "\\( 1\\frac{7}{12} \\)", "option_d_en": "\\( \\frac{19}{24} \\)", "option_a_zh": "\\( \\frac{8}{10} \\)", "option_b_zh": "\\( \\frac{8}{12} \\)", "option_c_zh": "\\( 1\\frac{7}{12} \\)", "option_d_zh": "\\( \\frac{19}{24} \\)", "answer": "C", "question_type": "MCQ", "difficulty_estimate": 2, "linked_objectives": ["MATH.S1.FRACTION.ADD"], "grade": "S1", "topic": "Number and Algebra", "subtopic": "Fractions" }, { "id": "demo-q2", "stem_en": "Solve for x: \\( 3x - 7 = 14 \\)", "stem_zh": "求 x 的值：\\( 3x - 7 = 14 \\)", "answer": "x = 7", "question_type": "FILL_IN", "difficulty_estimate": 2, "linked_objectives": ["MATH.S1.ALGEBRA.EQUATION1"], "grade": "S1", "topic": "Number and Algebra", "subtopic": "Linear Equations" }, { "id": "demo-q3", "stem_en": "The radius of a circle is 5 cm. Find its area. (Take π = 3.14)", "stem_zh": "一個圓的半徑為5厘米。求其面積。（取π = 3.14）", "answer": "78.5 cm²", "question_type": "OPEN_ENDED", "difficulty_estimate": 2, "linked_objectives": ["MATH.S1.MEASURE.CIRCLE"], "grade": "S1", "topic": "Measures, Shape and Space", "subtopic": "Circles" } ] }