Senior Mathematical Challenge （SMC）高年级数学个人挑战赛是UKMT赛事体系中面向16-19岁的学生的竞赛，其中最好的一千名讲参加英国数学奥赛BMO，中间最优秀的学生将有机会代表英国参加国际奥林匹克竞赛的选拔体系。对应英国和威尔士小于13年级，北爱尔兰小于14年级以及苏格兰小于S6年级的学生。
SMC成绩最好的1000名左右的学生会被邀请参加BMO1，Senior Kangaroo（SK）高级袋鼠竞赛会邀请大约6000名学生。
学员须知
英国高级数学思维挑战活动（SMC）
活动语言：中英文
活动时间：每年11月
参与资格：12年级（高三年级）及以下学生
活动形式：笔试，25道单项选择题
评分标准：起始分数25分，答对得4分，答错扣1分
课程大纲
Number theory
TOPICS：
Divisor Problems of integers
*Remainder Problems of integers
Digit Problems *in different base representations
Divisibility Problems
Details：
Exponents, Prime factorization, Number of divisors, LCM and GCD
Modulus, Congruence and its properties, simple Modular algebra
Base-10 digit representation, *Base-2 representation, *Different base conversion
Divisibility rules; Venn diagram, Sets, *Union formula for two/three sets
Number Theory Total:
Algebra
TOPICS：
Sequences
Algebraic Operations
Coodinate System and Functions
Solving Equations
Inequalities and Extreme Value Problems
Details：
Arithmetic Sequences, Geometric sequences, Simple Repeating Sequence
Expansion and Factorization Formulas; *Binomial theorem, Pascal Triangle; Radical Calculations
Linear Functions, Quadratic Functions, Rational Functions, Absolute Value Functions,Trigonometric Functions, Exponential Functions
Linear equations and quadratic equations, Vieta’s theorem for quadratic equations; Functional Equations
Linear inequalities and System of linear inequalities; Absolute value inequality, *AM-GM inequality
Algebra
Total:
Geometry
TOPICS：
Triangles
Polygons
Circles
Simple Solid Geometry
Details：
Similar and Congruent; Angle bisector and the *Angle Bisector Theorem,Median and the Centroid; Pythagorean Theorem, *Heron's formula
Trapezoid, Parallelogram, Rhombus, Rectangle, Square
Chords, Arcs, Angles and Areas; Inscribed Circles and Circumscribed Circles; *Four Concyclic Points
Rectangular Box, Prisms, and Pyramids; Sphere and Cones; Lines and Planes in Space
Geometry
Total:
Combinatorics
Counting Problems
Permutation Problems and Combination Problems
Simple Probability Problems
Details：
Sum rules and Product rules
Permutation Numbers and Combination Numbers; *Balls into Boxes Problems
The Concept of Probability and basic Properties; Simple Geometric Probability
Combinatorics Total:
