Gaokao Mathematics case studies
Gaokao Mathematics · Put your knowledge to work in context.
The Gaokao mathematics paper is the mathematics component of China's National College Entrance Examination, the main route into undergraduate study for senior secondary graduates. Candidates sit it at the end of three years of senior high school, and the score enters the composite that provincial admission offices use when placing students into universities and programmes. It is an academic selection test rather than a professional certification, and it is written to discriminate finely across a very large, heavily practised cohort. Coverage runs across sets and logic, functions and derivatives, trigonometry and triangle solving, sequences, inequalities, vectors and complex numbers, solid geometry, analytic geometry, probability and statistics, and counting principles. The Gaokao Mathematics case studies are 5 cases and about 1,651 words.
1Scholarship Cutoffs and Set Inclusion
A district scholarship uses two screening rules on a 100-point mathematics score M and a 100-point physics score P. Rule A requires M at least 90 and P at least 85.
352 words, about 2 min2Production Level and a Cost Parameter
A workshop models daily profit in hundreds of yuan by f(x)=x^3-3ax+1, where x in [0,2] is the production level in hundreds of units and a is a nonnegative supplier-cost parameter. The current contract sets a=1.
360 words, about 2 min3The Surveyor's Ambiguous Triangle
A surveyor measures a triangular plot ABC from point B. The baseline BA is 7.00 m, the distance AC is 5.00 m, and angle ABC is 30°.
360 words, about 2 min4A Production Recurrence with a Wrong Guess
A small factory starts with 1 thousand units produced in week 1. Each week output is set by a {n+1}=2a n+n, where a n is output in week n, in thousands of units.
311 words, about 2 min5Defect Rate and the Wrong Conditional
A factory has two assembly lines. Line A makes 60% of the daily output and Line B makes 40%.
268 words, about 1 min