Description of problems

.
№ of the problem	Content (section of curriculum)	Topic	Description of problems	Level of complexity	Criteria
A	В	С	D
	Trigonometric Equations	Graphs of trigonometric functions	Knowledge of graphs of trigonometric functions = 1 mark (A) Application of horizontal translation = 1 mark (B)	Basic	+	+
	Solutions of trigonometric equations	Knowledge of manipulation of sine function = 1 mark (A) Analysis of periodic property of sine function = 1 mark (C)	Basic	+		+
	Solutions of trigonometric equations	Knowledge of manipulation of cosine function = 1 mark (A) Application of rearranging function to make x the subject = 1 mark (B) Analysis of periodic property of cosine function = 1 mark (C)	Basic	+	+	+
	Solutions of trigonometric equations	Knowledge of manipulation of sine function = 1 mark (A) Application of rearranging function to make x the subject = 1 mark (B) Communication of solution in mathematical language = 1 mark (D)	Basic	+	+		+
	Solutions of trigonometric equations	Knowledge of manipulation of sine function = 1 mark (A) Application of rearranging function to make x the subject = 1 mark (B) Communication of solution in mathematical language = 1 mark (D)	Basic	+	+		+
	Graphs of trigonometric functions	Knowledge of graphs of trigonometric functions = 1 mark (A) Application of effect of coefficients = 1 mark (B) Using graphs to solve a problem = 1 mark (D)	Basic	+	+		+
	Обратные тригонометри-ческие функции	Свойства обратных тригонометрических функций	Знает область определения обратных тригонометрических функций = 1 балл (А) Составляет и решает неравенство по условию задачи = 1 балл (С)	Б	+		+
	Нахождение значений обратных тригонометрических функций	Знает свойства аркфункций = 1 балл (А) Применяет свойства аркфункций и тригонометрических функций = 1 балл (В)	Б	+	+
	Свойства обратных тригонометрических функций	Знает область значений обратных тригонометрических функций = 1 балл (А) Применяет свойства аркфункций = 1 балл (В)	Б	+	+
	Преоразование обратных тригонометрических функций	Применяет свойства аркфункций = 1 балл (В) Находит метод решения задачи = 1 балл (С)	Б		+	+
	Геометричес-кие фигуры	Параллельные, пересекающиеся и скрещивающиеся прямые	Знает расположение прямых в пространстве = 1 балл (А) Применяю признаки параллельности прямых = 1 балл (В)	Б	+	+
	Взаимное расположение прямых и плоскостей в пространстве	Применяет свойства фигур = 1 балл (В) Анализирует данные при решении задачи = 1 балл (С)	Б		+	+
	Угол между прямыми в пространстве	Знает определение угла между прямыми в пространстве = 1 балл (А) Анализирует данные при решении задачи = 1 балл (С)	Б	+		+
Total

Part 2

№ of problems

Content (sections of the curriculum)

Topic

Description of problems

Level of comlexity

Criteria

A

В

С

D

Geometrical figures

Intersection of two planes Parallelism of lines

Knowledge of line of intersection between planes = 1 mark (A) Writing proof in logical mathematical language that can be understood = 1 mark (D)

Medium

+

+

Geometrical figures

Distance between two points

Find distance from base corner to middle of 1 side = 1 mark (A) Distance from corner to middle of base = 1 mark (B) Distance from apex to corner = 1 mark (C)

Medium

+

+

+

Geometrical figures

Section construction Perimeter of section

Correctly draw and shade section = 1 mark (D) Calculate length of side = 1 mark (C) Calculate perimeter = 1 mark (B)

Medium

+

+

+

Trigonometric Equations

Solutions of trigonometric equations

Sketch 2 trigonometric functions = 2 marks (D) State number of solutions in correct domain = 1 mark (A)

Medium

+

++

Обратные тригонометри-ческие функции

Нахождение значения обратных тригонометрических функций

Знает свойства обратных тригонометрических функций = 1 балл (А) Находит связь между тригонометри-ческими функциями = 1 балл (С)

В

+

+

Нахождение значения обратных тригонометрических функций

Применяет свойства обратных тригонометрических функций = 1 балл (А) Представляет решение задачи в четкой и лаконичной форме = 1 балл (D)

В

+

+

Total

Part Three

№ of the problem

Content (section of curriculum)

Topic

Description of problems

Level of complexity

Criteria

A

В

С

D

Геометрические фигуры

Построение сечения фигур плоскостью

Анализирует данные для выполнения построения = 1 балл (C) Обосновывает этапы построения и делает выводы = 1 балл (C) Выполняет чертеж в четкой последовательности = 1 балл (D) Правильно оформляет решение задачи = 1 балл (D) Грамотно показывает результат построения = 1 балл (D)

П

++

+++

Тригонометрия

Доказательство тригонометрических тождеств

Применяет формулы тригонометрии = 1 балл (В) Проводит достоверные доказательства = 1 балл (С) Анализирует данные для решения проблемы = 1 балл (С) Оценивает полученные результаты = 1 балл (D) Представляет решение задачи в четкой и лаконичной форме = 1 балл (D)

П

+

++

++

Trigonometric Equations

Solutions of trigonometric equations Use of identities Substitution

Use identity to manipulate function = 1 mark (C) Manipulate equation correctly in mathematical language to match other equation = 1 mark (D) Use correct substitution to solve for sinφ = 1 mark (C) Solve for φ = 1 mark (B) Communicate correct number of solutions in given domain = 1 mark (D)

Difficult

+

++

++

Total

Criteria	Expected outcomes
АKnowledge and understanding (max 6)	The student is able to give a meaningful definition of terms, concepts; The student is able to use the language of mathematics, law, laws, terms and concepts; The student is able to explain the scientific information.
В Application (max 6)	The student is able to select and use appropriate mathematical knowledge, skills; The student is able to do consistent findings; The student is able to make reliable mathematical proofs; The student is able to illustrate the theoretical concepts learned from their examples and facts; The student is able to relate the learned material to previously required knowledge; The student is able to transfer acquired knowledge to explain other phenomena and facts; The student is able to point to interdisciplinary communication, if available.
СAnalysis and synthesis (scientific investigation) (max 6)	The student is able to analyze data to solve a given problem and support conclusions; The student is able to reflect on the meaning and methods of solution studies, the reliability of their findings, and other alternative approaches of problem solving; The student is able to find rational solutions to problems; A student can form an idea of ​​the related concepts and methods, as important means of mathematical modeling of real processes and phenomena; The student is able to break down the material into simple sections; The student demonstrates the ability of learning the whole in different terms; The student demonstrates the ability to organize, classify, group the objects; The student is able to find patterns; The student is able to evaluate the results of decisions; The student is able to generalize the results; The student is able to allocate practical ideas in the study of materials, to express his attitude towards them.
DCommunication (max 6)	The student is able to transmit scientific information logically and sequentially; The student is able to provide information and solve problems in a clear and concise manner; The student demonstrates the ability to transmit information of mathematical literacy in the form of oral and written communications; The student is able to properly use information and communications technology, and various forms of information (pictures, graphs, charts, drawings, diagrams, models); The student is able to properly execute the task; The student is able to correctly record the result; The student is able to defend his point of view, arguing it; The student is able to critically evaluate his own opinion; The student is able to listen to others and be ready to change their point of view. The student is able to organize the training of group interaction (assign roles, agree with each other, etc.); The student is able to anticipate (predict) the impact of collective decision-making; The student is able to analyze and evaluate the activities (own and classmates).

Дата добавления: 2015-11-05