Ti li畛u tr狸nh by 畛 thi th畛 畉i h畛c m担n To叩n cho h畛c sinh l畛p 12, bao g畛m c叩c ph畉n chung v t畛 ch畛n. 畛 thi bao g畛m nhi畛u c但u h畛i v畛 kh畉o s叩t hm s畛, gi畉i ph動董ng tr狸nh, t狸m nguy棚n hm v t鱈nh th畛 t鱈ch h狸nh ch坦p, k竪m theo c叩c i畛u ki畛n v b畉t ph動董ng tr狸nh. Th鱈 sinh c坦 th畛 ch畛n lm m畛t trong hai ph畉n t畛 ch畛n 畛 hon thnh bi thi.
Ti li畛u l 畛 thi to叩n cho th鱈 sinh kh畛i A, B, D nm h畛c 2011-2012, g畛m nhi畛u bi to叩n li棚n quan 畉n kh畉o s叩t hm s畛, gi畉i ph動董ng tr狸nh, t鱈nh t鱈ch ph但n v t鱈nh th畛 t鱈ch h狸nh ch坦p. 畛 thi chia thnh hai ph畉n: ph畉n chung cho t畉t c畉 th鱈 sinh v ph畉n ri棚ng theo ch動董ng tr狸nh chu畉n ho畉c n但ng cao. Th鱈 sinh ph畉i tu但n th畛 quy 畛nh kh担ng s畛 d畛ng ti li畛u trong khi lm bi.
Ti li畛u l 畛 thi ki畛m tra ch畉t l動畛ng m担n To叩n c畛a h畛c sinh trung h畛c ph畛 th担ng, bao g畛m c叩c c但u h畛i v畛 hm s畛, ph動董ng tr狸nh, t鱈ch ph但n v h狸nh h畛c. C叩c c但u h畛i y棚u c畉u gi畉i quy畉t c叩c bi to叩n li棚n quan 畉n t鱈nh to叩n, ch畛ng minh v ph但n t鱈ch h狸nh h畛c trong kh担ng gian ba chi畛u. 畛 thi c滴ng bao g畛m c叩c ph動董ng tr狸nh ph畛c t畉p v bi t畉p v畛 畉i s畛, gi畉i t鱈ch.
1. The document discusses integration and properties of integrals. It shows that the integral of the derivative of a function equals the function evaluated from negative infinity to positive infinity.
2. Several integral properties are demonstrated, including properties related to adding or subtracting integrals and integrating with respect to different variables.
3. The document also explores integrals of functions over all real numbers and shows some integrals equal zero while others do not, depending on the properties of the functions.
1. The document provides information about a math exam, including the exam time of 180 minutes and 6 questions ranging from 1 to 2 points each. The questions cover topics such as solving equations, finding roots of equations, integrals, geometry problems, and systems of equations.
2. The responses provide solutions to each question, showing the steps and reasoning for obtaining the answers. Solutions include solving equations, finding integrals, using geometry relationships, and solving a system of inequalities.
3. Diagrams and calculations are shown to visually depict the solutions to the geometry problems involving shapes, angles, and areas.
Ti li畛u l 畛 thi ki畛m tra ch畉t l動畛ng m担n To叩n c畛a h畛c sinh trung h畛c ph畛 th担ng, bao g畛m c叩c c但u h畛i v畛 hm s畛, ph動董ng tr狸nh, t鱈ch ph但n v h狸nh h畛c. C叩c c但u h畛i y棚u c畉u gi畉i quy畉t c叩c bi to叩n li棚n quan 畉n t鱈nh to叩n, ch畛ng minh v ph但n t鱈ch h狸nh h畛c trong kh担ng gian ba chi畛u. 畛 thi c滴ng bao g畛m c叩c ph動董ng tr狸nh ph畛c t畉p v bi t畉p v畛 畉i s畛, gi畉i t鱈ch.
1. The document discusses integration and properties of integrals. It shows that the integral of the derivative of a function equals the function evaluated from negative infinity to positive infinity.
2. Several integral properties are demonstrated, including properties related to adding or subtracting integrals and integrating with respect to different variables.
3. The document also explores integrals of functions over all real numbers and shows some integrals equal zero while others do not, depending on the properties of the functions.
1. The document provides information about a math exam, including the exam time of 180 minutes and 6 questions ranging from 1 to 2 points each. The questions cover topics such as solving equations, finding roots of equations, integrals, geometry problems, and systems of equations.
2. The responses provide solutions to each question, showing the steps and reasoning for obtaining the answers. Solutions include solving equations, finding integrals, using geometry relationships, and solving a system of inequalities.
3. Diagrams and calculations are shown to visually depict the solutions to the geometry problems involving shapes, angles, and areas.