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Triangles
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triangles
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Triangles
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Triangles
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Triangles
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Triangle Theorems
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Geometry of Triangles
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Areas of Triangles
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Triangles and radians
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Triangle congruence
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Right Triangles
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Area of Triangles
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Classifying triangles
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EQUAL TRIANGLES
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Geometry of a Triangle
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Anterior triangle
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General Triangles
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Triangles and Trigonometry
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Flashcards (1825)
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Special triangles
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Notes on Lines, line segments, and rays. Notes on Properties if planes, lines, and points. Notes on Describe intersections in a plane. Notes on Additive property of lengths. Notes on congruent line segments. Notes on Construct a congruent segment. Notes on Distance formula. Notes on Construct the midpoint or perpendicular bisector of a segment. Notes on Midpoint. Notes on angle vocabulary. Notes on Construct an angle bisector. Notes on Construct a congruent angle. Notes on parts of a circle. Notes on arc length. Notes on slopes of parallel and perpendicular lines. Notes on equations of parallel and perpendicular lines. Notes on find the distance between a point and a line. Notes on find the distance between two parallel lines. Notes on Construct an equilaterial triangle inscribed in a circle. Notes on Construct a square inscribed in a circle. Notes on Construct a regular hexagon inscribed in a circle. Notes on Construct a equilaterial triangle or regular hexagon. Notes on Construct a square. Notes on translations write the rule. Notes on Reflections graph the image. Notes on Reflections find the coordinates. Notes on rotate polygons about a point. Notes on rotations graph the image. Notes on rotations find the coornates. Make Notes detailed on paper all notes on each topic detailed throughly.Notes on Lines, line segments, and rays. Notes on Properties if planes, lines, and points. Notes on Describe intersections in a plane. Notes on Additive property of lengths. Notes on congruent line segments. Notes on Construct a congruent segment. Notes on Distance formula. Notes on Construct the midpoint or perpendicular bisector of a segment. Notes on Midpoint. Notes on angle vocabulary. Notes on Construct an angle bisector. Notes on Construct a congruent angle. Notes on parts of a circle. Notes on arc length. Notes on slopes of parallel and perpendicular lines. Notes on equations of parallel and perpendicular lines. Notes on find the distance between a point and a line. Notes on find the distance between two parallel lines. Notes on Construct an equilaterial triangle inscribed in a circle. Notes on Construct a square inscribed in a circle. Notes on Construct a regular hexagon inscribed in a circle. Notes on Construct a equilaterial triangle or regular hexagon. Notes on Construct a square. Notes on translations write the rule. Notes on Reflections graph the image. Notes on Reflections find the coordinates. Notes on rotate polygons about a point. Notes on rotations graph the image. Notes on rotations find the coornates. Make Notes detailed on paper all notes on each topic detailed throughly.Notes on Lines, line segments, and rays. Notes on Properties if planes, lines, and points. Notes on Describe intersections in a plane. Notes on Additive property of lengths. Notes on congruent line segments. Notes on Construct a congruent segment. Notes on Distance formula. Notes on Construct the midpoint or perpendicular bisector of a segment. Notes on Midpoint. Notes on angle vocabulary. Notes on Construct an angle bisector. Notes on Construct a congruent angle. Notes on parts of a circle. Notes on arc length. Notes on slopes of parallel and perpendicular lines. Notes on equations of parallel and perpendicular lines. Notes on find the distance between a point and a line. Notes on find the distance between two parallel lines. Notes on Construct an equilaterial triangle inscribed in a circle. Notes on Construct a square inscribed in a circle. Notes on Construct a regular hexagon inscribed in a circle. Notes on Construct a equilaterial triangle or regular hexagon. Notes on Construct a square. Notes on translations write the rule. Notes on Reflections graph the image. Notes on Reflections find the coordinates. Notes on rotate polygons about a point. Notes on rotations graph the image. Notes on rotations find the coornates. Make Notes detailed on paper all notes on each topic detailed throughly
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Geometry: Trigonometry
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Phil Final Ethical Triangle
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PRE-IB Chemistry Notes (based on your test) 1. Molecular Formula English A molecular formula shows the actual number of atoms in a molecule. Example: * H₂O = 2 hydrogen atoms and 1 oxygen atom * C₆H₁₂O₆ = 6 carbon, 12 hydrogen, 6 oxygen Important * Molecular formula = actual number * Empirical formula = simplest ratio Example: * Molecular formula: C₆H₁₂O₆ * Empirical formula: CH₂O Test question “What information does the molecular formula provide?” Correct answer: ✅ The actual numbers of atoms in a molecule ⸻ Русский Молекулярная формула показывает настоящее количество атомов в молекуле. Пример: * H₂O = 2 атома водорода и 1 атом кислорода * C₆H₁₂O₆ = 6 углеродов, 12 водородов, 6 кислородов Важно * Molecular formula = настоящее количество * Empirical formula = простое соотношение ⸻ 2. Isotopes English Isotopes are atoms of the same element with: * same number of protons * different number of neutrons Example: * Carbon-12 * Carbon-14 Both have: * 6 protons But different neutrons. Formula Neutrons = mass number − atomic number ⸻ Русский Изотопы — это атомы одного элемента: * одинаковое количество протонов * разное количество нейтронов Формула: Нейтроны = массовое число − атомный номер ⸻ 3. Protons, Neutrons and Electrons English Proton number = atomic number Electron number Neutral atom: electrons = protons Ion: * positive ion → lost electrons * negative ion → gained electrons Example ^{43}_{20}Ca^{2+} * protons = 20 * neutrons = 43 − 20 = 23 * electrons = 20 − 2 = 18 ⸻ Русский Протоны = атомный номер Электроны У нейтрального атома: электроны = протоны Ион: * плюс → потерял электроны * минус → получил электроны Пример: Ca²⁺: * 20 протонов * 23 нейтрона * 18 электронов ⸻ 4. Electron Configuration English Electrons fill shells. Rules * 1st shell = 2 electrons * 2nd shell = 8 * 3rd shell = 8 Examples Mg (12): 2,8,2 Cl (17): 2,8,7 Al (13): 2,8,3 Outer shell electrons Mg → 2 Cl → 7 ⸻ Русский Электроны распределяются по оболочкам. Примеры: * Mg = 2,8,2 * Cl = 2,8,7 * Al = 2,8,3 Внешние электроны: * Mg → 2 * Cl → 7 ⸻ 5. Ionic Bonding English Ionic bonding happens when electrons are transferred. * metals lose electrons * non-metals gain electrons Example: Mg + Cl Mg loses 2 electrons. Each chlorine gains 1. Formula: MgCl₂ ⸻ Русский Ионная связь появляется, когда электроны переходят от одного атома к другому. * металл теряет электроны * неметалл получает Пример: MgCl₂ ⸻ 6. Relative Atomic Mass and Relative Formula Mass English Relative Atomic Mass (Ar) Average mass of atoms compared with carbon-12. Example: Cl = 35.5 Relative Formula Mass (Mr) Total of all atomic masses in a formula. Example: H₂O = 2(1) + 16 = 18 ⸻ Русский Relative Atomic Mass Средняя масса атомов элемента. Relative Formula Mass Сумма всех атомных масс в формуле. Пример: H₂O = 18 ⸻ 7. Moles English Formula triangle n=\frac{m}{M} n = moles m = mass M = molar mass Example NaCl: M = 23 + 35.5 = 58.5 If mass = 117 g 117 ÷ 58.5 = 2 mol ⸻ Русский Формула: n = m / M n — моли m — масса M — молярная масса ⸻ 8. Concentration English Formula: c=\frac{n}{V} c = concentration n = moles V = volume in dm³ Important 1000 cm³ = 1 dm³ ⸻ Русский Формула: c = n / V V обязательно в dm³ 1000 cm³ = 1 dm³ ⸻ 9. Acids and Alkalis English Acid Produces H⁺ ions Alkali Produces OH⁻ ions Examples: * HCl = acid * NaOH = alkali ⸻ Русский Кислота выделяет H⁺ Щёлочь выделяет OH⁻ ⸻ 10. Strong and Weak Acids English Strong acid Fully ionizes in water. Example: HCl Weak acid Partially ionizes. Example: CH₃COOH Important Strong ≠ concentrated ⸻ Русский Сильная кислота полностью распадается. Слабая — только частично. ⸻ 11. Amphoteric Compounds English Amphoteric substances can act as: * acid * base Example: Al₂O₃ ⸻ Русский Амфотерные вещества могут быть: * кислотой * основанием ⸻ 12. pH and Indicators English pH scale * below 7 = acid * 7 = neutral * above 7 = alkali Indicators Litmus: * acid → red * alkali → blue Phenolphthalein: * acid → colorless * alkali → pink ⸻ Русский pH: * меньше 7 = кислота * 7 = нейтрально * больше 7 = щёлочь ⸻ 13. Acid-Base Titration English Titration is used to find concentration. Steps 1. Add indicator 2. Add acid/base slowly 3. Endpoint color change 4. Use formula Common indicators * phenolphthalein * methyl orange ⸻ Русский Титрование используют для нахождения концентрации. Шаги: 1. Добавить индикатор 2. Медленно добавлять раствор 3. Смотреть изменение цвета ⸻ 14. Redox Reactions English Oxidation Loss of electrons Reduction Gain of electrons OIL RIG: * Oxidation Is Loss * Reduction Is Gain ⸻ Русский Окисление = потеря электронов Восстановление = получение электронов ⸻ 15. Hydrophobic and Hydrophilic English Hydrophobic “Water-fearing” Does not mix with water. Example: oil Hydrophilic “Water-loving” Mixes with water. Example: salt ⸻ Русский Hydrophobic: не смешивается с водой Hydrophilic: смешивается с водой ⸻ 16. Organic Chemistry Naming (IMPORTANT FOR TEST) English Alkane Only single bonds General formula: C_nH_{2n+2} Alkene Contains double bond General formula: C_nH_{2n} Alkyne Contains triple bond General formula: C_nH_{2n-2} ⸻ Русский Алкан: только одинарные связи Алкен: двойная связь Алкин: тройная связь ⸻ 17. IUPAC Naming Quick Rules English Step 1 Find longest chain. Step 2 Count carbons: * meth = 1 * eth = 2 * prop = 3 * but = 4 * pent = 5 * hex = 6 Step 3 Find double bond. Step 4 Number chain from nearest double bond. Step 5 Name branches: * methyl * ethyl ⸻ Русский 1. Найти самую длинную цепь 2. Посчитать углероды 3. Найти двойную связь 4. Нумеровать с ближайшей двойной связи 5. Назвать ответвления ⸻ 18. Combustion English Combustion = burning in oxygen. Example: C_5H_{12}+8O_2\rightarrow5CO_2+6H_2O Products: * carbon dioxide * water ⸻ Русский Горение — реакция с кислородом. Продукты: * CO₂ * H₂O ⸻ 19. Activity Series English More reactive metals replace less reactive metals. Mg is more reactive than H: → reacts with acid Cu is less reactive than Fe: → cannot replace Fe ⸻ Русский Более активный металл вытесняет менее активный
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triangulation
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🧠 CH 9: Intelligence & Neuropsych Testing Q: What does Spearman’s theory of intelligence propose? A: A general intelligence factor called g underlies all cognitive abilities. Q: What did Thurstone contribute to intelligence theory? A: Proposed multiple primary mental abilities instead of one general intelligence. Q: What is fluid intelligence? A: Problem-solving and reasoning in new situations. Q: What is crystallized intelligence? A: Learned knowledge and experience-based skills. Q: Who developed the Wechsler intelligence tests? A: David Wechsler. Q: What are the 3 Wechsler scales? A: WAIS (adults), WISC (children), WPPSI (preschool). Q: What are the 4 WAIS index scores? A: Verbal Comprehension, Perceptual Reasoning, Working Memory, Processing Speed. Q: What is the Stanford-Binet test used for? A: Measuring general intelligence (IQ), especially in children. Q: What is neuropsychological testing used for? A: Assessing brain functioning (injury, dementia, learning disorders, etc.). Q: Name two major neuropsych batteries. A: Halstead-Reitan, Luria-Nebraska. ⸻ 🧠 CH 10: Personality Assessment Q: What is multimethod assessment? A: Using multiple types of assessment (tests, interviews, observation). Q: What is the MMPI-2? A: A true/false personality test measuring psychopathology. Q: What are MMPI validity scales used for? A: Detecting inconsistent answers, exaggeration, or faking. Q: What is malingering? A: Faking or exaggerating symptoms for external gain. Q: What is empirical criterion keying? A: MMPI method of selecting test items based on real group differences. Q: What is the MCMI-IV? A: Personality inventory based on Millon’s theory of personality disorders. Q: What is the Big Five model? A: Openness, Conscientiousness, Extraversion, Agreeableness, Neuroticism. Q: What is the Beck Depression Inventory? A: Self-report measure of depression severity. Q: What is the Rorschach test? A: Inkblot test used to assess personality and unconscious processes. Q: What is the TAT? A: Storytelling test using ambiguous pictures. Q: What is behavioral assessment? A: Direct measurement of behavior through observation or recording. ⸻ 🧠 CH 15: Cognitive Therapy Q: Who developed CBT? A: Aaron Beck. Q: Who developed REBT? A: Albert Ellis. Q: What are automatic thoughts? A: Immediate, involuntary thoughts that affect emotions. Q: What is the cognitive triad? A: Negative views of self, world, and future. Q: What are cognitive distortions? A: Irrational thinking patterns (e.g., catastrophizing). Q: What is the goal of cognitive therapy? A: Change maladaptive thoughts to improve emotions/behavior. Q: What is the ABCDE model? A: Activating event → Beliefs → Consequences → Disputation → Effect. Q: What is mindfulness? A: Nonjudgmental awareness of thoughts and feelings. Q: What is ACT? A: Therapy focusing on acceptance and values-based action. Q: What is DBT used for? A: Emotion regulation and distress tolerance skills. ⸻ 🧠 CH 16: Group & Family Therapy Q: What did Yalom emphasize in group therapy? A: Interpersonal learning and universality. Q: What is universality? A: Realizing others share similar struggles. Q: What is group cohesiveness? A: Sense of belonging within the group. Q: What are the stages of group therapy? A: Initial, transition, working stage. Q: What is the main idea of family therapy? A: The system is the problem, not the individual. Q: What is circular causality? A: Each person influences others in a cycle. Q: What is an identified patient? A: The family member labeled as “the problem.” Q: What are boundaries in family systems? A: Rules defining closeness or separation (enmeshed vs disengaged). Q: What is a triangle in family therapy? A: When tension between two people involves a third person. ⸻ 🧠 CH 17: Child & Adolescent Psych Q: What are externalizing disorders? A: Outward behaviors (aggression, ADHD, conduct problems). Q: What are internalizing disorders? A: Inward distress (anxiety, depression). Q: Which are easier to detect? A: Externalizing disorders. Q: What is a developmental perspective? A: Considering age-related changes in behavior. Q: What is resilience? A: Ability to adapt despite adversity. Q: What are Grotberg’s resilience categories? A: I have, I am, I can. Q: What is play therapy? A: Therapy using play to express emotions in children. Q: What are two types of play therapy? A: Directive and nondirective. ⸻ 🧠 CH 18: Health Psychology Q: What is health psychology? A: Study of psychological factors in health and illness. Q: Who developed General Adaptation Syndrome? A: Hans Selye. Q: What are the 3 stages of GAS? A: Alarm, resistance, exhaustion. Q: What is cortisol? A: Stress hormone released by the body. Q: What is psychoneuroimmunology? A: Study of mind–brain–immune system interactions. Q: What is chronic stress linked to? A: Increased illness risk and immune suppression. Q: What is coping? A: Strategies to manage stress. Q: What is biofeedback? A: Using feedback to control physiological functions. ⸻ 🧠 CH 19: Forensic Psychology Q: What is forensic psychology? A: Application of psychology to the legal system. Q: What is competency to stand trial? A: Ability to understand legal proceedings and assist defense. Q: What is insanity defense? A: Not guilty by reason of mental illness at time of crime. Q: What is civil commitment? A: Court-ordered psychiatric hospitalization. Q: What is an expert witness? A: Psychologist who provides testimony in court. Q: What is voir dire? A: Jury selection questioning process. Q: What is malingering in forensic settings? A: Faking symptoms for legal advantage. Q: Which test is preferred in forensic assessment and why? A: MMPI-2 because validity scales detect deception. Q: Why are projective tests not preferred legally? A: Low reliability and subjective interpretation
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Iron Triangle Relationship
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revision of triangle geometry
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TRIANGLES OF THE NECK
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Triangulation
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