Functions in Mathematics

Mathematics: Functions Fundamentals

• Relations need to be determined as functions in multiple-choice questions
• Find f(2), f(-1), f(0), and f(1/2) for the function f(x) = 2x² - 3x + 1
• Identify the domain and range for g(x) = √(x-3), h(x) = 5/x, and k(x) = |2x+4| - 3
• Determine which graph passes the vertical line test, given four graphs with various relations
• Find the value of x where f(x) = g(x), with f(x) = 2x + 3 and g(x) = x² - 4
• Find (f ∘ g)(2), (g ∘ f)(1), and (f ∘ f)(-1) for f(x) = x² - 5x + 2 and g(x) = 3x - 4
• Given f(x) = ax² + bx + c has zeros at x = 2 and x = -3, and if f(1) = 4, find the values of a, b, and c, then write the function in standard form
• Identify the domain of f(x) = (x-1)/(x² - 4) and g(x) = √(x² - 9)
• Find all values of x where h(x) = |x - 2| + 3 = 5
• Sketch graphs of f(x) = x² - 6x + 8, g(x) = |x + 2| - 3, and h(x) = 1/(x-1), showing intercepts and vertices
• On a graph, identify/label the domain, range, x-intercepts, y-intercepts, and locations of any asymptotes
• Draw a mapping diagram for f(x) = 2x - 3 with the domain {-2, -1, 0, 1, 2}
• Create a sketch of f(x) = x³ and identify key features

Mathematics: Test Review

• Focus review on questions pertaining to functions and transformations
• Focus on identifying common errors
• Identify areas where points were lost
• Rework 3-5 struggled-with problems from scratch
• Compare new solutions with original answers to those problems
• Note any improvements in understanding
• Summarize key lessons learned from past errors

English: Focus on Poetry Analysis Fundamentals

• Study the list of tone and mood words
• Create flashcards for 20 unfamiliar words from the prepared list.
• Group words into categories like positive, negative, and neutral
• Practice identifying tone in short excerpts using precise vocabulary and explaining which words/phrases create that tone
• Complete a tone-mapping exercise, listing 5 specific tone words for 3 emotions (joy, grief, anger) and providing a sample phrase that would exemplify each tone
• Read Vernon Scannell's poem "Nettles," annotating for initial impressions.
• Circle unfamiliar words, underline phrases with strong imagery or emotions, and note questions/observations
• Analyze literary techniques, identifying 3-5 examples each of imagery (visual, tactile, etc.), diction (word choice), and sound devices (alliteration, assonance, etc.)
• Explain the effect that they create in the poem
• Determine the poem's theme and purpose, considering the universal human experience and the poet's intent, and analyze how the techniques support that purpose
• Connect the poem to the assigned area of focus
• Analyze how the poem relates to art/creativity, science/environment, or beliefs/values
• Practice writing an effective introduction for an analysis of "Nettles," including a hook, title/author, directional statement, and thesis
• Practice writing a PEEL paragraph about imagery, including point (topic sentence), evidence (quote), explanation (analysis), and link (to theme/purpose)
• Self-assess the writing against English assessment criteria and pinpoint one strength and one area to improve upon

Biology: Photosynthesis

• Answer 15 multiple-choice questions covering light-dependent reactions, the Calvin cycle, photosynthesis factors, the chloroplast, and cellular respiration
• Self-check answers using the provided key
• Complete a detailed diagram of a chloroplast, labeling all major structures and indicating where reactions take place
• Complete a flowchart of the photosynthesis process, filling in missing reactants, products, processes, and indicating energy transfers
• Sketch/label a graph showing the effect of light intensity, CO2 concentration, and temperature on the photosynthesis rate
• Explain the role of water in photosynthesis
• Describe how ATP is generated during light-dependent reactions
• Compare and contrast C3 and C4 photosynthesis
• Explain why photosynthesis is important for all living organisms
• Describe the adaptations of leaves for maximizing photosynthesis

Spanish: Environmental Vocabulary

• Learn 20 key terms related to environmental protection and sustainability
• Create flashcards with Spanish terms and English meanings
• Practice pronunciation of each term
• Read a passage about environmental initiatives in a Spanish-speaking country
• Answer comprehension questions about the content and identify new vocabulary
• Write 5-8 sentences about environmental issues in the community using at least 10 vocabulary terms and focusing on correct verb conjugation and sentence structure

Arabic: Reading Comprehension

• Review 15 vocabulary words related to current topics and practice using each in a sentence
• Read a one-page text on a contemporary issue
• Annotate unfamiliar words to look up meanings and identify main ideas/supporting details
• Answer 5-7 questions with complete sentences and correct grammar/structure

Humanities: Source Analysis Techniques

• Review the OPVL (Origin, Purpose, Value, Limitation) framework
• Study examples of effective source analysis
• Analyze a primary source document (historical letter, speech, image), applying the OPVL framework, and identifying potential biases and contextual factors
• Write a short paragraph analyzing the source's reliability
• Explain how the source could be used in a historical investigation
• Consider what additional sources would complement this one

Daily Review and Reflection

• Summarize what was learned in each subject
• Identify particularly challenging concepts
• Note questions to ask teachers
• Prepare study materials for the next session