Grade 7 Math Sets PDF

MATH I. Sets Definition of a Set A set is a well-defined collection of objects, called elements. Sets are usually written using curly braces {}. The elements of a set must be distinct and follow a specific rule or characteristic. II. How to Define Sets Sets can be defined in three ways:...

MATH I. Sets Definition of a Set A set is a well-defined collection of objects, called elements. Sets are usually written using curly braces {}. The elements of a set must be distinct and follow a specific rule or characteristic. II. How to Define Sets Sets can be defined in three ways: Roster Form 1. Listing all elements inside curly braces. 2. Example: {1, 2, 3, 4, 5} 3. Used when the set has a small number of elements. 4. Example: {red, blue, green} represents a set of colors. Set-builder Notation 1. Describing the properties of elements in a set using a condition. 2. Example: {x | x is a natural number less than 6} 3. This reads as "the set of all x such that x is a natural number less than 6." 4. Example: {y | y is an even number between 1 and 10} Descriptive Form 1. Writing a description of the set in words. 2. Example: "The set of all even numbers between 1 and 10." 3. Example: "The set of vowels in the English alphabet." III. Comparing Sets Using Symbols  Equal Sets (A = B)   o Two sets are equal if they have exactly the same elements. o Example: {1, 2, 3} = {3, 1, 2} (Order does not matter)  Subset (A ⊆ B)  o Set A is a subset of Set B if all elements of A are also in B. o Example: {1, 2} ⊆ {1, 2, 3, 4}  Proper Subset (A ⊂ B)  o Set A is a proper subset of Set B if A is a subset of B but A ≠ B. o Example: {1, 2} ⊂ {1, 2, 3}  Superset (A ⊇ B)  o Set A is a superset of Set B if A contains all elements of B. o Example: {1, 2, 3, 4} ⊇ {1, 2}  Proper Superset (A ⊃ B)  o Set A is a proper superset of Set B if A contains all elements of B and A ≠ B. o Example: {1, 2, 3} ⊃ {1, 2}  Disjoint Sets  o Two sets are disjoint if they have no common elements. o Example: {1, 2, 3} ∩ {4, 5, 6} = ∅ IV. Comparing Subsets  Subset (⊆)   o A subset contains some or all elements of another set. o Example: {a, b} ⊆ {a, b, c, d}  Proper Subset (⊂)  o A proper subset contains some but not all elements of another set. o Example: {x, y} ⊂ {x, y, z}  Power Set  o The power set includes all possible subsets, including the empty set and the set itself. o Example: If A = {1, 2}, the power set of A is {∅, {1}, {2}, {1, 2}}. V. Cardinality of a Set The cardinality of a set refers to the number of elements in the set. It is denoted by |A| for a set A.  Finite Set Cardinality  o If a set has a specific number of elements, its cardinality is a non-negative integer. o Example: If A = {1, 2, 3, 4}, then |A| = 4.  Infinite Set Cardinality  o If a set has an unlimited number of elements, its cardinality is infinite. o Example: The set of natural numbers {1, 2, 3,...} has infinite cardinality.  Empty Set Cardinality  o The empty set has a cardinality of zero. o Example: |∅| = 0 VI. Operations with Integers 1. Addition 2. o Same signs: Add the absolute values and keep the common sign. Example: (-5) + (-3) = -8, (-7) + 4 = -3 o Different signs: Subtract the smaller absolute value from the larger absolute value and take the sign of the larger number. 3. Subtraction 4. o Change the subtraction into addition by adding the opposite. o Example: 5 - (-3) = 5 + 3 = 8, (-2) - 4 = -2 + (-4) = -6 5. Multiplication and Division 6. o Same signs: The result is positive. Example: (-6) × (-2) = 12, (-8) ÷ 4 = -2 o Different signs: The result is negative. VII. Order of Operations (PEMDAS) 1. Parentheses – Solve expressions inside parentheses first. 2. Exponents – Evaluate powers and square roots. 3. Multiplication and Division – From left to right. 4. Addition and Subtraction – From left to right. Example: 5 + (3 × 2) - 4² ÷ 2 = 5 + 6 - 16 ÷ 2 = 5 + 6 - 8 = 11 - 8 = 3 Grade 7 English Reviewer I. The Writing Process The writing process is a step-by-step approach to creating clear and organized writing. It consists of five stages: 1. Prewriting (Planning & Brainstorming) 2. 1. Think about your topic and purpose. 2. Brainstorm ideas using mind maps or lists. 3. Identify your audience (Who will read your work?). 4. Gather relevant information and organize your thoughts. 3. Drafting (Writing the First Version) 4. 1. Start writing without worrying about grammar and spelling. 2. Focus on expressing ideas clearly. 3. Follow a structure: introduction, body, and conclusion. 5. Revising (Improving Content & Structure) 6. 1. Read your work and improve clarity. 2. Check if your ideas flow logically. 3. Add, remove, or reorganize sentences if needed. 4. Ask for feedback from others. 7. Editing (Correcting Mistakes) 8. 1. Fix grammar, spelling, and punctuation errors. 2. Ensure sentence structure is correct. 3. Replace unclear or repetitive words with better choices. 9. Publishing (Sharing the Final Version) 10. 1. Write the final, polished version. 2. Present your work by printing, posting online, or submitting it. II. Expository Text Structures with Diagrams Expository texts aim to explain, inform, or describe a topic clearly. To make them more effective, they use the following structures: 1. Sequence/Chronological Order (Time Order)  Definition: Information is arranged in the order it happens.  Purpose: Used for explaining processes, historical events, or step-by-step instructions.  Examples: o Life cycle of a butterfly o Steps in a scientific experiment  Diagram Used: Timeline or Flowchart 2. Compare & Contrast  Definition: Highlights similarities and differences between two or more things.  Purpose: Helps readers understand two subjects better.  Examples: o Comparing basketball and soccer o Differences between reptiles and mammals  Diagram Used: Venn Diagram or T-Chart 3. Cause & Effect  Definition: Explains why something happens (cause) and what happens as a result (effect).  Purpose: Used in science, history, and problem-solving writing.  Examples: o Causes and effects of global warming o Why eating junk food leads to health problems  Diagram Used: Cause and Effect Diagram (Fishbone Diagram) or Concept Map 4. Problem & Solution  Definition: Identifies an issue and suggests ways to fix it.  Purpose: Used in persuasive writing and problem-solving discussions.  Examples: o How to prevent bullying in schools o Solutions to pollution  Diagram Used: Problem-Solution Chart or Flowchart III. Unity, Cohesion, and Coherence in Writing These three elements make writing clear, logical, and connected: 1. Unity  All sentences in a paragraph should relate to the main idea.  Example: ❌Incorrect: “I love pizza. The Eiffel Tower is in Paris. My brother likes soccer.” (No unity) ✅Correct: “I love pizza because it’s cheesy and delicious. My favorite kind is pepperoni.” (Has unity) 2. Cohesion  Sentences should be smoothly connected using transition words like: o Addition: Furthermore, Moreover, In addition o Comparison: Similarly, Likewise o Contrast: However, On the other hand o Cause & Effect: Therefore, As a result, Consequently 🔹 Example: "I love reading books. Furthermore, it helps improve my vocabulary and imagination." 3. Coherence  Ideas should be organized in a logical order.  Example: ❌Incorrect: “He finally arrived at school. He woke up late. He missed the bus.” ✅Correct: “He woke up late, so he missed the bus. As a result, he arrived at school late.” IV. Block vs. Point-by-Point Method in Compare & Contrast Essays Compare & Contrast essays can be structured in two ways: 1. Block Method  Discusses one subject entirely, then the next subject.    Example:  Paragraph 1 (Dogs):  o Friendly, need exercise, trainable Paragraph 2 (Cats): o Independent, low-maintenance, use a litter box 🔹 Best for short essays or when comparing fewer topics. 2. Point-by-Point Method  Discusses one point at a time for both subjects.   Example:  Paragraph 1: Personality  o Dogs are social and playful. o Cats are independent and quiet. Paragraph 2: Care Needs o Dogs need daily walks. o Cats need a litter box. 🔹 Best for detailed comparisons and longer essays.