Grade 9 Mathematics Review
DepEd MELC-Based Quarterly Exam Reviewer
Total: 107 questions across 4 quarters
Choose Your Quarter
Select a quarter to start practicing. Each quiz covers specific topics from the DepEd curriculum.
Quarter 1: Quadratic Equations
Solving quadratics, discriminant, roots, quadratic inequalities
TOPICS COVERED:
- •Quadratic Equations
- •Solving by Factoring
- •Completing the Square
- •Quadratic Formula
- •Discriminant and Nature of Roots
Quarter 2: Functions & Rational Functions
Domain, range, function notation, rational functions, asymptotes
TOPICS COVERED:
- •Functions and Relations
- •Domain and Range
- •Function Composition
- •Inverse Functions
- •Rational Functions and Asymptotes
Quarter 3: Variations & Statistics
Direct, inverse, joint variation, measures of central tendency
TOPICS COVERED:
- •Direct Variation
- •Inverse Variation
- •Joint and Combined Variation
- •Measures of Central Tendency
- •Measures of Dispersion
Quarter 4: Logic & Reasoning
Logical statements, conditional, biconditional, arguments
TOPICS COVERED:
- •Logical Statements
- •Conditional Statements
- •Biconditional Statements
- •Valid Arguments
- •Deductive and Inductive Reasoning
Grade 9 Math Learning Milestones
Key skills your child should master throughout the school year:
| Skill | Quarter | Description |
|---|---|---|
| Solving quadratic equations | Q1 | Factor, complete square, use formula |
| Discriminant analysis | Q1 | Determine nature of roots before solving |
| Function notation | Q2 | Evaluate f(x) and work with function rules |
| Domain and range | Q2 | Identify valid inputs and outputs |
| Inverse functions | Q2 | Find and verify inverse relationships |
| Direct and inverse variation | Q3 | Write and solve variation equations |
| Central tendency | Q3 | Calculate mean, median, mode accurately |
| Logical statements | Q4 | Identify and write conditional statements |
| Valid arguments | Q4 | Recognize valid and invalid reasoning |
| Mathematical proofs | Q4 | Construct deductive and inductive proofs |
Quarter-by-Quarter Learning Guide
Q1: Quadratic Equations
- • Identify quadratic equations (ax^2 + bx + c = 0)
- • Solve by extracting square roots
- • Solve by factoring (trial and error, grouping)
- • Solve by completing the square
- • Apply the quadratic formula
- • Analyze discriminant and nature of roots
Q2: Functions & Rational Functions
- • Distinguish functions from relations
- • Use function notation f(x)
- • Find domain and range
- • Perform function operations
- • Find and verify inverse functions
- • Graph rational functions with asymptotes
Q3: Variations & Statistics
- • Write direct variation equations (y = kx)
- • Write inverse variation equations (y = k/x)
- • Solve joint and combined variation
- • Calculate measures of central tendency
- • Calculate measures of dispersion
- • Interpret statistical data
Q4: Logic & Reasoning
- • Identify and write logical statements
- • Form conditional statements (if-then)
- • Write converse, inverse, contrapositive
- • Evaluate biconditional statements
- • Construct valid arguments
- • Apply deductive and inductive reasoning
Tips for Parents: Supporting Grade 9 Math Learning
Do's
- ✓Encourage graphing calculators and apps to visualize functions
- ✓Relate quadratics to real-world scenarios (projectile motion, areas)
- ✓Practice logical puzzles and brain teasers together
- ✓Connect statistics to news, sports, and everyday data
- ✓Encourage showing complete solutions with explanations
Don'ts
- ✗Don't skip understanding in favor of memorizing formulas
- ✗Avoid rushing through word problems - read carefully
- ✗Don't neglect checking answers by substitution
- ✗Avoid skipping steps in proofs and logical arguments
- ✗Don't ignore graphing - it builds visual understanding
Recommended Weekly Study Schedule
Monday
Quadratic Equations Practice
Tuesday
Functions & Graphing
Wednesday
Variations & Word Problems
Thursday
Statistics & Data Analysis
Friday
Logic & Comprehensive Review
Recommended: 60 minutes daily, with problem-solving sessions on weekends
Frequently Asked Questions
What topics are covered in Grade 9 Mathematics?
Grade 9 Math covers four main areas: Quadratic Equations (Q1), Functions & Rational Functions (Q2), Variations & Statistics (Q3), and Logic & Reasoning (Q4). These are advanced algebra topics that prepare students for senior high school mathematics.
What is the quadratic formula and when do I use it?
The quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / 2a. Use it to solve any quadratic equation ax^2 + bx + c = 0, especially when factoring is difficult. It always works and gives both roots.
What is the discriminant and what does it tell us?
The discriminant is b^2 - 4ac from the quadratic formula. If positive: 2 real roots. If zero: 1 repeated real root. If negative: 2 complex (imaginary) roots. It determines the nature of roots without solving.
What is the difference between direct and inverse variation?
Direct variation: y = kx (when x increases, y increases proportionally). Inverse variation: y = k/x (when x increases, y decreases). Joint variation combines multiple variables: y = kxz.
How do I find the domain and range of a function?
Domain: all possible input (x) values. Range: all possible output (y) values. For rational functions, exclude x-values that make the denominator zero. For square roots, exclude x-values that make the radicand negative.
What are conditional and biconditional statements?
Conditional (if-then): "If p, then q" (p implies q). Biconditional (if and only if): "p if and only if q" (p and q are logically equivalent). The converse, inverse, and contrapositive are related forms.
Is Grade 9 Math aligned with DepEd MELC curriculum?
Yes, all questions in this reviewer are aligned with the Department of Education Most Essential Learning Competencies (MELC) for Grade 9 Mathematics, covering all four quarters of the school year.
How can I improve my problem-solving skills in Grade 9 Math?
Practice different types of quadratic problems, understand function behavior through graphing, work on word problems involving variations, and develop logical reasoning through proof-based exercises.
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About Grade 9 Math
This reviewer covers the complete Grade 9 Mathematics curriculum based on DepEd's Most Essential Learning Competencies (MELC). Topics include quadratic equations, functions, variations, and logical reasoning.
Grade 9 Math builds on algebraic foundations and introduces more advanced concepts preparing students for senior high school and beyond.
Note: Questions are designed as single-word terminology to help you master mathematical vocabulary and concepts efficiently.