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- Arithmetic
  - Addition
    - Basic Addition 68
    - Carrying Over 1
    - Word Problems 109
    - Mental Math 20
    - Large Numbers 13
  - Subtraction
    - Basic Subtraction 57
    - Borrowing 11
    - Number Line 9
  - Multiplication
    - Times Tables 22
    - Multi Digit 8
    - Area Models 5
    - Estimation 17
  - Division
    - Basic Division 26
    - Long Division 7
    - Remainders 4
  - Fractions
    - Fraction Basics 5
    - Equivalent Fractions 5
    - Comparing Fractions 9
    - Fraction Operations 55
    - Mixed Numbers 10
  - Decimals
    - Decimal Basics 5
    - Place Value 45
    - Decimal Operations 37
    - Comparing Decimals 8
    - Rounding Decimals 28
  - Percentages
    - Percent Basics 7
    - Finding Percents 28
    - Percent Increase 3
    - Percent Decrease 9
    - Real Life Percent 5
  - Ratios & Proportions
    - Ratio Basics 2
    - Simplifying Ratios 9
    - Proportion Basics 2
    - Solving Proportions 14
    - Real World Ratios 3
  - Exponents & Roots
    - Exponent Basics 3
    - Square Roots 21
    - Cube Roots 5
    - Exponent Rules 23
  - Order of Operations
    - PEMDAS 1
    - Nested Expressions 3
    - With Exponents 13
    - Multi Step Problems 13
- Algebra
  - Algebraic Expressions
    - Algebraic Terms 4
    - Simplifying Expressions 43
    - Like Terms 6
    - Distributive Property 11
    - Evaluating Expressions 15
  - Linear Equations
    - One Variable Equations 13
    - Two Variable Equations 4
    - Solving Equations 41
    - Graphing Lines 13
  - Quadratic Equations
    - Quadratic Form 6
    - Factoring Method 11
    - Quadratic Formula 2
    - Completing Square 4
    - Graphing Parabolas 12
  - Polynomials
    - Polynomial Basics 3
    - Polynomial Operations 17
    - Degree of Polynomial 2
    - Polynomial Identities 6
  - Factoring
    - Common Factors 10
    - Difference of Squares 1
    - Trinomial Factoring 6
    - Special Products 2
  - Inequalities
    - Linear Inequalities 17
    - Compound Inequalities 1
    - Graphing Inequalities 6
    - Absolute Inequalities 6
  - Algebraic Functions
    - Function Basics 11
    - Domain & Range 6
    - Evaluating Functions 7
    - Function Graphs 12
    - Function Notation 2
  - Systems of Equations
    - Solving by Graphing 5
    - Substitution Method 6
    - Elimination Method 2
    - Real World Systems 2
    - No Infinite Solutions 2
  - Exponential & Logarithmic
    - Exponential Growth 4
    - Exponential Decay 2
    - Logarithm Basics 11
    - Logarithm Properties 16
  - Complex Numbers
    - Complex Operations 2
    - Complex Conjugates 1
    - Polar Form 6
    - Quadratic with Complex 2
- Geometry
  - Geometry Basics
    - Undefined Terms 3
    - Line Segments 4
    - Mathematical Rays 1
    - Intersections 3
    - Midpoint Formula 2
    - Distance Formula 3
  - Angles
    - Angle Types 26
    - Complementary Angles 13
    - Vertical Angles 7
    - Angle Bisector 4
    - Angle Addition 4
  - Triangles
    - Triangle Types 7
    - Angle Sum 3
    - Triangle Inequality 6
    - Triangle Congruence 14
    - Special Triangles 8
    - Pythagoras Theorem 18
    - Triangle Centers 4
    - Medians & Altitudes 6
  - Quadrilaterals
    - Types of Quads 1
    - Quad Properties 14
    - Midsegment Rule 5
  - Circles
    - Circle Parts 4
    - Arcs & Angles 2
    - Inscribed Angles 2
    - Arc Length 1
    - Circle Equation 3
    - Tangents 1
  - Polygons
    - Polygon Types 13
    - Angle Sums 7
    - Regular Polygons 5
    - Polygon Diagonals 3
    - Tessellations 4
  - Perimeter & Area
    - Perimeter 18
    - Area Formulas 10
    - Composite Areas 6
    - Circle Area 11
  - Surface Area & Volume
    - Surface Area 4
    - Volume of Solids 11
    - Composite Solids 8
    - Math Density 2
    - Cross Sections 5
  - Coordinate Geometry
    - Metric Distance 2
    - Midpoint 5
    - Slope 7
    - Line Equation 10
  - Transformations
    - Geometric Translation 10
    - Geometric Rotation 1
    - Geometric Reflection 3
    - Dilation 5
    - Symmetry 5
    - Similarity 9
- Trigonometry
  - Trigonometric Ratios
    - Sine Cosine Tangent 5
    - Reciprocal Ratios 4
    - Right Triangle Ratios 4
    - Triangle Sides 9
  - Trigonometric Identities
    - Pythagorean Identities 6
    - Reciprocal Identities 5
    - Quotient Identities 5
    - Co Function Identities 1
    - Even Odd Identities 5
    - Double Angle Formulas 5
    - Half Angle Formulas 4
    - Sum & Difference 4
  - Trig Graphs
    - Sine Graph 4
    - Cosine Graph 5
    - Tangent Graph 2
    - Cotangent Graph 5
    - Secant Graph 5
    - Cosecant Graph 2
    - Amplitude & Period 4
    - Phase Shift 5
    - Vertical Shift 5
  - Inverse Trig
    - Inverse Sine 5
    - Inverse Cosine 4
    - Inverse Tangent 6
    - Graphs of Inverses 4
    - Principal Values 4
    - Real World Use 2
  - Solving Triangles
    - SOHCAHTOA Method 8
    - Law of Sines 5
    - Law of Cosines 3
    - Ambiguous Case 2
    - Finding Sides 3
    - Finding Angles 4
    - Area of Triangle 5
    - Heron Formula 5
  - Real World Applications
    - Heights & Distances 3
    - Angle of Elevation 6
    - Angle of Depression 5
    - Navigation Bearings 5
    - Shadows & Towers 5
    - Sound & Light Waves 5
    - Engineering Design 4
    - Astronomy & Orbits 5
- Calculus
  - Limits
    - Limit Basics 4
    - One Sided Limits 5
    - Infinite Limits 5
    - Limits at Infinity 6
    - Piecewise Functions 7
    - lhopitals Rule 5
  - Derivatives
    - Definition of Derivative 4
    - Power Rule 4
    - Product Rule 11
    - Quotient Rule 3
    - Chain Rule 2
    - Derivatives of Trig 5
    - Implicit Differentiation 6
    - Tangents & Slopes 4
    - Optimization Problems 4
  - Integrals
    - Indefinite Integrals 7
    - Definite Integrals 2
    - Fundamental Theorem 3
    - Integration by Substitution 4
    - Integration by Parts 6
    - Improper Integrals 5
    - Integration of Trig 1
  - Differential Equations
    - First Order Equations 4
    - Separable Equations 5
    - Exact Equations 1
    - Homogeneous Equations 4
    - Growth & Decay 5
  - Sequences & Series
    - Arithmetic Sequences 51
    - Geometric Sequences 8
    - Convergence Tests 1
    - Infinite Series 3
    - Partial Sums 4
    - Power Series 6
    - Taylor Series 5
    - Maclaurin Series 5
  - Multivariable Calculus
    - Partial Derivatives 4
    - Gradient Vectors 8
    - Vector Fields 1
    - Line Integrals 5
    - Divergence & Curl 5
- Statistics & Probability
  - Data Handling
    - Types of Data 17
    - Primary Secondary Data 1
    - Frequency Tables 3
    - Bar Graphs 5
    - Pie Charts 8
    - Line Graphs 16
    - Histograms 7
    - Stem & Leaf 6
    - Dot Plots 9
  - Central Tendency
    - Arithmetic Mean 6
    - Median 15
    - Mode 6
    - Weighted Mean 3
  - Data Dispersion
    - Range 5
    - Interquartile Range 6
    - Variance 5
    - Standard Deviation 1
    - Mean Absolute Deviation 6
    - Box & Whisker 3
  - Probability Concepts
    - Theoretical Probability 2
    - Experimental Probability 5
    - Sample Space 6
    - Mutually Exclusive Events 6
    - Independent Events 7
    - Conditional Probability 5
    - Complementary Events 5
  - Probability Distributions
    - Probability Tables 3
    - Binomial Distribution 6
    - Normal Distribution 9
    - Uniform Distribution 2
    - Poisson Distribution 2
    - Cumulative Distribution 5
  - Inferential Statistics
    - Population & Sample 5
    - Sampling Methods 12
    - Hypothesis Testing 16
    - Confidence Intervals 4
    - Margin of Error 7
    - Z & T Tests 3
    - Chi Square Test 3
- Number Theory
  - Prime Numbers
    - Prime Basics 6
    - Prime Factorization 13
    - Sieve of Eratosthenes 5
    - Twin Primes 5
    - Primality Tests 1
  - Divisibility Rules
    - Divisibility by 2 6
    - Rules Application 2
    - Remainder Concepts 6
    - Number Puzzles 2
    - Divisibility Proofs 5
  - GCD & LCM
    - GCD Basics 5
    - LCM Basics 5
    - Euclidean Algorithm 4
    - GCD LCM Practice 2
    - Coprime Numbers 2
  - Modular Arithmetic
    - Congruence 9
    - Modulo Basics 5
    - Congruence Relations 6
    - Modular Addition 5
    - Modular Multiplication 3
    - Modular Inverses 3
    - Math in Coding 2
  - Diophantine Equations
    - Pythagorean Triples 3
- Mathematical Topology
  - Set Types
    - Open Sets 4
    - Closed Sets 4
    - Interior Points 3
    - Closure of Sets 3
    - Boundary Points 3
    - Limit Points 3
  - Continuity
  - Compactness
    - Compact Sets 3
    - Open Covers 4
  - Connectedness
    - Connected Sets 3
    - Disconnected Sets 3
    - Path Connectedness 3
    - Connected Components 3
    - Continuous Images 3
  - Metric Spaces
    - Metric Definition 2
    - Open Balls 3
    - Convergence in Metric 3
    - Completeness 3
    - Boundedness 4
    - Induced Mathematical Topology 3
- Combinatorics
  - Permutations
    - Permutation Basics 3
    - Without Repetition 5
    - With Repetition 2
    - Circular Permutations 1
    - Permutation Problems 1
  - Combinations
  - Pigeonhole
    - Basic Principle 5
    - Generalized Form 3
    - Number Problems 1
  - Inclusion Exclusion
    - Principle Basics 5
    - Two Sets 5
    - Three Sets 4
    - Venn Diagram Use 5
    - Advanced Problems 2
  - Graph Theory
    - Graph Terminology 4
    - Types of Graphs 2
    - Degree of Vertex 5
    - Euler Paths 4
    - Hamiltonian Paths 3
    - Graph Representations 3
- Mathematical Logic
  - Propositional Logic
    - Logical Statements 9
    - Truth Tables 4
    - Logical Connectives 4
    - Tautologies 1
    - Contradictions 5
    - Logical Equivalence 5
  - Predicate Logic
    - Predicate Statements 4
    - Logical Quantifiers 4
    - Universal Statements 4
    - Existential Statements 6
    - Validity & Models 5
  - Set Theory
    - Set Notation 4
    - Venn Diagrams 7
    - Union & Intersection 4
    - Subsets & Power Sets 5
    - Complements & Differences 3
    - Cartesian Products 4
    - Countable Sets 3
  - Proof Techniques
    - Direct Proof 4
    - Contrapositive Proof 4
    - Contradiction Method 4
    - Inductive Proof 4
    - Case Analysis 4
    - Counterexamples 4
  - Boolean Algebra
    - Boolean Variables 5
    - Boolean Laws 4
    - Simplification Rules 4
    - Logic Circuits 4
    - Karnaugh Maps 3
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Direct Proof Quizzes, Questions & Answers

Top Trending Direct Proof Quizzes

Direct Proof in Algebra, Functions, and Sets

Think you can turn everyday math facts into solid proofs? This quiz lets you put that to the test using direct proofs in number theory, algebra, and functions. You’ll write integers as multiples, express rational numbers as...

Questions: 15 | Attempts: 17 | Last updated: Dec 12, 2025

Sample Question 1
In a direct proof that "If a|b and b|c, then a|c" (where | means divides), which is the first appropriate statement?

Assume a|c

Assume a|b and b|c

Let b = ak and c = bm for integers k,m

Let c = an for some integer n

Sample Question 2
To directly prove "If x > y > 0, then x² > y²," the first step is to:

Assume x² > y²

Write x = y + d where d > 0

Assume x > y > 0

Factor x² - y² = (x-y)(x+y)

Direct Proof Basics: From Hypothesis to Conclusion

Are you ready to see how formal proofs actually work step by step? In this quiz, you’ll practice the core idea of a direct proof: start by assuming the hypothesis is true and then use logic, definitions, and simple algebra...

Questions: 15 | Attempts: 13 | Last updated: Dec 12, 2025

Sample Question 1
What is the first step in a direct proof of "If P, then Q"?

Assume Q is true

Assume P is true

Assume P is false

Assume Q is false

Sample Question 2
In a direct proof of "If n is even, then n² is even," what do we assume first?

N² is even

N is odd

N² is odd

N is even

Recent Direct Proof Quizzes

Direct Proof Quiz: Strengthen Step-by-Step Logical Arguments

Direct reasoning is the foundation of most mathematical arguments, and this direct proof quiz helps you practice it in a clear, approachable way. You’ll work through statements that require building a logical chain from...

Questions: 20 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
In proving "If a relation R is symmetric and transitive, and every element is related to at least one element, then R is reflexive" directly, we need to:

Assume aRa is false for some a

Prove the contrapositive statement

Use induction on the number of elements

For each a, find b such that aRb, then use symmetry and transitivity to show aRa

Direct Proof in Advanced Structures and Mappings

Ready to level up your proof skills in more abstract settings? In this quiz, you’ll use direct proofs to explore sets, relations, sequences, and algebraic structures like rings. You’ll practice showing when one set is...

Questions: 15 | Attempts: 10 | Last updated: Dec 12, 2025

Sample Question
In proving "If a relation R is symmetric and transitive, and every element is related to at least one element, then R is reflexive" directly, we need to:

Assume aRa is false for some a

Prove the contrapositive statement

Use induction on the number of elements

For each a, find b such that aRb, then use symmetry and transitivity to show aRa