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공개 퀴즈 목록 (256개 중 121-140)
| ID | 과목 | 파일명 | 문제 수 | 퀴즈 타입 | 소유자 | 통계 조회/가져오기 |
등록일 | 작업 |
|---|---|---|---|---|---|---|---|---|
| 328 | 🔬 Science |
science_quiz1_8_chemical_bonding
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 327 | 🔬 Science |
science_quiz1_7_atomic_structure_isotopes
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 326 | 🔬 Science |
science_quiz1_6_properties_of_matter
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 325 | 🔬 Science |
science_quiz1_5_states_of_matter
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 324 | 🔬 Science |
science_quiz1_4_chemical_formulas
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 323 | 🔬 Science |
science_quiz1_3_molecules_compounds
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 322 | 🔬 Science |
science_quiz1_2_the_periodic_table
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25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 321 | 🔬 Science |
science_quiz1_1_atoms_and_elements
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25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 320 | 🔢 Mathematics |
math_quiz8_8_patterns_and_sequences_review
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25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 319 | 🔢 Mathematics |
math_quiz8_7_sequence_problem_solving
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 318 | 🔢 Mathematics |
math_quiz8_6_recursive_formulas
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 317 | 🔢 Mathematics |
math_quiz8_5_special_sequences
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 316 | 🔢 Mathematics |
math_quiz8_4_comparing_and_applying_sequences
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 315 | 🔢 Mathematics |
math_quiz8_3_geometric_sequences
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 314 | 🔢 Mathematics |
math_quiz8_2_arithmetic_sequences
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 313 | 🔢 Mathematics |
math_quiz8_1_introduction_to_patterns
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 312 | 🔢 Mathematics |
math_quiz7_8_applications_of_ratios_and_proportions
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
| 311 | 🔢 Mathematics |
math_quiz7_7_inverse_proportion
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 310 | 🔢 Mathematics |
math_quiz7_6_direct_proportion
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
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| 309 | 🔢 Mathematics |
math_quiz7_5_solving_proportion_problems
|
25문제 | 🛡️ 교강사 | admin | 👁️ 0 / 📥 0 | 2025-11-25 14:16:20 |
|
📖 science_quiz1_8_chemical_bonding
Why do atoms form bonds?
1. To become unstable
2. To lose all electrons
3. To achieve a full outer shell ✓
4. Randomly
The octet rule states that atoms want:
1. 2 valence electrons
2. 8 valence electrons ✓
3. 18 electrons total
4. No electrons
An ionic bond forms between:
1. Two metals
2. A metal and a non-metal ✓
3. Two non-metals
4. Noble gases
A covalent bond forms between:
1. Two metals
2. Only noble gases
3. A metal and a non-metal
4. Two non-metals ✓
In ionic bonding, electrons are:
1. Shared equally
2. Destroyed
3. Transferred ✓
4. Created
In covalent bonding, electrons are:
1. Shared ✓
2. Transferred
3. Lost forever
4. Not involved
An atom that loses electrons becomes a:
1. Cation (positive ion) ✓
2. Anion (negative ion)
3. Neutral atom
4. Molecule
An atom that gains electrons becomes a:
1. Cation (positive ion)
2. Anion (negative ion) ✓
3. Neutral atom
4. Molecule
Sodium (2,8,1) typically forms:
1. Na⁻ (anion)
2. Na₂
3. Na⁺ (cation) ✓
4. Na does not form ions
Chlorine (2,8,7) typically forms:
1. Cl⁺ (cation)
2. Cl does not form ions
3. Cl₂ only
4. Cl⁻ (anion) ✓
Ionic compounds typically have:
1. Low melting points
2. High melting points ✓
3. No definite structure
4. Cannot form crystals
Covalent compounds typically have:
1. High melting points
2. Always conduct electricity
3. Low melting points ✓
4. Are always metals
Which is a property of ionic compounds?
1. Conduct electricity when dissolved ✓
2. Soft and flexible
3. Low melting points
4. Cannot form crystals
Which is a property of covalent compounds?
1. Always solid at room temperature
2. High electrical conductivity
3. Do not conduct electricity ✓
4. Always form crystals
Table salt (NaCl) is an example of:
1. Covalent bonding
2. No bonding
3. Metallic bonding
4. Ionic bonding ✓
Water (H₂O) is an example of:
1. Ionic bonding
2. Metallic bonding
3. Covalent bonding ✓
4. No bonding
Metallic bonding involves:
1. A "sea" of delocalized electrons ✓
2. Electron sharing between two atoms
3. Electron transfer
4. No electrons
Why are metals good electrical conductors?
1. They are heavy
2. They are solid
3. They are shiny
4. They have free-moving electrons ✓
Why are metals malleable?
1. Layers of atoms can slide past each other ✓
2. They are soft
3. They have low density
4. They are brittle
A double bond consists of:
1. One shared pair of electrons
2. No shared electrons
3. Three shared pairs of electrons
4. Two shared pairs of electrons ✓
Nitrogen gas (N₂) has what type of bond?
1. Single
2. Triple ✓
3. Double
4. Ionic
Predict the bond type for MgO:
1. Covalent
2. Ionic ✓
3. Metallic
4. No bond
Predict the bond type for CO₂:
1. Covalent ✓
2. Ionic
3. Metallic
4. No bond
Predict the bond type for copper wire:
1. Metallic ✓
2. Covalent
3. Ionic
4. No bond
Why are ionic compounds brittle?
1. They are too soft
2. They conduct electricity
3. They have weak bonds
4. Like charges repel when layers shift ✓
📖 science_quiz1_7_atomic_structure_isotopes
Which subatomic particle has a positive charge?
1. Electron
2. Neutron
3. Proton ✓
4. Nucleus
Where are electrons located in an atom?
1. In the nucleus
2. In electron shells around the nucleus ✓
3. Outside the atom
4. Mixed with protons
The maximum number of electrons in the first shell is:
1. 1
2. 2 ✓
3. 8
4. 18
The maximum number of electrons in the second shell is:
1. 2
2. 4
3. 18
4. 8 ✓
Valence electrons are electrons in the:
1. Nucleus
2. First shell
3. Outermost shell ✓
4. Innermost shell
An atom with electron configuration 2,8,1 has how many valence electrons?
1. 1 ✓
2. 2
3. 8
4. 11
In atomic notation ¹²₆C, the 6 represents:
1. Atomic number (protons) ✓
2. Number of neutrons
3. Mass number
4. Number of electrons
In atomic notation ¹²₆C, the 12 represents:
1. Atomic number
2. Mass number (protons + neutrons) ✓
3. Number of electrons
4. Number of neutrons only
For ²³₁₁Na, how many neutrons are there?
1. 11
2. 23
3. 12 ✓
4. 34
What are isotopes?
1. Atoms with different protons
2. Different elements entirely
3. Atoms with different electrons
4. Atoms of the same element with different neutrons ✓
Carbon-12 and Carbon-14 are isotopes. They have the same number of:
1. Neutrons
2. Electrons and protons ✓
3. Mass
4. Neutrons and protons
Which hydrogen isotope has no neutrons?
1. Deuterium
2. Tritium
3. Protium ✓
4. All have neutrons
Deuterium (²H) has how many neutrons?
1. 1 ✓
2. 0
3. 2
4. 3
Carbon-14 is used for:
1. Nuclear power
2. Medical imaging
3. Dating ancient objects ✓
4. Water purification
Why do isotopes of the same element have similar chemical properties?
1. Same mass
2. Same neutrons
3. Same density
4. Same number of electrons ✓
The average atomic mass on the periodic table is:
1. Always a whole number
2. The mass of the most common isotope
3. A weighted average of isotopes ✓
4. The mass of the nucleus
Chlorine has an average atomic mass of 35.5 amu because:
1. It's a mix of Cl-35 (75%) and Cl-37 (25%) ✓
2. All atoms weigh 35.5 amu
3. Chlorine is unstable
4. It's a calculation error
A radioactive isotope is one that:
1. Has extra electrons
2. Never changes
3. Has no neutrons
4. Is unstable and decays over time ✓
Which isotope is used to treat thyroid cancer?
1. Iodine-131 ✓
2. Carbon-14
3. Uranium-235
4. Hydrogen-3
An atom with 8 protons, 8 neutrons, and 8 electrons is:
1. Carbon
2. Nitrogen
3. Neon
4. Oxygen ✓
An element with electron configuration 2,8,8,2 has how many valence electrons?
1. 8
2. 2 ✓
3. 18
4. 20
The octet rule states that atoms are most stable with:
1. 2 valence electrons
2. 8 valence electrons ✓
3. 4 valence electrons
4. 18 valence electrons
Noble gases are stable because they have:
1. Full outer shells ✓
2. No electrons
3. No protons
4. Only one shell
For ⁴⁰₂₀Ca, how many protons, neutrons, and electrons are there?
1. 20, 20, 20 ✓
2. 20, 40, 20
3. 40, 20, 40
4. 20, 20, 40
Which property changes between isotopes of the same element?
1. Chemical reactivity
2. Number of protons
3. Number of electrons
4. Mass ✓
📖 science_quiz1_6_properties_of_matter
A physical property can be observed:
1. Only by changing the substance
2. Only with special equipment
3. Without changing the substance ✓
4. Never directly
Which is a chemical property?
1. Color
2. Flammability ✓
3. Density
4. Melting point
Density is defined as:
1. Mass times volume
2. Mass divided by volume ✓
3. Volume divided by mass
4. Mass plus volume
If an object has a density less than water, it will:
1. Sink
2. Evaporate
3. Dissolve
4. Float ✓
Which is an intensive property?
1. Mass
2. Volume
3. Melting point ✓
4. Total energy
Which is an extensive property?
1. Mass ✓
2. Color
3. Density
4. Boiling point
The ability to be hammered into thin sheets is called:
1. Malleability ✓
2. Ductility
3. Conductivity
4. Solubility
The ability to be drawn into wires is called:
1. Malleability
2. Ductility ✓
3. Brittleness
4. Hardness
On the Mohs scale, which mineral is the hardest?
1. Talc
2. Quartz
3. Diamond ✓
4. Gold
Copper is a good electrical conductor because:
1. It's heavy
2. It's orange
3. It's shiny
4. It has free-moving electrons ✓
Which property helps identify pure substances?
1. Mass
2. Melting point ✓
3. Volume
4. Shape
"Like dissolves like" means:
1. All substances dissolve in water
2. Solids don't dissolve
3. Polar dissolves polar, nonpolar dissolves nonpolar ✓
4. Only liquids dissolve
Which is a chemical property?
1. Reactivity with acid ✓
2. Mass
3. Boiling point
4. Color
Rust forming on iron is an example of:
1. A physical change
2. Melting
3. Oxidation ✓
4. Sublimation
A substance with mass 50g and volume 25cm³ has a density of:
1. 1.0 g/cm³
2. 75 g/cm³
3. 25 g/cm³
4. 2.0 g/cm³ ✓
Which material is the best thermal conductor?
1. Wood
2. Plastic
3. Copper ✓
4. Air
Gasoline is:
1. Highly flammable ✓
2. Slightly flammable
3. Non-flammable
4. Cannot burn
Gold is chemically stable, meaning it:
1. Reacts with everything
2. Changes color quickly
3. Is radioactive
4. Doesn't tarnish or corrode easily ✓
Which property is used in distillation to separate liquids?
1. Boiling point ✓
2. Density
3. Color
4. Mass
An insulator is a material that:
1. Conducts electricity well
2. Conducts heat well
3. Is always metal
4. Does not conduct electricity ✓
Which is true about intensive properties?
1. They depend on the amount
2. They don't depend on the amount ✓
3. They are always chemical properties
4. They cannot be measured
The melting point of pure water is:
1. -10°C
2. 0°C ✓
3. 50°C
4. 100°C
Which property would help identify an unknown white powder as salt?
1. It dissolves in water and tastes salty ✓
2. It's white
3. It's a powder
4. It exists at room temperature
Why are cooking pots often made of aluminum or copper?
1. They have high thermal conductivity ✓
2. They are cheap
3. They are light
4. They are colorful
Which is a use of properties in forensic science?
1. Cooking food
2. Making music
3. Building bridges
4. Identifying unknown substances ✓
📖 science_quiz1_5_states_of_matter
Which state of matter has a definite shape and volume?
1. Gas
2. Liquid
3. Solid ✓
4. Plasma
Which state of matter has no definite shape or volume?
1. Solid
2. Gas ✓
3. Liquid
4. Ice
In which state do particles slide past each other?
1. Solid
2. Liquid ✓
3. Gas
4. Plasma
What phase change occurs when a solid becomes a liquid?
1. Freezing
2. Sublimation
3. Condensation
4. Melting ✓
What phase change occurs when a liquid becomes a gas?
1. Melting
2. Freezing
3. Vaporization ✓
4. Deposition
What is sublimation?
1. Solid to gas directly ✓
2. Liquid to gas
3. Solid to liquid
4. Gas to liquid
Dry ice (solid CO₂) undergoes:
1. Sublimation ✓
2. Freezing
3. Melting
4. Condensation
What happens to particles when a substance is heated?
1. They move slower
2. They move faster ✓
3. They stop moving
4. They disappear
At what temperature does water freeze?
1. 100°C
2. 32°C
3. 0°C ✓
4. -10°C
At what temperature does water boil at sea level?
1. 0°C
2. 50°C
3. 212°C
4. 100°C ✓
Which state has particles that are far apart and move rapidly?
1. Solid
2. Gas ✓
3. Liquid
4. All states
What is plasma?
1. Super-cooled solid
2. Dense liquid
3. Superheated gas with ions ✓
4. Frozen gas
Which is an example of plasma?
1. Lightning ✓
2. Water
3. Steam
4. Ice
When water vapor condenses, it becomes:
1. Ice
2. Steam
3. Liquid water ✓
4. Plasma
Why does sweating cool you down?
1. Sweat is cold
2. It doesn't cool you
3. Sweat blocks heat
4. Evaporation absorbs heat from skin ✓
Which has the strongest forces between particles?
1. Gases
2. Liquids
3. Solids ✓
4. Plasma
Which state is most compressible?
1. Gas ✓
2. Liquid
3. Solid
4. They are equally compressible
Frost forming on a window is an example of:
1. Melting
2. Freezing
3. Sublimation
4. Deposition ✓
What property do liquids and gases share?
1. Ability to flow ✓
2. Definite shape
3. Fixed volume
4. High density
In which state do particles only vibrate in place?
1. Plasma
2. Liquid
3. Gas
4. Solid ✓
What is the most common state of matter in the universe?
1. Solid
2. Plasma ✓
3. Gas
4. Liquid
Which phase change releases energy?
1. Melting
2. Freezing ✓
3. Vaporization
4. Sublimation
Which phase change requires adding energy?
1. Melting ✓
2. Condensation
3. Freezing
4. Deposition
Water is unique because it exists naturally on Earth as:
1. Solid, liquid, and gas ✓
2. Only liquid
3. Only solid
4. Only gas
Temperature measures:
1. Total energy
2. Type of matter
3. Number of particles
4. Average kinetic energy of particles ✓
📖 science_quiz1_4_chemical_formulas
What does a chemical formula represent?
1. Only the mass of a substance
2. The color of a substance
3. The composition of a substance using symbols and numbers ✓
4. The physical state only
What does the subscript in a chemical formula indicate?
1. Number of molecules
2. Number of atoms of an element ✓
3. Charge of the atom
4. Mass of the element
In the formula H₂O, how many hydrogen atoms are there?
1. 1
2. 2 ✓
3. 3
4. 4
If no subscript is written after an element symbol, it means:
1. Zero atoms
2. The element is absent
3. Two atoms
4. One atom ✓
What is the difference between H₂O and H₂O₂?
1. They are the same substance
2. Different number of hydrogen atoms
3. Different number of oxygen atoms ✓
4. Only the temperature
A coefficient is written:
1. In front of the formula ✓
2. As a subscript
3. After the formula
4. Inside parentheses
In 2H₂O, what does the "2" in front represent?
1. 2 molecules of water ✓
2. 2 oxygen atoms
3. 2 hydrogen atoms
4. 2 different substances
How many total atoms are in 2H₂O?
1. 3
2. 6 ✓
3. 4
4. 8
What is the molecular formula for glucose?
1. CO₂
2. CH₂O
3. C₆H₁₂O₆ ✓
4. C₁₂H₂₂O₁₁
An empirical formula shows:
1. The exact number of atoms
2. The bonds between atoms
3. The mass of the molecule
4. The simplest whole-number ratio ✓
In Ca(OH)₂, how many total atoms are there?
1. 3
2. 5 ✓
3. 4
4. 6
Parentheses in a formula indicate:
1. A mistake
2. An optional part
3. A group that repeats ✓
4. The charge
How many hydrogen atoms are in 3H₂SO₄?
1. 6 ✓
2. 3
3. 2
4. 12
What is the chemical formula for table salt?
1. CaCl₂
2. NaOH
3. NaCl ✓
4. KCl
In chemical formulas, which element is usually written first?
1. Non-metal
2. Halogen
3. Noble gas
4. Metal ✓
How many total atoms are in C₆H₁₂O₆?
1. 3
2. 6
3. 24 ✓
4. 18
What is the formula for carbon dioxide?
1. CO₂ ✓
2. CO
3. C₂O
4. C₂O₂
The formula NH₃ represents:
1. Nitrogen oxide
2. Ammonium
3. Nitric acid
4. Ammonia ✓
Changing a subscript in a formula:
1. Changes the substance completely ✓
2. Changes the amount only
3. Has no effect
4. Changes the temperature
How many oxygen atoms are in 2CO₂?
1. 1
2. 2
3. 3
4. 4 ✓
In Al₂O₃, the ratio of aluminum to oxygen is:
1. 1:1
2. 2:3 ✓
3. 2:1
4. 3:2
What does the formula NaHCO₃ represent?
1. Sodium chloride
2. Baking soda ✓
3. Sodium hydroxide
4. Salt water
Why do scientists use chemical formulas?
1. For universal communication ✓
2. To make chemistry difficult
3. Only for advanced research
4. To confuse students
In 2Ca(OH)₂, how many calcium atoms are there?
1. 2 ✓
2. 1
3. 3
4. 4
The formula for water is always H₂O because:
1. It's a rule with no reason
2. Scientists decided arbitrarily
3. Water changes composition
4. Compounds have fixed ratios of elements ✓
📖 science_quiz1_3_molecules_compounds
What is a molecule?
1. A single atom
2. Only atoms of different elements
3. Two or more atoms bonded together ✓
4. A type of element
What is a compound?
1. A substance made of only one type of atom
2. A substance made of two or more different elements bonded together ✓
3. A mixture of different substances
4. A molecule made of the same element
Which of the following is a diatomic molecule?
1. O₃ (ozone)
2. O₂ (oxygen gas) ✓
3. H₂O (water)
4. CO₂ (carbon dioxide)
Which statement is TRUE about compounds?
1. Compounds have the same properties as their elements
2. All molecules are compounds
3. Compounds can only contain two elements
4. All compounds are molecules ✓
What is the correct formula for water?
1. H₃O
2. HO₂
3. H₂O ✓
4. H₂O₂
Which of these is NOT a compound?
1. N₂ ✓
2. CO₂
3. H₂O
4. NaCl
The mnemonic "HONClBrIF" helps us remember:
1. Elements that exist as diatomic molecules ✓
2. Elements that form compounds
3. Noble gases
4. Metals
What type of bond involves sharing electrons?
1. Ionic bond
2. Covalent bond ✓
3. Metallic bond
4. Hydrogen bond
What type of bond involves transferring electrons?
1. Covalent bond
2. Metallic bond
3. Ionic bond ✓
4. Double bond
Sodium chloride (NaCl) is formed from:
1. Two sodium atoms
2. Sodium and oxygen
3. Only chlorine atoms
4. Sodium metal and chlorine gas ✓
Which property of water is DIFFERENT from its elements (H and O)?
1. Water is a gas at room temperature
2. Water extinguishes fires ✓
3. Water is flammable
4. Water is explosive
Carbon dioxide (CO₂) consists of:
1. 1 carbon and 1 oxygen
2. 2 carbon and 1 oxygen
3. 1 carbon and 2 oxygen ✓
4. 2 carbon and 2 oxygen
Ammonia (NH₃) is used in:
1. Fertilizer production ✓
2. Drinking water
3. Jewelry making
4. Battery production
What is the ratio of hydrogen to oxygen in water (H₂O)?
1. 1:1
2. 1:2
3. 2:1 ✓
4. 3:1
Ozone (O₃) is classified as:
1. A compound
2. An element
3. A diatomic molecule
4. A polyatomic molecule ✓
Which statement about compounds is TRUE?
1. Compounds can be separated by physical means
2. Compounds have varying ratios of elements
3. Compounds have properties different from their elements ✓
4. Compounds contain only one type of atom
Methane (CH₄) is commonly known as:
1. Natural gas ✓
2. Table salt
3. Vinegar
4. Sugar
Which of these is a characteristic of compounds?
1. Variable composition
2. Physical combination only
3. Same properties as their elements
4. Fixed ratio of elements ✓
Glucose (C₆H₁₂O₆) contains how many different elements?
1. 3 ✓
2. 2
3. 1
4. 4
Which molecule protects Earth from UV radiation?
1. O₂ (oxygen)
2. H₂O (water)
3. CO₂ (carbon dioxide)
4. O₃ (ozone) ✓
When sodium (Na) and chlorine (Cl) form table salt, the result is:
1. A poisonous gas
2. A harmless white crystal ✓
3. An explosive metal
4. A flammable liquid
Which is TRUE about diatomic molecules?
1. They contain different elements
2. They always contain two atoms of the same element ✓
3. They are always compounds
4. They cannot exist naturally
What is the common name for NaCl?
1. Table salt ✓
2. Baking soda
3. Sugar
4. Vinegar
Covalent bonds are most common between:
1. Non-metals and non-metals ✓
2. Metals and non-metals
3. Metals and metals
4. Noble gases
Which formula represents a compound?
1. O₂
2. N₂
3. H₂
4. CO₂ ✓
📖 science_quiz1_2_the_periodic_table
Who created the first widely recognized periodic table?
1. Albert Einstein
2. Isaac Newton
3. Dmitri Mendeleev ✓
4. Marie Curie
How are elements arranged in the modern periodic table?
1. By atomic mass
2. By atomic number ✓
3. By element name
4. By discovery date
What are the horizontal rows in the periodic table called?
1. Groups
2. Periods ✓
3. Families
4. Series
What are the vertical columns in the periodic table called?
1. Periods
2. Rows
3. Sections
4. Groups ✓
Where are most metals located on the periodic table?
1. Right side
2. Top only
3. Left side and center ✓
4. Bottom only
Where are nonmetals located on the periodic table?
1. Right side ✓
2. Center
3. Left side
4. Bottom
Which property is common to all metals?
1. They conduct electricity ✓
2. They are gases at room temperature
3. They are dull in appearance
4. They break easily
What does the period number tell us about an element?
1. Number of protons
2. Number of electron shells ✓
3. Number of neutrons
4. Number of valence electrons
Which group contains the most reactive metals?
1. Group 17 (Halogens)
2. Group 2 (Alkaline earth metals)
3. Group 1 (Alkali metals) ✓
4. Group 18 (Noble gases)
Why are Group 18 elements called noble gases?
1. They are expensive
2. They are colorful
3. They are radioactive
4. They are unreactive ✓
How many valence electrons do halogens (Group 17) have?
1. 1
2. 7 ✓
3. 2
4. 8
Which elements are called metalloids?
1. All elements in Period 1
2. All elements in Group 1
3. Elements between metals and nonmetals ✓
4. Only radioactive elements
What is silicon (Si) primarily used for?
1. Computer chips and solar panels ✓
2. Making steel
3. Water purification
4. Making jewelry
Why do elements in the same group have similar properties?
1. They have the same atomic mass
2. They were discovered at the same time
3. They have the same number of valence electrons ✓
4. They have the same number of neutrons
What happens to atomic size as you move down a group?
1. It decreases
2. It doubles
3. It stays the same
4. It increases ✓
What happens to metallic character as you move from left to right across a period?
1. It increases
2. It stays the same
3. It decreases ✓
4. It varies randomly
Which element is used in balloons because it is lighter than air and safe?
1. Helium ✓
2. Hydrogen
3. Oxygen
4. Nitrogen
An element is in Group 2, Period 3. What can you determine about it?
1. It has 2 electron shells and 3 valence electrons
2. It is a noble gas
3. It has 2 protons and 3 neutrons
4. It has 3 electron shells and 2 valence electrons ✓
Why did Mendeleev leave gaps in his periodic table?
1. He predicted undiscovered elements ✓
2. He ran out of space
3. He made mistakes
4. He wanted to confuse people
What trend occurs in reactivity of alkali metals (Group 1) going down the group?
1. Reactivity decreases
2. Reactivity alternates
3. Reactivity stays the same
4. Reactivity increases ✓
What trend occurs in reactivity of halogens (Group 17) going down the group?
1. Reactivity increases
2. Reactivity decreases ✓
3. Reactivity stays the same
4. Reactivity doubles
How many elements are currently confirmed on the periodic table?
1. 92
2. 118 ✓
3. 108
4. 100
What is the most reactive nonmetal?
1. Fluorine ✓
2. Chlorine
3. Oxygen
4. Nitrogen
Why do noble gases rarely form compounds?
1. They have full outer electron shells ✓
2. They are too heavy
3. They are radioactive
4. They are too small
Which statement about periodic trends is correct?
1. Atomic size increases from left to right
2. Electron shells decrease down a group
3. Reactivity of metals decreases down a group
4. Metallic character increases from right to left ✓
📖 science_quiz1_1_atoms_and_elements
What is an atom?
1. A chemical compound
2. A type of molecule
3. The smallest unit of an element ✓
4. A subatomic particle
Which subatomic particle has a positive charge?
1. Electron
2. Proton ✓
3. Neutron
4. Nucleus
Which subatomic particle has NO charge?
1. Proton
2. Neutron ✓
3. Electron
4. Ion
Where are electrons found in an atom?
1. In the nucleus
2. Between neutrons
3. Inside protons
4. In electron shells around the nucleus ✓
What determines the identity of an element?
1. Number of neutrons
2. Number of electrons
3. Number of protons ✓
4. Mass number
What is the atomic number?
1. Number of protons ✓
2. Number of electrons
3. Number of neutrons
4. Number of atoms
In a neutral atom, the number of protons equals the number of:
1. Electrons ✓
2. Neutrons
3. Nuclei
4. Energy levels
Which particle has the smallest mass?
1. Proton
2. Electron ✓
3. Neutron
4. All have equal mass
What is the mass number of an atom?
1. Number of protons only
2. Number of electrons + protons
3. Number of protons + neutrons ✓
4. Number of neutrons only
An atom has 6 protons. What element is it?
1. Oxygen
2. Nitrogen
3. Helium
4. Carbon ✓
If an atom has 8 protons and 8 neutrons, what is its mass number?
1. 8
2. 16 ✓
3. 24
4. 0
What does the standard notation ¹²C tell us?
1. Carbon has 12 protons
2. Carbon has 12 electrons
3. Carbon has mass number 12 ✓
4. Carbon has 12 neutrons
How many electrons can the first electron shell hold?
1. 2 ✓
2. 8
3. 18
4. 32
Which element has the symbol 'Au'?
1. Silver
2. Aluminum
3. Gold ✓
4. Argon
What holds the nucleus together despite the repulsion between positive protons?
1. Gravitational force
2. Electromagnetic force
3. Weak nuclear force
4. Strong nuclear force ✓
Which of the following is an element?
1. Water (H₂O)
2. Salt (NaCl)
3. Oxygen (O₂) ✓
4. Carbon dioxide (CO₂)
A neutral sodium atom has 11 protons. How many electrons does it have?
1. 11 ✓
2. 10
3. 12
4. 22
An atom has an atomic number of 17 and a mass number of 35. How many neutrons does it have?
1. 17
2. 52
3. 35
4. 18 ✓
Which statement about the size of an atom is correct?
1. The nucleus is much smaller but contains most of the mass ✓
2. The nucleus occupies most of the atom's volume
3. The nucleus is larger than the electron cloud
4. Electrons occupy the same space as the nucleus
What is the most abundant element in the human body?
1. Carbon
2. Hydrogen
3. Nitrogen
4. Oxygen ✓
Why do different elements have different properties?
1. They have different masses
2. They have different numbers of protons ✓
3. They have different colors
4. They exist in different states
What percentage of an atom's volume does the nucleus occupy?
1. About 99%
2. Less than 1% ✓
3. About 50%
4. Exactly 10%
Which particle was discovered by J.J. Thomson in 1897?
1. Electron ✓
2. Neutron
3. Proton
4. Nucleus
What did Ernest Rutherford's gold foil experiment reveal?
1. Atoms have a small, dense nucleus ✓
2. Atoms are solid spheres
3. Electrons have negative charge
4. Atoms can be divided
Why is carbon-14 useful for dating ancient objects?
1. It's the most common form of carbon
2. It's found only in living organisms
3. It doesn't react with other elements
4. It's radioactive and decays at a known rate ✓
📖 math_quiz8_8_patterns_and_sequences_review
What is the explicit formula for an arithmetic sequence?
1. aₙ = a₁ × r^(n-1)
2. aₙ = n²
3. aₙ = a₁ + (n-1)d ✓
4. aₙ = aₙ₋₁ + aₙ₋₂
What is the explicit formula for a geometric sequence?
1. aₙ = a₁ + (n-1)d
2. aₙ = a₁ × r^(n-1) ✓
3. aₙ = nd
4. aₙ = n × r
What is the formula for the nth triangular number?
1. n²
2. n(n+1)/2 ✓
3. n³
4. 2n + 1
What is the recursive rule for the Fibonacci sequence?
1. Fₙ = Fₙ₋₁ + 2
2. Fₙ = 2Fₙ₋₁
3. Fₙ = n²
4. Fₙ = Fₙ₋₁ + Fₙ₋₂ ✓
Which sequence type grows faster in the long run?
1. Arithmetic always grows faster
2. They grow at the same rate
3. Geometric (with r > 1) eventually grows faster ✓
4. It depends on the starting values only
What indicates a sequence is arithmetic?
1. Constant differences between consecutive terms ✓
2. Constant ratios between consecutive terms
3. Each term is a perfect square
4. Terms increase exponentially
What indicates a sequence is geometric?
1. Constant ratios between consecutive terms ✓
2. Constant differences between consecutive terms
3. Linear growth
4. All terms are even
A problem says 'investment grows 6% per year.' What type is this?
1. Arithmetic (constant addition)
2. Geometric (multiply by 1.06) ✓
3. Neither
4. Fibonacci
A problem says 'add $50 each month.' What type is this?
1. Geometric
2. Fibonacci
3. Arithmetic (constant addition) ✓
4. Special sequence
Why is the Fibonacci sequence naturally defined recursively?
1. Because it's too difficult otherwise
2. Because it only works with recursion
3. Because it has no pattern
4. Because each term depends on the two previous terms ✓
Find the 20th term of: 8, 15, 22, 29, 36, ...
1. 148
2. 141 ✓
3. 155
4. 162
Find the 8th term of: 5, 15, 45, 135, ...
1. 98,415
2. 32,805
3. 10,935 ✓
4. 295,245
What is the 10th triangular number?
1. 55 ✓
2. 50
3. 45
4. 60
If F₈=21 and F₉=34, what is F₁₁?
1. 55
2. 68
3. 144
4. 89 ✓
Savings: start $400, add $90/month. Total after 15 months?
1. $1,840
2. $1,740
3. $1,750 ✓
4. $1,650
Bacteria: 500 cells, doubles every 3 hours. After 15 hours (5 doublings)?
1. 8,000
2. 12,000
3. 16,000 ✓
4. 32,000
In sequence 6, 13, 20, 27, ..., which term is 97?
1. 13th
2. 14th ✓
3. 15th
4. 16th
Write recursive formula for: 10, 17, 24, 31, ...
1. a₁=10, aₙ=aₙ₋₁+17
2. a₁=10, aₙ=7aₙ₋₁
3. a₁=7, aₙ=aₙ₋₁+10
4. a₁=10, aₙ=aₙ₋₁+7 ✓
Sequence: 4, 9, 16, 25, 36. What pattern? What's next?
1. Square numbers (n²); Next: 49 ✓
2. Add 5 each time; Next: 41
3. Fibonacci; Next: 61
4. Geometric; Next: 72
Jobs: A starts $45k, +$3k/yr. B starts $43k, +5%/yr. Compare Year 12.
1. A: $78k beats B: $76,980 ✓
2. B: $76,980 beats A: $78k
3. They are equal
4. Cannot determine
Sequence: 3, 7, 13, 21, 31. Differences: 4, 6, 8, 10. What's the 7th term?
1. 55
2. 43
3. 57 ✓
4. 61
At what term does 2, 4, 8, 16, ... first exceed 100, 120, 140, 160, ...?
1. 5th term
2. 7th term
3. 6th term
4. 8th term ✓
Investment: $5k for 3 years adding $500/year, then 6%/year for 5 more years. Final value?
1. $8,500
2. $8,734 ✓
3. $9,014
4. $9,500
Student says: 'All sequences with positive terms that increase are geometric.' Evaluate this claim.?
1. False, arithmetic sequences also increase with positive terms ✓
2. True, all increasing sequences are geometric
3. True, but only if they double
4. False, no sequences increase
What is the most important skill learned in this Patterns and Sequences unit?
1. Memorizing all formulas perfectly
2. Drawing graphs
3. Calculating very large numbers
4. Recognizing patterns and choosing appropriate mathematical models ✓
📖 math_quiz8_7_sequence_problem_solving
What is the first step in solving a sequence problem?
1. Write the formula immediately
2. Calculate all terms
3. Identify the pattern and type of sequence ✓
4. Graph the sequence
To determine if a sequence is arithmetic, what should you check?
1. If the ratios between consecutive terms are constant
2. If the differences between consecutive terms are constant ✓
3. If all terms are positive
4. If the terms are whole numbers
To determine if a sequence is geometric, what should you check?
1. If the differences are constant
2. If the ratios between consecutive terms are constant ✓
3. If the terms increase
4. If the formula has an exponent
What information do you need to write an explicit formula for an arithmetic sequence?
1. Only the first term
2. Only the common difference
3. All terms in the sequence
4. The first term (a₁) and common difference (d) ✓
A sequence is 5, 10, 20, 40, 80. What strategy identifies this as geometric?
1. Check differences: 5, 10, 20, 40 (not constant)
2. Plot on a graph
3. Check ratios: 10/5=2, 20/10=2, 40/20=2 (constant) ✓
4. Count the terms
Why might you choose a recursive formula over an explicit formula?
1. When you need to find the 100th term quickly
2. When you need to show the step-by-step development ✓
3. When the sequence is arithmetic
4. Recursive formulas are always better
A problem states: 'Population grows by 200 people per year.' What type is this?
1. Geometric (constant multiplication)
2. Arithmetic (constant addition) ✓
3. Fibonacci
4. Special sequence
A problem states: 'Value increases by 5% each year.' What type is this?
1. Arithmetic (constant addition)
2. Geometric (multiply by 1.05) ✓
3. Linear function
4. Special sequence
What does it mean if a problem asks for the 'nth term formula'?
1. List all terms
2. Find an explicit formula ✓
3. Find a recursive formula
4. Find the first term only
When should you suspect a sequence is neither arithmetic nor geometric?
1. When it has more than 10 terms
2. When it starts with 1
3. When it has negative terms
4. When differences AND ratios are both not constant ✓
Sequence: 7, 14, 21, 28, 35. Find the 15th term.
1. 105 ✓
2. 98
3. 112
4. 119
Sequence: 4, 12, 36, 108. Find the 8th term.
1. 2,916
2. 26,244
3. 8,748 ✓
4. 78,732
You save $100 first month, then $125, $150, $175. How much in month 10?
1. $275 ✓
2. $300
3. $325
4. $350
Bacteria count: 200, 400, 800, 1600. How many after 8 hours (at hour 8)?
1. 12,800
2. 51,200
3. 25,600 ✓
4. 102,400
In sequence 3, 7, 11, 15, ..., which term equals 83?
1. 23rd
2. 21st ✓
3. 22nd
4. 20th
Theater rows: 18, 21, 24, 27 seats. Which row has 39 seats?
1. 6th row
2. 8th row
3. 7th row ✓
4. 9th row
Pattern: Each layer of pyramid has one fewer block. Top has 1, next 2, then 3. Total in 8-layer pyramid?
1. 36 ✓
2. 32
3. 28
4. 40
Car value: $24,000, depreciates 12% yearly. Value after 5 years? (0.88^5 ≈ 0.528)?
1. $12,000
2. $14,208
3. $13,440
4. $12,672 ✓
Two jobs: A starts $40k, +$2k/year. B starts $38k, +5%/year. Which pays more in year 10?
1. Job A: $58k ✓
2. Job B: $61,870
3. They are equal
4. Cannot determine
A sequence starts 5, 8, 13, 20, 29. What pattern? (Differences: 3, 5, 7, 9)?
1. Fibonacci-like
2. Geometric
3. Differences increase by 2 (consecutive odd numbers) ✓
4. Arithmetic
Problem: Find when geometric 2,4,8,16,... exceeds arithmetic 50,60,70,80,... Answer: 7th term. Why?
1. Because geometric always wins
2. Because 128 > 110 (exponential overtakes linear) ✓
3. Because 7 is prime
4. Random coincidence
A problem gives first 3 terms: 2, 6, 18. Multiple students find different formulas that work. Why possible?
1. They all made mistakes
2. Three terms aren't enough to uniquely determine the pattern ✓
3. All sequences are the same
4. Math is inconsistent
Investment doubles every 7 years (Rule of 72). $5,000 becomes how much in 21 years?
1. $20,000
2. $15,000
3. $30,000
4. $40,000 ✓
Student claims: 'Any three numbers can start either arithmetic or geometric sequence.' Evaluate this claim.
1. False, some combinations like 0,5,10 can't be geometric ✓
2. True, always
3. True, but only with positive numbers
4. False, three numbers determine exactly one sequence type
Which approach is best for real-world problems: memorize formulas or understand concepts?
1. Memorize formulas - faster
2. Both are equally important but concepts provide flexibility
3. Neither - just guess
4. Understand concepts - can adapt to new situations and choose right approach ✓
📖 math_quiz8_6_recursive_formulas
What is a recursive formula?
1. A formula that gives the nth term directly
2. A formula for finding sums
3. A formula that defines each term using previous term(s) ✓
4. A formula that only works for arithmetic sequences
What are the two parts of a recursive definition?
1. First term and last term
2. Initial condition(s) and recursive rule ✓
3. Sum and difference
4. Common difference and common ratio
In the notation aₙ = aₙ₋₁ + 3, what does aₙ₋₁ represent?
1. The first term
2. The previous term (one before current) ✓
3. The last term
4. The nth term
What is the recursive form of the Fibonacci sequence?
1. Fₙ = Fₙ₋₁ + 2
2. Fₙ = 2Fₙ₋₁
3. Fₙ = n²
4. Fₙ = Fₙ₋₁ + Fₙ₋₂ ✓
Given a₁ = 5, aₙ = aₙ₋₁ + 3. What is a₃?
1. 11 ✓
2. 8
3. 14
4. 17
For a₁ = 10, aₙ = aₙ₋₁ - 4, what type of sequence is this?
1. Arithmetic with d = -4 ✓
2. Geometric with r = -4
3. Fibonacci
4. Neither arithmetic nor geometric
What is an advantage of recursive formulas?
1. Can find any term directly without previous terms
2. Shows the relationship between consecutive terms clearly ✓
3. Always shorter than explicit formulas
4. Only works for small sequences
What is a disadvantage of recursive formulas?
1. They are too simple
2. Must calculate all previous terms to find a specific term ✓
3. They only work for arithmetic sequences
4. Cannot be programmed
Given a₁ = 2, aₙ = 3aₙ₋₁. What is a₃?
1. 18 ✓
2. 9
3. 6
4. 27
Why does the Fibonacci sequence require TWO initial conditions (F₁ and F₂)?
1. Because it's a special sequence
2. Because each term uses the two previous terms ✓
3. It doesn't need two initial conditions
4. Because it starts with 1, 1
Given a₁ = 7, aₙ = aₙ₋₁ + 5. Find a₅.
1. 27
2. 22 ✓
3. 32
4. 37
For a₁ = 4, aₙ = 2aₙ₋₁. Find a₆.
1. 64
2. 96
3. 128 ✓
4. 256
Write the recursive formula for: 6, 11, 16, 21, 26, ...
1. a₁ = 6, aₙ = aₙ₋₁ + 5 ✓
2. a₁ = 6, aₙ = 5aₙ₋₁
3. a₁ = 1, aₙ = aₙ₋₁ + 6
4. a₁ = 6, aₙ = aₙ₋₁ + 11
Write the recursive formula for: 3, 12, 48, 192, ...
1. a₁ = 3, aₙ = aₙ₋₁ + 9
2. a₁ = 3, aₙ = 3aₙ₋₁
3. a₁ = 3, aₙ = 4aₙ₋₁ ✓
4. a₁ = 12, aₙ = 4aₙ₋₁
Given a₁ = 100, aₙ = aₙ₋₁ - 8. Find a₇.
1. 44
2. 48
3. 56
4. 52 ✓
Convert to explicit: a₁ = 5, aₙ = aₙ₋₁ + 4. What is the explicit formula?
1. aₙ = 4n + 5
2. aₙ = 4n + 1 ✓
3. aₙ = 5n + 4
4. aₙ = 5n + 1
For F₁=1, F₂=1, Fₙ=Fₙ₋₁+Fₙ₋₂, find F₆.?
1. 8 ✓
2. 5
3. 13
4. 21
A savings account starts at $150 and adds $50/month. Write recursive formula.
1. a₁ = 200, aₙ = aₙ₋₁ + 50
2. a₁ = 50, aₙ = aₙ₋₁ + 150
3. a₁ = 150, aₙ = 50aₙ₋₁
4. a₁ = 150, aₙ = aₙ₋₁ + 50 ✓
Given a₁ = 1, a₂ = 3, aₙ = 2aₙ₋₁ - aₙ₋₂. Find a₄.
1. 9
2. 7 ✓
3. 11
4. 13
Population: 5,000 people, grows 3%/year. After 3 years using Pₙ = 1.03Pₙ₋₁?
1. 5,304
2. 5,409
3. 5,463 ✓
4. 5,618
Given a₁ = 5, aₙ = aₙ₋₁ + n. What pattern forms? (a₁=5, a₂=7, a₃=10, a₄=14, ...)?
1. Arithmetic sequence
2. Differences increase by 1 each time ✓
3. Geometric sequence
4. Fibonacci-like
Which is more efficient for finding a₁₀₀: recursive or explicit formula?
1. Recursive, because it shows steps
2. Explicit, because you can calculate directly ✓
3. Both equally efficient
4. Depends on the sequence type
A sequence has a₁=2, aₙ=n·aₙ₋₁. This grows: 2, 4, 12, 48, 240. What is this related to?
1. Factorials (n!) ✓
2. Fibonacci numbers
3. Perfect squares
4. Prime numbers
When would you prefer a recursive formula over an explicit formula?
1. When modeling step-by-step processes or programming ✓
2. When finding the 1000th term
3. When you need speed
4. Never, explicit is always better
A student says: 'Recursive formulas are useless because you can't find terms quickly.' Evaluate this claim.?
1. True, they have no practical use
2. False, recursive formulas are faster than explicit
3. True, explicit formulas are always better
4. False, they show relationships clearly and are useful for programming and modeling ✓
📖 math_quiz8_5_special_sequences
What is the rule for the Fibonacci sequence?
1. Add a constant to each term
2. Multiply each term by 2
3. Each term is the sum of the previous two terms ✓
4. Each term is the square of its position
What is the formula for the nth triangular number?
1. n²
2. n(n+1)/2 ✓
3. n³
4. 2n + 1
What is a prime number?
1. A number divisible by 2
2. A number greater than 1 with exactly two factors: 1 and itself ✓
3. Any odd number
4. A number that can be squared
What is the formula for square numbers?
1. n + n
2. n(n+1)/2
3. n² ✓
4. n × 2
What is the 7th Fibonacci number? Sequence: 1, 1, 2, 3, 5, 8, __?
1. 11
2. 12
3. 13 ✓
4. 14
Which of these is a triangular number?
1. 15 ✓
2. 12
3. 18
4. 20
The Golden Ratio (approximately 1.618) is connected to which sequence?
1. Fibonacci sequence ✓
2. Prime numbers
3. Square numbers
4. Cube numbers
What is the pattern in the differences between consecutive square numbers? (4-1=3, 9-4=5, 16-9=7, ...)?
1. Consecutive even numbers
2. All differences are 2 ✓
3. Consecutive odd numbers
4. Fibonacci numbers
Why is 1 NOT considered a prime number?
1. Because it's too small
2. Because it's odd
3. Because it has only one factor (itself), not two ✓
4. Because it can't be divided
The 5th triangular number is 15. What does this represent visually?
1. A 5×5 square
2. 5 cubes stacked
3. 5 groups of 3
4. Dots arranged in a triangle: 1+2+3+4+5 ✓
Find the 10th Fibonacci number. (Start: 1, 1, 2, 3, 5, 8, 13, 21, 34, __)
1. 44
2. 55 ✓
3. 65
4. 75
Calculate the 8th triangular number using the formula n(n+1)/2.
1. 28
2. 32
3. 36 ✓
4. 40
What is 13²?
1. 169 ✓
2. 156
3. 182
4. 196
Calculate 6³ (6 cubed).
1. 18
2. 36
3. 216 ✓
4. 108
If F₈ = 21 and F₉ = 34, what is F₁₀?
1. 45
2. 50
3. 60
4. 55 ✓
Is 91 a triangular number? Use: n(n+1)/2 = 91?
1. Yes, T₁₂
2. Yes, T₁₃ ✓
3. No
4. Yes, T₁₄
Which of these is a perfect square: 120, 144, 150, 168?
1. 144 ✓
2. 120
3. 150
4. 168
Calculate the ratio F₉/F₈ where F₉=34 and F₈=21. How close is it to the Golden Ratio (1.618)?
1. 1.524
2. 1.800
3. 1.714
4. 1.619 ✓
A sunflower has spirals in 34 and 55 directions. What is significant about these numbers?
1. They are consecutive Fibonacci numbers ✓
2. They are prime numbers
3. They are triangular numbers
4. They are perfect squares
Compare growth rates at n=10: Triangular (55), Square (100), Cube (1000), Fibonacci (55). Which grows fastest?
1. Fibonacci
2. Square
3. Cube ✓
4. Triangular
The sum of first n odd numbers equals n². Verify: 1+3+5+7+9
1. 20
2. 25 ✓
3. 30
4. 36
Why do many flowers have Fibonacci numbers of petals (3, 5, 8, 13)?
1. Random coincidence
2. Efficient packing and growth patterns in nature ✓
3. Farmers plant them that way
4. All flowers have these numbers
If triangular numbers represent sums 1+2+3+..., what does T₁₀ - T₉ equal?
1. 1
2. 9
3. 10 ✓
4. 19
A student claims: 'All even numbers except 2 are not prime.' Is this correct?
1. Yes, because all other even numbers are divisible by 2 ✓
2. No, many even numbers are prime
3. No, 4 is also prime
4. Only sometimes true
Why are special sequences like Fibonacci important beyond just mathematics?
1. They were invented recently
2. They are only theoretical with no real use
3. They are easier to calculate than other sequences
4. They appear in nature, art, and have practical applications ✓
📖 math_quiz8_4_comparing_and_applying_sequences
What is the main difference between arithmetic and geometric sequences?
1. Arithmetic uses division, geometric uses subtraction
2. Arithmetic is faster, geometric is slower
3. Arithmetic adds a constant, geometric multiplies by a constant ✓
4. There is no difference
What type of growth is associated with geometric sequences?
1. Linear growth
2. Exponential growth ✓
3. Constant growth
4. Negative growth
What type of growth is associated with arithmetic sequences?
1. Exponential growth
2. Linear growth ✓
3. Quadratic growth
4. No growth
In the long run, which type of sequence with positive growth will always grow faster?
1. Depends on the starting value
2. Geometric (with r > 1) ✓
3. They grow at the same rate
4. Arithmetic
Classify: A savings account where you deposit $100 every month (no interest).
1. Neither
2. Geometric sequence
3. Arithmetic sequence ✓
4. Both
Classify: An investment that earns 5% compound interest annually.
1. Arithmetic sequence
2. Geometric sequence ✓
3. Neither
4. Linear function
Why does exponential growth eventually outpace linear growth?
1. Because the rate of increase itself increases in exponential growth ✓
2. Because exponential starts larger
3. Because linear growth stops after a while
4. It doesn't always
Which sequence: 5, 10, 20, 40, 80? Type and key value?
1. Geometric, r = 2 ✓
2. Arithmetic, d = 5
3. Arithmetic, d = 10
4. Geometric, r = 5
Which sequence: 10, 20, 30, 40, 50? Type and key value?
1. Arithmetic, d = 5
2. Geometric, r = 2
3. Arithmetic, d = 10 ✓
4. Geometric, r = 10
What happens to the graph of a geometric sequence with r > 1?
1. Downward curve
2. Curve that gets steeper (exponential curve) ✓
3. Horizontal line
4. Straight line
Sequence A: 10, 20, 30, 40, ... vs Sequence B: 5, 10, 20, 40, ... Which is larger at term 6?
1. B is larger (160 vs 60) ✓
2. A is larger (60 vs 160)
3. They are equal
4. Cannot determine
At which term does geometric sequence 2, 4, 8, 16, ... first exceed arithmetic sequence 10, 20, 30, 40, ...?
1. 6th term ✓
2. 5th term
3. 4th term
4. 7th term
Job A: $50,000 start, +$3,000/year. Job B: $48,000 start, +5%/year. Year 5 salary for each?
1. A: $62,000; B: $61,271 ✓
2. A: $65,000; B: $60,000
3. A: $62,000; B: $58,000
4. A: $60,000; B: $61,271
Bacteria double every hour, starting with 200. How many after 5 hours?
1. 1,600
2. 6,400
3. 3,200 ✓
4. 12,800
Save $150/month for 12 months (no interest). Total savings?
1. $1,650
2. $2,100
3. $1,950
4. $1,800 ✓
Population 100,000 grows 3% yearly. Population after 3 years? (Use 1.03^3 ≈ 1.093)?
1. 109,300
2. 106,000
3. 103,000 ✓
4. 112,000
Compare aₙ = 15n at n=8 vs aₙ = 3^(n-1) at n=8. Which is larger?
1. 3^(n-1) is larger (2,187 vs 120) ✓
2. 15n is larger (120 vs 2,187)
3. They are equal
4. Cannot compare
Car depreciates 15% yearly. Starting value $25,000. Value after 4 years? (0.85^4 ≈ 0.522)?
1. $12,000
2. $15,625
3. $14,500
4. $13,050 ✓
Two savings plans: A saves $200/month for 5 years. B invests $10,000 at 4% for 5 years. Which is better? (1.04^5 ≈ 1.217)?
1. A is better ($12,000 vs $12,170) ✓
2. B is better ($12,170 vs $12,000)
3. They are equal
4. Need more information
A disease spreads: Day 1: 10 sick, Day 2: 20, Day 3: 40. What type? Predict Day 7.?
1. Arithmetic, Day 7: 70 sick
2. Geometric (r=10), Day 7: 700 sick
3. Neither type
4. Geometric (r=2), Day 7: 640 sick ✓
Why might a real population not follow pure geometric growth forever?
1. Because math formulas don't apply to real life
2. Because resources become limited and growth slows ✓
3. Because populations always grow arithmetically
4. Because populations decrease over time
A sequence starts arithmetic (d=10) for 3 terms, then geometric (r=2) for 3 terms. Start: 20. What is term 6?
1. 100
2. 80 ✓
3. 120
4. 160
Technology doubles power every 2 years. After 20 years (10 doublings), how many times more powerful? 2^10 = ?
1. 1,024 times ✓
2. 512 times
3. 100 times
4. 2,048 times
A student says: 'Geometric sequences are always better than arithmetic because they grow faster.' Is this correct?
1. No, depends on context, values, and time frame ✓
2. Yes, geometric always beats arithmetic
3. Yes, because exponential growth is always fastest
4. No, arithmetic is actually faster
The 'Rice and Chessboard' legend teaches us about geometric growth. What is the main lesson?
1. Always accept modest-sounding rewards
2. Chessboards have 64 squares
3. Arithmetic growth is faster than geometric
4. Never underestimate the power of exponential growth ✓
📖 math_quiz8_3_geometric_sequences
What is a geometric sequence?
1. A sequence where you add a constant to get the next term
2. A sequence of perfect squares
3. A sequence where you multiply by a constant to get the next term ✓
4. A sequence that increases by doubling
What is the common ratio in a geometric sequence?
1. The difference between consecutive terms
2. The constant value multiplied to get from one term to the next ✓
3. The first term
4. The sum of all terms
What is the formula for the nth term of a geometric sequence?
1. aₙ = a₁ + (n-1)d
2. aₙ = a₁ × r^(n-1) ✓
3. aₙ = a₁ + nr
4. aₙ = a₁ × (n-1)r
How do you find the common ratio r in a sequence?
1. Add consecutive terms
2. Subtract consecutive terms
3. Multiply consecutive terms
4. Divide any term by the previous term ✓
Which sequence is geometric?
1. 3, 6, 9, 12, 15
2. 1, 4, 9, 16, 25
3. 2, 4, 8, 16, 32 ✓
4. 5, 10, 15, 20, 25
What is the common ratio in: 5, 15, 45, 135?
1. 3 ✓
2. 2
3. 5
4. 10
In the sequence 80, 40, 20, 10, 5, what is the common ratio?
1. 0.5 or 1/2 ✓
2. 2
3. -2
4. -0.5
What type of growth does a geometric sequence with r > 1 represent?
1. Exponential growth ✓
2. Linear growth
3. Exponential decay
4. No growth
What happens when the common ratio r is between 0 and 1 (0 < r < 1)?
1. The sequence decays exponentially ✓
2. The sequence stays constant
3. The sequence grows exponentially
4. The sequence becomes negative
What is special about a geometric sequence with negative common ratio?
1. All terms are negative
2. The sequence is constant
3. The sequence decreases
4. The sequence alternates between positive and negative ✓
Find the 7th term of: 2, 6, 18, 54, ...
1. 1,620
2. 1,458 ✓
3. 486
4. 4,374
Find the 9th term of: 1000, 500, 250, 125, ...
1. 2.906
2. 3.125
3. 3.906 ✓
4. 4.5
What is the 6th term of: 3, 12, 48, 192, ...?
1. 3,072 ✓
2. 6,144
3. 12,288
4. 24,576
A bacteria culture starts with 100 cells and doubles every hour. How many after 6 hours?
1. 3,200
2. 4,800
3. 6,400 ✓
4. 12,800
Find the 5th term of: 5, -10, 20, -40, ... (r = -2)
1. -80
2. 80 ✓
3. -160
4. 160
$2,000 invested at 6% annual interest (compounded). Value after 5 years? Use aₙ = 2000 × (1.06)^4
1. $2,475
2. $2,625
3. $2,525 ✓
4. $2,675
Find the 8th term of: 1, 4, 16, 64, ...
1. 16,384 ✓
2. 8,192
3. 4,096
4. 32,768
A machine worth $20,000 depreciates by 20% yearly. Value after 3 years? (r = 0.80)?
1. $9,600
2. $12,800
3. $11,520
4. $10,240 ✓
In a geometric sequence, a₃ = 36 and a₅ = 324. What is the common ratio?
1. 2 ✓
2. 3
3. 4
4. 6
Compare: Arithmetic sequence 5, 10, 15, 20, ... vs Geometric sequence 5, 10, 20, 40, .... At which term does geometric first exceed arithmetic by more than 100?
1. 8th term
2. 6th term
3. 7th term
4. 5th term ✓
A ball drops from 10m and bounces to 60% of previous height each time. After 4 bounces, approximately what height?
1. 1.3 m
2. 1.0 m ✓
3. 1.6 m
4. 2.2 m
After how many terms does the sequence 1, 3, 9, 27, ... first exceed 500?
1. 7th term
2. 6th term ✓
3. 8th term
4. 9th term
In a geometric sequence, a₁ = 12 and a₃ = 324. Find a₂.
1. 36
2. 62 ✓
3. 108
4. 72
Which situation is best modeled by a geometric sequence?
1. Saving $50 per month in a piggy bank
2. Investment growing with compound interest ✓
3. Distance traveled at constant speed
4. Temperature increasing by 2°C per hour
Why does exponential growth (geometric with r > 1) eventually outpace linear growth (arithmetic) no matter the starting values?
1. Because multiplication is faster than addition
2. This is not always true
3. Because geometric sequences always start larger
4. Because the rate of increase itself increases in exponential growth ✓
📖 math_quiz8_2_arithmetic_sequences
What is an arithmetic sequence?
1. A sequence where each term is multiplied by a constant
2. A sequence of perfect squares
3. A sequence where each term is found by adding a constant to the previous term ✓
4. A sequence that doubles each time
What is the common difference in an arithmetic sequence?
1. The sum of all terms
2. The constant value added to get from one term to the next ✓
3. The first term
4. The last term minus the first term
What is the formula for the nth term of an arithmetic sequence?
1. aₙ = a₁ × n
2. aₙ = a₁ + (n-1)d ✓
3. aₙ = a₁ + nd
4. aₙ = a₁ × (n-1)d
How do you find the common difference d in a sequence?
1. Multiply consecutive terms
2. Add consecutive terms
3. Divide consecutive terms
4. Subtract any term from the next term ✓
Which sequence is arithmetic?
1. 2, 4, 8, 16, 32
2. 1, 4, 9, 16, 25
3. 5, 10, 15, 20, 25 ✓
4. 1, 2, 4, 7, 11
What is the common difference in: 7, 13, 19, 25, 31?
1. 7
2. 6 ✓
3. 5
4. 8
In the sequence 50, 45, 40, 35, 30, what is the common difference?
1. 5
2. -5 ✓
3. 10
4. -10
What does it mean if the common difference d is negative?
1. The sequence is decreasing ✓
2. The sequence is increasing
3. The sequence is constant
4. The sequence is not arithmetic
In the formula aₙ = a₁ + (n-1)d, what does n represent?
1. The common difference
2. The position number (which term) ✓
3. The first term
4. The value of the term
Why is (n-1) used in the formula instead of just n?
1. To avoid negative numbers
2. Because we add the common difference (n-1) times to get from term 1 to term n ✓
3. It's a mathematical convention
4. To make calculations easier
Find the 15th term of: 4, 9, 14, 19, 24, ...
1. 69
2. 74 ✓
3. 79
4. 84
Find the 20th term of: 100, 94, 88, 82, ...
1. -14 ✓
2. -8
3. -2
4. 4
What is the general formula for: 3, 8, 13, 18, 23, ...? (Simplified form aₙ = __)?
1. aₙ = 5n - 2 ✓
2. aₙ = 5n + 3
3. aₙ = 3n + 5
4. aₙ = 8n - 5
Find the missing term: 64, 32, __, 8, 4. Wait - is this arithmetic?
1. Yes, missing term is 20
2. No, this is not arithmetic (differences not constant) ✓
3. Yes, missing term is 16
4. Yes, missing term is 24
In the sequence 6, 13, 20, 27, ..., which term equals 104?
1. 13th term
2. 16th term
3. 15th term
4. 14th term ✓
You save $25 per week starting with $50. How much after 12 weeks? (Week 0: $50, Week 1: $75, ...)?
1. $325
2. $350
3. $375 ✓
4. $400
Find the 30th term of: 2, 7, 12, 17, 22, ...
1. 147 ✓
2. 142
3. 152
4. 157
Theater rows: Row 1 has 20 seats, Row 2 has 24, Row 3 has 28. How many in Row 10?
1. 52
2. 64
3. 60
4. 56 ✓
A sequence has a₃ = 14 and a₇ = 30. What is the common difference?
1. 3
2. 4 ✓
3. 5
4. 6
Is 150 a term in the sequence 7, 15, 23, 31, ...? (Common difference = 8)?
1. Yes, it's the 20th term
2. Yes, it's the 19th term
3. No, because solving gives a non-integer value for n ✓
4. Yes, it's the 18th term
In sequence: 5, 9, 13, 17, ..., temperature starts at 12°C and increases by 2°C/hour. After 8 hours, temperature is 28°C. Which concept is similar?
1. One is arithmetic, the other is geometric
2. Both follow arithmetic sequence with constant addition ✓
3. They are completely different
4. Both involve multiplication
A sequence has first term 5 and 10th term 50. What is the common difference?
1. 4
2. 4.5 ✓
3. 5
4. 5.5
You owe $500 and pay $25/month. After how many months will you owe $200?
1. 12 months ✓
2. 11 months
3. 10 months
4. 13 months
Which formula is better for finding the 100th term: listing all terms or using aₙ = a₁ + (n-1)d?
1. Using the formula is better because it's much faster and more efficient ✓
2. Listing is better because it's more accurate
3. Both are equally good
4. Listing is better because you can see the pattern
A student writes the general term for 10, 15, 20, 25 as aₙ = 10 + 5n. Is this correct?
1. Yes, completely correct
2. No, should be aₙ = 5n + 5
3. No, should be aₙ = 5n (when n starts from 2)
4. Partially correct but simplified form is better: aₙ = 5(n + 2) or aₙ = 5n + 5 when adjusted ✓
📖 math_quiz8_1_introduction_to_patterns
What is a pattern in mathematics?
1. A random arrangement of numbers
2. Any list of numbers
3. A regular, repeated arrangement following a specific rule ✓
4. A mathematical equation
What is the sequence of even numbers?
1. 1, 3, 5, 7, 9, ...
2. 2, 4, 6, 8, 10, ... ✓
3. 1, 2, 3, 4, 5, ...
4. 0, 2, 4, 6, 8, ...
What are square numbers?
1. Numbers that can be arranged in a square
2. Numbers that are perfect squares (1, 4, 9, 16, ...) ✓
3. Numbers with four digits
4. Numbers divisible by 4
To find the rule in a growing pattern, what should you look at first?
1. The last term
2. The middle term
3. The sum of all terms
4. The difference or ratio between consecutive terms ✓
What is the next term in the pattern: 3, 7, 11, 15, 19, __?
1. 21
2. 22
3. 23 ✓
4. 24
What is the rule for the pattern: 5, 10, 20, 40, 80?
1. Multiply by 2 each time ✓
2. Add 5 each time
3. Add 10 each time
4. Multiply by 5 each time
In the pattern 100, 90, 80, 70, 60, ..., what type of pattern is this?
1. Shrinking pattern ✓
2. Growing pattern
3. Repeating pattern
4. Multiplying pattern
What is the difference between consecutive terms in: 8, 14, 20, 26, 32?
1. 4
2. 6 ✓
3. 5
4. 7
Which pattern shows powers of 2?
1. 2, 4, 6, 8, 10
2. 2, 4, 8, 12, 16
3. 1, 2, 4, 8, 16 ✓
4. 1, 4, 9, 16, 25
In the sequence 1, 4, 9, 16, 25, what mathematical operation creates each term?
1. Adding 3, then 5, then 7
2. Squaring consecutive integers (1², 2², 3², ...)
3. Multiplying by 4
4. Adding consecutive odd numbers ✓
Find the next three terms: 7, 12, 17, 22, 27, __, __, __
1. 31, 35, 39
2. 32, 37, 42 ✓
3. 30, 33, 36
4. 28, 29, 30
Find the missing term: 64, 32, __, 8, 4
1. 20
2. 18
3. 16 ✓
4. 14
What is the next term in: 3, 6, 12, 24, 48, __?
1. 108
2. 84
3. 96 ✓
4. 72
A staircase pattern has 1 square in Figure 1, 3 squares in Figure 2, 6 squares in Figure 3. How many in Figure 5? (Pattern: 1, 3, 6, 10, ...)?
1. 12
2. 13
3. 15 ✓
4. 14
You save $10 on Week 1 and increase by $5 each week. How much do you save in Week 6?
1. $45
2. $35
3. $40
4. $30 ✓
Find the 10th term in the sequence: 4, 8, 12, 16, 20, ... (each term = 4n)
1. 36
2. 38
3. 40 ✓
4. 42
What is the next term: 2, 5, 11, 23, 47, __? (Rule: multiply by 2, then add 1)?
1. 95 ✓
2. 93
3. 91
4. 97
A plant is 5 cm tall and grows 2 cm per day. How tall after 8 days?
1. 19 cm
2. 20 cm
3. 22 cm
4. 21 cm ✓
Which description best fits the pattern 5, 8, 13, 20, 29?
1. Square numbers plus 1
2. Add 3 each time
3. Add consecutive integers: +3, +5, +7, +9 ✓
4. Multiply by 2, subtract 2
In a Fibonacci-style sequence where each term is the sum of previous two: 2, 3, 5, 8, 13, __, what is the 6th term?
1. 18
2. 19
3. 20
4. 21 ✓
A pattern alternates between two rules: add 2, then add 4. Starting with 1, what is the 8th term? (1, 3, 7, 9, 13, 15, 19, ...)?
1. 21
2. 23 ✓
3. 25
4. 27
A border pattern has perimeters: 4, 8, 12, 16 dots (for 1×1, 2×2, 3×3, 4×4 squares). What formula gives the perimeter for an n×n square?
1. 2n
2. 4n ✓
3. 3n
4. n²
Cinema seats per row: Row 1 has 20, Row 2 has 24, Row 3 has 28. Row 10 has how many seats?
1. 56 ✓
2. 52
3. 60
4. 64
A student claims that 2, 6, 18, 54 follows the rule 'add 4, then add 12, then add 36.' Is this the best description?
1. No, the rule 'multiply by 3' is simpler and better ✓
2. Yes, that's the clearest rule
3. Yes, because it shows all the differences
4. No, there is no rule for this pattern
Which pattern would be most useful for calculating the 100th term without listing all previous terms?
1. A pattern where you add consecutive terms (Fibonacci-style)
2. A pattern where you add increasing amounts
3. A pattern that alternates between two rules
4. A pattern with formula: term = 3n + 2 ✓
📖 math_quiz7_8_applications_of_ratios_and_proportions
When solving a ratio problem, what is the first step?
1. Calculate the answer immediately
2. Cross multiply
3. Identify total parts in the ratio ✓
4. Convert to percentages
In a direct proportion problem, what relationship exists between the variables?
1. One increases, the other decreases
2. Both increase or decrease together proportionally ✓
3. They remain constant
4. They are unrelated
What type of proportion is used when more workers means less time for a job?
1. Direct proportion
2. Inverse proportion ✓
3. Simple ratio
4. Equivalent ratio
In medication dosage problems, what is the dosage typically proportional to?
1. Age of patient
2. Time of day
3. Height
4. Body weight ✓
Three partners invest in ratio 3:4:5. If total investment is $60,000, what does one 'part' represent?
1. $3,000
2. $4,000
3. $5,000 ✓
4. $12,000
A scale drawing shows 1 cm = 50 m. This is an example of which type of proportion?
1. Direct proportion ✓
2. Inverse proportion
3. No proportion
4. Combined proportion
Why is currency exchange an example of direct proportion?
1. Because more of one currency gives proportionally more of another ✓
2. Because money increases over time
3. Because exchange rates change daily
4. Because it involves multiplication
In a recipe scaling problem, if you triple the servings, what happens to each ingredient amount?
1. Stays the same
2. Triples ✓
3. Doubles
4. Depends on the ingredient
A car's fuel consumption (liters per 100 km) relates to distance traveled through which concept?
1. Simple ratio
2. Inverse proportion
3. Direct proportion ✓
4. Percentage
The Golden Ratio (approximately 1.618:1) is primarily used in which field?
1. Medicine
2. Finance
3. Chemistry
4. Art and Design ✓
Three business partners share profit in ratio 2:3:5. If total profit is $50,000, how much does the third partner receive?
1. $20,000
2. $15,000 ✓
3. $25,000
4. $30,000
A medication requires 1.5 mg per kg of body weight. What dose for a 60 kg patient?
1. 80 mg
2. 85 mg
3. 90 mg ✓
4. 95 mg
A scale drawing uses 1:150. If a room measures 8 cm on the plan, what is the actual length in meters?
1. 12 m ✓
2. 11 m
3. 10 m
4. 13 m
Mix chemicals in ratio 3:7. To make 400 mL total, how much of the first chemical?
1. 100 mL
2. 140 mL
3. 120 mL ✓
4. 160 mL
A car uses 7 liters for 100 km. How much fuel for 250 km?
1. 15.5 L
2. 16.5 L
3. 18.5 L
4. 17.5 L ✓
8 workers complete a job in 12 days. How many days for 6 workers?
1. 14 days
2. 15 days
3. 16 days ✓
4. 18 days
Exchange rate: 1 EUR = 1.20 USD. Convert 150 EUR to USD?
1. $180 ✓
2. $175
3. $170
4. $185
A recipe for 6 servings uses 2.5 cups flour. How much for 15 servings?
1. 5.75 cups
2. 6.00 cups
3. 6.50 cups
4. 6.25 cups ✓
A project budget: materials, labor, overhead in ratio 5:8:2. Materials split into wood, metal, plastic in ratio 3:2:1. Total budget $45,000. How much for metal?
1. $5,000 ✓
2. $4,500
3. $4,000
4. $5,500
A bacteria culture doubles every 3 hours, starting with 600 cells. After doubling once, cells are split into 4 containers. How many cells per container?
1. 200
2. 250
3. 350
4. 300 ✓
Three cities A, B, C on a line. Distance A-B to B-C is 2:3. Total A-C is 150 km. What is distance A-B?
1. 50 km
2. 60 km ✓
3. 70 km
4. 80 km
Worker A takes 15 hours for a job, Worker B takes 20 hours. Working together, approximately how long?
1. 8.0 hours
2. 7.5 hours ✓
3. 8.6 hours
4. 9.0 hours
A journey takes 4 hours at 75 km/h. Speed needed to complete in 3 hours?
1. 100 km/h ✓
2. 95 km/h
3. 90 km/h
4. 105 km/h
A store sells tea blend (ratio 3:2:5) for $18/kg. Individual teas cost $15, $20, $18/kg. What is the profit per kg?
1. $0.50 ✓
2. $0.40
3. $0.30
4. $0.60
Comparing two problems: (A) Share $60,000 in ratio 3:5:4. (B) 6 workers take 10 days, find time for 8 workers. Which uses which concept?
1. A uses inverse proportion, B uses ratios
2. A uses ratios, B uses inverse proportion ✓
3. Both use inverse proportion
4. Both use direct proportion
📖 math_quiz7_7_inverse_proportion
What is the equation form for inverse proportion?
1. y = x + k
2. y = k/x ✓
3. y = kx
4. y = x - k
In inverse proportion, what remains constant?
1. The sum of the two quantities
2. The product of the two quantities ✓
3. The difference of the two quantities
4. The ratio of the two quantities
What happens to y when you double x in an inverse proportion?
1. y doubles
2. y halves ✓
3. y stays the same
4. y quadruples
What type of curve does an inverse proportion graph create?
1. Circle
2. Parabola
3. Hyperbola ✓
4. Straight line
Which situation represents inverse proportion?
1. Cost of apples and weight purchased
2. Distance traveled and time at constant speed
3. Time to complete a job and number of workers ✓
4. Perimeter of square and side length
In the equation y = 60/x, what is the value of k?
1. 60 ✓
2. y
3. x
4. Cannot determine
Why does the graph of inverse proportion never touch the axes?
1. Because neither variable can be zero ✓
2. Because the line is too short
3. Because k is always positive
4. Because it's a curve
How do direct and inverse proportion differ when x increases?
1. Direct: y decreases; Inverse: y increases
2. Direct: y increases; Inverse: y decreases ✓
3. Both: y increases
4. Both: y decreases
If xy = 48 for all values, what type of relationship exists between x and y?
1. Direct proportion
2. Linear with y-intercept
3. Inverse proportion ✓
4. No relationship
In a lever balance problem, why are weight and distance inversely proportional?
1. Because heavier weights sink more
2. Because they use different units
3. Because distance is always greater than weight
4. Because their product (moment) must be constant for balance ✓
Given this table, is y inversely proportional to x? x: 4,6,8,12 and y: 18,12,9,6?
1. Yes, k = 60
2. Yes, k = 72 ✓
3. No, products are not constant
4. Cannot determine
If y is inversely proportional to x and y = 24 when x = 5, what is k?
1. 100
2. 110
3. 120 ✓
4. 130
If y = 36 when x = 4, and y is inversely proportional to x, find y when x = 9?
1. 14 ✓
2. 16
3. 18
4. 20
8 workers complete a job in 12 days. How many days will 6 workers take?
1. 14 days
2. 15 days
3. 16 days ✓
4. 18 days
A car traveling at 80 km/h takes 3 hours for a journey. How long at 60 km/h?
1. 3.5 hours
2. 5 hours
3. 4.5 hours
4. 4 hours ✓
A gas has volume 4 liters at pressure 6 atmospheres. Find volume at 8 atmospheres?
1. 3 liters
2. 2.5 liters
3. 2 liters ✓
4. 3.5 liters
On a lever, a 50 kg weight is 6 meters from the fulcrum. Where should a 75 kg weight be placed to balance?
1. 3 meters
2. 4 meters ✓
3. 5 meters
4. 8 meters
If 10 taps fill a pool in 4 hours, how long will 8 taps take?
1. 4.5 hours
2. 6 hours
3. 5.5 hours
4. 5 hours ✓
A journey of 360 km takes 4 hours at a certain speed. What speed is needed to complete it in 3 hours?
1. 120 km/h ✓
2. 110 km/h
3. 100 km/h
4. 130 km/h
12 machines take 15 days for a job. After 5 days, 3 machines break down. When will the job be completed?
1. 23 days total
2. 21 days total
3. 22 days total
4. 20 days total ✓
If y is inversely proportional to x, and y decreases from 30 to 10, by what factor did x change?
1. Increased by factor of 2
2. Decreased by factor of 2 ✓
3. Increased by factor of 3
4. Decreased by factor of 3
Two gears are connected. Gear A (30 teeth) makes 40 rotations while Gear B makes 24 rotations. How many teeth does Gear B have?
1. 40 teeth
2. 50 teeth ✓
3. 45 teeth
4. 55 teeth
A rectangle has fixed area 120 cm². If the length is 15 cm, what is the width? What is the perimeter?
1. Width = 8 cm, Perimeter = 46 cm ✓
2. Width = 8 cm, Perimeter = 48 cm
3. Width = 10 cm, Perimeter = 50 cm
4. Width = 12 cm, Perimeter = 54 cm
A student claims: 'In inverse proportion, if I triple one variable, the other also triples.' Is this correct?
1. No, the other variable becomes one-third ✓
2. Yes, always correct
3. Yes, but only for positive values
4. No, the other variable stays the same
Comparing two problems: (A) 5 workers take 12 days; find time for 8 workers. (B) Apples cost $2 per kg; find cost of 8 kg. Which uses inverse proportion?
1. Both A and B
2. Neither
3. Only B
4. Only A ✓
📖 math_quiz7_6_direct_proportion
What does it mean when two quantities are in direct proportion?
1. When one increases, the other decreases
2. They are always equal
3. The ratio between them remains constant ✓
4. One is twice the other
What is the equation form for direct proportion?
1. y = x + k
2. y = kx ✓
3. y = k/x
4. y = x - k
What is the constant k in the equation y = kx called?
1. The variable
2. The constant of proportionality ✓
3. The y-intercept
4. The denominator
What point must the graph of a direct proportion always pass through?
1. (1, 1)
2. (0, 1)
3. (1, 0)
4. (0, 0) ✓
If y is directly proportional to x and you double x, what happens to y?
1. y is halved
2. y stays the same
3. y doubles ✓
4. y quadruples
Which table represents direct proportion?
1. x: 2,4,6,8 and y: 6,12,18,24 ✓
2. x: 2,4,6,8 and y: 5,10,16,22
3. x: 2,4,6,8 and y: 3,6,10,14
4. x: 2,4,6,8 and y: 4,8,13,18
What does the constant of proportionality represent in the equation d = 60t (where d is distance in km and t is time in hours)?
1. The speed (60 km/h) ✓
2. The total time
3. The total distance
4. The starting position
Why is the relationship F = (9/5)C + 32 NOT a direct proportion?
1. It's not linear
2. It doesn't pass through the origin ✓
3. The ratio is too large
4. It uses fractions
If y/x = 5 for all values, what is the equation relating y and x?
1. y = x + 5
2. y = x - 5
3. y = 5x ✓
4. y = x/5
Which real-world situation represents direct proportion?
1. The number of people and the time to complete a task
2. Your age and the current year
3. Temperature in Celsius and Fahrenheit
4. The cost of apples at $3 per kg ✓
Given this table, is y directly proportional to x? x: 3,6,9,12 and y: 12,24,36,48?
1. Yes, k = 3
2. Yes, k = 4 ✓
3. No, ratios are not constant
4. Cannot determine
If y is directly proportional to x and y = 35 when x = 7, what is the constant of proportionality?
1. 3
2. 4
3. 5 ✓
4. 6
If y = 48 when x = 8, and y is directly proportional to x, find y when x = 12?
1. 72 ✓
2. 66
3. 60
4. 78
A car travels 180 km in 3 hours at constant speed. What is the equation relating distance d and time t?
1. d = 70t
2. d = 50t
3. d = 60t ✓
4. d = 180t
If bananas cost $2.40 per kg, how much do 5.5 kg cost?
1. $12.20
2. $13.00
3. $13.80
4. $13.20 ✓
The perimeter P of a regular octagon is directly proportional to side length s. If P = 40 cm when s = 5 cm, find P when s = 8 cm?
1. 56 cm
2. 60 cm
3. 64 cm ✓
4. 72 cm
A printer prints at 18 pages per minute. How many pages does it print in 12 minutes?
1. 216 pages ✓
2. 206 pages
3. 196 pages
4. 226 pages
If y is directly proportional to x with constant 3.5, find y when x = 20?
1. 65
2. 80
3. 75
4. 70 ✓
A graph passes through (0,0) and (5,30). What is the constant of proportionality and equation?
1. k = 6, y = 6x ✓
2. k = 5, y = 5x
3. k = 25, y = 25x
4. k = 30, y = 30x
Shop A: 6 kg for $18. Shop B: 10 kg for $28. Which offers better value (lower price per kg)?
1. Shop A ($3.00/kg)
2. Cannot determine
3. Both same price
4. Shop B ($2.80/kg) ✓
If y is directly proportional to x, and z is directly proportional to y, with y = 15 when x = 3, and z = 60 when y = 15, find z when x = 7?
1. 120
2. 140 ✓
3. 130
4. 150
A water tank fills at a constant rate. After 10 minutes it has 75 liters. The tank capacity is 240 liters. When will it be full?
1. 28 minutes
2. 32 minutes ✓
3. 30 minutes
4. 34 minutes
Person A runs 1,500 m in 5 minutes. Person B runs 2,400 m in 8 minutes. Who runs faster?
1. Both same speed (300 m/min) ✓
2. Person B (300 m/min)
3. Person A (300 m/min)
4. Person A (320 m/min)
A student claims that the relationship between hours worked and wages is always direct proportion. Is this correct?
1. No, only if there's a fixed hourly rate with no bonuses or overtime rates ✓
2. Yes, always true
3. No, never true
4. Yes, but only for part-time workers
Three students graphed direct proportions. All graphs pass through (0,0). Graph A passes through (2,10), Graph B through (2,6), Graph C through (2,14). Which has the steepest slope and largest constant of proportionality?
1. Graph A (k=5)
2. Graph B (k=3)
3. All have same slope
4. Graph C (k=7) ✓
📖 math_quiz7_5_solving_proportion_problems
What is the first step in solving a proportion word problem?
1. Cross multiply immediately
2. Write the answer
3. Read and understand the problem ✓
4. Calculate the unit rate
In the 5-step method for solving proportions, what comes after 'Set Up'?
1. Check
2. Solve ✓
3. Answer
4. Understand
When setting up a proportion from a word problem, what is most important?
1. Using the largest numbers
2. Keeping corresponding quantities in matching positions ✓
3. Always putting the unknown first
4. Using decimals instead of fractions
What should you always include with your final answer in a proportion problem?
1. The original proportion
2. All calculations
3. A graph
4. Appropriate units ✓
If 5 apples cost $3.75, which proportion correctly represents the cost of 12 apples?
1. 5/3.75 = 12/x ✓
2. 3.75/5 = 12/x
3. Both A and B are correct
4. 5/12 = 3.75/x
A car travels 180 km in 3 hours. What does the ratio 180/3 represent?
1. The speed (km per hour) ✓
2. The total distance
3. The time taken
4. The number of stops
On a map scale of 1 cm : 25 km, what does 1 cm on the map represent?
1. 25 km in reality ✓
2. 25 cm in reality
3. 1 km in reality
4. 25 meters in reality
When scaling a recipe from 6 servings to 15 servings, what factor are you multiplying by?
1. 2
2. 2.5 ✓
3. 3
4. 9
If a machine produces 240 items in 8 hours, how would you find the production rate per hour?
1. Multiply 240 × 8
2. Divide 8 ÷ 240
3. Divide 240 ÷ 8 ✓
4. Add 240 + 8
In a proportion problem about currency exchange, if 3 USD = 2.4 EUR, what does the ratio 2.4/3 represent?
1. The total amount of Euros
2. The number of dollars per Euro
3. The exchange fee
4. The number of Euros per dollar ✓
If 4 pencils cost $2.80, how much would 9 pencils cost?
1. $5.60
2. $6.30 ✓
3. $6.00
4. $7.00
A train travels 240 km in 3 hours. At the same speed, how far will it travel in 7 hours?
1. 480 km
2. 520 km
3. 560 km ✓
4. 600 km
On a map, 3 cm represents 45 km. If two towns are 8 cm apart on the map, what is the actual distance?
1. 120 km ✓
2. 110 km
3. 100 km
4. 130 km
A recipe for 8 servings uses 3 cups of sugar. How much sugar is needed for 20 servings?
1. 6 cups
2. 6.5 cups
3. 7.5 cups ✓
4. 7 cups
A factory produces 600 items in 10 hours. How many items can it produce in 16 hours?
1. 900 items
2. 1200 items
3. 1000 items
4. 960 items ✓
If 6 US dollars equals 4.8 British pounds, how many pounds can you get for 20 US dollars?
1. 15 pounds
2. 17 pounds
3. 16 pounds ✓
4. 18 pounds
To make green paint, mix blue and yellow in ratio 5:3. If you use 25 liters of blue, how much yellow do you need?
1. 15 liters ✓
2. 12 liters
3. 18 liters
4. 20 liters
A printer prints 180 pages in 12 minutes. How long will it take to print 270 pages?
1. 16 minutes
2. 22 minutes
3. 20 minutes
4. 18 minutes ✓
In a survey of 120 people, 72 prefer Brand A. In a city of 2,000 people, how many would you expect to prefer Brand A?
1. 1,200 people ✓
2. 1,100 people
3. 1,000 people
4. 1,300 people
A car travels 210 km in 3 hours, then continues at the same speed for 2 more hours. What is the total distance?
1. 300 km
2. 330 km
3. 420 km
4. 350 km ✓
A model airplane has a scale of 1:40. If the model's wingspan is 30 cm, what is the actual wingspan in meters?
1. 10 m
2. 12 m ✓
3. 11 m
4. 13 m
A town with 9,600 people has an area of 16 km². At the same density, what would be the population of a region with 35 km²?
1. 19,200 people
2. 21,000 people ✓
3. 20,000 people
4. 22,400 people
Machine A produces 150 items in 6 hours. Machine B produces 200 items in 10 hours. Working together at these rates, how many items can they produce in 4 hours?
1. 160 items ✓
2. 180 items
3. 200 items
4. 220 items
Store A sells 5 pens for $7.50. Store B sells 8 pens for $11.20. Which store offers the better price per pen and by how much?
1. Store B, cheaper by $0.10 per pen ✓
2. Store A, cheaper by $0.10 per pen
3. Store A, cheaper by $0.20 per pen
4. Store B, cheaper by $0.20 per pen
A student sets up the proportion 8/12 = 20/x to find how much 20 items cost if 8 items cost $12. Another student says it should be 8/12 = x/20. Who is correct?
1. First student has correct setup but will get wrong answer
2. Second student; x represents the cost of 20 items
3. Both are wrong; should be 12/8 = 20/x
4. First student; x represents the cost of 20 items ✓
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