Common misconceptions

Does doubling mean adding the same amount each time? — “The doubling pattern 3, 6, 12 continues with 18.”

Which angle opens wider? — “The angle with longer arms is larger.”

Do the same digits make the same number? — “352 and 523 have the same value because they use the same digits.”

What does one picture stand for? — “Five symbols mean five books.”

Is 1 a prime number? — “1 is prime because it can be divided by 1 and itself.”

Does equal fencing give equal area? — “Rectangles with the same perimeter enclose the same area.”

Can you add the bottom numbers? — “1/2 + 1/3 = 2/5”

Do equal sides guarantee a square? — “Four equal sides always make a square.”

Does a turn guarantee a mirror line? — “A figure with rotational symmetry always has a mirror line.”

Which is warmer, −3 °C or −8 °C? — “−8 °C is warmer because 8 is bigger than 3.”

What turns a guess into a conclusion? — “A sensible guess is enough to settle the question.”

Does a whale count as a fish? — “A whale is a fish because it lives in water.”

Does filling food supply everything the body needs? — “A diet that provides enough energy gives all needed nutrients.”

Do all metals stick to magnets? — “An aluminium can sticks because it is metal.”

What if the ruler starts at 2 cm? — “A pencil from 2 cm to 9 cm is 9 cm long.”

Does a powder count as a liquid because it pours? — “Dry sand is a liquid because it pours and takes the shape of a cup.”

Does touch measure temperature reliably? — “Metal feels colder than wood, so the metal must have a lower temperature.”

Can water evaporate without boiling? — “A puddle can dry only if the water boils.”

Can a filter catch dissolved salt? — “Filter paper separates salt from clear salt water.”

Is everything that moves alive? — “A moving toy car is alive.”

Can renewable resources run out locally? — “Groundwater can never run low because rain renews it.”

Is the Moon a light source like the Sun? — “The Moon makes its own visible light.”

Can the same digit have different values? — “The two 7s in 707,000 are worth the same.”

Must every operation be done left to right? — “8 + 2 × 3 = 30”

Which decimal is larger? — “0.35 is greater than 0.4 because 35 is greater than 4.”

Do like terms multiply when you add them? — “3x + 2x = 5x²”

Are alternate angles always equal? — “Alternate angles are equal even when a transversal crosses two nonparallel lines.”

Can an even total prove both addends are even? — “If a sum is even, both numbers were even.”

Can any three side lengths make a triangle? — “Sides 2, 3 and 6 make a triangle.”

Must multiplication make a fraction larger? — “½ × ⅔ must be bigger than ⅔.”

Does the same shape guarantee congruence? — “A 3–4–5 triangle and a 6–8–10 triangle are congruent.”

What does subtracting a negative do? — “3 − (−2) = 1”

When do you need a common factor? — “The greatest equal packet size for 12 blue beads and 18 red beads is 36.”

Does a trailing zero make a decimal bigger? — “0.50 is bigger than 0.5.”

Which group has the higher average? — “The group with the larger total always has the larger mean.”

Is every line through the midpoint a perpendicular bisector? — “Passing through the midpoint is enough.”

What happens when you move a term across an equals sign? — “From x + 3 = 10, move +3 to the right as +3 and get x = 13.”

Does one matching result establish a scientific rule? — “If a wide bowl of water dries before a narrow cup once, the bowl shape must be the cause.”

Does one unchanged litmus strip prove neutrality? — “If blue litmus stays blue, the liquid must be neutral.”

Does current get used up by a bulb? — “Less current leaves the bulb than enters it in a steady series circuit.”

Is a shiny substance always a metal? — “Shiny iodine must be a metal.”

Does melting make a new substance? — “Melted ice has turned into a new substance.”

Does the start of puberty mean growth is complete? — “The first visible sign of puberty means someone has finished growing.”

Does heat only travel upward? — “Heat from a heater reaches only places above it.”

Do stops count when you calculate average speed? — “A trip's average speed counts only the time spent moving.”

Is the stomach where digestion finishes? — “All digestion is finished in the stomach.”

Do plants get their food from the soil? — “Roots absorb the plant’s food from the soil.”

Is a shadow a reflection? — “A shadow is a dark image reflected by the object.”

Is every new moon a solar eclipse? — “The Moon is between Earth and Sun at new moon, so an eclipse must happen each month.”

Do factors always come in different pairs? — “Every number has an even number of factors.”

What does an exponent count? — “2³ = 6”

Does an extra digit always make a number larger? — “IX is larger than X because IX has two symbols.”

Is one pair of parallel sides enough for a parallelogram? — “A quadrilateral with one pair of parallel sides is a parallelogram.”

Can a pattern of examples establish a number rule? — “If n² + n + 41 is prime for the first several whole numbers, it must always be prime.”

Does the outside factor reach both terms? — “3(x + 2) = 3x + 2”

Does adding the same amount preserve a recipe? — “A 2:3 syrup-to-water ratio stays the same at 3:4.”

Does a percent already give a count? — “A 25% discount always means 25 rupees off.”

Can the theorem be used on any triangle? — “For two sides 3 cm and 4 cm, the third side must be 5 cm.”

Do more workers always take more time? — “If workers double, the time for a fixed task doubles.”

Can a boundary grow when its individual segments get shorter? — “A Koch-curve step shortens the boundary because every replacement segment is shorter.”

Can the average come from just the smallest and largest values? — “The mean of 2, 2, 2 and 10 is 6.”

Can you square a sum term by term? — “(x + 3)² = x² + 9”

Which side is the height of a slanted parallelogram? — “Multiply the base by the slanted side to find area.”

Does a difference in one trial establish a reliable effect? — “Setup B always evaporates more water because it lost 5 mL while setup A lost 4 mL in the first trial.”

Are all microbes harmful? — “All bacteria make people ill.”

Do antibiotics treat viral infections? — “An antibiotic kills the virus that causes a cold.”

Does insulation remove the current in a wire? — “A coated wire cannot produce a magnetic effect.”

Does a push have to cause motion? — “There is no force on a box that stays still while I push it.”

Does the same force always create the same pressure? — “A sharp and blunt end press equally because I use the same force.”

Do particles themselves expand when a gas expands? — “Heating a gas makes each molecule bigger.”

Is a uniform mixture a compound? — “Salt water is a compound because it looks uniform.”

Does a dissolved solid disappear from the mass? — “When sugar dissolves, it stops adding to the mass.”

Why do mirror images look reversed? — “A plane mirror swaps left and right in space.”

Does the Moon itself change shape? — “The Moon physically gets thinner during a crescent phase.”

Do aquatic animals need oxygen? — “Fish have no need for oxygen because they live underwater.”

Does being closer to the Sun always make a planet hotter at its surface? — “Mercury must have a hotter average surface than Venus because it is closer to the Sun.”

Does the order of coordinates matter? — “(2, 5) and (5, 2) give the same point.”

Can a variable in a denominator be linear? — “1/x + 2 is a linear polynomial.”

Can a calculator's finite display prove a number is rational? — “√2 is rational because a calculator displays 1.414213562, a terminating decimal.”

Does expanding a product mean multiplying only matching terms? — “(x + 2)(x + 3) = x² + 6”

Does every chord cross the centre? — “A chord must go through the centre of a circle.”

What happens to area when lengths double? — “Doubling all side lengths doubles the area.”

Is every named outcome equally likely? — “A spinner with red and blue has a ½ chance of red.”

Does an increasing sequence always add the same number? — “2, 4, 8, 16 is arithmetic because every term is larger than the previous one.”

Can one seedling per group settle an experiment? — “Fertiliser makes seedlings grow faster because my one fertilised seedling grew more than my one untreated seedling.”

Do plant cells have cell membranes? — “Plant cells have walls in place of membranes.”

Do all cells in a tissue have the same shape? — “A tissue can contain only one cell shape.”

Can displacement be zero after travelling? — “A runner who travels 400 m must be 400 m from the start.”

Does clear water have to be pure? — “A clear liquid must be pure water.”

Does constant motion require a net force? — “A trolley moving steadily must have a forward net force.”

Does holding a heavy load do mechanical work on it? — “I do mechanical work on a bag because my arms get tired while I hold it still.”

Does losing an electron change the element? — “A sodium atom becomes a different element when it loses an electron.”

Can you change subscripts to balance an equation? — “Change H₂O to H₂O₂ to balance the oxygen atoms.”

Do air particles travel all the way from speaker to listener? — “The speaker sends its air particles across the room.”

Can reproduction happen with one parent? — “Every living thing needs two parents to reproduce.”

Does a similar habitat mean close classification? — “A dolphin and a shark belong to the same group because both swim.”

Does energy cycle through ecosystems like matter? — “Energy comes back to producers as dead material breaks down.”

Can an endless decimal be rational? — “Every decimal that goes on forever is irrational.”

Are the zeros the coefficients? — “The zeros of x² − 5x + 6 are −5 and 6.”

Does every pair of lines have one solution? — “Two linear equations always give one solution.”

Can you divide away a possible solution? — “Divide x² = 3x by x and keep only x = 3.”

Is the first term one step from itself? — “The nth term is a + nd.”

Does similarity mean equal areas? — “Similar triangles have the same area.”

Can opposite coordinate signs cancel the distance? — “The distance from (−3, 0) to (3, 0) is zero.”

Can you label a side opposite without choosing an angle? — “A leg stays the opposite side when I switch the reference angle.”

Which height does an elevation angle measure? — “The height calculated from eye level is the whole tower height.”

Does a line through one point on a circle have to be a tangent? — “Any line drawn through a marked point on the circle is a tangent.”

Does half the radius give half the area? — “A circle of radius 3 has half the area of one of radius 6.”

Do joined faces still count as outer surface? — “Add both full surface areas when two cubes are joined face to face.”

Can you ignore frequencies in the mean? — “If scores are 1 and 5, the mean is 3.”

Does a losing streak change the next fair toss? — “After three tails, heads is more likely on the next toss.”

Can balancing change a chemical formula? — “Write NH₃ as NH₆ to account for all six hydrogen atoms.”

Does one pH step mean one equal unit of acidity? — “A solution at pH 3 has twice the hydrogen ion concentration of pH 6.”

Do all metals react with water in the same way? — “Copper reacts with cold water like sodium because both are metals.”

Can a double bond count as just one bond toward carbon’s valency? — “Each carbon in ethene makes only three bonds.”

Does photosynthesis release oxygen taken from carbon dioxide? — “The oxygen gas comes from carbon dioxide because CO₂ contains oxygen.”

Is a reflex a deliberate decision? — “You think about moving your hand before a withdrawal reflex.”

Does regrowing a body part count as reproduction? — “A lizard reproduces when it regrows a lost tail.”

Does dominant mean more common? — “A dominant allele must be found in most people.”

Does a convex lens always form a real image? — “A converging lens always projects an image onto a screen.”

Which lens corrects near-sightedness? — “Near-sightedness needs a converging lens to make distant objects clear.”

Does a larger series resistor use up more current? — “Less current flows just after a 4 Ω resistor than just after a 2 Ω resistor in the same series loop.”

Does reversing current reverse the magnetic field? — “The compass deflects the same way after reversing the current.”

Does energy increase higher up a food chain? — “Top predators receive the most energy because they eat other animals.”

Does a shared genus mean the same species? — “Two organisms with the same genus name belong to the same species.”

Can a virus multiply on nutrient medium by itself? — “A virus grows on nutrient agar like bacteria.”

Do seed plants need flowers to make seeds? — “A pine produces spores only because it has no flowers.”

Do wings and a streamlined shape make bats and birds one animal class? — “A bat belongs in the same animal class as birds because both fly with wings.”

Do roots only absorb water? — “A root can only take up water and minerals.”

Does phloem always carry sugars downward? — “Food moves down through phloem in every plant.”

Can an organ be made of just one tissue type? — “The stomach is made entirely of muscle because it squeezes food.”

Can cells without a nucleus make proteins? — “A bacterium has no ribosomes because it lacks a nucleus.”

Are all enzymes proteins? — “Every biological catalyst must be a protein.”

Does DNA replication double the chromosome count immediately? — “After S phase a cell has twice as many chromosomes.”

Does doubling light always double the rate of photosynthesis? — “If light intensity doubles, the rate of photosynthesis must double at every light level.”

Do plants only respire at night? — “Photosynthesis replaces respiration in daylight.”

Does growth mean only getting bigger? — “A bigger plant organ always has more cells.”

Is moving air into the lungs the same as cellular respiration? — “Breathing air into the lungs is cellular respiration.”

Do arteries always carry oxygenated blood? — “Every artery carries oxygen-rich blood.”

Is everything filtered by the kidney lost in urine? — “All filtered glucose ends up in urine.”

Do muscles push bones to move them? — “The biceps pushes the forearm up.”

Is every synapse a continuous electrical wire? — “An impulse jumps directly between cells at a chemical synapse.”

Does a hormone affect every cell it reaches? — “Insulin acts on all cells equally because blood carries it everywhere.”

Do equal masses contain equal numbers of molecules? — “18 g of water and 18 g of CO₂ contain the same number of molecules.”

Is an orbital a path drawn around the nucleus? — “An electron travels on the line shown for its orbital.”

Does an atom get bigger as electrons are added across a period? — “A chlorine atom is larger than a sodium atom because it has more electrons.”

Do polar bonds always give a polar molecule? — “CO₂ is polar because its C=O bonds are polar.”

Does an exothermic reaction always proceed spontaneously? — “A negative enthalpy change alone guarantees spontaneity.”

Does chemical equilibrium mean the reactions stop? — “The forward and reverse reactions stop at equilibrium.”

Can something be oxidised without oxygen? — “Sodium cannot be oxidised in a reaction with chlorine because there is no oxygen.”

Does bond breaking always split the electrons evenly? — “When a C–Cl bond breaks, each atom always gets one shared electron.”

Does a benzene ring react like three independent double bonds? — “Benzene should readily add bromine like an alkene.”

Can you switch an element and a subset? — “1 is a subset of {1, 2}.”

Can a function send one input to two outputs? — “The relation {(1, 2), (1, 3)} is a function.”

Does a sine value identify just one angle? — “If sin θ = ½, θ must be 30°.”

Does a negative discriminant mean a quadratic has no solutions at all? — “x² + 1 = 0 has no solutions because a square cannot be negative.”

Can you multiply an inequality by a negative without reversing it? — “From −2x < 6, divide by −2 to get x < −3.”

When does order count? — “Choosing A then B is always different from choosing B then A.”

Can you raise each part of a sum to a power separately? — “(x + 1)³ = x³ + 1”

Is a term the same as the sum up to it? — “For 2, 4, 8, the third partial sum is 8.”

Is the slope of a vertical line zero? — “A vertical line has slope 0 because there is no horizontal change.”

Does the denominator determine a parabola’s axis? — “In y² = 8x, the axis is vertical because y is squared.”

Is the xy-plane where x and y are zero? — “The xy-plane is defined by x = y = 0.”

Must a limit equal the function value? — “If f(2) is undefined, the limit as x tends to 2 cannot exist.”

Does equal mean imply equal spread? — “Two sets with mean 5 must have the same spread.”

Do mutually exclusive events count as independent? — “Two outcomes that cannot happen together must be independent.”

Do more decimal places guarantee accuracy? — “A reading of 10.50 cm must be accurate because it includes hundredths.”

Does negative acceleration always mean slowing down? — “A car with acceleration −2 m/s² is slowing down.”

Does a projectile have upward acceleration while rising? — “An upward-moving projectile accelerates upward.”

Do action and reaction cancel on one object? — “Equal action and reaction forces cancel, so nothing accelerates.”

Does effort always mean positive work on an object? — “The brake force does positive work because it acts on the moving car.”

Does force alone decide how easily a door turns? — “The same push turns the door equally well anywhere.”

Is an astronaut weightless because gravity is absent? — “Astronauts float because gravity has stopped acting.”

Does elastic mean easy to stretch? — “Rubber has a larger Young’s modulus than steel because it stretches easily.”

Does liquid pressure depend on container shape? — “The wide tank has greater water pressure at the same depth.”

Can a temperature rise be used as the only measure of energy added? — “If ice stays at 0 °C while melting, it absorbs no energy.”

Does zero heat transfer mean constant temperature? — “An insulated gas stays at the same temperature when compressed.”

Does equal temperature mean equal molecular speed? — “Helium and oxygen molecules have the same average speed at the same temperature.”

Where does a spring mass move fastest? — “The mass moves fastest at maximum stretch because the spring pulls hardest there.”

Do particles travel along a wave? — “A pulse carries the particles of a string to the far end.”

Does pollination produce a seed immediately? — “Once pollen lands on the stigma, fertilisation is complete.”

Where does fertilisation usually happen? — “Fertilisation usually occurs in the uterus because that is where the baby develops.”

Do all contraceptive methods reduce STI transmission? — “Any method that prevents pregnancy also reduces the chance of a sexually transmitted infection.”

Can dominance tell you the frequency of an allele? — “A dominant allele must be carried by most members of the population.”

Does a cell transcribe all its DNA at once? — “A cell must copy its whole genome into RNA whenever it needs a protein.”

Does a bacterium evolve because it needs to survive? — “An antibiotic makes each bacterium develop the resistance it needs.”

Does receiving antibodies build long-term immune memory? — “Ready-made antibodies give lasting immunity because the body now has the antibodies it needs.”

Does fermentation always make the same product? — “Every microbe that ferments sugar produces alcohol.”

Does antibiotic survival prove the target gene is present? — “Every colony that grows on the antibiotic must contain the desired DNA insert.”

Does Bt maize protect against every insect? — “A crop carrying a Bt gene resists all insect pests.”

Does a population grow exponentially forever? — “A population that doubles once should keep doubling indefinitely.”

Does all the energy fixed by plants become new biomass? — “All of the energy that plants fix by photosynthesis stays in their new biomass.”

Can species count alone describe biodiversity? — “Two habitats with the same number of species have equal biodiversity in every respect.”

Does molarity stay constant when a solution is warmed? — “The molarity remains unchanged because the amount of solute stays the same.”

Does the anode always have a negative sign? — “Every anode is negative because the anode is negative in a galvanic cell.”

Why are the rates for two reactants different? — “In 2A + B → products, A and B disappear at the same rate.”

Is every d-block element a transition element? — “Zinc is a transition element because it sits in the d block.”

Is coordination number the number of ligands? — “In [Co(en)₃]³⁺, the coordination number is 3 because there are three ligands.”

Should chlorobenzene react like chloroethane? — “Chlorobenzene readily substitutes chloride under the same conditions as chloroethane.”

Is phenol as weak an acid as ethanol? — “Phenol and ethanol are equally acidic because both contain an –OH group.”

Will every carbonyl compound give a silver mirror? — “Both ethanal and propanone give a positive Tollens test because both have C=O.”

Do carbon atoms determine the amine class? — “Ethylamine is secondary because its ethyl group has two carbons.”

Is every disaccharide made with glucose reducing? — “Sucrose must be reducing because one of its units is glucose.”

Does every function have an inverse function? — “Squaring can be undone by square root for every real input.”

Does inverse sine always recover the original angle? — “sin⁻¹(sin 150°) is 150°.”

Can you reverse a matrix product? — “If A and B are square, AB must equal BA.”

What happens to the determinant when every entry doubles? — “Doubling every entry doubles the determinant.”

Does a continuous curve always have a tangent slope? — “Every continuous function is differentiable.”

Does a zero derivative guarantee a maximum or minimum? — “Every point where f′(x) = 0 is a turning point.”

Does the power integration rule work for 1/x? — “Integrating x⁻¹ gives x⁰/0 by the usual power rule.”

Can areas above and below the x-axis cancel? — “The area between y = x and the x-axis from −1 to 1 is zero.”

Does an initial value only check a solution? — “All curves y = Ceˣ solve y′ = y, so any one works when y(0) = 2.”

Does a zero dot product mean a vector is zero? — “If two vectors have dot product 0, at least one has length 0.”

Must nonparallel lines meet in space? — “Two nonparallel lines always intersect.”

Can you optimise using just one constraint at a time? — “A point is feasible if it satisfies at least one constraint.”

Can you swap the event and the condition? — “The probability of a heart given red equals the probability of red given a heart.”

Does zero enclosed charge mean zero field everywhere on a surface? — “If the net electric flux is zero, the electric field must vanish at every point of the surface.”

Can the electric potential be zero while the field is nonzero? — “If electric potential is zero at a point, the electric field there must also be zero.”

Is the same current through two resistors proof of the same voltage drop? — “Two resistors in series have identical voltage drops because they carry the same current.”

Does a magnetic field push a moving charge along the field? — “A positive charge is pushed in the direction the magnetic field points.”

Can you separate the north pole by cutting a magnet? — “Cutting a bar magnet in half gives one north pole and one south pole.”

Will a stationary magnet keep inducing current? — “A strong magnet held inside a coil keeps inducing a current.”

Can AC with zero average current still heat a resistor? — “A resistor on AC cannot heat because the current averages to zero.”

Do higher-frequency electromagnetic waves travel faster in a vacuum? — “X-rays cross a vacuum faster than radio waves because their frequency is higher.”

Do mirrors always form images you can catch on a screen? — “A screen behind a plane mirror can catch the image I see there.”

Does a dark fringe mean the light's energy disappeared? — “Two waves destroy their energy when they make a dark fringe.”

Can brighter light always release photoelectrons? — “Light below the threshold frequency ejects electrons if it is bright enough.”

Is an emitted photon set by the upper energy level alone? — “The photon energy equals the atom's energy at the upper level.”

Does half-life remove the same number of nuclei each time? — “If the first half-life removes an expected 800,000 of 1,600,000 nuclei, the next removes another 800,000.”

Does a diode conduct as soon as any positive voltage appears? — “A silicon diode behaves like a short circuit at any forward voltage.”