Hiroshima Entrance Science common mistakes
Hiroshima Entrance Science · Understand the traps and how to avoid them.
When a quadratic or rational function is given with a parameter and the question asks for the range of the parameter for which the equation has two distinct real roots, the candidate computes the discriminant and stops at D > 0, ignoring the separate conditions that the leading coefficient is nonzero and that any excluded value (where the denominator vanishes or the roots coincide with a boundary) is not attained.
Discriminant-only training is heavily drilled, so D > 0 becomes an automatic reflex. The habit forms because most textbook problems are engineered so that D > 0 is the only condition, and candidates rarely meet problems where the coefficient of x² can vanish or where a root must be rejected because it makes a denominator zero.
What to do instead
Before solving, list every condition that must hold: leading coefficient nonzero, discriminant sign, denominator nonzero, and any stated restriction on the variable. Write them as a system of inequalities and take the intersection. Then test the boundary parameter values by substituting back into the original equation to confirm the root count. Build a habit of a final substitution check for each endpoint of the parameter interval.
In trigonometric problems the candidate solves sin θ = k or cos θ = k and reports only the principal value, or reports solutions in degrees when the problem is set in radians, or forgets that squaring an equation can introduce extraneous roots and never checks the original equation.
The inverse-trig function on a calculator returns one value, and candidates trust that output. The general-solution structure (θ = α + 2nπ, or π − α + 2nπ for sine) is often memorised as a formula without understanding the unit circle symmetry, so it collapses under time pressure or when the interval is restricted to something like 0 ≤ θ < 2π.
What to do instead
Always draw the unit circle, mark the reference angle, and read off all solutions in the required interval before writing the general form. State the interval explicitly at the top of the working. If you squared the equation at any step, substitute every candidate solution back into the unsquared equation and discard failures. Practise converting between degrees and radians until the conversion is automatic, and check whether the question specifies the unit.
When a mechanics problem involves a body on an incline, in a lift, or connected over a pulley, the candidate writes Newton's second law for the whole system as if it were a single particle, adding forces that act on different bodies, or omits the normal force or tension from the free-body diagram of one body.
Candidates learn F = ma early and apply it globally. The discipline of isolating each body and drawing a separate free-body diagram is a procedural step that is easy to skip when the answer seems obvious, and connected-body problems are visually simple but conceptually require per-body accounting.
What to do instead
Draw one free-body diagram per body, label every force with its source, and choose a positive direction per body (consistent along the string for connected bodies). Write ΣF = ma separately for each body, then solve the simultaneous equations. For lifts and inclines, resolve along and perpendicular to the acceleration direction. Check that internal forces (tension, contact) cancel when you add the equations for the whole system.
In electricity and magnetism questions the candidate treats the magnetic flux through a loop as B × A without considering the angle between the field and the area normal, or applies Faraday's law using the change in flux over the whole time interval when the question asks for the instantaneous induced emf at a moment when the flux is changing non-uniformly.
The formula Φ = BA is learned first and the cosine factor is treated as decoration. Average-versus-instantaneous distinction is blurred because most school problems use uniform rates, so the derivative form ε = −dΦ/dt is not internalised as the definition.
What to do instead
Write Φ = BA cos θ explicitly and identify θ as the angle between B and the normal to the area, not the plane of the loop. For induced emf, decide first whether the question wants average emf (use ΔΦ/Δt over the interval) or instantaneous emf (differentiate Φ with respect to t). If the flux graph is given, read the instantaneous emf as the gradient of the tangent, not the gradient of the chord.
In stoichiometry and solution problems the candidate mixes units - using volume in mL with concentration in mol/L, or mass in grams with molar mass in g/mol but then treating the result as if it were in mmol - and reports a numerical answer with no unit or with the wrong unit.
The arithmetic is correct but the unit bookkeeping is skipped because candidates treat units as labels added at the end rather than as part of the calculation. Under time pressure, converting mL to L feels like an unnecessary step when the numbers are small.
What to do instead
Carry units through every line of working as if they were algebraic quantities, so that mL × mol/L visibly fails to give moles. Convert all volumes to litres and all masses to grams at the start, before any calculation. Write the final answer with its unit and check the order of magnitude against an estimate (for example, 25 mL of 0.1 mol/L is 2.5 mmol, not 2.5 mol).
When asked to predict the products of a reaction or to identify an unknown ion, the candidate writes a balanced equation that is chemically impossible - for example, placing a metal above hydrogen in the activity series as a product of displacement by a less reactive metal, or forgetting that a precipitate does not form when the putative product is soluble.
Candidates pattern-match on the appearance of the reagents rather than reasoning from the reactivity series and solubility rules. The rules are learned as lists but not applied as a filter on the proposed product, so a plausible-looking equation is accepted without a feasibility check.
What to do instead
Before writing products, run two checks: (1) is the reaction feasible thermodynamically - does the displacing species lie above the displaced one in the reactivity series, and is a gas, precipitate, or weak electrolyte formed? (2) is the proposed salt soluble under the stated conditions? Keep a solubility table and a reactivity series at hand and cite the relevant entry in your working. For ion identification, confirm that the test distinguishes the ion from all others that would give the same observation.
In genetics and cell-division questions the candidate confuses the number of chromatids with the number of chromosomes, or applies a dominant/recessive ratio to a cross without checking whether the genes are linked or whether the parents' genotypes are actually as assumed.
Chromosome and chromatid counts are taught with diagrams that look similar, and the distinction only matters at specific stages (after S phase, at anaphase). Ratio problems are drilled as 3:1 and 9:3:3:1 templates, so candidates apply the template without verifying the assumptions of independent assortment and complete dominance.
What to do instead
For every cell-stage question, state the ploidy, the number of chromosomes, and the number of chromatids separately before answering. For crosses, write out the parental genotypes explicitly, check whether the genes are on the same chromosome (linkage changes the ratio), and confirm that dominance is complete and that no lethal genotype is involved. If the observed ratio deviates from the template, test it against the expected ratio with a chi-square calculation rather than assuming an error.
When interpreting an experiment on enzyme activity, photosynthesis, or osmosis, the candidate identifies the dependent variable as the one that was deliberately changed, or concludes that a correlation across a range of conditions proves a causal mechanism without identifying the controlled variables.
The vocabulary of independent and dependent variables is learned as definitions but not practised on real experimental descriptions. Candidates also over-generalise from a single graph because the mechanism was taught separately and is assumed to explain any trend.
What to do instead
For each experiment, write three lines: what the experimenter changed (independent), what was measured (dependent), and what was held constant (controlled). Then state the conclusion strictly in terms of the measured variable, and separately state whether the proposed mechanism is supported or merely consistent. If a control group is missing, say so explicitly rather than inferring causation.
In earth and environmental science questions the candidate treats the greenhouse effect, ozone depletion, and acid rain as a single pollution topic, attributing ozone depletion to carbon dioxide or acid rain to chlorofluorocarbons, and ignoring the different spatial scales (global, stratospheric, regional).
The three topics are taught together in environmental units and share the vocabulary of 'pollution' and 'atmosphere', so the specific gases and mechanisms blur. The spatial-scale distinction is rarely tested in school, so it is not reinforced.
What to do instead
Build a comparison table with one row per phenomenon and columns for primary pollutants, mechanism, affected layer or region, and principal consequence. Greenhouse effect: CO₂, CH₄, N₂O trap outgoing infrared in the troposphere, global scale. Ozone depletion: CFCs release chlorine radicals in the stratosphere, polar enhancement, global but concentrated over Antarctica. Acid rain: SO₂ and NOₓ form sulfuric and nitric acids, regional scale, damages soils and fresh water. Recall the table before answering any question that names one of the three.
When a question presents tabulated or graphed data and asks for a conclusion, the candidate reads a single data point as representative, extrapolates beyond the measured range, or reports a trend without quantifying it (for example, 'increases' instead of 'increases by about 0.4 units per 10 °C').
Data-interpretation questions are often answered by pattern recognition on the shape of the graph, and candidates are not trained to attach numbers to trends. Extrapolation feels natural because the graph continues, but the axes stop where the measurements stop.
What to do instead
Before writing a conclusion, state the range of the independent variable that was actually measured and restrict the claim to that range. Quantify the trend using at least two points: compute the gradient or the ratio between successive values and quote it with units. Check for scatter and state whether the trend is monotonic. If the question asks about behaviour outside the measured range, answer that the data do not support a conclusion rather than extrapolating.