Niigata Public High School Entrance Examination - Science cheat sheet

Average speed = distance ÷ time; velocity adds direction, so a round trip can have zero average velocity but nonzero average speed.

Acceleration = change in velocity ÷ time (m/s²); on a velocity–time graph, slope gives acceleration and the area under the line gives displacement.

Newton's first law: with no net force, a stationary object stays still and a moving object keeps constant velocity; friction is the usual net force stopping motion.

Newton's second law: F = ma; the same force gives smaller acceleration to a larger mass, and acceleration is always in the direction of the net force.

Newton's third law: forces act in equal-and-opposite pairs on two different objects, so the pair never cancels on a single object.

Weight = mass × gravitational acceleration (about 9.8 N/kg on Earth); mass in kg is unchanged on the Moon but weight is about one-sixth.

Work = force × distance moved along the force (J); holding a load still does no work because there is no displacement.

Kinetic energy = ½mv²; gravitational potential energy = mgh. With friction ignored, mechanical energy is conserved and PE lost equals KE gained.

Pressure = force ÷ area (Pa); a smaller contact area gives greater pressure, which is why a sharp edge cuts and wide tires float on soft ground.

Ohm's law: V = IR. For a fixed resistor, current is proportional to voltage; a steeper straight line on an I–V graph means smaller resistance.

Series circuit: current is the same everywhere, total resistance R = R1 + R2, and the supply voltage splits in proportion to resistance.

Parallel circuit: voltage is the same across each branch, total current is the sum of branch currents, and total resistance is less than any single branch resistance.

Electric power P = VI = I²R = V²/R (W); energy used = power × time, and 1 kWh = 3.6 × 10⁶ J.

Charge Q = It (C); current is the rate of charge flow, and conventional current is taken from + to − outside the source.

A current-carrying wire has a magnetic field around it; reversing the current reverses the field, and a coil with a soft-iron core becomes an electromagnet.

A wire carrying current in a magnetic field feels a force (motor effect); reversing either the current or the field reverses the force direction.

Electromagnetic induction: a magnet moving into or out of a coil induces a voltage; faster motion or more turns gives a larger induced voltage.

Wave speed = frequency × wavelength (v = fλ); frequency is set by the source and does not change when a wave enters a new medium, but speed and wavelength do.

A pure substance has a fixed melting and boiling point; an impurity lowers the melting point and raises the boiling point over a range.

Physical change alters state or shape without new substances; chemical change produces new substances and is shown by gas, precipitate, colour change, or heat.

Mixtures are separated by physical means: filtration for insoluble solids, distillation for dissolved solids or liquids with different boiling points, chromatography for dyes.

Density = mass ÷ volume (g/cm³); a substance less dense than water floats, and density is a property usable to identify a pure substance.

Combustion of a hydrocarbon in enough oxygen gives carbon dioxide and water; in limited oxygen, carbon monoxide and soot also form.

Reduction removes oxygen from a compound; oxidation adds oxygen. In a blast furnace, carbon reduces iron oxide to iron.

Exothermic reactions release heat (combustion, neutralisation, respiration); endothermic ones absorb heat (thermal decomposition, photosynthesis).

Metals react with oxygen to form basic oxides, non-metals form acidic oxides, and neutralisation of an acid with a base gives a salt plus water.

An atom has a positive nucleus of protons and neutrons, with electrons outside; proton number (atomic number) fixes the element.

Mass number = protons + neutrons; isotopes have the same proton number but different neutron numbers, so chemical properties are nearly identical.

An ion forms when an atom gains or loses electrons: metals lose electrons to become positive cations, non-metals gain electrons to become negative anions.

A chemical formula gives the element symbols and the ratio of atoms; the subscript applies only to the symbol just before it, as in Ca(OH)₂.

Balancing an equation: change only coefficients, never subscripts, and check that each element's atom count is equal on both sides.

Mole relationship: 1 mol contains 6.0 × 10²³ particles and has a mass in grams equal to the molar mass; molar mass of H₂O is 18 g/mol.

Avogadro's law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, so volume ratios equal mole ratios.

Ionic compounds conduct electricity when melted or dissolved because ions become free to move, but not as solids, where ions are fixed in the lattice.

Precipitation occurs when ions in solution combine into an insoluble compound, such as Ag⁺ with Cl⁻ giving AgCl.

Producers fix energy by photosynthesis; energy passes to consumers along food chains, and arrows point in the direction energy flows.

Only about 10% of energy passes to the next trophic level, so food chains are short and top predators are few; matter cycles but energy flows one way.

Decomposers break down dead organisms and waste, returning carbon and nitrogen compounds to soil and water for producers to reuse.

Carbon cycle: photosynthesis removes CO₂; respiration, combustion, and decomposition release it. Nitrogen is fixed by bacteria and lightning for use in proteins.

Population size is limited by food, space, predators, disease, and climate; a predator–prey graph shows the prey peak slightly before the predator peak.

Competition and symbiosis: mutualism benefits both species, parasitism benefits one and harms the other, and competition harms both.

Adaptation suits an organism to its habitat; organisms with favourable inherited variation survive and leave more offspring, so the trait spreads.

Environmental change such as warming or habitat loss shifts species ranges and can break the timing links between plants, insects, and predators.

Digestion: amylase in saliva breaks starch to sugar; stomach acid and pepsin digest protein; bile from the liver emulsifies fat and lipase in the small intestine completes fat digestion.

Villi in the small intestine give a large surface with thin walls and dense capillaries, so digested glucose and amino acids are absorbed into blood.

Blood: red cells carry oxygen with haemoglobin, white cells defend the body, platelets clot blood, and plasma carries nutrients, CO₂, and hormones.

Double circulation: the right side of the heart sends blood to the lungs and the left side sends it around the body; arteries carry blood away, veins return it.

Respiration: inhaled air has more oxygen than exhaled air, which has more carbon dioxide; alveoli give a large, thin, moist surface for gas exchange.

Excretion: kidneys filter blood and reabsorb useful substances, producing urine; the liver detoxifies and controls blood glucose.

Nervous coordination: a reflex arc runs receptor → sensory neurone → spinal cord → motor neurone → muscle, giving a fast response without conscious thought.

Human reproduction: sperm from the testis fertilises the egg in the oviduct; the zygote implants in the uterus and the placenta exchanges materials with the mother.

Earth's interior: crust, mantle, outer core (liquid iron, source of the magnetic field), and inner core (solid); the mantle's slow convection moves plates.

Plate boundaries: divergent (mid-ocean ridge, new crust), convergent (subduction, earthquakes, volcanoes), and transform (plates slide past, causing earthquakes).

Earthquakes: P waves arrive first and travel through solids and liquids; S waves arrive later and cannot pass through liquid, showing the outer core is liquid.

Igneous rock forms from cooled magma or lava, sedimentary from compacted deposits in layers, and metamorphic from heat and pressure; fossils occur mainly in sedimentary rock.

Weathering and erosion break and carry away rock; deposition builds layers, and rivers sort particles by size, carrying fine mud farthest.

Air pressure falls with altitude; wind blows from high to low pressure, and on a weather map tight isobars mean strong winds.

Warm, humid air rising cools and condenses into cloud; fronts bring rain, and a warm front typically gives steady rain followed by warmer air.

Seasons come from Earth's 23.4° axial tilt changing the Sun's height and day length, not from Earth's distance from the Sun.

Moon phases arise from the changing angle between Earth, Moon, and Sun; a solar eclipse needs a new moon, and a lunar eclipse needs a full moon.