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Tokyo Metropolitan Public High School Entrance Examination - Science study materials
Tokyo Metropolitan Public High School Entrance Examination - Science study resources

Tokyo Metropolitan Public High School Entrance Examination - Science practice questions

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Question 1Physics: measurements, energy and circuits

A car travels at a constant speed of 20 m/s for 30 seconds. What distance does it cover?

  1. 600 m Correct answer.
  2. 50 m
  3. 1.5 m
  4. 900 m

Explanation

Distance = speed × time = 20 m/s × 30 s = 600 m. Constant speed means the object covers equal distances in equal time intervals.

Question 2Physics: measurements, energy and circuits

An object starting from rest accelerates uniformly at 2 m/s² for 5 seconds. What is its final speed?

  1. 10 m/s Correct answer.
  2. 25 m/s
  3. 2.5 m/s
  4. 7 m/s

Explanation

Final speed = initial speed + acceleration × time = 0 + 2 m/s² × 5 s = 10 m/s. Uniform acceleration means velocity increases by equal amounts each second.

Question 3Physics: measurements, energy and circuits

A cart is released from the top of a ramp and rolls down. Ignoring friction, which statement best describes the energy change as it descends?

  1. Potential energy and kinetic energy both decrease
  2. Kinetic energy decreases while potential energy increases
  3. Potential energy decreases while kinetic energy increases, and their total stays constant Correct answer.
  4. Potential energy and kinetic energy both increase

Explanation

As the cart loses height, its gravitational potential energy falls, and that energy is converted into kinetic energy, so the cart speeds up. With friction ignored, the sum of the two - the mechanical energy - remains constant. This is the law of conservation of mechanical energy (力学的エネルギーの保存).

Question 4Physics: measurements, energy and circuits

A force of 10 N is applied to push a box 5 m along a straight horizontal surface. How much work is done by this force?

  1. 50 J Correct answer.
  2. 5 J
  3. 2 J
  4. 15 J

Explanation

Work = force × distance = 10 N × 5 m = 50 J. Work requires both a force and displacement in the direction of the force.

Question 5Physics: measurements, energy and circuits

Which statement correctly describes the relationship between the force applied to a spring and its extension, within the elastic limit?

  1. Force is directly proportional to extension Correct answer.
  2. Force is independent of extension
  3. Force is inversely proportional to extension
  4. Force is proportional to the square of extension

Explanation

Hooke's law states that within the elastic limit, the force applied to a spring is directly proportional to its extension (F = kx). Beyond the elastic limit the spring deforms permanently and this linear relationship no longer holds.

Question 6Physics: measurements, energy and circuits

A block of mass 500 g rests on a horizontal surface. What is the normal force exerted by the surface on the block? (Take g = 9.8 m/s².)

  1. 4.9 N Correct answer.
  2. 0.5 N
  3. 9.8 N
  4. 500 N

Explanation

Weight = mass × g = 0.5 kg × 9.8 m/s² = 4.9 N. On a horizontal surface with no vertical acceleration, the normal force equals the weight. The mass must be converted from grams to kilograms before calculating.

Question 7Physics: measurements, energy and circuits

The pressure at a depth h in a liquid of density ρ is given by P = ρgh. What is the pressure 2 m below the surface of water? (ρ = 1000 kg/m³, g = 9.8 m/s².)

  1. 2000 Pa
  2. 9800 Pa
  3. 4900 Pa
  4. 19600 Pa Correct answer.

Explanation

P = ρgh = 1000 kg/m³ × 9.8 m/s² × 2 m = 19600 Pa. Pressure in a fluid increases with depth and depends on the fluid density and gravitational acceleration.

Question 8Physics: measurements, energy and circuits

A battery of 6 V is connected across a resistor of 3 Ω. What current flows through the resistor?

  1. 18 A
  2. 0.5 A
  3. 2 A Correct answer.
  4. 9 A

Explanation

By Ohm's law, I = V/R = 6 V / 3 Ω = 2 A. Current is directly proportional to voltage and inversely proportional to resistance.

Question 9Physics: measurements, energy and circuits

A current of 0.5 A flows through a 12 Ω resistor. What is the voltage across it?

  1. 12.5 V
  2. 6 V Correct answer.
  3. 24 V
  4. 0.042 V

Explanation

By Ohm's law, V = IR = 0.5 A × 12 Ω = 6 V. The voltage across a resistor equals the product of the current through it and its resistance.

Question 10Physics: measurements, energy and circuits

A 4 Ω resistor and a 2 Ω resistor are connected in series. What is their combined resistance?

  1. 8 Ω
  2. 1.33 Ω
  3. 6 Ω Correct answer.
  4. 2 Ω

Explanation

For resistors in series, the total resistance is the sum: R = 4 Ω + 2 Ω = 6 Ω. Series connections always increase total resistance.

Question 11Physics: measurements, energy and circuits

A 6 Ω resistor and a 3 Ω resistor are connected in parallel. What is their combined resistance?

  1. 9 Ω
  2. 18 Ω
  3. 3 Ω
  4. 2 Ω Correct answer.

Explanation

For parallel resistors, 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so R = 2 Ω. The parallel combination is always smaller than either individual resistor.

Question 12Physics: measurements, energy and circuits

A light bulb draws 0.5 A from a 100 V supply. What is the electric power consumed?

  1. 25 W
  2. 100.5 W
  3. 200 W
  4. 50 W Correct answer.

Explanation

Electric power P = VI = 100 V × 0.5 A = 50 W. Power equals the rate at which electrical energy is converted to other forms such as heat and light.

Question 13Physics: measurements, energy and circuits

A 100 W light bulb is operated for 10 seconds. How much electrical energy is consumed?

  1. 10000 J
  2. 1000 J Correct answer.
  3. 10 J
  4. 100 J

Explanation

Energy = power × time = 100 W × 10 s = 1000 J. One watt equals one joule per second, so power multiplied by time gives energy in joules.

Question 14Physics: measurements, energy and circuits

Which of the following correctly describes the magnetic field produced by a straight current-carrying wire?

  1. Circular field lines centered on the wire Correct answer.
  2. No magnetic field is produced
  3. Radial lines pointing outward from the wire
  4. Straight lines parallel to the wire

Explanation

A current-carrying wire produces a magnetic field whose field lines form concentric circles around the wire. The direction can be found using the right-hand rule.

Question 15Physics: measurements, energy and circuits

A sound wave has a frequency of 500 Hz and travels at 340 m/s in air. What is its wavelength?

  1. 2.21 m
  2. 0.68 m Correct answer.
  3. 0.0015 m
  4. 170000 m

Explanation

Wave speed = frequency × wavelength, so wavelength = speed / frequency = 340 m/s / 500 Hz = 0.68 m. Wavelength is inversely proportional to frequency for a fixed wave speed.

Question 16Physics: measurements, energy and circuits

Light strikes a plane mirror at an angle of 30° to the mirror surface. What is the angle of reflection measured from the normal?

  1. 60° Correct answer.
  2. 90°
  3. 0°
  4. 30°

Explanation

The angle of incidence is measured from the normal. Since the ray makes 30° with the mirror surface, it makes 60° with the normal (90° − 30° = 60°). By the law of reflection, the angle of reflection equals the angle of incidence, so it is 60°.

Question 17Physics: measurements, energy and circuits

When light passes from air into water, which property of the light remains unchanged?

  1. Direction of travel
  2. Frequency Correct answer.
  3. Speed
  4. Wavelength

Explanation

When light enters a denser medium like water, its speed and wavelength decrease, and it bends (refracts). However, the frequency of the wave is determined by the source and does not change as light passes from one medium to another.

Question 18Physics: measurements, energy and circuits

A boy of mass 40 kg climbs a vertical height of 3 m. How much gravitational potential energy does he gain? (g = 9.8 m/s².)

  1. 400 J
  2. 120 J
  3. 1176 J Correct answer.
  4. 392 J

Explanation

Gravitational potential energy = mgh = 40 kg × 9.8 m/s² × 3 m = 1176 J. The gained energy depends on mass, gravitational acceleration, and the change in height.

Question 19Physics: measurements, energy and circuits

Two forces of 3 N and 4 N act on the same point at right angles to each other. What is the magnitude of the resultant force?

  1. 7 N
  2. 5 N Correct answer.
  3. 1 N
  4. 12 N

Explanation

When two forces act at right angles, the resultant is found by the Pythagorean theorem: R = √(3² + 4²) = √(9 + 16) = √25 = 5 N. This is a 3-4-5 right triangle.

Question 20Physics: measurements, energy and circuits

A lever has an effort arm of 0.8 m and a load arm of 0.2 m. If the load to be lifted is 40 N, what effort force is needed? (Assume the lever is in equilibrium.)

  1. 10 N Correct answer.
  2. 160 N
  3. 50 N
  4. 32 N

Explanation

By the principle of moments, effort × effort arm = load × load arm. So effort = (40 N × 0.2 m) / 0.8 m = 10 N. A lever with a longer effort arm requires less effort force.

Question 21Physics: measurements, energy and circuits

An object of mass 2 kg is pushed with a net force of 8 N. What is its acceleration?

  1. 0.25 m/s²
  2. 10 m/s²
  3. 16 m/s²
  4. 4 m/s² Correct answer.

Explanation

By Newton's second law, a = F/m = 8 N / 2 kg = 4 m/s². Acceleration is directly proportional to net force and inversely proportional to mass.

Question 22Physics: measurements, energy and circuits

Which of the following is true about the motion of an object moving at constant velocity?

  1. There are no forces acting on the object
  2. The net force is in the direction of motion
  3. The net force is perpendicular to the velocity
  4. The net force on the object is zero Correct answer.

Explanation

By Newton's first law, an object at constant velocity has zero net force acting on it. There may be individual forces, but they balance out. Zero net force means zero acceleration, so velocity stays constant.

Question 23Physics: measurements, energy and circuits

A rectangular block measures 2 cm × 3 cm × 5 cm and has a mass of 60 g. What is its density?

  1. 10 g/cm³
  2. 0.5 g/cm³
  3. 4 g/cm³
  4. 2 g/cm³ Correct answer.

Explanation

Volume = 2 × 3 × 5 = 30 cm³. Density = mass / volume = 60 g / 30 cm³ = 2 g/cm³. Density is the mass per unit volume of a substance.

Question 24Physics: measurements, energy and circuits

Which correctly describes how an electroscope detects electric charge?

  1. The leaves spread due to gravitational repulsion
  2. Like charges on the leaves repel, causing them to spread apart Correct answer.
  3. The leaves attract each other when charged
  4. The device measures the voltage of nearby objects

Explanation

When a charged object touches the electroscope, charge flows to the gold leaves. Since the leaves acquire the same type of charge, they repel each other and spread apart. This is a demonstration of like-charge repulsion.

Question 25Physics: measurements, energy and circuits

Two identical resistors of 4 Ω each are connected in parallel across a 12 V battery. What is the total current drawn from the battery?

  1. 3 A
  2. 1.5 A
  3. 6 A Correct answer.
  4. 12 A

Explanation

Parallel resistance: 1/R = 1/4 + 1/4 = 2/4 = 1/2, so R = 2 Ω. Total current I = V/R = 12 V / 2 Ω = 6 A. The parallel combination halves the resistance compared to one resistor.

Question 26Chemistry: particles, reactions and mass

Which state of matter has both a definite volume and a definite shape?

  1. Liquid
  2. Gas
  3. Solid Correct answer.
  4. Plasma

Explanation

Solids have a fixed shape and a fixed volume because their particles are tightly packed in a regular arrangement with strong intermolecular forces. Liquids have fixed volume but take the shape of their container, and gases have neither fixed shape nor fixed volume.

Question 27Chemistry: particles, reactions and mass

Which of the following is a pure substance, not a mixture?

  1. Milk
  2. Brass
  3. Distilled water Correct answer.
  4. Air

Explanation

Distilled water (H₂O) is a single compound and therefore a pure substance. Air is a mixture of gases (nitrogen, oxygen, etc.), brass is a mixture of copper and zinc, and milk is a mixture of water, fat, proteins, and other components.

Question 28Chemistry: particles, reactions and mass

What is the atomic number of an element whose neutral atom has 11 electrons?

  1. 12
  2. 11 Correct answer.
  3. 23
  4. 22

Explanation

The atomic number is the number of protons in the nucleus. An atom is neutral only when its protons and electrons balance, so 11 electrons means 11 protons and an atomic number of 11. This element is sodium (Na).

Question 29Chemistry: particles, reactions and mass

An atom has a mass number of 23 and an atomic number of 11. How many neutrons does it have?

  1. 34
  2. 12 Correct answer.
  3. 11
  4. 23

Explanation

Number of neutrons = mass number − atomic number = 23 − 11 = 12. The mass number is the total count of protons and neutrons in the nucleus.

Question 30Chemistry: particles, reactions and mass

Which of the following correctly gives the charge of a chloride ion (Cl⁻)?

  1. −1 Correct answer.
  2. 0
  3. −2
  4. +1

Explanation

A chlorine atom gains one electron to achieve a stable outer electron shell, forming a chloride ion with charge −1. The gain of a negatively charged electron gives the ion a net negative charge.

Question 31Chemistry: particles, reactions and mass

In the chemical reaction H₂ + O₂ → H₂O, what are the coefficients when the equation is balanced?

  1. 1, 2, 1
  2. 2, 2, 2
  3. 2, 1, 2 Correct answer.
  4. 1, 1, 1

Explanation

The balanced equation is 2H₂ + O₂ → 2H₂O. Counting atoms: 4 H and 2 O on each side. Balancing ensures the same number of each type of atom on both sides, satisfying the law of conservation of mass.

Question 32Chemistry: particles, reactions and mass

Which type of reaction is represented by the equation CaCO₃ → CaO + CO₂?

  1. Synthesis
  2. Combustion
  3. Decomposition Correct answer.
  4. Single displacement

Explanation

A single compound (CaCO₃) breaks down into two or more simpler substances (CaO and CO₂), which is a decomposition reaction. This specific reaction is the thermal decomposition of limestone.

Question 33Chemistry: particles, reactions and mass

Which of the following is a characteristic property of an acid?

  1. Turns red litmus paper blue
  2. Feels slippery to the touch
  3. Turns blue litmus paper red Correct answer.
  4. Has a pH greater than 7

Explanation

Acids turn blue litmus paper red, have a pH less than 7, and typically taste sour. The other options listed are properties of bases, which turn red litmus blue, have pH above 7, and feel slippery.

Question 34Chemistry: particles, reactions and mass

Dilute hydrochloric acid is gradually added to sodium hydroxide solution containing a few drops of BTB (bromothymol blue). What colour sequence is observed?

  1. Green throughout, with no colour change
  2. Red, then colourless, then red again
  3. Yellow, then green at neutrality, then blue
  4. Blue, then green at neutrality, then yellow Correct answer.

Explanation

BTB is blue in alkaline solution, green when neutral and yellow in acid. Sodium hydroxide solution starts alkaline, so the indicator is blue; as acid is added the mixture is neutralised and turns green; further acid makes the solution acidic and the indicator turns yellow.

Question 35Chemistry: particles, reactions and mass

Hydrochloric acid (HCl) is neutralized by sodium hydroxide (NaOH). What are the products of this neutralization reaction?

  1. NaCl and H₂O Correct answer.
  2. NaOH and Cl₂
  3. Na and H₂O
  4. NaCl and H₂

Explanation

A neutralization reaction between an acid and a base produces a salt and water: HCl + NaOH → NaCl + H₂O. NaCl is common table salt. The H⁺ from the acid and OH⁻ from the base combine to form water.

Question 36Chemistry: particles, reactions and mass

Which of the following is an example of an oxidation reaction?

  1. Ice melting into water
  2. Iron rusting in moist air Correct answer.
  3. Water boiling to form steam
  4. Salt dissolving in water

Explanation

Rusting is an oxidation reaction in which iron reacts with oxygen to form iron oxide (Fe₂O₃). Oxidation involves a substance combining with oxygen or losing electrons. The other options are physical changes, not chemical reactions.

Question 37Chemistry: particles, reactions and mass

In the reaction CuO + H₂ → Cu + H₂O, which substance is reduced?

  1. CuO Correct answer.
  2. Cu
  3. H₂
  4. H₂O

Explanation

Reduction is the loss of oxygen (or gain of electrons). CuO loses oxygen to become Cu, so copper oxide is reduced. Simultaneously, H₂ gains oxygen to become H₂O, so hydrogen is oxidized. This is a redox reaction.

Question 38Chemistry: particles, reactions and mass

Which property is generally characteristic of metals?

  1. Poor conductor of heat
  2. Good conductor of electricity Correct answer.
  3. Brittle when solid
  4. Low melting point

Explanation

Metals are generally good conductors of electricity and heat due to their free (delocalized) electrons. They are also typically malleable, ductile, and have high melting points. Brittleness and poor conductivity are characteristic of non-metals.

Question 39Chemistry: particles, reactions and mass

When a piece of zinc is placed in dilute hydrochloric acid, what gas is produced?

  1. Hydrogen Correct answer.
  2. Chlorine
  3. Oxygen
  4. Carbon dioxide

Explanation

Zinc reacts with hydrochloric acid in a single displacement reaction: Zn + 2HCl → ZnCl₂ + H₂. Hydrogen gas is evolved, which can be tested with a burning splint producing a 'pop' sound.

Question 40Chemistry: particles, reactions and mass

Which of the following elements is a noble gas?

  1. Nickel
  2. Neon Correct answer.
  3. Sodium
  4. Nitrogen

Explanation

Neon (Ne) is a noble gas in Group 18 of the periodic table. Noble gases have full outer electron shells, making them very stable and chemically unreactive. Nitrogen is a non-metal gas but not noble; sodium is a reactive metal; nickel is a transition metal.

Question 41Chemistry: particles, reactions and mass

How many molecules are represented by the formula 3H₂O?

  1. 2
  2. 3 Correct answer.
  3. 5
  4. 6

Explanation

The coefficient 3 in front of H₂O indicates three water molecules. Each H₂O molecule contains 2 hydrogen atoms and 1 oxygen atom, so 3H₂O contains 6 H atoms and 3 O atoms in total.

Question 42Chemistry: particles, reactions and mass

Which of the following reactions produces a precipitate when aqueous solutions of silver nitrate (AgNO₃) and sodium chloride (NaCl) are mixed?

  1. NaNO₃ (white precipitate)
  2. No precipitate forms
  3. AgNa (precipitate)
  4. AgCl (white precipitate) Correct answer.

Explanation

The reaction is AgNO₃ + NaCl → AgCl + NaNO₃. Silver chloride (AgCl) is insoluble in water and forms a white precipitate. NaNO₃ remains dissolved. This is a precipitation reaction.

Question 43Chemistry: particles, reactions and mass

In an experiment, an electric current is passed through dilute hydrochloric acid. Toward which electrode do the hydrogen ions (H⁺) move, and what is produced there?

  1. The cathode (negative electrode), where hydrogen gas is produced Correct answer.
  2. The anode (positive electrode), where oxygen gas is produced
  3. The anode (positive electrode), where hydrogen gas is produced
  4. The cathode (negative electrode), where chlorine gas is produced

Explanation

Hydrogen ions carry a positive charge, so they are attracted to the negatively charged electrode, the cathode. There each H⁺ gains an electron and pairs up to form hydrogen gas. Meanwhile the negatively charged chloride ions (Cl⁻) travel to the anode, where chlorine gas is released.

Question 44Chemistry: particles, reactions and mass

Which of the following correctly describes what happens when an acid is added to water?

  1. The acid releases OH⁻ ions
  2. No ions are formed
  3. The water becomes neutral
  4. The acid dissociates to release H⁺ ions Correct answer.

Explanation

When an acid dissolves in water, it dissociates to release hydrogen ions (H⁺), which make the solution acidic. The H⁺ ions bond with water to form hydronium ions (H₃O⁺). This is why acids conduct electricity in aqueous solution.

Question 45Chemistry: particles, reactions and mass

In the electrolysis of water, what gases are produced at the cathode and anode respectively?

  1. Both hydrogen at both electrodes
  2. Both oxygen at both electrodes
  3. Oxygen at cathode, hydrogen at anode
  4. Hydrogen at cathode, oxygen at anode Correct answer.

Explanation

During electrolysis of water, hydrogen is produced at the cathode (negative electrode) and oxygen at the anode (positive electrode). The volume of hydrogen is twice that of oxygen, reflecting the 2:1 ratio of hydrogen to oxygen in water.

Question 46Chemistry: particles, reactions and mass

Which of the following is the correct chemical formula for calcium carbonate?

  1. Ca(OH)₂
  2. CaCl₂
  3. CaO
  4. CaCO₃ Correct answer.

Explanation

Calcium carbonate is CaCO₃, composed of calcium (Ca²⁺), carbonate (CO₃²⁻). The charges balance in a 1:1 ratio. It is found in limestone, chalk, and seashells.

Question 47Chemistry: particles, reactions and mass

When 4.0 g of copper powder is heated in air until no further change occurs, 5.0 g of copper oxide forms. What mass of oxygen combined with the copper?

  1. 1.0 g Correct answer.
  2. 4.0 g
  3. 0.8 g
  4. 9.0 g

Explanation

Mass is conserved in a chemical reaction, so the mass of oxygen that combined equals the increase in mass: 5.0 g − 4.0 g = 1.0 g. This copper-to-oxygen ratio of 4:1 by mass is the standard result of the 中学 heating experiment and reflects the law of conservation of mass (質量保存の法則).

Question 48Chemistry: particles, reactions and mass

When magnesium ribbon burns in air, the main product is magnesium oxide. What type of oxide is MgO?

  1. Amphoteric oxide
  2. Basic oxide Correct answer.
  3. Acidic oxide
  4. Neutral oxide

Explanation

Magnesium is a metal, and metal oxides are generally basic. MgO is a basic oxide that reacts with acids to form salt and water. Non-metal oxides like CO₂ are generally acidic.

Question 49Chemistry: particles, reactions and mass

Which of the following describes the change in state directly from solid to gas without passing through the liquid phase?

  1. Condensation
  2. Deposition
  3. Sublimation Correct answer.
  4. Evaporation

Explanation

Sublimation is the direct change from solid to gas, bypassing the liquid phase. Dry ice (solid CO₂) and iodine are common examples. The reverse process (gas to solid) is called deposition.

Question 50Chemistry: particles, reactions and mass

An alloy of copper and zinc is called brass. If a sample of brass contains 35% zinc by mass, how much zinc is in 200 g of brass?

  1. 70 g Correct answer.
  2. 165 g
  3. 35 g
  4. 100 g

Explanation

Zinc mass = 35% × 200 g = 0.35 × 200 = 70 g. The percentage by mass gives the fraction of the total mass that is the specified component.