NCEA L1 Science cheat sheet

Electric current is the rate of flow of charge: I = Q/t, measured in amperes (A); one ampere is one coulomb of charge passing a point per second.

Voltage (potential difference) is energy transferred per unit charge: V = E/Q, measured in volts (V); one volt is one joule per coulomb.

Ohm's law applies to ohmic conductors at constant temperature: V = IR, so current is proportional to voltage and inversely proportional to resistance.

Electrical power is P = VI; combining with Ohm's law gives P = I²R and P = V²/R, all in watts (W).

Energy used is E = Pt; household energy is billed in kilowatt-hours (kWh), where 1 kWh = 3.6 × 10⁶ J.

In a series circuit the current is the same everywhere and voltages add; in a parallel circuit the voltage is the same across each branch and currents add.

A magnetic field surrounds any current-carrying wire; the field direction follows the right-hand grip rule, and field strength increases with current and decreases with distance.

A wire carrying current in an external magnetic field experiences a force (F = BIL when perpendicular); this is the basis of electric motors and loudspeakers.

Electromagnetic induction: a changing magnetic flux through a coil induces a voltage; a generator converts kinetic energy to electrical energy this way, and a transformer changes AC voltage levels.

Wave speed equation: v = fλ, where v is speed (m/s), f is frequency (Hz) and λ is wavelength (m); frequency is set by the source and does not change on refraction.

The wave equation for light in a vacuum is c = 3.0 × 10⁸ m/s; sound travels far slower in air, about 340 m/s at room temperature.

Reflection: the angle of incidence equals the angle of reflection, both measured from the normal; plane mirrors form virtual, laterally inverted images.

Refraction occurs because wave speed changes between media; light bending towards the normal means it has slowed down (entering a denser medium).

Total internal reflection occurs when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle; this underlies optical fibres.

Sound frequency determines pitch and amplitude determines loudness; sound needs a medium, so it cannot travel through a vacuum.

The electromagnetic spectrum from longest to shortest wavelength is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma; all travel at c in a vacuum.

Resonance occurs when a driving frequency matches an object's natural frequency, producing large amplitude vibrations, as in musical instruments and some structural failures.

Speed is distance divided by time (v = d/t); velocity is speed with direction, and acceleration is change in velocity divided by time (a = Δv/t).

Distance-time graphs: gradient gives speed. Velocity-time graphs: gradient gives acceleration and area under the graph gives displacement.

Newton's second law: net force equals mass times acceleration (F = ma); the net force, not any single force, determines acceleration.

Weight is the force of gravity on a mass: W = mg, with g ≈ 9.8 N/kg on Earth; mass in kilograms stays the same anywhere.

Friction and air resistance oppose motion and convert kinetic energy into heat; they can be reduced by streamlining or lubrication.

Work done equals force times distance moved in the direction of the force (W = Fd), measured in joules; power is work done per second (P = W/t).

Kinetic energy is EK = ½mv²; gravitational potential energy is EP = mgh; in the absence of friction, mechanical energy is conserved.

Pressure is force per unit area (P = F/A) in pascals; for a fluid at rest, pressure increases with depth, explaining why dams are thicker at the base.

A chemical reaction rearranges atoms; mass is conserved, so equations must be balanced with coefficients, not by changing subscripts.

Acids release hydrogen ions (H⁺) in solution and have pH below 7; bases release hydroxide ions (OH⁻) or accept H⁺ and have pH above 7; pH 7 is neutral.

Acid + base → salt + water (neutralisation); acid + metal carbonate → salt + water + carbon dioxide, which is the test for carbonates.

The reactivity series (e.g. K, Na, Ca, Mg, Al, Zn, Fe, Pb, Cu, Ag, Au) predicts displacement: a more reactive metal displaces a less reactive one from its salt solution.

Combustion of a hydrocarbon in sufficient oxygen gives carbon dioxide and water; incomplete combustion gives carbon monoxide and soot.

Rates of reaction increase with higher temperature, higher concentration, greater surface area and the presence of a catalyst; a catalyst lowers activation energy.

Exothermic reactions release energy to the surroundings (temperature rises); endothermic reactions absorb energy (temperature falls).

Corrosion of iron (rusting) requires both oxygen and water; galvanising or painting prevents it by excluding these or by sacrificial protection.

Earth's interior is layered: crust, mantle, outer core (liquid) and inner core (solid); the mantle's slow convection drives plate movement.

Tectonic plates move a few centimetres per year; at divergent boundaries plates separate and new crust forms, at convergent boundaries one plate subducts, and at transform boundaries plates slide past.

Earthquakes occur when stress built up at plate boundaries is suddenly released; the focus is underground and the epicentre is directly above it.

Seismic waves: P waves are fastest, longitudinal and travel through solids and liquids; S waves are slower, transverse and cannot pass through liquids.

Volcanoes form at subduction zones, mid-ocean ridges and hot spots; magma composition affects eruption style - runny basaltic lava flows, viscous andesitic or rhyolitic magma erupts explosively.

The rock cycle links igneous (cooled magma or lava), sedimentary (compacted and cemented layers) and metamorphic (heat and pressure) rocks; any type can transform into another.

Erosion wears away rock and transport moves the material; deposition builds layers, and fossils and cross-cutting relationships give relative ages of rock strata.

Soil formation depends on parent rock, climate, organisms and time; nutrient-rich topsoil is lost quickly through erosion once vegetation is removed.

Earth rotates on its axis once every 24 hours from west to east, causing day and night and the apparent daily movement of the Sun and stars.

Earth orbits the Sun once every 365.25 days; the 0.25-day surplus is handled by a leap year every four years.

Earth's axis is tilted about 23.5° to the plane of its orbit; this tilt, not distance from the Sun, causes the seasons.

Solstices occur when a hemisphere is tilted most towards or away from the Sun; equinoxes occur when day and night are nearly equal everywhere.

The Moon orbits Earth in about 27.3 days (sidereal month); the synodic month of lunar phases is about 29.5 days.

The phases of the Moon arise from the changing angle between the Sun, Earth and Moon as seen from Earth, not from Earth's shadow.

Solar eclipses occur at new Moon when the Moon passes between Sun and Earth; lunar eclipses occur at full Moon when Earth's shadow falls on the Moon.

Tides are caused mainly by the Moon's gravitational pull, producing two high tides and two low tides daily; spring tides occur at new and full Moon, neap tides at quarter phases.