LOWKEY SMART

Check an expansion or a solution by putting a small number (like x = 2) back into both sides.

Animal and plant cells are eukaryotic: their DNA is inside a nucleus, which controls the cell's activities. Both also have cytoplasm (where most chemical reactions happen), a cell membrane (controls what goes in and out), mitochondria (where aerobic respiration releases energy) and ribosomes (where proteins are made). Plant cells also have a cell wall made of cellulose that strengthens the cell, a permanent vacuole filled with cell sap, and chloroplasts, which absorb light for photosynthesis. Bacteria are prokaryotic: they are much smaller, have no nucleus, and their DNA is a single loop in the cytoplasm, often with extra small rings of DNA called plasmids. Bacteria also have a cell wall, but it is not made of cellulose.

Magnification = image size ÷ real size, so real size = image size ÷ magnification, and image size = magnification × real size. Always put both sizes in the same units first: 1 mm = 1000 micrometres (µm). A light microscope magnifies up to about ×2000 and shows cells and nuclei; an electron microscope has a much higher magnification and resolution, so it shows tiny structures such as ribosomes. Resolution is the ability to tell two points that are close together apart. The total magnification of a light microscope = eyepiece lens magnification × objective lens magnification.

An atom has a tiny central nucleus containing protons (relative charge +1, relative mass 1) and neutrons (charge 0, mass 1), with electrons (charge -1, almost no mass) in shells around it. The atomic number is the number of protons, and in a neutral atom the number of electrons equals the number of protons, so the atom has no overall charge. The mass number is the number of protons + neutrons, so neutrons = mass number - atomic number. Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, such as carbon-12 and carbon-14. Electrons fill shells in order: up to 2 in the first shell, then up to 8 in the second and 8 in the third, so sodium (11 electrons) is 2,8,1. The nucleus is about 10 000 times smaller across than the whole atom.

An element contains only one type of atom, and a compound contains two or more elements chemically bonded in fixed proportions, such as water (H₂O) or carbon dioxide (CO₂). A mixture contains substances that are not chemically joined, so it can be separated by physical methods. Filtration separates an insoluble solid from a liquid, and crystallisation gets a soluble solid back from a solution by evaporating some of the water and leaving it to form crystals. Simple distillation separates a liquid from a solution (for example pure water from salt water) by boiling it and then cooling the vapour so it condenses; fractional distillation separates liquids with different boiling points. Paper chromatography separates dissolved substances such as the dyes in ink: the more soluble a dye is in the solvent, the further it travels up the paper.

Energy is held in stores such as kinetic (moving objects), gravitational potential (raised objects), elastic potential (stretched or squashed objects), thermal, chemical and nuclear. Kinetic energy = ½ × mass × speed², or E = ½mv², with mass in kg and speed in m/s. Gravitational potential energy = mass × gravitational field strength × height, or E = mgh, where g = 10 N/kg on Earth; all energy is measured in joules (J). Heating an object transfers energy to its thermal store. Energy cannot be created or destroyed, only transferred, stored or dissipated, which means spread out and wasted, usually as heat to the surroundings.

Power is the rate of energy transfer: power = energy transferred ÷ time, or P = E/t, measured in watts (W), where 1 W = 1 J per second and 1 kW = 1000 W. Efficiency = useful output energy ÷ total input energy, and you multiply by 100 to give a percentage; the same formula works with useful output power ÷ total input power. Wasted energy = total input energy - useful output energy. No device is 100% efficient, because some energy is always dissipated, usually as heat. Lubrication reduces friction between moving parts, and thermal insulation reduces heat loss, so both make things more efficient.