LOWKEY SMART

To expand brackets, multiply the outside by EACH term inside: 3(x + 4) = 3x + 12. Two minuses make a plus: 5 - (-4) = 9.

This one is about speed, not method — answer what you know instantly and come back to the rest. It is testing quick multiplication and division facts, squares and roots and percentage change (find 10% first, then build up, and add on or take off).

All living things are made of CELLS. Every cell has a NUCLEUS, which controls the cell and holds the DNA, CYTOPLASM, where the reactions happen, a CELL MEMBRANE holding it together, and MITOCHONDRIA, where respiration releases energy. A plant cell has three extras: a CELL WALL for strength, CHLOROPLASTS holding the green pigment CHLOROPHYLL for photosynthesis, and a VACUOLE of sap that keeps it firm. Cells that do a particular job are SPECIALISED, and the shape follows the job: a root hair cell is drawn out into a long spike to give a bigger surface area for absorbing water. Every cell in your body holds the SAME DNA, so a muscle cell and a skin cell end up different only because different GENES are switched on in each. Cells build up in a fixed order: cell, then TISSUE (similar cells together), then ORGAN, then ORGAN SYSTEM. GOING FURTHER: magnification = image size / actual size, with both in the SAME unit, so a 0.05 mm cell drawn 100 mm across is magnified 100 / 0.05 = ×2000. Cells take in GLUCOSE and OXYGEN for respiration and must get rid of CARBON DIOXIDE and WATER, all by diffusion across the membrane. The number of mitochondria follows the energy demand: muscle and sperm cells are packed with them, a fat cell has very few.

Adding and subtracting: move right for +, left for -, and two minuses together turn into a plus, so 5 - (-4) = 9. Multiplying and dividing: SAME signs give a positive (-12 ÷ -4 = 3), DIFFERENT signs give a negative (-5 × 3 = -15).

Everything is made of tiny particles. In a SOLID they are packed in a fixed pattern, held by strong forces, and can only vibrate on the spot, which is why a solid keeps its shape. In a LIQUID they touch but slide past each other, so it flows. In a GAS they are far apart and moving fast, so a gas can be squashed and fills its container. Heating gives particles more energy: melting, then evaporating or boiling; cooling gives condensing and freezing. The particles themselves never change size or number, only their arrangement and how fast they move, so when a puddle dries up the MASS is unchanged, the particles have just spread into the air. Gas particles COLLIDE with the container walls, and those collisions ARE pressure, so heating a sealed can raises the pressure inside. DIFFUSION is particles spreading from where they are crowded to where they are not, and it is faster when warm because the particles move faster. GOING FURTHER: pressure IS the collisions of gas particles with the walls, so it rises two ways — heat the gas and each particle hits harder and more often, or squash it and the same particles hit a smaller area more often. Halving the volume at a fixed temperature DOUBLES the pressure. Evaporation cools what is left because only the fastest particles have enough energy to escape, which drags the average energy of the rest down. That is why sweating works.

Common denominator to add (2/3 + 1/4 = 8/12 + 3/12 = 11/12); straight across to multiply (3/4 × 2/5 = 3/10); and to DIVIDE, flip the second fraction and multiply (3/4 ÷ 1/8 = 3/4 × 8/1 = 6). Decimal to percentage: × 100, so 0.2 = 20%.

The pH scale runs 0 to 14: below 7 is ACIDIC, 7 is NEUTRAL, above 7 is ALKALINE. An INDICATOR shows pH by changing colour. The scale is not a straight count, each step of 1 is a factor of TEN, so pH 4 is ten times more acidic than pH 5. Three reactions to know: acid + alkali gives SALT + WATER, which is NEUTRALISATION; acid + base gives SALT + WATER too; acid + metal gives SALT + HYDROGEN. Neutralisation is what an indigestion tablet does to stomach acid, and what a farmer's lime does to soil that is too acidic. To get a dry salt out of the reaction, add alkali until it is neutral, then EVAPORATE the water and the salt is left behind as crystals. GOING FURTHER: the ACID decides the second half of the salt's name and the METAL decides the first. Hydrochloric acid gives CHLORIDES, sulfuric acid gives SULFATES, nitric acid gives NITRATES. So sulfuric acid + potassium hydroxide gives potassium sulfate + water. Underneath it all, an acid releases H+ ions in water and an alkali releases OH- ions; neutralisation is simply H+ + OH- joining to make H2O.

Simplify by dividing both sides by the same number (24:36 both ÷12 = 2:3). To share, add the parts to get the number of shares, divide the total by that, then multiply out: £60 in 2:3 is 5 shares of £12 = £24 and £36. For pricing, find the cost of ONE first.

SPEED = distance / time, in metres per second, so 100 m in 20 s is 5 m/s. Check the units first: 1.5 km in 5 minutes is 1500 m in 300 s, which is 5 m/s. Rearranged, distance = speed x time, so 8 m/s for 12 s covers 96 m. Force is measured in NEWTONS. When several forces act, add the ones pointing the same way and subtract the opposing ones to get the RESULTANT force: 30 N forwards against 18 N backwards is 12 N forwards. A resultant of zero means BALANCED forces and no change in motion, which is why a car at a steady speed still has balanced forces on it. MASS is how much matter there is, in kilograms. WEIGHT is the force of gravity on that mass, in newtons: weight = mass x g, and g = 10 N/kg on Earth, so a 45 kg person weighs 450 N. GOING FURTHER: acceleration = change in speed / time, in m/s², so 5 m/s to 25 m/s in 8 s is 20 / 8 = 2.5 m/s². Force, mass and acceleration are tied together by F = m x a, so 1200 kg accelerating at 2 m/s² needs 2400 N. A falling skydiver speeds up, and the faster she goes the bigger the air resistance, until air resistance EQUALS weight: resultant force zero, no more acceleration, steady terminal velocity.

Collect like terms (5a + 3a - 2a = 6a). To expand, multiply the outside by EVERY term inside, keeping the signs: 2(3x - 5) = 6x - 10. To solve, undo in reverse and do the same to both sides: 2x + 3 = 11 becomes 2x = 8, so x = 4.

Current only flows round a COMPLETE circuit. Current is measured in AMPS with an ammeter, voltage in VOLTS with a voltmeter. In a SERIES circuit everything is in one loop: the CURRENT is the SAME everywhere in it, the supply VOLTAGE is SHARED between the components, so a 12 V battery across two identical bulbs gives 6 V each, and adding another bulb makes them ALL dimmer. Break the loop anywhere and everything stops. In a PARALLEL circuit the components are on separate branches: each branch gets the FULL supply voltage, the current splits between them, adding another branch does not dim the others, and if one breaks the rest carry on. That is why houses are wired in parallel: every appliance gets full voltage, each has its own switch, and one blown bulb does not black out the house. GOING FURTHER: two formulae carry most of GCSE electricity. V = I x R, so 12 V driving 0.5 A means R = 12 / 0.5 = 24 Ω. P = V x I, so that lamp uses 12 x 0.5 = 6 W. Resistors in SERIES simply add, so two 6 Ω resistors give 12 Ω and the current falls. Resistors in PARALLEL give LESS than either one on its own, because you have opened a second path for the current.

A prime has exactly two factors — 51 is not prime because 3 × 17 = 51. HCF is the BIGGEST number that divides into both (12 and 18 share 6); LCM is the SMALLEST number both go into (4 and 6 both go into 12). Square rooting undoes squaring: √144 = 12.

Every question here takes more than one step, so write the steps down. Read it twice, decide what is being asked, then work through. It pulls together percentage change (find 10% first, then build up, and add on or take off), time (count on in whole hours first, then the minutes), area and perimeter (triangle area is base × height ÷ 2, and area is in square units) and speed and other compound measures (distance ÷ time, with the units carried through).

A food chain starts with a PRODUCER, a plant that makes its own food by photosynthesis, so ALL the energy in the chain came originally from the SUN. Then come the CONSUMERS: a PREDATOR hunts, and the animal it hunts is its PREY. A FOOD WEB is many food chains joined up. Only about 10% of the energy passes on at each step, the rest being lost in movement, warmth and waste. That single fact explains most of the questions: it is why food chains are rarely longer than four or five links, why there are many producers but only one top predator, and why the fox in grass to rabbit to fox has the least energy available to it. INTERDEPENDENCE means species rely on each other for food, shelter and pollination, so removing one species ripples out through the whole web. GOING FURTHER: only about 10% of the energy at one trophic level is passed on. The rest is lost as heat from respiration, in movement, and in waste and uneaten parts. That is why the levels form a PYRAMID and why a chain runs out of energy after four or five links. A poison behaves the opposite way to energy: it is not lost at each step, so it concentrates as it goes up. That is BIOACCUMULATION, and it is why the top predator is harmed first.

Multiplying powers of the same letter ADDS the indices (x² × x³ = x⁵); dividing SUBTRACTS them (x⁵ ÷ x² = x³). Anything to the power 0 is 1. Standard form is a number between 1 and 10 times a power of ten: 400 = 4 × 10².

A flower is the plant's reproductive organ. The STAMEN is the male part and makes POLLEN; the CARPEL is the female part, with the STIGMA on top and the OVARY at the base holding the ovules. POLLINATION is pollen moving from a stamen to a stigma, by INSECT (bright petals, scent, nectar, sticky pollen) or by WIND (dull petals, no nectar, and masses of light pollen, because so little of it lands on the right flower). FERTILISATION is the later step where the pollen joins an OVULE. The fertilised ovule becomes the SEED and the whole ovary becomes the FRUIT. To GERMINATE, a seed needs water, warmth and oxygen. Humans reproduce sexually too: a sperm fertilises an egg, the fertilised egg develops in the UTERUS, and the PLACENTA passes oxygen and food from the mother to the baby and carries waste back. GOING FURTHER: the menstrual cycle is run by hormones. OESTROGEN, from the ovaries, rebuilds and thickens the uterus lining; PROGESTERONE keeps it in place; FSH and LH from the pituitary control the release of the egg. In plants the gametes are the POLLEN NUCLEUS and the EGG CELL inside the OVULE. Cross-pollination brings genes from two different plants together, so the offspring VARY — and variation is what a species needs to survive a change in its environment.

The gap between terms is the number in front of n: 5, 8, 11, 14 goes up 3, so it starts 3n. Then compare 3n (3, 6, 9, 12) with the sequence to find what to add — here +2, giving 3n + 2. Now any term is one substitution away: the 10th is 32.

PHOTOSYNTHESIS happens in the CHLOROPLASTS and uses light energy: carbon dioxide + water -> glucose + oxygen. It takes CO2 in and gives oxygen out. RESPIRATION is the near opposite and happens in EVERY living cell, plant and animal, all the time: glucose + oxygen -> carbon dioxide + water, releasing energy. Plants respire as well as photosynthesise, which is why a plant kept in the dark still respires but cannot make food, so it will not grow. At dawn the two rates match exactly for a moment and the plant gives out no gas at all. The RATE of photosynthesis is limited by whichever of LIGHT INTENSITY, CARBON DIOXIDE and TEMPERATURE is in shortest supply, which is called the limiting factor. GOING FURTHER: in symbols, photosynthesis is 6CO2 + 6H2O → C6H12O6 + 6O2, and respiration is that same equation read backwards. A LIMITING FACTOR is whichever one is in shortest supply and so sets the rate: light intensity, carbon dioxide concentration, or temperature. Raising the others changes nothing until you raise the limiting one. A plant photosynthesises only in the light but respires DAY AND NIGHT; in bright light photosynthesis is simply the faster of the two.

They all follow the same shape: speed = distance ÷ time, density = mass ÷ volume, pressure = force ÷ area. To compare two speeds, work both out in the same units first — 120km in 2h is 60km/h and 150km in 3h is 50km/h, so the first is faster.

Light travels in STRAIGHT LINES and is a wave. REFLECTION is light bouncing off a surface, and the angle of incidence EQUALS the angle of reflection, both measured from the NORMAL, the line drawn at 90 degrees to the surface where the ray hits. REFRACTION is light BENDING as it passes into a different material, because it changes SPEED. Going into a denser material such as glass or water it slows down and bends TOWARDS the normal; coming back out it speeds up and bends AWAY. That is why a straw looks broken at the water's surface: the light from the underwater part bends as it leaves, so your eye traces it back along the wrong line. Materials are TRANSPARENT (see through), TRANSLUCENT (light gets through but no clear image) or OPAQUE (no light at all). Light also travels about a million times faster than sound, which is why you see lightning before you hear thunder. GOING FURTHER: both angles are always measured from the NORMAL, the line at 90° to the surface, and for reflection they are equal. Refraction is about SPEED: light slows entering glass or water and bends TOWARDS the normal, and speeds up leaving and bends AWAY from it. Every wave obeys v = f x λ (speed = frequency x wavelength), so 5 Hz and 3 m give 15 m/s.

Probability = wanted ÷ total, so heads is 1/2 and a six is 1/6. For two events happening together, list the outcomes systematically (HH, HT, TH, TT) or multiply along the branches. All the probabilities of one event add up to 1.

A magnet has a NORTH and a SOUTH pole. LIKE poles repel, OPPOSITE poles attract. Only iron, steel, nickel and cobalt are attracted to magnets, so a plastic ruler is not. A current in a wire makes a magnetic field, and around a straight wire that field is a set of CIRCLES around it. Coil the wire round an iron core and you have an ELECTROMAGNET, and there are three ways to make it stronger: more CURRENT, more TURNS of wire, and an IRON CORE. Soft iron is used rather than steel because it loses its magnetism the moment the current stops, which is how a scrapyard crane drops the car. Reversing the CURRENT reverses the POLES. A compass is just a tiny magnet, so its north pole swings to point at the SOUTH pole of a nearby magnet. GOING FURTHER: three levers make an electromagnet stronger — more TURNS, more CURRENT, and an IRON CORE. Iron is chosen because it is magnetically SOFT: it magnetises strongly and then loses it the instant the current stops, which is the whole point of a crane magnet or a relay. Steel stays magnetised, so it makes permanent magnets instead. A current-carrying wire in a magnetic field feels a force, and FLEMING'S LEFT-HAND RULE gives its direction: first finger Field, second finger Current, thumb Motion. That force is what spins a motor. The field AROUND a current-carrying wire has its own rule, the RIGHT-HAND GRIP rule: thumb along the current, curled fingers give the circular field.

On a straight line angles add to 180°, around a point 360°. On parallel lines: alternate angles (the Z shape) are EQUAL, corresponding angles (the F shape) are EQUAL, and co-interior angles (the C or U shape) add to 180°.

Elements are arranged in order of ATOMIC NUMBER. A GROUP is a column, and everything in it behaves alike because it has the SAME NUMBER OF OUTER ELECTRONS. Metals are on the left and in the middle, non-metals on the right. GROUP 1, the ALKALI METALS, are soft and very reactive and give off HYDROGEN with water. GROUP 7, the HALOGENS, are reactive non-metals. GROUP 0, the NOBLE GASES, are unreactive because their outer shell is already FULL. Going DOWN a group each element gains another electron shell, so the outer electron sits further from the nucleus. Group 1 reacts by LOSING that electron, and further out means easier to lose, so reactivity INCREASES down the group: potassium beats sodium. Group 7 reacts by GAINING an electron, and a bigger atom grabs one less easily, so reactivity DECREASES down the group: chlorine beats iodine. GOING FURTHER: the GROUP number is the number of outer electrons, and the outer electrons decide the chemistry — which is why a whole group behaves alike. Group 1 must LOSE one electron, and further down the group the outer shell is further from the nucleus and easier to lose, so reactivity RISES down the group. Group 7 must GAIN one, and further down it is harder to attract one in, so reactivity FALLS. Alkali metal + water always gives a metal hydroxide + hydrogen.

Start counting significant figures from the first non-zero digit, then round on the next digit: 3456 to 2 s.f. is 3500, and 0.0678 to 2 s.f. is 0.068 (the leading zeros do not count). To estimate, round each number to 1 s.f. first — 29 × 41 becomes 30 × 40 = 1200.

NON-RENEWABLE resources will run out: coal, oil and gas, which release CARBON DIOXIDE when burned, plus nuclear fuel, which does not. RENEWABLE resources are replaced as fast as they are used: wind, solar, hydroelectric, tidal and geothermal. They release no CO2 when generating, but wind and solar are UNRELIABLE, which is why a country usually uses both. TIDAL is the most reliable renewable, because the tides are set by the Moon and can be predicted years ahead. EFFICIENCY = useful energy out / total energy in, times 100 for a percentage: a motor given 400 J that usefully transfers 300 J is 75% efficient, and a power station at 40% turns 1000 MJ of fuel into 400 MJ of electricity. The wasted energy is not destroyed, it spreads into the surroundings as thermal energy. GOING FURTHER: energy in kilowatt-hours = power in kW x time in hours, so a 2 kW heater for 3 hours uses 6 kWh — that is the unit your electricity bill charges for. Nuclear power gives huge, reliable output with no carbon dioxide while it runs, but leaves radioactive waste dangerous for thousands of years and costs a fortune to decommission. The National Grid uses transformers to step the voltage UP to hundreds of thousands of volts for transmission, because the same power at a higher voltage needs a smaller current, and it is current that heats the cables and wastes energy.

This one is about speed, not method — answer what you know instantly and come back to the rest. It is testing quick multiplication and division facts, squares and roots and percentage change (find 10% first, then build up, and add on or take off).

In a chemical reaction the starting substances are the REACTANTS and the new substances made are the PRODUCTS. Atoms are only REARRANGED, never created or destroyed, so mass is CONSERVED: 10 g of magnesium plus 6.6 g of oxygen gives 16.6 g of magnesium oxide. That is also why a symbol equation must be BALANCED, with the same number of each atom on both sides. Balance by putting big numbers in FRONT of formulae, never by changing the small ones, so H2 + O2 -> H2O becomes 2H2 + O2 -> 2H2O, and Mg + O2 -> MgO becomes 2Mg + O2 -> 2MgO. Two experiments look like they break the rule and neither does: heat a metal in an open dish and the mass appears to RISE, because it has combined with oxygen from the air; heat a carbonate in an open tube and it appears to FALL, because carbon dioxide gas has escaped. In a sealed container nothing changes at all. GOING FURTHER: balancing means the same number of each atom on both sides. You may only change the BIG numbers in front, never the small ones inside a formula, because changing those changes the substance. H2 + O2 → H2O has two oxygens on the left and one on the right, so it balances to 2H2 + O2 → 2H2O. This works because of the LAW OF CONSERVATION OF MASS: atoms are only rearranged. A mass that appears to rise or fall always means a gas has joined in or escaped — magnesium gains the mass of the oxygen it burns with.

In a right-angled triangle a² + b² = c², where c is the hypotenuse — the longest side, opposite the right angle. Square the two short sides, add them, then square root: 5 and 12 give 25 + 144 = 169, so c = 13. Learn 3-4-5, 5-12-13 and 8-15-17 by heart.

In a SERIES circuit there is one loop. The CURRENT is the same at every point, the supply voltage is SHARED, so a 9 V battery across three identical bulbs gives 3 V each, and resistances simply ADD, so two 4 ohm resistors in series make 8 ohms. Adding a bulb makes them all dimmer, and one blown bulb breaks the loop and stops everything, which is what happens to Christmas lights. In a PARALLEL circuit the components are on separate branches. Every branch gets the FULL supply voltage, which is the key fact, so adding another bulb does NOT dim the ones already there. The current splits between the branches and rejoins afterwards, and if one branch breaks the others carry on. Houses are wired in parallel for exactly those reasons. GOING FURTHER: two IDENTICAL resistors in parallel give HALF the resistance of one, so two 4 Ω give 2 Ω — adding a second path always makes it easier for current to flow. To find the total current in a parallel circuit, work out each branch separately with I = V / R and add them: 6 V across 3 Ω gives 2 A, across 6 Ω gives 1 A, so the battery supplies 3 A. Because every branch gets the FULL supply voltage, adding a lamp does not dim the others — it just makes the battery work harder.

Interior angles sum to (n - 2) × 180°, so a hexagon is 4 × 180 = 720° and an octagon is 6 × 180 = 1080°. Exterior angles ALWAYS sum to 360°, so each one in a regular polygon is 360 ÷ number of sides.

The nervous system carries information as fast electrical impulses. The order never changes: STIMULUS, RECEPTOR (which detects it), SENSORY neurone, CNS, MOTOR neurone, EFFECTOR, RESPONSE. The CENTRAL NERVOUS SYSTEM is the brain and the spinal cord. An EFFECTOR is whatever carries out the response, either a MUSCLE that contracts or a GLAND that releases a hormone. Between two neurones is a tiny gap called a SYNAPSE; the impulse cannot jump it, so the first neurone releases a chemical that diffuses across and starts a new impulse in the next one. A REFLEX skips the conscious brain: the signal goes through the SPINAL CORD only, so there are fewer synapses and no decision to make, which is why it is so much faster and why you cannot stop it happening. Pulling your hand off something hot and blinking are both reflexes. GOING FURTHER: the reflex arc runs RECEPTOR → SENSORY NEURONE → RELAY NEURONE (in the spinal cord) → MOTOR NEURONE → EFFECTOR, which is a muscle or a gland. It is fast because it bypasses the conscious brain entirely — you pull your hand back BEFORE you feel the pain. Neurones never actually touch: at the SYNAPSE a chemical called a neurotransmitter diffuses across the gap and starts the impulse again on the other side. That tiny diffusion step is the slowest part of the whole journey.

If the same letter has the same coefficient in both equations, ADD them when the signs are opposite and SUBTRACT when they match — that cancels one letter out. x + y = 10 plus x - y = 2 gives 2x = 12, so x = 6; put x back into either equation to find y = 4.

The RATE of a reaction is how much product forms per unit of time, so 40 cm3 of gas in 20 s is an average rate of 2 cm3 per second. Plot the amount of product against time and the RATE IS THE GRADIENT: steepest at the start when the reactants are most concentrated, flattening as they are used up, and completely FLAT once a reactant has run out and the reaction has finished. Four things speed a reaction up, and they all work the same way, by making the particles COLLIDE more often or harder: higher TEMPERATURE (the particles move faster, so they collide more often and with more energy), higher CONCENTRATION, bigger SURFACE AREA (powder exposes far more of the solid than a single lump), and a CATALYST, which speeds it up without being used up. GOING FURTHER: COLLISION THEORY explains every one of them. A reaction happens when particles collide with at least the ACTIVATION ENERGY. Heat makes them move faster, so collisions are more frequent AND harder. More concentration or more pressure packs them closer, so collisions are more frequent. Grinding a solid to powder exposes far more surface, so more particles are available to be hit. A CATALYST does something different: it does not speed the particles up, it offers a route with a LOWER activation energy, so a bigger fraction of the collisions succeed. It is not used up, so a tiny amount lasts.

To multiply, multiply the front numbers and ADD the powers: (3 × 10³) × (2 × 10²) = 6 × 10⁵. To divide, divide the fronts and SUBTRACT the powers. To add or subtract, the powers must already match — then just add the fronts.

Eight planets orbit the SUN, held in orbit by its GRAVITY, and each orbit is an ELLIPSE rather than a perfect circle. The further out a planet is, the longer its orbit and the longer its year, which is why a year on Neptune is far longer than a year on Earth. The Moon stays with us for the same reason: the Earth's gravity keeps pulling it towards us. Earth has SEASONS because its axis is TILTED, so through the year each hemisphere gets more or less direct sunlight. Beyond the solar system, stars are gathered into GALAXIES, and ours is the MILKY WAY. The distances are almost unimaginable: sunlight takes about 8 minutes to reach us, while light from even the nearest stars takes YEARS. Faint stars are easier to see from the countryside because there is less light pollution. GOING FURTHER: an orbit is a permanent fall. Gravity pulls the satellite towards the planet at 90° to its motion, which changes its DIRECTION but never its speed, so it curves round instead of flying off. The further out the orbit, the longer the path and the slower the speed, so Neptune's year is about 165 Earth years. Distances get too big for kilometres, so we use the LIGHT YEAR: the DISTANCE light covers in a year, about 9.5 million million km. It is a distance, not a time — which is the trick the question is testing.

MULTIPLY along the branches, ADD between them. WITH replacement the second pick has the same probability as the first (3/5 × 3/5 = 9/25). WITHOUT replacement both the wanted count and the total drop by one (3/5 × 2/4 = 3/10).

Every question here takes more than one step, so write the steps down. Read it twice, decide what is being asked, then work through. It pulls together percentage change (find 10% first, then build up, and add on or take off), time (count on in whole hours first, then the minutes), Pythagoras (a² + b² = c², so square, add, then square root), angles (straight line 180°, around a point 360°), quick multiplication and division facts, ratio (add the parts to get the shares, divide, then multiply), speed and other compound measures (distance ÷ time, with the units carried through) and area and perimeter (triangle area is base × height ÷ 2, and area is in square units).

VARIATION is the differences between individuals of the same species, and it comes from GENES and from the ENVIRONMENT. The genetic variation ultimately comes from MUTATIONS in DNA and from the mixing of genes in sexual reproduction. NATURAL SELECTION follows in steps: individuals vary; those whose characteristics suit the environment are more likely to SURVIVE and REPRODUCE; they pass those characteristics on THROUGH THEIR GENES; and over MANY generations the useful version becomes common. An individual does not evolve during its own lifetime. The peppered moth is the classic case, dark moths surviving better on sooty bark because predators could not see them. ANTIBIOTIC RESISTANCE is the same process happening now: a few bacteria survive the drug, only those reproduce, and the whole population ends up resistant. FOSSILS are the evidence, showing how organisms changed over millions of years. GOING FURTHER: natural selection needs four things in order — VARIATION within a species, COMPETITION for limited food and space, SURVIVAL of the individuals whose features suit the conditions, and those individuals PASSING ON the genes. Antibiotic resistance is the same process running in front of us: a chance mutation makes one bacterium resistant, the antibiotic kills its rivals, and it inherits the whole population. CONTINUOUS variation takes any value on a scale, like height or mass; DISCONTINUOUS variation falls into separate groups, like blood group or eye colour.

This one is about speed, not method — answer what you know instantly and come back to the rest. It is testing quick multiplication and division facts, squares and roots, percentage change (find 10% first, then build up, and add on or take off) and ratio (add the parts to get the shares, divide, then multiply).

The REACTIVITY SERIES ranks metals from most to least reactive: potassium, sodium, calcium, magnesium, aluminium, CARBON, zinc, iron, tin, lead, copper, silver, gold. In a DISPLACEMENT reaction a more reactive metal pushes a less reactive one out of its compound, so zinc + copper sulfate gives zinc sulfate + copper, while copper added to zinc sulfate does nothing at all, because copper is lower down. Carbon's place in that list decides how a metal is extracted: metals BELOW carbon, like iron, can be pulled out of their ore by heating with carbon, which is cheap; metals ABOVE carbon, like aluminium, cannot, so electrolysis is the only way, and it is expensive. Gold is so unreactive it is found as the pure metal in the ground, while iron is always found combined as an ore. Aluminium is an odd case: it IS reactive, but it forms a tough oxide layer that seals the metal underneath, so it does not corrode away. GOING FURTHER: where a metal sits relative to CARBON in the reactivity series decides how it is extracted. Metals BELOW carbon (iron, zinc, copper) can be reduced by heating with carbon in a furnace. Metals ABOVE it (aluminium, magnesium, sodium) hold their oxygen too tightly, so they need ELECTROLYSIS, which is why aluminium was a precious metal until electricity was cheap. A more reactive metal always displaces a less reactive one from its compound. Rusting needs BOTH oxygen and water, which is why oil, paint and galvanising all work by keeping one of them away.

Compound means each year's growth is worked out on the NEW amount, not the original. Use a multiplier: +5% is × 1.05, so two years is × 1.05 twice — £1000 becomes £1050 then £1102.50. A decrease of 10% would be × 0.9.

Air travels down the TRACHEA, branches into the BRONCHI and then the bronchioles, and ends in millions of tiny air sacs called ALVEOLI. Everything about an alveolus makes DIFFUSION fast: a huge total SURFACE AREA, walls only ONE CELL thick so the distance to cross is tiny, a good blood supply that carries the oxygen away, and a moist lining. Diffusion runs from HIGH concentration to LOW, so oxygen moves from the alveolus, where there is plenty, into the blood, where it has just been used up, and carbon dioxide goes the other way. Breathing in, the DIAPHRAGM contracts and flattens and the ribs move up and out, so the chest volume rises, the pressure inside FALLS, and air rushes in. Breathing out reverses it. Exercise raises your breathing rate because the muscles need more oxygen and make more carbon dioxide, so both have to be moved faster. GOING FURTHER: every gas exchange surface in biology is built the same way — a huge SURFACE AREA, walls ONE CELL thick for a short diffusion path, a rich BLOOD SUPPLY to carry the gas away and keep the gradient steep, and a moist lining. The steeper that concentration gradient, the faster the net diffusion, which is why the blood never stops moving. Breathing in is active: the diaphragm CONTRACTS and flattens, the ribs swing up and out, the chest volume rises, the pressure inside drops below the air outside, and air flows in.

Circumference = π × diameter (or 2πr) — that is the distance around. Area = π × r², so square the radius FIRST, then multiply by π. Radius 6cm gives a circumference of 3.14 × 12 = 37.68cm; radius 3cm gives an area of 3.14 × 9 = 28.26cm².

The EM spectrum is one family of waves that ALL travel at the SPEED OF LIGHT in a vacuum, differing only in wavelength. In order of decreasing wavelength, and so increasing frequency and increasing ENERGY: RADIO, MICROWAVES, INFRARED, VISIBLE LIGHT, ULTRAVIOLET, X-RAYS, GAMMA. Visible light is the only part we can see. The uses follow the properties: radio for broadcasting, microwaves for cooking (their frequency is absorbed by the WATER in the food, heating it from within) and satellites, infrared for remote controls and thermal cameras, X-rays for imaging bones because they pass through soft tissue but are absorbed by bone, and gamma for treating cancer. From UV upwards the waves are IONISING, energetic enough to damage the DNA in cells, which is why too much UV burns skin and why X-rays are used in small doses only. GOING FURTHER: the order, longest wavelength to shortest, is radio, microwaves, infrared, visible light, ultraviolet, X-rays, gamma. As the wavelength falls the FREQUENCY and the energy rise, and it is the energy that makes the short end dangerous: ultraviolet, X-rays and gamma are IONISING, meaning they can knock electrons off atoms and so damage cells and mutate DNA. Every one of them, from radio to gamma, travels at the same speed in a vacuum: 300 000 000 m/s, or 3 x 10⁸ m/s. Each band has its uses: radio for broadcasting, MICROWAVES for mobile phones and satellites, infrared for heating and remote controls, X-rays for imaging bone.

A vector is written as a column: the top number is how far right (negative = left) and the bottom is how far up (negative = down). To ADD vectors, add the tops together and the bottoms together: (5,1) + (2,3) = (7,4).

HOMEOSTASIS is the body holding its internal conditions steady: TEMPERATURE at about 37 C, plus blood GLUCOSE and WATER levels. It runs on NEGATIVE FEEDBACK, which means the response always pushes the level back the OPPOSITE way, towards normal. Temperature is monitored by the BRAIN, in the hypothalamus. Too hot: you SWEAT, and the evaporating water carries energy away from the skin, while blood vessels near the surface WIDEN so more warm blood flows near the skin and more heat is lost. Too cold: you SHIVER, because rapidly contracting muscles respire faster and respiration releases energy as heat, and the surface vessels NARROW to keep blood away from the cold surface. Blood glucose works the same way: too high and INSULIN, from the PANCREAS, brings it down; too low and glucagon brings it up. GOING FURTHER: homeostasis works by NEGATIVE FEEDBACK — a receptor detects that something has moved away from the set point, and the response pushes it back the other way. Blood glucose is the clearest case: too high and the PANCREAS releases INSULIN, which makes the liver store glucose as glycogen; too low and it releases GLUCAGON, which does the reverse. Temperature works the same way. Too cold, and you shiver (muscles contracting fast, releasing heat by respiration), your hair stands up and blood vessels constrict; too hot, and you sweat and the vessels dilate.

Solve them exactly like equations — do the same to both sides: x + 9 > 11 gives x > 2. On a number line an OPEN circle means < or > (the value itself is not included) and a FILLED circle means ≤ or ≥. If you multiply or divide by a negative, flip the sign round.

Static builds up when two INSULATORS are rubbed together and ELECTRONS are transferred by FRICTION. Only electrons move, never the positive nuclei. Whatever GAINS electrons becomes NEGATIVELY charged, whatever LOSES them becomes POSITIVELY charged. Like charges REPEL, opposite charges ATTRACT. A charged rod even attracts uncharged paper, because it pushes the paper's own electrons away and leaves the near side oppositely charged. Charge can only build up on an INSULATOR, since there is nothing for it to flow through; on an EARTHED metal it flows straight to the ground, which is what earthing is for. Static is not a current: it sits still until it discharges, sometimes as a spark, which is the small shock off a door handle and, on an enormous scale, lightning. A spark near fuel vapour is why an aircraft is earthed before refuelling. GOING FURTHER: only ELECTRONS move — the protons are locked in the nuclei. Rub two insulators together and electrons transfer from one to the other: the one that GAINS them becomes NEGATIVE, the one that LOSES them becomes POSITIVE. A build-up of charge will eventually jump as a spark, and a spark near fuel vapour is a catastrophe, so aircraft and fuel tankers are EARTHED first: a conducting path lets the charge drain harmlessly away.

DIRECT: as one doubles, so does the other — scale both the same way. INVERSE: as one doubles, the other HALVES, because the product stays fixed. So 10 workers take half as long as 5 workers, but 12 cakes need one and a half times the flour of 8.

Every question here takes more than one step, so write the steps down. Read it twice, decide what is being asked, then work through. It pulls together percentage change (find 10% first, then build up, and add on or take off), time (count on in whole hours first, then the minutes), ratio (add the parts to get the shares, divide, then multiply), speed and other compound measures (distance ÷ time, with the units carried through) and volume (area of the cross-section × the length).

From the outside in, the Earth is CRUST (thinnest), MANTLE, OUTER CORE (the liquid one) and INNER CORE. The crust is cracked into huge TECTONIC PLATES that move a few centimetres a year. EARTHQUAKES and VOLCANOES happen at PLATE BOUNDARIES because that is where plates grind, collide or pull apart: they lock together, strain builds, then they slip suddenly. The evidence that they move includes the jigsaw fit of South America into Africa, with matching rocks and fossils on both coasts. Three rock types come out of it. IGNEOUS forms when magma COOLS and solidifies, so it has interlocking crystals and NEVER holds fossils, because the heat destroys any remains. SEDIMENTARY forms from layers of sediment squashed together, shows visible layers, and is the ONLY type with fossils. METAMORPHIC forms when an existing rock is changed by HEAT AND PRESSURE without melting. GOING FURTHER: heat from the Earth's core sets up CONVECTION CURRENTS in the mantle, and those currents drag the plates. Where plates move APART the boundary is CONSTRUCTIVE: magma rises into the gap and makes new crust, as along the mid-Atlantic ridge. Where they push TOGETHER it is DESTRUCTIVE: one plate is forced under the other, and you get deep earthquakes, mountains and violent volcanoes. Where they grind past each other it is a CONSERVATIVE boundary, earthquakes but no volcanoes. Geologists can say WHERE, but not WHEN, because the stress accumulates invisibly and releases unpredictably.

This one is about speed, not method — answer what you know instantly and come back to the rest. It is testing quick multiplication and division facts, percentage change (find 10% first, then build up, and add on or take off), time (count on in whole hours first, then the minutes) and squares and roots.

An atom has a tiny NUCLEUS of PROTONS (charge +1) and NEUTRONS (no charge), with ELECTRONS (charge -1) in shells around it. Nearly all the mass is in the nucleus. The ATOMIC NUMBER is the number of PROTONS and it is what makes an element that element. The MASS NUMBER is protons + neutrons, so an atom with 15 protons and 16 neutrons has mass number 31, and one with atomic number 8 and mass number 18 has 18 - 8 = 10 neutrons. A neutral atom has EQUAL numbers of protons and electrons, so the charges cancel exactly. Lose or gain an electron and you have an ION: 13 protons with only 10 electrons is 3+. ISOTOPES are atoms of the same element with the same protons but DIFFERENT neutrons. Because chemistry is decided by the ELECTRONS, and isotopes have identical electron arrangements, isotopes behave exactly the same chemically. GOING FURTHER: the ATOMIC NUMBER is the number of protons and it is what makes the element what it is. The MASS NUMBER is protons + neutrons, so 17 protons and 18 neutrons give a mass number of 35. ISOTOPES are atoms of the same element with different neutron counts — same chemistry, different mass. Electrons fill shells 2, then 8, then 8, so magnesium's 12 electrons arrange as 2, 8, 2, and those two outer electrons are exactly why magnesium sits in Group 2.

In y = mx + c, m is the GRADIENT (how steep, and negative means downhill) and c is the Y-INTERCEPT (where it crosses the y-axis). So y = 5x + 7 has gradient 5 and crosses at (0, 7), and y = 7x - 6 crosses at (0, -6).

The heart has FOUR chambers: the two ATRIA on top receive blood, the two VENTRICLES below pump it out, and VALVES stop it flowing backwards. It is a DOUBLE circulatory system, so blood passes through the heart TWICE for one trip round the body: once out to the lungs for oxygen, once out to the body through the AORTA. The LEFT ventricle wall is much thicker than the right because it has to push blood all the way round the body, while the right only has to reach the lungs. The three vessels match their jobs: an ARTERY carries blood AWAY from the heart at high pressure and has a thick muscular wall; a VEIN carries it back at low pressure with a thin wall, a wide lumen and valves; a CAPILLARY is only ONE cell thick, so the diffusion distance to the tissues is as short as possible. GOING FURTHER: the heart is a DOUBLE pump. The right side sends blood the short distance to the lungs; the left side sends it round the entire body, so its ventricle wall is far thicker and more muscular. The naming trips people up: arteries carry blood AWAY from the heart and veins TOWARDS it, which is why the PULMONARY ARTERY carries deoxygenated blood and the PULMONARY VEIN carries oxygenated blood — the only pair that breaks the usual pattern. Arteries have thick elastic walls for high pressure; veins have thin walls, wide lumens and VALVES, because their low-pressure blood would otherwise slide back down.

Reflecting in the x-axis flips the sign of y: (6, 1) becomes (6, -1). Reflecting in the y-axis flips the sign of x. A rotation needs THREE things described — the centre, the angle and the direction. A translation just slides, with no turning or flipping.

DNA is the chemical in the NUCLEUS that carries genetic information, coiled up into CHROMOSOMES. A GENE is a short section of DNA coding for one characteristic. You inherit TWO sets of chromosomes, one from each parent, so genes come in pairs, and the two versions of the same gene are ALLELES. A DOMINANT allele (capital letter) shows whenever it is present; a RECESSIVE one (small letter) only shows if BOTH alleles are recessive. So with B brown and b blue, Bb is brown and only bb is blue. GENOTYPE is which alleles you carry (Bb); PHENOTYPE is what you actually see (brown eyes). A Bb x Bb cross gives BB, Bb, Bb, bb, so one QUARTER are expected to be bb, and two brown-eyed parents can only have a blue-eyed child if both are Bb. Sex is decided by one pair, XX female and XY male, so it is the SPERM that decides it. GOING FURTHER: draw a PUNNETT SQUARE. Bb x Bb gives BB, Bb, Bb, bb — so a 3 in 4 chance of showing the dominant characteristic and a 1 in 4 chance of bb. GENOTYPE is the pair of alleles you carry; PHENOTYPE is what actually shows, which is why a carrier looks no different from BB. Body cells hold 46 chromosomes in 23 pairs; gametes hold 23 singles, so that fertilisation restores 46 rather than doubling it every generation.

Multiply every term in the first bracket by every term in the second (FOIL), then collect the middle terms: (x + 1)(x + 8) = x² + 8x + x + 8 = x² + 9x + 8. Watch the signs — (x - 4)(x - 5) gives -4x - 5x = -9x and a POSITIVE 20.

A MOMENT is the turning effect of a force about a pivot: moment = force x distance from the pivot, in newton-metres (Nm). So 12 N at 0.5 m gives 6 Nm and 10 N at 1.5 m gives 30 Nm. Because the distance multiplies the force, the same push further out turns harder, which is why a long spanner undoes a tight bolt and why a door handle is fitted as far from the hinges as possible. Every lever has three parts: the PIVOT, the EFFORT and the LOAD. When something balances, the PRINCIPLE OF MOMENTS applies: total clockwise moment EQUALS total anticlockwise moment. Use it to find a missing force or distance. A 500 N child 1 m out gives 500 Nm, so a 250 N child must sit at 500 / 250 = 2 m. A beam with 60 N at 0.5 m gives 30 Nm, so the force at 0.25 m is 30 / 0.25 = 120 N. Lighter always means further out. GOING FURTHER: moment = force x perpendicular distance from the pivot, measured in newton metres, so 25 N at 0.6 m gives 15 Nm. When something balances, the total CLOCKWISE moment equals the total ANTICLOCKWISE moment — that is the principle of moments, and it lets you solve for whatever is missing. 50 N at 0.4 m is 20 Nm, so a 25 N weight needs 20 / 25 = 0.8 m on the other side. It is also why a long spanner loosens a bolt a short one cannot: more distance, more moment, same effort.

The hypotenuse is the longest side, opposite the right angle. Then SOH: sin = opposite ÷ hypotenuse. CAH: cos = adjacent ÷ hypotenuse. TOA: tan = opposite ÷ adjacent. Label the three sides from the angle you are working with before you choose.

OHM'S LAW is V = I x R: voltage in VOLTS = current in AMPS x resistance in OHMS. Rearrange as needed: V = 4 x 6 = 24 V; I = 18 / 3 = 6 A; and a 10 V supply across a 5 ohm resistor gives 10 / 5 = 2 A. More resistance for the same voltage means LESS current. In SERIES, resistances add, so 4 ohms and 6 ohms make 10 ohms; in PARALLEL the total is LOWER than either one, because you have given the current extra routes. Plot current against voltage for a fixed resistor and you get a STRAIGHT line through the origin, and if you compare two, the STEEPER line is the LOWER resistance, since more current flows for the same voltage. A filament lamp is the exception: as it heats up its resistance RISES, so its graph curves. A longer wire has more resistance, because the electrons collide with more ions on the way through. GOING FURTHER: V = I x R rearranges to R = V / I, so 20 V and 0.4 A give 50 Ω. A component OBEYS Ohm's law only if its resistance stays constant, which gives a straight line through the origin on an I-V graph — a fixed resistor does, a filament lamp does not. As the filament heats, its metal ions vibrate harder, the electrons collide with them more often, and the resistance climbs, so the graph curves. Power is P = V x I, so a 230 V heater at 6 A is 1380 W, which is why big appliances need thick cable and a 13 A fuse.

y ∝ x means y = kx; y ∝ 1/x means y = k/x. Always find k FIRST by substituting the pair you are given: x = 4 and y = 20 gives 20 = 4k, so k = 5. Then use y = 5x for any other value — x = 7 gives y = 35.

Every question here takes more than one step, so write the steps down. Read it twice, decide what is being asked, then work through. It pulls together Pythagoras (a² + b² = c², so square, add, then square root), angles (straight line 180°, around a point 360°), area and perimeter (triangle area is base × height ÷ 2, and area is in square units), percentage change (find 10% first, then build up, and add on or take off) and time (count on in whole hours first, then the minutes).

Read the axes first, because the two graphs mean different things. On a DISTANCE-TIME graph the GRADIENT is the SPEED: horizontal means stationary, steeper means faster, and a line curving upwards means the speed is increasing. A straight line from (0,0) to (8 s, 32 m) is a speed of 32 / 8 = 4 m/s. On a VELOCITY-TIME graph the GRADIENT is the ACCELERATION and the AREA under the line is the DISTANCE travelled. So a horizontal line above zero there is not stationary, it is a steady speed with no acceleration. ACCELERATION = change in velocity / time, in m/s2, so 0 to 20 m/s in 8 s is 20 / 8 = 2.5 m/s2. For distance, the area of a rectangle is height x width, so a constant 7 m/s for 20 s covers 140 m. GOING FURTHER: the two graphs are read differently and mixing them up costs marks. On a DISTANCE-time graph the gradient is the SPEED, and a horizontal line means stationary. On a VELOCITY-time graph the gradient is the ACCELERATION, a horizontal line means steady speed, and the AREA UNDERNEATH is the distance travelled. For 0 to 16 m/s in 6 s that area is a triangle: ½ x 6 x 16 = 48 m.