LOWKEY SMART

BODMAS: Brackets first, then Indices (powers), then ÷ and ×, then + and −, left to right.

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 and squares and roots.

A force is a push or a pull. Gravity is the pull that brings things down to Earth. Friction is a force that slows things down when two surfaces rub together. Air resistance slows things falling through the air (like a parachute). GOING FURTHER. Forces are measured in NEWTONS (N) using a newton meter. When something is not moving, the forces on it are BALANCED: a book on a table has gravity pulling it down and the table pushing up by exactly the same amount.

Work in BIDMAS order: Brackets, Indices (powers), Division and Multiplication left to right, then Addition and Subtraction. Powers come BEFORE the × and ÷, so 2² + 3 × 4 is 4 + 12 = 16, and 5 × 3² is 5 × 9 = 45.

Solids keep their shape. Liquids flow and fill the bottom of a container. Gases spread out to fill all the space. Heating melts a solid to liquid; cooling freezes liquid to solid. When a liquid turns to gas it is called evaporation. GOING FURTHER. A gas can be squashed because its particles have big gaps between them; a liquid cannot, because its particles are already touching. The temperature a solid melts at is its MELTING POINT, and the temperature a liquid boils at is its BOILING POINT. Water melts at 0°C and boils at 100°C. Evaporation can happen at ANY temperature, not just when it is hot — which is why a puddle dries up on a cold day.

To ADD or SUBTRACT, make the denominators the same first: 2/3 + 1/6 = 4/6 + 1/6 = 5/6. To MULTIPLY, just go straight across the top and the bottom: 2/3 × 3/4 = 6/12 = 1/2. Always simplify at the end.

Living things grow, feed and reproduce. Plants make their own food using sunlight, water and carbon dioxide (photosynthesis). Animals eat plants or other animals for energy. Animals that eat only plants are herbivores. GOING FURTHER. All living things do seven things: movement, respiration, sensitivity, growth, reproduction, excretion and nutrition. Plants make their own food by PHOTOSYNTHESIS, using light, water and carbon dioxide — so a plant left in the dark cannot feed itself and goes pale and weak.

Find 10% by dividing by 10, then build the rest from it. To INCREASE by 20%, find 20% and add it on (60 + 12 = 72); to DECREASE, take it off. Working BACKWARDS, if 10% = 7 then 100% = 7 × 10 = 70.

The Earth spins once a day, giving day and night. It orbits the Sun once a year. The Moon orbits the Earth. The Sun is a star; the Earth is one of eight planets. GOING FURTHER. The Sun does not travel across the sky — the EARTH is spinning, and that is what makes the Sun appear to move. Because the Earth is a sphere, only the half facing the Sun is lit, so it is day here and night on the other side of the world. One full orbit of the Sun takes a year and gives us the seasons.

To simplify a ratio, divide both sides by the same number: 18:24 both ÷6 = 3:4. To SHARE in a ratio, add the parts to get the total number of shares, divide, then multiply: £45 in 2:3 is 5 shares of £9, so £18 and £27. For rates, find the cost of ONE first.

Sound is made by vibrations. It travels as waves through air (and other materials) to our ears. The faster something vibrates, the higher the pitch; the bigger the vibration, the louder the sound. Sound cannot travel through a vacuum (empty space). GOING FURTHER. Sound needs a MATERIAL to travel through — air, water or a solid — so in space, where there is no air, there is no sound at all. A tighter or shorter string vibrates faster and gives a HIGHER pitch.

You can only collect LIKE terms: 4a + 5a = 9a, and 7x - 2x + x = 6x. To substitute, swap the letter for its number and work it out: if x = 5 then 3x + 2 = 15 + 2 = 17. Remember 2y² means square y FIRST, then double.

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 quick multiplication and division facts.

The heart pumps blood around the body through blood vessels. Blood carries oxygen and nutrients to cells and carries waste away. Arteries carry blood away from the heart; veins carry blood back to the heart. GOING FURTHER. Blood goes round in a loop, which is why it is called CIRCULATION. It picks up oxygen at the LUNGS and delivers it to every cell, all the time, because cells need oxygen constantly and their waste has to be carried away.

Multiplying by 10, 100 or 1000 moves every digit LEFT one place per zero (3.6 × 100 = 360); dividing moves them RIGHT (45 ÷ 100 = 0.45). The decimal point never really moves — the digits do.

Light travels in straight lines from a source (like the Sun or a lamp). We see objects when light bounces off them into our eyes. A shadow forms when an opaque object blocks light — it's the same shape as the object but can change size. GOING FURTHER. Materials are TRANSPARENT (light passes through clearly), TRANSLUCENT (some light passes through, blurred) or OPAQUE (no light passes through). Because light travels in straight lines, an opaque object blocks a patch of light the same shape as itself — that is the shadow. When the Sun is low, the light hits at a shallow angle and the shadow stretches out long.

Area of a rectangle = length × width, and its perimeter is the distance all the way round. Area of a triangle = (base × height) ÷ 2, so base 10cm and height 4cm gives 20cm². Area is always in square units (cm²), perimeter in plain units (cm).

A circuit needs a complete loop for electricity to flow: a power source (battery), wires, and a component (like a bulb). A switch can break the loop to turn things off. If the loop is broken anywhere, nothing works. GOING FURTHER. A circuit must be a complete, unbroken LOOP or nothing flows, and a switch works by breaking or completing that loop. If you add a second bulb to the same cell, both bulbs are dimmer, because one cell is now doing twice the work.

Find the gap between one term and the next. If the gap is the same every time (3, 7, 11, 15 goes up 4 each time) keep adding it. If the terms DOUBLE (2, 4, 8, 16) the rule is multiply. A falling sequence like 20, 17, 14 has a subtract rule.

A habitat is where a living thing naturally lives (e.g. a pond, a desert, a forest) — it provides what the animal or plant needs to survive. We classify (group) living things by shared features: animals WITH a backbone are vertebrates, without are invertebrates. GOING FURTHER. A HABITAT is the place something lives; the ENVIRONMENT is the conditions there — how warm, how wet, how light. Animals are suited to their own habitat and usually could not survive in another: a polar bear's thick fur and fat would make it overheat in a rainforest.

MEAN: add them all up and divide by how many there are. MODE: the one that appears MOST. MEDIAN: put them in order and take the middle one. RANGE: biggest minus smallest. Order the list first for median and range.

Living things go through a life cycle: born or germinated, grow, reproduce, then eventually die. A flowering plant's cycle: seed → germination → seedling → mature plant → flower → seed. Animals like frogs go through METAMORPHOSIS: egg → tadpole → froglet → adult frog. GOING FURTHER. The flowering plant cycle runs: seed, germination, growth, pollination, then seed dispersal. Seeds are spread away from the parent so they are not all competing for the same light, water and space.

Count on in whole hours first, then the minutes: 14:20 + 1h = 15:20, + 50m = 16:10. To find a duration, count up from the start time to the next whole hour, then on to the end time. There are 60 minutes in an hour, so 130 minutes is 2h 10m.

Some changes can be undone (REVERSIBLE) — like melting ice (can freeze back) or dissolving sugar (can evaporate the water back). Others CAN'T be undone (IRREVERSIBLE) — like baking a cake or burning wood; a new substance is made. GOING FURTHER. In an IRREVERSIBLE change a NEW material is made and you cannot get the original back — burning is the clearest example. The clues that a new material has been made are a gas given off, a colour change, or heat and light being produced. Dissolving looks dramatic but is REVERSIBLE: evaporate the water and the solid comes back.

With the SAME top number, the bigger the bottom number the SMALLER the fraction, because you are cutting the same thing into more pieces: 1/2 is bigger than 1/3. To compare different fractions, give them the same denominator: 3/4 = 9/12 and 2/3 = 8/12, so 3/4 wins.

Food travels: mouth (chewed, mixed with saliva) → oesophagus (food pipe) → stomach (churned with acid) → small intestine (nutrients absorbed into blood) → large intestine (water absorbed) → waste leaves the body. GOING FURTHER. Food travels mouth, oesophagus, stomach, small intestine, large intestine. The small intestine is where the digested nutrients are ABSORBED into the blood — which is the whole reason food has to be broken down first: the pieces have to be small enough to pass into the blood.

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 and squares and roots.

The skeleton supports the body, protects organs (like the skull protecting the brain), and lets us move. Muscles work in PAIRS at a joint — when one contracts (shortens) it pulls a bone, and the other relaxes; muscles can only pull, never push. GOING FURTHER. The biceps and triceps are a pair: the biceps contracts to BEND the arm and the triceps contracts to straighten it. Joints have CARTILAGE and fluid to cushion the bones and stop them wearing away. Exercise makes bones denser and stronger, not just muscles.

Picture a number line. Adding moves you RIGHT, subtracting moves you LEFT: -3 + 5 lands on 2, and 4 - 9 takes you past zero to -5. Starting below zero and subtracting takes you further down: -2 - 3 = -5.

Rocks are grouped by how they form: igneous (cooled from magma/lava), sedimentary (layers of squashed sediment, often containing fossils), and metamorphic (changed by heat and pressure). Soil forms from broken-down rock mixed with humus (decayed plants and animals). GOING FURTHER. There are three types of rock: IGNEOUS (cooled from molten rock), SEDIMENTARY (laid down in layers, and the type that holds fossils) and METAMORPHIC (changed by heat and pressure). WEATHERING is rock being worn away by water, ice, wind or plant roots.

Under 90° is ACUTE, exactly 90° is a RIGHT angle, between 90° and 180° is OBTUSE. Angles on a straight line add to 180°, angles in a triangle add to 180°, and angles in a quadrilateral add to 360°.

Offspring inherit characteristics from both parents but aren't identical to them — this difference is called variation. Over many generations, characteristics that help an animal survive are more likely to be passed on — the simple starting idea behind evolution. GOING FURTHER. INHERITED features come from your parents; ACQUIRED ones, like a scar or a skill, happen during your life and are not passed on. If a feature helps an animal SURVIVE, it lives longer and has more young, so more of the next generation has it — over very many generations that is how species change.

Coordinates are written (x, y) — along the corridor first, then up the stairs. So 3 right and 2 up from the origin is (3, 2), and in (2, 5) the x-coordinate is 2. For the line y = x, whatever x is, y is the same.

Micro-organisms are tiny living things too small to see without a microscope, including bacteria, viruses, and fungi. Some are harmful and cause disease; others are helpful, like the bacteria used to make yoghurt or the fungi used in bread and in penicillin. GOING FURTHER. Most micro-organisms are harmless or useful: yeast makes bread rise, bacteria make yoghurt and cheese, and mould gave us penicillin. Only some cause disease. A fridge does not kill them, it just slows their growth, which is why cold food keeps longer.

Probability = (the outcomes you want) ÷ (all the outcomes possible). A coin has 2 sides so heads is 1/2; a dice has 6 faces so a six is 1/6; 3 red out of 5 balls is 3/5. Certain = 1, impossible = 0.

Plants make their own food through photosynthesis, using sunlight, water, and carbon dioxide, releasing oxygen as a by-product. Roots absorb water and minerals; the stem transports them up to the leaves, where most photosynthesis happens. GOING FURTHER. In photosynthesis a plant takes IN carbon dioxide and water and gives OUT oxygen. Roots do two jobs: anchoring the plant and absorbing water and minerals. Leaves are flat and wide to catch as much light as possible.

Substituting just means swapping the letter for its number, then doing the sum: if x = 5, 3x - 2 means 15 - 2 = 13. Remember 2x means 2 × x, and letters next to each other are multiplied.

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 quick multiplication and division facts.

Melting and freezing are opposite changes that happen at the same temperature for a substance (its melting point). Evaporation and condensation are opposite changes too. These are all PHYSICAL changes — no new substance is made, so they can be reversed. GOING FURTHER. EVAPORATION happens from the surface at any temperature; BOILING happens all through the liquid, only at its boiling point. Warm air holds water vapour, and when it touches a cold window it cools and CONDENSES into droplets. Melting does not change the MASS: the same particles are there, just arranged differently.

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 and squares and roots.

Different methods separate different mixtures: sieving separates solids of different sizes, filtering separates an insoluble solid from a liquid, and evaporation separates a DISSOLVED solid from a liquid by evaporating the liquid away. GOING FURTHER. To separate sand, salt and water: FILTER first to catch the sand, then EVAPORATE the water to leave the salt. Filtering only catches particles too big to pass through the paper, and dissolved salt goes straight through. CHROMATOGRAPHY is the method that separates the different dyes in an ink.

Volume of a cuboid = length × width × height, so 5 × 2 × 6 = 60cm³. A cube has all three the same, so side 4cm gives 4 × 4 × 4 = 64cm³. Volume is always in CUBIC units (cm³).

A food chain shows what eats what, starting with a producer (usually a plant) that makes its own food. Arrows point in the direction energy flows, towards the eater. A food web shows many connected food chains. GOING FURTHER. Every food chain starts with a PRODUCER — a plant, because it makes its own food using the Sun. The arrows point towards the eater and show which way the ENERGY goes. Remove one animal and everything above it in the chain suffers.

The CIRCUMFERENCE is the distance all the way round. The DIAMETER goes right across through the centre; the RADIUS goes from the centre to the edge and is always half the diameter — so a 10cm diameter means a 5cm radius.

Breathing brings oxygen into the body and removes carbon dioxide. Air travels down the windpipe (trachea) into the lungs, where oxygen passes into the blood and carbon dioxide passes out. GOING FURTHER. BREATHING moves air in and out of the lungs; RESPIRATION is releasing energy from food inside every cell. They are not the same word for the same thing. We breathe in more oxygen than we breathe out, and breathe out more carbon dioxide than we breathe in. Running makes you breathe faster AND deeper because your muscles need more oxygen and make more carbon dioxide.

They are three ways of saying the same thing. Fraction to decimal: divide top by bottom (1/2 = 0.5). Decimal to percentage: multiply by 100 (0.3 = 30%). Percentage to fraction: put it over 100 and simplify (25% = 25/100 = 1/4).

Magnets attract magnetic materials like iron and steel, but not materials like wood or plastic. Every magnet has a north and south pole — like poles repel, unlike poles attract — and magnetic force can act without touching. GOING FURTHER. Like poles REPEL and unlike poles ATTRACT. Magnetism is a NON-CONTACT force: it works across a gap without touching. Only iron, steel, nickel and cobalt are magnetic — copper and aluminium are metals but are not.

Find the value of ONE first, then scale up: if 6 apples cost £3 then one costs 50p, so 10 cost £5. For best value, work out the price per item for each option and compare — the cheaper per item wins.

The Moon doesn't make its own light — we see it because it reflects sunlight, and its phases happen because we see different amounts of its lit side as it orbits Earth. The seasons happen because Earth's tilted axis means different parts get more or less direct sunlight through the year. GOING FURTHER. The Moon takes about 28 days to orbit the Earth, and its phases are the different amounts of its sunlit half that we can see. The seasons are caused by the Earth's TILT: when your half is tilted towards the Sun it is higher in the sky, the days are longer, and that is summer.

FACTORS divide into a number exactly (find them in pairs: 1×12, 2×6, 3×4). MULTIPLES are its times table (4, 8, 12, 16, 20). A PRIME has exactly two factors, 1 and itself — so 17 is prime but 21 is not, because 3 × 7 = 21.

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), volume (area of the cross-section × the length) and quick multiplication and division facts.

A balanced diet gives the body the right nutrients in the right amounts. Regular exercise keeps the heart and muscles healthy. Substances like medicines, alcohol and tobacco affect the body — some help when used correctly, but many can harm health, especially in the wrong amounts. GOING FURTHER. CARBOHYDRATES like bread, pasta and rice give you most of your energy. Someone who is very active uses more energy and so needs more food. Regular exercise makes the heart stronger, so it pumps more blood with every beat.

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 and squares and roots.

The water cycle describes how water moves around our planet. The Sun heats water in oceans, rivers and lakes, causing it to EVAPORATE (turn into water vapour) and rise into the air. As it rises and cools, the vapour CONDENSES back into tiny water droplets, forming clouds. When those droplets get too heavy, they fall as PRECIPITATION — rain, snow or hail. GOING FURTHER. Condensation and precipitation both happen because the air is getting COLDER, which is why clouds form high up where it is cold. Only the water evaporates from the sea and the salt is left behind, so rain is fresh water, not salty.

Undo the operations in reverse order, doing the same to BOTH sides. For 2x + 3 = 11, take the 3 off first (2x = 8), then divide by 2 (x = 4). Always check by putting your answer back in.

Simple machines make jobs easier by changing the size or direction of a force. A LEVER is a rigid bar that pivots around a fixed point (a fulcrum) to lift things with less effort. A PULLEY is a wheel with a rope or chain around it that changes the direction of a pulling force. GEARS are wheels with teeth that lock together — when one gear turns, it turns the next, which can change speed or force. GOING FURTHER. A LEVER turns about a PIVOT and lets a small force move a big load. A ramp does the same trade: less force, but you push over a longer distance. Simple machines never give you something for nothing — they swap force for distance.

Find 10% by dividing by 10, then build up: 20% is double that, 5% is half of it. Then ADD for an increase and SUBTRACT for a decrease — £70 + 20% is £70 + £14 = £84, and £60 - 15% is £60 - £9 = £51.

Living things have ADAPTATIONS — special features or behaviours that help them survive in their habitat. For example, a camel has wide feet to stop it sinking in sand, and a cactus has spines instead of leaves to save water in the desert. Adaptations can be part of an animal's body, like fur or webbed feet, or the way it behaves, like hibernating in winter. GOING FURTHER. An ADAPTATION is an inherited feature that suits an animal or plant to its habitat — not a habit it learned. A cactus has spines instead of leaves so it loses less water, and a thick stem that stores it. A polar bear is white for CAMOUFLAGE in the snow.

Angles on a straight line add to 180°, so if one is 110° the other is 70°. Angles all the way around a point add to 360°. Vertically opposite angles — the pair across an X crossing — are always equal.

Circuit diagrams use standard SYMBOLS instead of drawings — a zigzag line for a resistor, a circle with a cross for a bulb, two parallel lines (one longer) for a cell/battery, and a break in a line with a small circle for a switch. In a SERIES circuit, components are connected in a single loop, one after another, so the same current flows through all of them. GOING FURTHER. Symbols are used in circuit diagrams because they are quick, clear and mean the same thing to every scientist in the world. In a SERIES circuit there is only one loop, so if one bulb breaks the loop is broken and every bulb goes out.

The TERM-TO-TERM rule is the gap: 5, 12, 19, 26 goes up 7 each time. The nth TERM rule lets you jump straight to any term: with 3n - 1, the 10th term is 3 × 10 - 1 = 29. To find the rule, the gap is the number in front of n.

Scientists sort living things into groups using CLASSIFICATION, based on features they share. A big first split is between VERTEBRATES (animals with a backbone, like fish, birds and mammals) and INVERTEBRATES (animals without a backbone, like insects and worms). A CLASSIFICATION KEY uses yes/no questions to help you work out which group a living thing belongs to. GOING FURTHER. Animals with a backbone are VERTEBRATES, and they fall into five groups: fish, amphibians, reptiles, birds and mammals. A classification KEY is a set of yes/no questions used to identify something you have never seen before.

You cannot add fractions until the bottoms match. Find a common denominator, change BOTH fractions, then add or subtract the tops only: 2/5 + 1/3 = 6/15 + 5/15 = 11/15. The bottom number stays the same in the answer.

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), angles (straight line 180°, around a point 360°), area and perimeter (triangle area is base × height ÷ 2, and area is in square units) and time (count on in whole hours first, then the minutes).

The Earth spins on its axis once every 24 hours, causing DAY and NIGHT — the side facing the Sun has daytime, while the side facing away has night. As the Earth spins, the Sun appears to move across the sky, which makes SHADOWS change length and direction through the day: they are long in the early morning and evening, and shortest around midday. GOING FURTHER. The Earth spins once every 24 hours, giving day and night. Shadows are SHORTEST around midday when the Sun is highest. The Sun rises in the east and sets in the west because the Earth spins from west to east.