Integers, Exponents, Prime Time, Lines & Angles, Kinematics, and Matter: quick revision, 18 bites

Exponent Laws: The Shortcut for Repeated Multiplication

Stop multiplying — start adding powers.

Exponents compress repeated multiplication into a single expression. Mastering the **laws of exponents** lets you simplify huge expressions in seconds.

Takeaway. Exponent laws turn long multiplication chains into simple addition or subtraction of powers.

Integers: The Number Family With Signs

Positive, negative, and zero — all integers.

Takeaway. Integers extend whole numbers to include negatives, enabling subtraction without restriction.

Sign Rules: The #1 Integer Trap

Two negatives don't always make a positive.

Takeaway. Brackets decide whether the negative sign is squared — read them carefully.

Prime Numbers: The Atoms of Arithmetic

Every number is built from primes.

A **prime** has exactly two factors: 1 and itself. Every composite number can be broken into a unique product of primes — the Fundamental Theorem of Arithmetic.

Takeaway. Primes are the building blocks; every composite number has exactly one prime factorisation.

Prime Factorisation in 3 Steps

Divide, divide, divide — until you hit primes.

Takeaway. Repeated division by the smallest prime gives the prime factorisation quickly.

Patterns in Mathematics: Nature's Hidden Rules

Numbers follow rhythms you can predict.

Takeaway. Recognising patterns lets you predict the next term without computing every step.

Lines & Angles: The Geometry Vocabulary

Every angle has a name and a rule.

Takeaway. Angle types are classified purely by their measure in degrees.

Angle Pairs: Complementary vs Supplementary

Two angles, one sum — 90 or 180?

Takeaway. Complementary pairs make a right angle; supplementary pairs make a straight line.

Parallel Lines: The Angle Rules That Save Time

One transversal unlocks six angles.

Takeaway. A single transversal across parallel lines creates equal or supplementary angle pairs you can use instantly.

Kinematics: Describing Motion Without Forces

Motion has a language — learn it.

Takeaway. Kinematics describes motion using distance, displacement, speed, velocity, and acceleration — no forces needed.

The Three Equations of Motion

Three formulas solve every uniform-acceleration problem.

Takeaway. Pick the equation that omits the quantity you don't know.

Distance vs Displacement: Not the Same Thing

Round trip? Displacement is zero.

Takeaway. Displacement depends only on start and end points; distance depends on the full path.

Matter: Made of Particles in Constant Motion

Everything around you is tiny moving particles.

Matter is anything with **mass and volume**, made of particles with **spaces between them** that are **in constant random motion** and **attract each other**.

Takeaway. The particle model explains diffusion, expansion, and states of matter.

Three States of Matter: Same Particles, Different Arrangement

Solid, liquid, gas — same stuff, different spacing.

Liquids sit between the two: particles close but free to slide, giving a fixed volume but no fixed shape.

Takeaway. State of matter depends on particle spacing and motion, not on the type of particle.

Change of State: The Six Transitions

Heat in, heat out — matter changes form.

Takeaway. Every change of state is driven by heat absorbed or released — temperature stays constant during the change.

Evaporation Cools — That's Why We Sweat

Sweat is your body's built-in AC.

Evaporation absorbs heat from the surroundings. When sweat evaporates from your skin, it pulls heat away — cooling you down. This is why evaporation is a **cooling process**.

Takeaway. Evaporation removes heat, making it nature's cooling mechanism.

Exam Tip: Match the Equation to the Missing Variable

Don't memorise — match and solve.

Takeaway. Identify the unknown first, then pick the equation that doesn't contain it.

Remember Angle Pairs With 'C' and 'S'

C for Corner, S for Straight.

Takeaway. C = 90°, S = 180° — the letter tells you the sum.