NSTSE cheat sheet

Speed = distance ÷ time; velocity adds direction, so a body moving at constant speed in a circle still accelerates because direction changes.

Newton's second law: F = ma. Weight = mg, where g ≈ 9.8 m/s² on Earth; mass is constant, weight varies with g.

Work = force × displacement along the force; power = work ÷ time. A force perpendicular to motion (e.g. centripetal) does zero work.

Density = mass ÷ volume; an object floats when its average density is less than the fluid's, and the upthrust equals the weight of fluid displaced.

Ohm's law: V = IR; resistors in series add (R₁+R₂), in parallel 1/R = 1/R₁ + 1/R₂. Power = VI = I²R = V²/R.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts with chlorophyll capturing light; respiration is the reverse energy release.

Acids turn blue litmus red and have pH < 7; bases turn red litmus blue with pH > 7; pH 7 is neutral at 25 °C.

In a food chain energy decreases about tenfold per trophic level, so top consumers are fewest; decomposers recycle nutrients, not energy.

Quadratic roots: for ax² + bx + c = 0, x = [−b ± √(b² − 4ac)] / 2a; the discriminant b² − 4ac decides real, equal, or complex roots.

Sum of first n natural numbers = n(n+1)/2; sum of squares = n(n+1)(2n+1)/6; nth term of an AP is a + (n−1)d.

Area formulas: triangle ½ × base × height; circle πr²; trapezium ½(a+b)h; volume of cylinder πr²h and of cone ⅓πr²h.

Pythagoras: in a right triangle a² + b² = c², where c is the hypotenuse; common triples are 3-4-5, 5-12-13, 8-15-17.

Percentage change = (change ÷ original) × 100; successive changes of x% and y% give a net change of x + y + xy/100 percent.

Simple interest = PRT/100; compound amount = P(1 + R/100)^T. Simple interest is constant each year, compound interest grows.

Probability of an event = favourable outcomes ÷ total equally likely outcomes, always between 0 and 1; P(not A) = 1 − P(A).

For similar figures, corresponding lengths scale by k, areas by k², and volumes by k³.

Number series: test successive differences, then ratios, then alternating or square/cube patterns before assuming a rule.

Coding-decoding: convert letters to positions (A=1 … Z=26); the common shifts are ±1, ±2, reversal (A↔Z), or position-squared.

Blood relations: draw a family tree with gender and generation levels; 'brother of my father' is uncle, 'son of my sister' is nephew.

Direction sense: net displacement uses Pythagoras when turns are at right angles; a 3 km east then 4 km north gives 5 km from start.

Clock problems: the minute hand gains 5.5° per minute on the hour hand; hands coincide every 65 5/11 minutes.

Syllogism: valid only if the conclusion holds in every diagram satisfying the premises; 'some A are B' does not imply 'some B are not A'.

Odd-one-out and analogy items: identify the shared attribute (category, function, part-whole, degree) before choosing the mismatched option.

Average speed for equal distances = 2xy/(x+y), not the arithmetic mean of the two speeds.