Mathematics: every concept, and where it is taught

Every idea in the mathematics courses, from ratio to the derivative. Each concept names the units that teach it, what it depends on, and what later work uses it, so you can start anywhere and follow the chain in either direction.

ratio

Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
Rate — A ratio of two different units, like miles per hour or dollars per pound.
Unit rate — A rate with denominator 1 — how much for exactly one.
Constant of proportionality — The unit rate, written k, in y = kx.
Percent — Parts per hundred. 37% = 37100 = 0.37.
Multiplier — The single number you multiply by. A 20% increase has multiplier 1.20.
Percent change — new - oldold × 100% — always divided by the original.
Markup — An increase / a decrease applied to a starting price.
Discount — An increase / a decrease applied to a starting price.
Proportional — Two quantities with a constant ratio: yx = k always.
Origin — The point (0, 0), which every proportional graph passes through.
Linear but not proportional — A straight line that misses the origin, like y = 3x + 5.
Scale factor — The number every length is multiplied by.
Scale drawing — A picture in proportion to the real thing, at a stated scale like 1 : 50.
Similar figures — Same shape, different size: equal angles, proportional sides.
Corresponding sides — Sides in matching positions in two similar figures.
Equivalent ratios — Ratios naming the same relationship, like 2:3 and 4:6.
Ratio table — A table of equivalent ratios, useful for scaling up or down.
Part-to-part — Comparing one part with another, like blue to yellow.
Part-to-whole — Comparing one part with the total, like blue to all the paint.
Better buy — The option with the lower unit price.
Constant speed — A rate that does not change, so distance and time stay proportional.
Conversion factor — A rate used to change units, like 12 inches per foot.
Percent of a number — A part found by multiplying, as in 25% of 80.
Percent increase — How much something grew, as a percentage of what it was.

number

Rational number — Any number you can write as a fraction ab with b ≠ 0.
Reciprocal — The flip of a fraction. The reciprocal of 35 is 53.
LCD — Least common denominator — the smallest number both denominators divide into.
Terminating — Every fraction becomes a decimal that either stops or repeats forever.
Repeating — Every fraction becomes a decimal that either stops or repeats forever.
Opposite — Same distance from zero, other side. The opposite of -7 is 7.
Absolute value — |x| — distance from zero, always positive or zero.
Additive inverse — The number you add to get 0. -7 + 7 = 0.
Integer — A whole number, positive, negative, or zero.
Base — The number being multiplied. In 53 the base is 5.
Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
Power — The whole expression, 53, and also its value, 125.
Scientific notation — A number written as a × 10n, where 1 ≤ a < 10.
Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
Radical — The √x symbol, and the expression under it.
Radicand — The number under the radical sign.
Rational — Any number writable as ab with integers a and b, b ≠ 0.
Irrational — A real number that cannot be written as a fraction — its decimal never repeats and never ends.
Factor — A number that divides evenly into another.
Multiple — The result of multiplying by a whole number: 12 is a multiple of 4.
GCF — Greatest common factor — the largest number dividing both.
LCM — Least common multiple — the smallest number both divide into.
Prime factorisation — A number written as a product of primes: 60 = 22 · 3 · 5.
Order of magnitude — The power of ten — roughly how many digits the number has.
Standard form — The ordinary way of writing a number, like 47,000.
Simplest radical form — No perfect square factors left under the root.
Rational exponent — x1/2 = √x and xm/n = √[n]xm.
Rationalise — Clear a radical out of a denominator.
Imaginary unit — i, defined by i2 = -1.
Complex number — Anything of the form a + bi, with a the real part and b the imaginary part.
Conjugate — a - bi is the conjugate of a + bi. Multiplying them clears the i entirely.
Complex plane — The plane where the horizontal axis is real and the vertical axis imaginary.
Place value — What each digit is worth, depending on its column.
Quotient — The answer to a division.
Terminating decimal — One that stops, like 0.75, rather than repeating forever.
Mixed number — A whole number with a fraction, like 212.
Improper fraction — One whose top is bigger than its bottom, like 52.
Opposite — The same distance from zero, on the other side. The opposite of -7 is 7.
Number line — A line with numbers increasing to the right.

data

Population — Every member of the group you care about.
Sample — The part of the population you actually measure.
Random sample — Every member has an equal chance of being picked — the only kind you can trust.
Mean — Two kinds of centre: the balance point, and the middle value.
Median — Two kinds of centre: the balance point, and the middle value.
MAD — Mean absolute deviation — the average distance from the mean; a measure of spread.
Outcome — One possible result of an experiment.
Sample space — The set of all possible outcomes.
Event — A collection of outcomes you care about, like "rolls an even number".
Complement — Everything except the event. P(not A) = 1 - P(A).
Theoretical vs experimental — What reasoning predicts vs what actually happened when you tried it.
Compound event — An event made of two or more simple events.
Independent — The first event does not change the second — like rolling a die twice.
Dependent — The first event changes the second — like drawing marbles without replacing them.
Tree diagram — A branching picture of all the ways a sequence can unfold.
Fundamental counting principle — If one stage has m ways and the next has n, together they have m × n ways.
Bar graph — Compares separate categories.
Line graph — Shows change over time.
Circle graph — Shows parts of one whole, as percentages summing to 100%.
Scale — What one grid step is worth — and where the axis starts.
Estimate — A deliberately rough answer used to check a precise one.
Scatter plot — A graph of paired data, one dot per case.
Association — A pattern linking the two variables.
Cluster — A group of dots bunched together.
Outlier — A dot far away from the rest of the pattern.
Linear association — The dots roughly follow a straight line.
Line of best fit — A straight line summarising a linear pattern in a scatter plot.
Interpolation — Predicting inside the range of the data. Usually safe.
Extrapolation — Predicting outside the range. Risky.
Residual — The gap between an actual value and the line's prediction.
Two-way table — A table of counts sorted by two categorical variables at once.
Joint frequency — A count in a single inner cell.
Marginal frequency — A row total or a column total, out at the margin.
Relative frequency — A count expressed as a fraction or percentage of some total.
Regression line — The line of best fit computed by a formula rather than by eye.
Correlation coefficient — r, between -1 and 1. Its sign gives the direction, its size the strength.
Residual plot — A plot of residuals against x, used to judge whether a line was the right model.
Interquartile range — Q3 - Q1, the spread of the middle half.
Standard deviation — A measure of typical distance from the mean.
Skew — A long tail on one side of the distribution.
Five-number summary — Minimum, Q1, median, Q3, maximum.
Normal distribution — The symmetric bell-shaped distribution described by its mean and standard deviation.
z-score — How many standard deviations a value sits from the mean: z = x - μσ.
Empirical rule — About 68%, 95% and 99.7% lie within one, two and three deviations.
Percentile — The percentage of the population at or below a value.
Bias — A flaw in how the sample was gathered that tilts the result in one direction.
Margin of error — How far the sample result might sit from the truth.
Confidence interval — The range formed by the estimate plus and minus the margin of error.
Permutation — An arrangement where order matters. P(n,r) = n!(n-r)!.
Combination — A selection where order does not matter. C(n,r) = n!r!(n-r)!.
Factorial — n! is the product of every whole number from 1 to n. 0! = 1.
Binomial theorem — The rule expanding (a+b)n using combinations as coefficients.
Statistical question — One that anticipates variability in the answers.
Data — The collected answers or measurements.
Distribution — The pattern of how the values are spread out.
Dot plot — A chart with one dot per value, stacked above a number line.
Mode — The value that appears most often.
Range — The largest value minus the smallest.
Mean absolute deviation — The average distance of the values from the mean.

algebra

Expression — A math phrase with no equals sign, like 3n + 5.
Term — A piece of an expression separated by + or -.
Coefficient — The number multiplying a variable — the 3 in 3n.
Like terms — Terms with exactly the same variable part; only these can be combined.
Arithmetic sequence — A list that grows by adding the same amount each time.
Variable — A letter standing for an unknown number.
Equation — A statement that two expressions are equal.
Inequality — A statement that one expression is less than or greater than another.
Solution — A value that makes the statement true.
Inverse operation — The operation that undoes another: + undoes -, × undoes ÷.
Isolate — Get the variable alone on one side.
Two-step equation — One needing two inverse operations, like 3x + 5 = 20.
Variables on both sides — An equation like 5x - 2 = 3x + 8.
Inequality symbols — < less than, > greater than, ≤ at most, ≥ at least.
Solution set — All the values that make the inequality true — usually infinitely many.
Open — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
Closed dot — Open excludes the endpoint (<, >); closed includes it (≤, ≥).
Compound inequality — Two conditions at once, like 3 < x ≤ 9.
Function — A rule pairing each input with exactly one output.
Input — The value you put in (x) and what comes out (y).
Output — The value you put in (x) and what comes out (y).
Slope — How much y changes for each 1 that x increases.
y-intercept — The output when x = 0 — where the line crosses the vertical axis.
Linear function — One whose graph is a straight line: y = mx + b.
Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
Rise — The vertical change, y2 - y1.
Run — The horizontal change, x2 - x1.
Slope-intercept form — y = mx + b, with m the slope and b the y-intercept.
x-intercept — The x value when y = 0 — where it crosses the x-axis.
Initial value — The same thing as b in a real-world context: the starting amount.
Domain — The set of allowed inputs.
Range — The set of outputs that actually occur.
Function notation — f(3) = 7 means: feed in 3, get out 7.
System — Two or more equations that must hold at the same time.
Solution of a system — The (x, y) pair that works in every equation.
Substitution — Solve one equation for a variable, then put that expression into the other.
Elimination — Add or subtract the equations so one variable disappears.
Degree — The largest exponent on the variable.
Equivalent expressions — Two expressions that give the same value for every input.
Literal equation — An equation with several letters, to be rearranged for one of them.
Properties of equality — You may add, subtract, multiply or divide both sides by the same thing (never divide by zero).
Extraneous solution — A value produced by the algebra that fails in the original equation.
Identity — An equation true for every value, like 2(x + 3) = 2x + 6.
Interval notation — A compact way of writing a solution set, like [3, ∞).
Point-slope form — y - y1 = m(x - x1). Best when you know a point and the slope.
Standard form — Ax + By = C. Best for finding intercepts fast.
Parallel — Same slope, different intercept.
Perpendicular — Slopes multiply to -1 — negative reciprocals.
Linear model — An equation of the form f(x) = mx + b fitted to a situation.
Rate of change — The slope, in the units of the situation.
Average rate of change — f(b) - f(a)b - a over an interval.
Transformation — A change to the function that moves or stretches its graph.
Consistent — Has a solution / has none.
Inconsistent — Has a solution / has none.
Feasible region — The shaded overlap for a system of inequalities.
Boundary line — The line you would get by replacing the inequality sign with =.
Exponential function — f(x) = a · bx with a ≠ 0, b > 0, b ≠ 1.
Growth factor — b itself. b > 1 means growth, 0 < b < 1 means decay.
Growth rate — The percentage change. b = 1 + r for growth, b = 1 - r for decay.
Asymptote — A line the graph approaches but never reaches — here, the x-axis.
Sequence — An ordered list of numbers. The nth one is an.
Explicit formula — A rule giving an directly from n.
Recursive formula — A rule giving an from an-1, plus a starting value.
Common difference — The constant added each time, in an arithmetic sequence.
Common ratio — The constant multiplied each time, in a geometric sequence.
Polynomial — A sum of terms, each a number times a whole-number power of the variable.
Binomial — A polynomial with two terms.
Closure — Polynomials added, subtracted or multiplied always give another polynomial.
Standard form — Terms written in order of decreasing degree.
Difference of squares — a2 - b2 = (a - b)(a + b).
Perfect square trinomial — a2 ± 2ab + b2 = (a ± b)2.
Prime polynomial — One that will not factor any further over the integers.
Parabola — The U-shaped graph of a quadratic function.
Vertex — The turning point — the minimum if it opens up, the maximum if it opens down.
Axis of symmetry — The vertical line through the vertex, x = -b2a.
Roots — The x values where y = 0.
Zeros — The x values where y = 0.
Vertex form — y = a(x - h)2 + k, with vertex at (h, k).
Zero product property — If AB = 0 then A = 0 or B = 0.
Quadratic formula — x = -b ± √b2 - 4ac2a.
Discriminant — b2 - 4ac. Its sign counts the real solutions.
Completing the square — Rewriting x2 + bx as a perfect square minus a constant.
Piecewise function — A function defined by different rules on different intervals.
Step function — A piecewise function that is constant on each piece, so its graph jumps.
Vertex of an absolute value graph — The corner, where the inside equals zero.
Composition — Running one function on the output of another, written (f ° g)(x) = f(g(x)).
Inverse function — The function that undoes another, written f-1. It sends every output back to the input it came from.
One-to-one — No two inputs share an output. Only a one-to-one function has an inverse that is itself a function.
Horizontal line test — If any horizontal line meets a graph twice, the function is not one-to-one.
Domain of a composition — The inputs that survive both machines — the inner function must produce something the outer one accepts.
Parent function — The plainest member of a family — y = x2, y = |x|, y = √x, y = 1x — before anything is done to it.
Vertical stretch — Multiplying the whole output: a f(x) pulls the graph away from the x-axis when |a| > 1.
Dividend — The polynomial being divided — the one inside the bracket.
Divisor — The polynomial you are dividing by.
Remainder — What is left when the divisor no longer fits. Always lower degree than the divisor.
Remainder theorem — Dividing f(x) by x - a leaves remainder f(a).
Factor theorem — If f(a) = 0 then x - a is a factor, and the other way round.
Degree — The highest power of x. It caps the number of roots and the number of turns.
Leading coefficient — The number in front of the highest power. Its sign decides which way the right end goes.
End behaviour — What the graph does far out to the left and right.
Multiplicity — How many times a root repeats. It decides whether the graph crosses or just touches.
Turning point — Where the graph changes from rising to falling or back. At most n - 1 of them.
Radical equation — An equation with the unknown underneath a root sign.
Principal root — The non-negative one. √25 = 5, never -5.
Index — The little number on the root. Square root has index 2, cube root index 3.
Domain restriction — A square root needs its inside to be ≥ 0, which limits the inputs allowed.
Rational expression — A fraction whose top and bottom are polynomials.
Excluded value — An input that makes the denominator zero. It can never be in the domain.
Vertical asymptote — A vertical line the graph approaches but never reaches, at an excluded value that does not cancel.
Horizontal asymptote — The height the graph settles towards far out to the left and right.
Least common denominator — The smallest expression every denominator divides into.
Logarithm — logb y is the exponent that turns b into y.
Common log — Base 10, usually written log with no base shown.
Natural log — Base e ≈ 2.718, written ln.
Change of base — logb x = log xlog b, which is how a calculator handles any base.
Argument — The thing inside the log. It must be strictly positive.
Half-life — The time for a decaying quantity to fall to half.
Doubling time — The time for a growing quantity to double.
Continuous growth — Growth compounding at every instant, modelled with A = Pert.
Series — The sum of the terms of a sequence.
Sigma notation — ∑k=1n ak — add ak for every k from 1 to n.
Matrix — A rectangular array of numbers, described by its rows then columns.
Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
Identity matrix — The square matrix with ones down the diagonal; it leaves everything unchanged.
Determinant — A single number computed from a square matrix; zero means it has no inverse.
Augmented matrix — The coefficients with the constants attached as a final column.
Parameter — The extra variable, usually t, that drives both coordinates.
Parametric equations — A pair x = f(t), y = g(t) describing a curve.
Eliminating the parameter — Combining the two equations to recover a relation in x and y alone.
Orientation — The direction the curve is traced as t increases.
Plane curve — The set of points traced out, with the timing stripped away.
Evaluate — To work out the value once you know what the variable is.
Check — Substituting your answer back to confirm it works.
At least — Greater than or equal to, written ≥.
At most — Less than or equal to, written ≤.
Open circle — A hollow dot showing the endpoint is not included.

geometry

Perimeter — Distance all the way around the outside.
Area — Space inside, measured in square units.
Circumference — The perimeter of a circle: C = 2π r.
Composite figure — A shape built from simpler ones.
π — The circumference of any circle divided by its diameter — about 3.14159.
Cross section — The 2-D face revealed when a plane cuts through a solid.
Plane — A perfectly flat surface extending forever.
Net — A 3-D shape unfolded flat.
Face — A flat surface; a line where two faces meet; a corner point.
Edge — A flat surface; a line where two faces meet; a corner point.
Vertex — A flat surface; a line where two faces meet; a corner point.
Volume — Space inside, in cubic units.
Surface area — Total area of all the outside faces, in square units.
Prism — A solid with two identical parallel bases joined by rectangles.
Lateral area — The side faces only, not counting the two bases.
Compass — Tools for drawing exact circles and lines — no measuring allowed.
Straightedge — Tools for drawing exact circles and lines — no measuring allowed.
Bisect — Cut exactly in half.
Complementary — Two angles summing to 90° / to 180°.
Supplementary — Two angles summing to 90° / to 180°.
Vertical angles — The opposite pair formed by two crossing lines — always equal.
Triangle inequality — Any two sides must sum to more than the third.
Unit rate for conversion — A fraction equal to 1, like 12 in1 ft.
Metric prefixes — kilo = 1000, centi = 1100, milli = 11000.
Precision — How finely a measurement is recorded — to the nearest cm, mm, and so on.
Radius — Centre to edge. Half the diameter.
Diameter — All the way across through the centre. d = 2r.
Arc — Part of the edge; a "pizza slice" bounded by two radii.
Sector — Part of the edge; a "pizza slice" bounded by two radii.
Leg — One of the two sides forming the right angle.
Hypotenuse — The side opposite the right angle — always the longest.
Pythagorean triple — Three whole numbers that fit: 3-4-5, 5-12-13, 8-15-17, 7-24-25.
Converse — If a2 + b2 = c2, then the triangle must be right-angled.
Pre-image — The shape you start with. Its corners are labelled A, B, C.
Image — The shape after the move. Its corners get primes: A', B', C'.
Rigid motion — A move that keeps every length and every angle. Slides, flips and turns are all rigid.
Translation — A slide. Every point moves the same distance in the same direction.
Reflection — A flip across a line, like a mirror.
Rotation — A turn about a fixed point, through a given angle and direction.
Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
Corresponding parts — The pieces that match up: A with D, side AB with side DE, and so on.
Sequence of transformations — Two or more moves done one after another.
Orientation — Whether the labels run clockwise or counter-clockwise around the shape.
Dilation — A resizing from a centre point by a scale factor k.
Centre of dilation — The one point that does not move.
Similar — Same shape, possibly different size. Written △ ABC ∼ △ DEF.
Transversal — A line that crosses two or more other lines.
Corresponding angles — Same position at each crossing. Equal when the lines are parallel.
Alternate interior angles — Between the parallels, on opposite sides of the transversal. Equal.
Co-interior angles — Between the parallels, same side. They add to 180°.
Exterior angle — The angle formed by extending one side of a triangle.
Distance formula — d = √(x2 - x1)2 + (y2 - y1)2.
Midpoint — The point halfway between two others: average the x values and average the y values.
Cylinder — Two parallel circles joined by a curved surface. V = π r2 h.
Cone — A circle tapering to a point. V = 13π r2 h.
Sphere — A ball. V = 43π r3.
Undefined term — Point, line and plane. Described but never defined, because any definition would use them.
Postulate — A statement accepted without proof, such as "two points determine exactly one line."
Theorem — A statement that has been proved from postulates and earlier theorems.
Segment — Two endpoints and everything between them. Written AB.
Ray — One endpoint and everything beyond it in one direction. Written AB.
Given — What the problem hands you. Always the first line of a proof.
Prove — The statement you must arrive at. Always the last line.
Two-column proof — Statements on the left, the reason for each on the right.
Counterexample — A single case that makes a claim false. One is enough.
Included angle — The angle between two named sides. The A in SAS must be included.
Included side — The side between two named angles. The S in ASA must be included.
CPCTC — Corresponding Parts of Congruent Triangles are Congruent — used after proving congruence.
Reflexive property — Anything is congruent to itself. A shared side is congruent to itself.
Hypotenuse-Leg — HL: for right triangles only, a matching hypotenuse and one leg are enough.
Polygon — A closed figure made of straight segments that meet only at endpoints.
Regular polygon — All sides equal and all angles equal.
Parallelogram — A quadrilateral with both pairs of opposite sides parallel.
Rhombus — A parallelogram with four congruent sides.
Trapezoid — A quadrilateral with exactly one pair of parallel sides.
Diagonal — A segment joining two non-adjacent vertices.
AA similarity — Two pairs of congruent angles prove two triangles similar.
SSS similarity — All three pairs of sides in the same ratio.
SAS similarity — Two pairs of sides in ratio with the included angles congruent.
Geometric mean — For a, x, b in proportion, x = √ab.
Central angle — An angle whose vertex is the centre. Equal to its arc.
Inscribed angle — An angle whose vertex is on the circle. Half its arc.
Chord — A segment joining two points on the circle.
Tangent — A line touching the circle at exactly one point.
Secant — A line that cuts the circle at two points.
Standard form — (x-h)2 + (y-k)2 = r2, centre (h,k) and radius r.
General form — x2 + y2 + Dx + Ey + F = 0, which hides the centre until you complete the square.
Midpoint formula — (x1+x22, y1+y22) — used to test bisecting.
Pyramid — A base tapering to a point. V = 13 Bh.
Solid of revolution — The solid swept out by spinning a flat shape about a line.
Cavalieri's principle — Same height and same cross sections at every level means same volume.
Vector — A quantity with both magnitude and direction.
Scalar — A quantity with size only, such as mass or temperature.
Magnitude — The length of the vector, written |v|.
Component form — A vector written as its horizontal and vertical parts, ⟨ a, b ⟩.
Resultant — The single vector that two or more vectors add up to.
Conic section — A curve obtained by slicing a cone with a plane.
Focus — A fixed point used to define the curve. An ellipse and a hyperbola have two.
Vertex — A turning point of the curve, on its axis.
Major axis — The longer axis of an ellipse.
Eccentricity — How far a conic is from being a circle. Zero is a circle; one is a parabola.
x-coordinate — The first number — how far across.
y-coordinate — The second number — how far up or down.
Quadrant — One of the four regions the axes divide the plane into.
Base — Any side of a triangle, chosen as the one to measure from.
Height — The perpendicular distance from the base to the opposite corner.
Cubic unit — A cube one unit on every edge.
Rectangular prism — A box — six rectangular faces meeting at right angles.
Edge length — The measurement along one side.
Capacity — How much a container holds, often in litres or gallons.

skills

Strategy — A general approach — draw it, tabulate it, work backwards, try a simpler case.
Work backwards — Start from the result and undo each step.
Guess — Make a sensible guess, test it, and use what you learn to guess better.
Check — Make a sensible guess, test it, and use what you learn to guess better.
Revise — Make a sensible guess, test it, and use what you learn to guess better.
Simpler case — Solve the same problem with small numbers, find the pattern, then scale up.

trig

Opposite — The side across the triangle from the angle you are using.
Adjacent — The side next to that angle which is not the hypotenuse.
Sine — sin θ = oppositehypotenuse.
Cosine — cos θ = adjacenthypotenuse.
Tangent — tan θ = oppositeadjacent.
Angle of elevation — The angle up from horizontal to a line of sight.
Radian — The angle whose arc length equals the radius. A full turn is 2π radians.
Unit circle — The circle of radius 1 centred at the origin.
Reference angle — The acute angle between the terminal side and the x-axis.
Coterminal angles — Angles that finish in the same place, differing by whole turns.
Terminal side — Where the rotating arm ends up after turning through the angle.
Amplitude — Half the distance from the top to the bottom — how tall the wave is.
Period — How long before the pattern repeats.
Midline — The horizontal line halfway between the peaks and troughs.
Phase shift — A horizontal slide — how far the wave has been moved sideways.
Frequency — How many full cycles fit in a given interval. The reciprocal of the period.
Pythagorean identity — sin2θ + cos2θ = 1.
Reciprocal identities — csc = 1sin, sec = 1cos, cot = 1tan.
Quotient identity — tanθ = sinθcosθ.
General solution — All the angles satisfying an equation, usually written with +2π n for the repeats.
Arcsine — The inverse of sine, restricted to outputs from -90° to 90°.
Arccosine — The inverse of cosine, restricted to outputs from 0° to 180°.
Arctangent — The inverse of tangent, restricted to outputs strictly between -90° and 90°.
Principal value — The single answer the restricted inverse returns.
Restricted domain — The stretch of the original function kept so that it is one-to-one.
Oblique triangle — Any triangle with no right angle.
Law of sines — asin A = bsin B = csin C.
Law of cosines — c2 = a2 + b2 - 2abcos C.
Ambiguous case — Two sides and a non-included angle, which can describe two different triangles.
Polar coordinates — A point given as (r, θ): distance from the origin, and direction.
Pole — The origin, where r = 0.
Polar axis — The ray pointing along positive x, from which θ is measured.
Rectangular form — The ordinary (x, y) description.
Modulus — The distance r, also written |z| for a complex number.

calculus

Limit — The value a function approaches as the input approaches some number.
One-sided limit — The value approached from the left, or from the right, alone.
Continuous — A function you could draw without lifting the pen — no holes, jumps or blow-ups.
Removable discontinuity — A single missing point; a hole that could be filled in.
Indeterminate form — 00, which means the limit needs more work — not that it fails to exist.
Secant line — A line through two points on a curve.
Tangent line — A line touching the curve at one point, with the same direction there.
Derivative — The slope of the tangent, written f'(x) or dydx.
Difference quotient — f(x+h)-f(x)h, the slope over a gap of h.
Riemann sum — An estimate of area made from rectangles under a curve.
Left sum — Rectangles whose heights come from the left edge of each strip.
Right sum — Rectangles whose heights come from the right edge.
Definite integral — The exact area, written ∫ab f(x)dx.
Accumulation — The total built up by a rate acting over an interval.

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