Full preview โ nothing is watermarked or held back.
Math ยท 10th Grade
The Equation of a Circle
Centre, radius, and the completing-the-square step that reveals both.
How to use it
If it is not in standard form, complete the square in x and in y separately.
Free ยท print-ready PDF ยท US Letter and A4
- Grade
- 10th Grade
- Ages
- 15โ16
- Subject
- Math
- Pages
- 1
The rest of the 10th Grade wall
49 more posters, all free to print.
Completing the SquareTurning any quadratic into vertex form โ and where the quadratic formula comes from.Vertex FormThe form that hands you the graph without any working at all.End Behaviour of PolynomialsWhat the graph does at the far left and far right, from two pieces of information.Sum and Difference of CubesTwo patterns worth memorising, and the sign rule that keeps them straight.Rational ExpressionsFractions with algebra in them โ and the values that are forbidden.Complex NumbersWhat happens when the discriminant is negative.LogarithmsA log is an exponent โ reading the definition backwards makes everything easier.SOH-CAH-TOAThree ratios, and the labelling step that decides which one you need.The Special TrianglesTwo triangles whose exact ratios are worth knowing without a calculator.The Unit CircleTrig beyond right triangles, and the sign pattern in each quadrant.Circle TheoremsSix results that solve almost every circle question.Coordinate ProofsProving a shape is what it claims to be, using only distance and slope.Ionic BondingElectrons handed over, not shared โ and the properties that follow.Covalent BondingElectrons shared between two non-metals, and why the properties are so different.Balancing EquationsConservation of mass, enforced with coefficients โ never with subscripts.The Five Reaction TypesRecognising the pattern tells you what the products will be.The MoleA counting unit for atoms โ and the three formulas that use it.Acids and BasesThe pH scale, what it measures, and the reaction that cancels both.The Gas LawsThree relationships between pressure, volume and temperature.Quadratics & PolynomialsCompleting the square, vertex form, the factoring patterns and end behaviour.Right-Triangle TrigSOH-CAH-TOA, the special triangles, and the unit circle in one place.Coordinate GeometryDistance, midpoint, slope proofs and circle equations on the plane.Function TransformationsHow a, h and k move any parent graph, with the inside/outside rule.Rhetorical AnalysisEthos, pathos, logos, the SOAPSTone frame and the analysis paragraph shape.SAT Word RootsThirty-six high-yield roots for standardised-test vocabulary.Bonding & ReactionsIonic vs covalent bonding, valence electrons and the five reaction types.US Government & CivicsThe branches plus how a bill becomes law, federalism and the key amendments.Sine and Cosine RulesTrigonometry for triangles that are not right-angled.Sequences and SeriesAdding versus multiplying, and the formulas for each.Systems with Three VariablesEliminating one variable twice to get back to familiar ground.Permutations and CombinationsDoes the order matter? That one question chooses the formula.The Normal DistributionThe bell curve, and the rule that covers almost everything.Electron ConfigurationWhere the electrons actually sit, and why the periodic table is shaped as it is.Why the Trends HappenTwo competing forces explain every periodic trend.Limiting ReactantsWhich ingredient runs out first, and why that decides the yield.The Rhetorical Analysis ParagraphThe shape of a paragraph that analyses persuasion rather than summarising it.SatireRidicule aimed at a target, and the two traditions it comes in.Standardised Test StrategyHow to spend the time, and when guessing is correct.Interest, Debt and CompoundingThe maths behind loans and savings โ the same formula pointing two ways.Writing a Personal StatementWhat admissions readers actually look for, and the openings to avoid.Radical EquationsSquaring both sides solves it โ and can invent answers that do not work.Inverse FunctionsUndoing a function, and the graph symmetry that reveals it.Piecewise FunctionsDifferent rules on different intervals, and where the graph breaks.Volume and Surface Area of SolidsThe formulas a geometry paper assumes you have.Angles in PolygonsTwo formulas that handle any polygon, however many sides.Energy in ReactionsExothermic and endothermic, and the bond-energy explanation.Solutions and ConcentrationThe vocabulary, and the formula that turns it into numbers.Carbon CompoundsWhy carbon builds more compounds than every other element combined.Logical FallaciesEight bad arguments that sound convincing until you name them.