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Quadratics & PolynomialsCompleting the square, vertex form, the factoring patterns and…10th GradeCOMPLETING THE SQUAREx² + 6x + 5 = 01. Move the constant: x² + 6x = −52. Add (b/2)² = 9 to both sides: x² + 6x + 9 = 43. Factor: (x + 3)² = 4 → x + 3 = ±2 → x = −1 or −5VERTEX FORMy = a(x − h)² + k → vertex (h, k)a > 0 opens up (minimum). a < 0 opens down (maximum).From standard form, the axis of symmetry is x = −b / 2a. Substitute to get k.FACTORING PATTERNSDifference of squaresa² − b² = (a + b)(a − b)x² − 16 = (x+4)(x−4)Perfect square trinomiala² ± 2ab + b² = (a ± b)²x² + 10x + 25 = (x+5)²Sum of cubesa³ + b³ = (a+b)(a² − ab + b²)x³ + 8Difference of cubesa³ − b³ = (a−b)(a² + ab + b²)x³ − 27Groupingax + ay + bx + by = (a+b)(x+y)four termsEnd behaviour: even degree → both ends together. Odd degree → ends opposite.Leading coefficient positive → right end rises.Quadratics & Polynomialslittleactivity.com

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Math · 10th Grade

Quadratics & Polynomials

Completing the square, vertex form, the factoring patterns and end behaviour.

How to use it

Vertex form tells you the graph. Standard form tells you the y-intercept.

Free · print-ready PDF · US Letter and A4

Grade
10th Grade
Ages
15–16
Subject
Math
Pages
1

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Right-Triangle Trig

The rest of the 10th Grade wall

7 more posters, all free to print.

Right-Triangle TrigSOH-CAH-TOA, the special triangles, and the unit circle in one…10th GradeSOH · CAH · TOAθadjacentoppositehypotenusesin θ = opp / hypcos θ = adj / hyptan θ = opp / adjName opposite, adjacent and hypotenuse relative to θ before you choose a ratio.THE SPECIAL TRIANGLES11√245°45–45–90 → 1 : 1 : √2√31230°30–60–90 → 1 : √3 : 2EXACT VALUESθ0°30°45°60°90°sin01/2√2/2√3/21cos1√3/2√2/21/20tan0√3/31√3—Missing an angle? Use the inverse: θ = sin⁻¹(opp/hyp).Not a right triangle? Law of sines a/sin A = b/sin B · Law of cosines c² = a² + b² − 2ab·cos CRight-Triangle Triglittleactivity.com
Math

Right-Triangle Trig

SOH-CAH-TOA, the special triangles, and the unit circle in one place.

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Coordinate GeometryDistance, midpoint, slope proofs and circle equations on the…10th Grade(x₁, y₁)(x₂, y₂)Distanced = √[(x₂−x₁)² + (y₂−y₁)²]MidpointM = ( (x₁+x₂)/2 , (y₁+y₂)/2 )Slopem = (y₂−y₁) / (x₂−x₁)Circle(x−h)² + (y−k)² = r²LINE RELATIONSHIPSParallelslopes are equalm₁ = m₂Perpendicularslopes are negative reciprocalsm₁ × m₂ = −1Collinearsame slope between every pair of pointsno trianglePROVING A SHAPE ON THE GRIDParallelogramboth pairs of opposite sides have equal slopesRectangleparallelogram + one pair of adjacent slopes multiply to −1Rhombusparallelogram + all four side lengths equalSquarerhombus + one right angleIsosceles triangletwo distances equalCoordinate Geometrylittleactivity.com
Math

Coordinate Geometry

Distance, midpoint, slope proofs and circle equations on the plane.

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Function TransformationsHow a, h and k move any parent graph, with the inside/outside…10th GradeTHE GENERAL FORMg(x) = a · f( b(x − h) ) + kOutside the bracket affects y and does what it says. Inside affects x and does the opposite.k > 0shift UP k unitsoutside — verticalk < 0shift DOWN |k| unitsoutside — verticalh > 0shift RIGHT h unitsinside — horizontal, reversedh < 0shift LEFT |h| unitsinside — horizontal, reversed|a| > 1vertical STRETCHtaller and thinner0 < |a| < 1vertical SHRINKshorter and widera < 0reflect over the x-axisflips upside downb < 0reflect over the y-axisflips left–rightWORKED — f(x) = x²g(x) = −2(x − 3)² + 5Reflected over the x-axis, stretched by 2, right 3, up 5. Vertex at (3, 5), opening down.Read the transformations in that order and the graph draws itself.Function Transformationslittleactivity.com
Math

Function Transformations

How a, h and k move any parent graph, with the inside/outside rule.

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Rhetorical AnalysisEthos, pathos, logos, the SOAPSTone frame and the analysis…10th GradeTHE THREE APPEALSETHOSCredibilityQualifications, fairness, shared values, careful tone.PATHOSEmotionStory, vivid image, loaded diction, appeal to fear or hope.LOGOSLogicData, cause and effect, concession, structured reasoning.SOAPSTone — read the text before you judge itSSpeakerWho is talking, and what do they want?OOccasionWhat moment prompted this?AAudienceWho is meant to hear it?PPurposeWhat should the audience do or believe?SSubjectIn one sentence.ToneAttitudeNamed with a precise adjective, not “negative”.ANALYSIS SENTENCEBy [device], the writer [verb: undercuts, magnifies, reassures] theaudience, so that [effect on their belief or feeling].Rhetorical Analysislittleactivity.com
Literacy

Rhetorical Analysis

Ethos, pathos, logos, the SOAPSTone frame and the analysis paragraph shape.

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SAT Word RootsThirty-six high-yield roots for standardised-test vocabulary.10th GradeOne root unlocks a dozen words. Learn the root, then collect the family.acrsharp, bitteracrid, acrimonyali / alterotheralias, alternativebelliwarbelligerent, rebelcandglowing, whitecandid, incandescentcarnfleshcarnivore, incarnatecir / circumaroundcircumventclamshoutclamour, proclaimculpblameculprit, culpabledignworthydignity, indignantdoc / doctteachdoctrine, indoctrinatedurhard, lastingendure, durableegoselfegotist, egocentricerrwandererratic, erroneouseugood, welleuphoria, eulogyfall / falsdeceivefallacy, falsifygratpleasinggratitude, ingratiategregherd, groupgregarious, segregateheterodifferentheterogeneoushomosamehomogeneous, homonymjectthrowconjecture, dejectedlaudpraiselaudable, laudatoryloqu / locuspeakeloquent, loquaciousluclightelucidate, lucidmutchangemutation, immutablenegdenynegate, renegepacpeacepacify, pacifistple / plenfullreplete, plenaryprobtest, proveprobity, reprobatepunctpointpunctual, punctuatequer / quisask, seekquery, inquisitivesanctholysanctuary, sanctifysomnsleepinsomnia, somnolenttac / ticsilenttaciturn, reticentten / tainholdtenacious, retainven / ventcomeconvene, intervenevoreat greedilyvoracious, carnivoreON A TESTSplit the unknown word, translate each part, then check it against the sentence.SAT Word Rootslittleactivity.com
Literacy

SAT Word Roots

Thirty-six high-yield roots for standardised-test vocabulary.

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Bonding & ReactionsIonic vs covalent bonding, valence electrons and the five…10th GradeIONIC — electrons transferredNa⁺Cl⁻Metal + non-metal. One gives, one takes.High melting point; conducts when dissolved.COVALENT — electrons sharedHHNon-metal + non-metal. Both pull, neither wins.Lower melting point; usually does not conduct.VALENCE ELECTRONS BY GROUPGroup 11 valence e⁻loses 1 → +1Group 22 valence e⁻loses 2 → +2Group 133 valence e⁻loses 3 → +3Group 144 valence e⁻shares 4Group 155 valence e⁻gains 3 → −3Group 166 valence e⁻gains 2 → −2Group 177 valence e⁻gains 1 → −1Group 188 valence e⁻full — unreactiveTHE FIVE REACTION TYPESSynthesisA + B → AB2H₂ + O₂ → 2H₂ODecompositionAB → A + B2H₂O₂ → 2H₂O + O₂Single replacementA + BC → AC + BZn + 2HCl → ZnCl₂ + H₂Double replacementAB + CD → AD + CBAgNO₃ + NaCl → AgCl + NaNO₃Combustionfuel + O₂ → CO₂ + H₂OCH₄ + 2O₂ → CO₂ + 2H₂OMass is conserved — the same atoms must appear on both sides.Bonding & Reactionslittleactivity.com
Science

Bonding & Reactions

Ionic vs covalent bonding, valence electrons and the five reaction types.

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US Government & CivicsThe branches plus how a bill becomes law, federalism and the…10th GradeLEGISLATIVECongressMakes the lawsEXECUTIVEPresidentCarries out the lawsJUDICIALSupreme CourtInterprets the lawsHOW A BILL BECOMES A LAW1A bill is introduced in the House or the Senate.2Committee studies it, amends it, and votes to send it on — or kills it.3The full chamber debates and votes. A simple majority passes it.4The other chamber repeats the process; differences go to a conference committee.5The President signs it, vetoes it, or lets it become law unsigned after 10 days.6Congress can override a veto with a two-thirds vote in both chambers.FEDERALISMFederal onlycurrency · treaties · war · postState onlyschools · licences · electionsSharedtaxes · courts · roadsAMENDMENTS TO KNOW1stspeech, religion, press, assembly4thno unreasonable searches5thdue process, no self-incrimination13thabolished slavery14thequal protection, citizenship19thwomen's right to voteUS Government & Civicslittleactivity.com
Social Studies

US Government & Civics

The branches plus how a bill becomes law, federalism and the key amendments.

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