ACT Math Flash Cards - PowerScore

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integerAny number in the set of positive and negative wholenumbers and zero:setA collection of numbers marked by brackets:{4, 6, 9, 13}{ –4, –3, –2, –1, 0, 1, 2, 3, 4 } Integers do not include fractions or decimals Integers are the most commonly used numbers onthe ACT It is important to remember that 0 is an integerFor more flash cards, visit PowerScore.com Copyright 2012 Sets can contain any amount of numbers Sets may have rules, such as “all even integers”For more flash cards, visit PowerScore.com Copyright 2012sumdigitThe numbers 0 through 9:{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}The amount obtained by adding numbers The sum of 2, 3, and 4 is 9: (2 3 4 9) The sum of x and y is x y Place is used to represent where in a number a digitoccurs The ones digit or units digit in 3748 is 8 The tens digit in 3748 is 4 The hundreds digit in 3748 is 7For more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012productThe amount obtained by multiplying numbers The product of 2, 3, and 4 is 24: (2 3 4 24) The product of x and y is xyFor more flash cards, visit PowerScore.com Copyright 2012multipleAn integer that is divisible by another integer withouta remainder Multiples of 3 include {–6, –3, 3, 6, 9, 12} Multiples of 4 include {–8, –4, 4, 8, 12, 16}For more flash cards, visit PowerScore.com Copyright 2012

DEFINITIONDEFINITIONsetintegerPowerScore ACT Mathematics Score ACT Mathematics NDEFINITIONmultipleproductPowerScore ACT Mathematics rScore ACT Mathematics Flashcards(800)545-1750PowerScore ACT Mathematics Flashcardswww.powerscore.comPowerScore ACT Mathematics Flashcards(800)545-1750www.powerscore.com

divisiblefactorDescribes a number capable of being divided withouta remainder. A number that is divisible by x is alsosaid to be a multiple of x.One of two or more numbers that divides into a largernumber without a remainder 18 is divisible by 1, 2, 3, 6, 9, and 18 xy is divisible by 1, x, y, and xyFor more flash cards, visit PowerScore.com Copyright 201210 prime numbers{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, .}Additional prime numbers under 100:{31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}For more flash cards, visit PowerScore.com Copyright 2012prime factorPrime numbers that divide into a larger numberwithout a remainder Factors of 18 are 1 and 18, 2 and 9, and 3 and 6;the prime factors are 2 and 3For more flash cards, visit PowerScore.com Copyright 2012 Factors of 18 are 1 and 18, 2 and 9, and 3 and 6 Factors of xy include 1 and xy, plus x and yFor more flash cards, visit PowerScore.com Copyright 2012prime numberAn integer that does not have any factors besidesitself and 1{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, .} One (1) is not a prime number When prime numbers are multiplied together, theproduct’s factors are limited to itself, one, and theprime numbers themselvesFor more flash cards, visit PowerScore.com Copyright 2012common factorA factor shared by two numbers Factors of 18 are 1 and 18, 2 and 9, and 3 and 6. Factors of 15 are 1 and 15 and 3 and 5. The common factors of 15 and 18 are 1 and 3.For more flash cards, visit PowerScore.com Copyright 2012

DEFINITIONDEFINITIONfactordivisiblePowerScore ACT Mathematics e ACT Mathematics NARITHMETICprime numberWhat are the first10 prime numbers?PowerScore ACT Mathematics e ACT Mathematics NDEFINITIONcommon factorprime factorPowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

Rules of Divisibility2: If the last digit of a number is even, it is a multiple of 2.3: If the sum of the digits is divisible by 3, the entireinteger is a multiple of 3.4: If the last two digits are a multiple of 4, the entirenumber is a multiple of 4.5: If the last digit ends in 0 or 5, the entire number isdivisible by 5.6: If the number is both divisible by 2 and 3, it is divisibleby 6.9: If the sum of the digits is divisible by 9, the entireinteger is a multiple of 9For more flash cards, visit PowerScore.com Copyright 2012Fraction Equivalent0.125For more flash cards, visit PowerScore.com Copyright 2012Fraction EquivalentAddition of Integerseven even evenodd odd evenodd even oddpositive positive positivenegative negative negativepositive negative can be eitherFor more flash cards, visit PowerScore.com Copyright 2012Multiplication of Integerseven even evenodd odd oddodd even evenpositive positive positivenegative negative positivepositive negative negativeFor more flash cards, visit PowerScore.com Copyright 2012Fraction Equivalent0.166For more flash cards, visit PowerScore.com Copyright 20120.2For more flash cards, visit PowerScore.com Copyright 2012

ARITHMETICS H O RT C U TAddition of IntegersRules of Divisibilityeven even odd odd odd even positive positive negative negative positive negative PowerScore ACT Mathematics CPowerScore ACT Mathematics Flashcards(800)545-1750www.powerscore.comD E C I M A L E Q U I VA L E N TMultiplication of Integers18even even odd odd odd even positive positive negative negative positive negative PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comD E C I M A L E Q U I VA L E N TD E C I M A L E Q U I VA L E N T1516PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

Fraction EquivalentFraction Equivalent0.25For more flash cards, visit PowerScore.com Copyright 2012Fraction Equivalent0.33For more flash cards, visit PowerScore.com Copyright 2012Fraction Equivalent0.5For more flash cards, visit PowerScore.com Copyright 2012Fraction Equivalent0.4For more flash cards, visit PowerScore.com Copyright 2012Fraction Equivalent0.66For more flash cards, visit PowerScore.com Copyright 20120.75For more flash cards, visit PowerScore.com Copyright 2012

D E C I M A L E Q U I VA L E N TD E C I M A L E Q U I VA L E N T1314PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comD E C I M A L E Q U I VA L E N TD E C I M A L E Q U I VA L E N T2512PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comD E C I M A L E Q U I VA L E N TD E C I M A L E Q U I VA L E N T3423PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

rate formulawhat percent?x100dr tr rated distanceor?100t timeFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012average rate of speedcombined work2 rate1 rate 2rate1 rate 21 1 1 1 t1 t2 t3 tTt1 time of first persont2 time of second persont3 time of third persontT time togetherFor more flash cards, visit PowerScore.com Copyright 2012plus, more than, added to,increased by, sum For more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012what? what number?x, n, ?, orother variableFor more flash cards, visit PowerScore.com Copyright 2012

T R A N S L AT EW O R K A N D R AT E SHow do you represent thephrase “what percent”?What is therate formula?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comW O R k A N D R AT E SW O R k A N D R AT E SWhat is the formula forcombined work problems?What is the formulafor average rate of speed?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750T R A N S L AT ET R A N S L AT EHow do you represent“what” or “what number?”PowerScore ACT Mathematics score.comHow do you represent“plus,” “more than,”“added to,” “increased by,”and “sum?”PowerScore ACT Mathematics Flashcards(800)545-1750www.powerscore.com

minus, less than, subtracted from,decreased by, reduced by, differenceof, times, product– (minus sign)(multiplication sign)For more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012per, out of, quotientis, equals, result (division sign)(equals sign)For more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 201290º angle60º angle60º90ºFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012

T R A N S L AT ET R A N S L AT EHow do you represent “of,”“times,” or “product?”How do you represent“minus,” “less than,”“subtracted from,”“decreased by,” “reducedby,” and “difference?”PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comT R A N S L AT ET R A N S L AT EHow do you represent “is,” How do you represent “per,”“out of,” or “quotient?”“equals,” or “result?”PowerScore ACT Mathematics e ACT Mathematics SBENCHMARKSIllustrate a 60º angle.Illustrate a 90º angle.PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

45º angle30º angle45ºFor more flash cards, visit PowerScore.com Copyright 201230ºFor more flash cards, visit PowerScore.com Copyright 2012divide by same basemultiply by same basexn xm xn–m(xn)(xm) xn mFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012multiply by same powerdivide by same power(xn)(yn) (xy)nxn yn (x y)nFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012

BENCHMARKSBENCHMARKSIllustrate a 30º angle.Illustrate a 45º angle.PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comEXPONENTS AND ROOTSEXPONENTS AND ROOTSMultiplication ofthe same base:Division ofthe same base:xn xm(xn)(xm)PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comEXPONENTS AND ROOTSEXPONENTS AND ROOTSDivision withthe same power:Multiplication withthe same power:xn yn(xn)(yn)PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

base–negativebase01nx130 1 and x0 1For more flash cards, visit PowerScore.com Copyright 2012single base with powersFor more flash cards, visit PowerScore.com Copyright 2012fractional exponentsnmn mn m(x ) xx xxFor more flash cards, visit PowerScore.com Copyright 2012powerrootmn root x powerFor more flash cards, visit PowerScore.com Copyright 2012classic form #2classic form #1(x y)2 x2 2xy y2(x y)(x – y) x2 – y2Examples:(t 5)2 t2 2(t)(5) 52 t2 10t 25(3a b)(3a b) 9a2 6ab b2y2 16y 64 y2 2(y)(8) 82 (y 8)236 12n n2 62 2(n)(6) n2 (6 n)2For more flash cards, visit PowerScore.com Copyright 2012Examples:(t – 5)(t 5) t2 – 52 t2 – 25(3a b)(3a – b) (3a)2 – b2 9a2 – b2y2 – 64 y2 – 82 (y 8)(y – 8)36 – n2 362 – n2 (6 n)(6 – n)For more flash cards, visit PowerScore.com Copyright 2012

EXPONENTS AND ROOTSEXPONENTS AND ROOTSWhen a base is raised to thepower of 0, what is the result?x–nFor example, what is 30 or x0?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comEXPONENTS AND ROOTSEXPONENTS AND ROOTSFractional exponents:Multiplication of a singlebase with multiple powers:xnmPowerScore ACT Mathematics rScore ACT Mathematics Flashcards(800)545-1750www.powerscore.comC L A S S I C Q U A D R AT I C F O R MC L A S S I C Q U A D R AT I C F O R M(x y)(x – y) (x y)2 PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

classic form #3direct variation(x – y)2 x2 – 2xy y2y cxExamples:(t – 5)2 t2 – 2(t)(5) 52 t2 – 10t 25(3a – b)(3a – b) 9a2 – 6ab b2y2 – 16y 64 y2 – 2(y)(8) 82 (y – 8)236 – 12n n2 62 – 2(n)(6) n2 (6 – n)2For more flash cards, visit PowerScore.com Copyright 2012area of a circleFor more flash cards, visit PowerScore.com Copyright 2012indirect variationA r2c xyrFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012circumference of a circlearea of a rectangleC 2 rA lwlrFor more flash cards, visit PowerScore.com Copyright 2012wFor more flash cards, visit PowerScore.com Copyright 2012

D I R E C T VA R I AT I O NC L A S S I C Q U A D R AT I C F O R MWhat is the formulafor direct variation?(x – y)2 PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comI N D I R E C T VA R I AT I O NCIRCLESWhat is the formulafor indirect variation?What is the formula for thearea of a circle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comQ U A D R I L AT E R A L SCIRCLESWhat is the formula forthe area of a rectangle?What is the formula for thecircumference of a circle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

area of a trianglevolume of a rectangular solid1bh2A V lwhhhwlbFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012volume of a cylinderPythagorean TheoremV r2ha2 b2 c2rhcbaFor more flash cards, visit PowerScore.com Copyright 201230º:60º:90º triangle2xFor more flash cards, visit PowerScore.com Copyright 201245º:45º:90º triangle60º x30ºx 3For more flash cards, visit PowerScore.com Copyright 2012s 2s 45ºs45ºFor more flash cards, visit PowerScore.com Copyright 2012

SOLIDSTRIANGLESWhat is the formulafor the volume of arectangular solid?What is the formula for thearea of a triangle?PowerScore ACT Mathematics e ACT Mathematics SOLIDSWhat is thePythagorean Theorem?What is the formulafor the volume of a rightcircular cylinder?PowerScore ACT Mathematics e ACT Mathematics TRIANGLESWhat are the assignedside ratios in a45º:45º:90º triangle?What are the assignedside ratios in a30º:60º:90º triangle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

degrees of arc in a circlesum of the angles in a triangle180º360ºx 35 50 x 50 35 180 For more flash cards, visit PowerScore.com Copyright 2012intersected parallel linesx 95 For more flash cards, visit PowerScore.com Copyright 2012perpendicular linesright angle21l21m2T12P1l mFor more flash cards, visit PowerScore.com Copyright 2012bisectPR TURUFor more flash cards, visit PowerScore.com Copyright 2012perimeter of a trianglebisect to divide in two equal partsNMx x perimeter s1 s2 s3POFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012

TRIANGLESCIRCLESWhat is the sum of of themeasures in degrees of theangles of a triangle?How many degrees of arcare in a circle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comLINES AND ANGLESLINES AND ANGLESWhat angle is createdby the intersection ofperpendicular lines?What relationship resultswhen two or more parallellines are intersectedby a transversal?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comBASIC TRIANGLESLINES AND ANGLESWhat is the formulafor finding theperimeter of a triangle?What is the definitionof "bisect?"PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

sum of the lengths of 2 sidessum of the angles in a triangleThe sum of the lengths ofany two sides of a triangleis always greater than thelength of the remaining side.180ºFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012Pythagorean Triplessimilar triangles3:4:55 : 12 : 137 : 24 : 258 : 15 : 179 : 40 : 4112 : 35 : 3720 : 21 : 29Triangles that have the exact same shape but differentarea. The corresponding angle measurements of similartriangles are equal, and the corresponding side lengths areproportionate:95 3y3x95 x50 y35 50 35 3zzFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012hidden triangleshidden trianglesTwo 30º:60º:90º triangles arehidden in every equilateral triangle:Two 45º:45º:90º triangles arehidden in every square:6ABA6s 6CD45 30 30 142x 1445 30 45 6x 3 7 360 60 60 x 7For more flash cards, visit PowerScore.com Copyright 2012s 2 6 245 45 D645 s 6CFor more flash cards, visit PowerScore.com Copyright 2012

BASIC TRIANGLESBASIC TRIANGLESWhat is the sum of of themeasures in degrees of theangles of a triangle?The sum of the lengths ofany two sides of a triangleis always greater than.PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comBASIC TRIANGLESSPECIAL TRIANGLESWhat aresimilar triangles?Name the most commonPythagorean Triples.PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comSPECIAL TRIANGLESSPECIAL TRIANGLESWhat is hiddenin a square?What is hidden in anequilateral triangle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

isosceles trianglesequilateral trianglesAn isosceles triangle has two sides of equal lengthand two angles of equal size. The two equal angles areopposite the two equal-length sides:Equilateral triangles have equal side lengths andequal angle measurements. Since the interior anglesof a triangle add up to 180 , the three angles of anequilateral triangle must each equal 60 :40 6104 670 70 660 6x ssx 60 60 sFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012perimeter of a rectanglearea of a squareP 2l 2wA lw or s2lwFor more flash cards, visit PowerScore.com Copyright 2012sFor more flash cards, visit PowerScore.com Copyright 2012area of a parallelogramperimeter of a squareA lhP 4shwslFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012

SPECIAL TRIANGLESBASIC TRIANGLESWhat is anequilateral triangle?What is anisosceles triangle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comQ U A D R I L AT E R A L SQ U A D R I L AT E R A L SWhat is the formula forthe area of a square?What is the formula for theperimeter of a rectangle?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comQ U A D R I L AT E R A L SQ U A D R I L AT E R A L SWhat is the formula forthe perimeter of a square?What is the formulafor the area of aparallelogram?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

regular polygonsinterior angles of a quadrilateralPolygons that have equal side lengths and equalangle measurements are called regular polygons.360º130 50 130 50 Regular PentagonRegular HexagonFor more flash cards, visit PowerScore.com Copyright 201290º 90º 90º 90º 360º50º 130º 50º 130º 360ºFor more flash cards, visit PowerScore.com Copyright 2012interior angles of a hexagoninterior angles of a pentagon720º540º120 120 120 108 108 120 108 120 120 120º 120º 120º 120º 120º 120º 720ºFor more flash cards, visit PowerScore.com Copyright 2012interior angles of a octagon108 108 108º 108º 108º 108º 108º 540ºFor more flash cards, visit PowerScore.com Copyright 2012circumference of a circle1080ºC 2πr135 135 135 135 135 135 r135 135 135º 135º 135º 135º 135º 135º 135º 135º 1080ºFor more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012

P O LY G O N SP O LY G O N SWhat is the sum ofthe interior anglesof a quadrilateral?What is a regular polygon?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comP O LY G O N SP O LY G O N SWhat is the sum ofthe interior angles of apentagon? What is themeasure of each angle in aregular pentagon?What is the sum of theinterior angles of ahexagon? What is themeasure of each angle in aregular hexagon?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.comCIRCLESP O LY G O N SWhat is the formulafor the circumferenceof a circle?What is the sum of theinterior angles of aoctagon? What is themeasure of each angle in aregular octagon?PowerScore ACT Mathematics e ACT Mathematics Flashcards(800)545-1750www.powerscore.com

tangentarea of a circleA πr2A tangent is a line that touches acircle at only one point. A radiusor diameter drawn to that point isperpendicular to the tangent.For more flash cards, visit PowerScore.com Copyright 2012rFor more flash cards, visit PowerScore.com Copyright 2012length of an arcarea of a sectorx The length of an arc (2 r)360 x 2The area of a sector (πr )360For more flash cards, visit PowerScore.com Copyright 2012For more flash cards, visit PowerScore.com Copyright 2012volume of a cubesurface area of a cubeV s3SA 6s2sssssFor more flash cards, visit PowerScore.com Copyright 2012sFor more flash cards, visit Po

PowerScore AC athematics Flashcards (800)545-1750 www.powerscore.com. PowerScore

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