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It covers factoring methods such as greatest common factor, difference of two perfect squares, and trinomial factoring, plus percent increase/decrease and arithmetic sequences. It includes radical operations (multiplication, division with rationalizing, and combining like radicals), triangle inequality, tangent properties, exterior angle sums, and motion problems using distance = rate × time. It also summarizes work-rate, investment/interest, coin problems, simultaneous equations, and permutation/combination definitions along with key geometry formulas like volume, surface area, slope, distance, and the quadratic formula.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/shsat-math-reference-sheet-quick-study-guide/274488/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/shsat-math-reference-sheet-quick-study-guide/274488.png","ImageObject",300,407,{"name":92,"@type":93},"Asher","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",31,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you factor out the greatest common factor (GCF) on this sheet?","Question",{"text":113,"@type":114},"Identify a common factor present in every term, then factor it out to create an equivalent expression. The remaining terms stay inside parentheses as a simplified polynomial.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are the rules for multiplying and dividing radicals here?",{"text":118,"@type":114},"For multiplication, multiply the coefficients and the radicands under the radical signs, then simplify. For division, rationalize the denominator by multiplying by an appropriate form of the radical.",{"name":120,"@type":111,"acceptedAnswer":121},"Which formulas and steps are provided for rate and work problems?",{"text":122,"@type":114},"Use distance = rate × time for motion. For combined work, add the individual rates and set up a proportion using the time variable, then solve with a common denominator and cross-multiplication.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},274488,1789477978,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":52},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","SHSAT Math Reference Sheet  \nFactor Completely:  \n1) Greatest Common Factor: Ex. (7x3 – 14x2 – 49x) GCFis 7x. A common factor to all terms of a polynomial can be factored out. All 3 terms contain a factor of 7x. Pulling out the GCF creates a new equivalent expression 7x(x2 – 2x – 7)  \n2) Difference of Two Perfect Squares: Anything in the form (a2 – b2 ) = (a+b)(a-b)  \n3) Factoring Trinomials: To factor a polynomial in the form y=ax2 +bx + c you need to find two binomials that would multiply together to create the polynomial. Consider factors of c that add to the b term. Ex. x2 + 7x + 12, consider factor pairs of the c term “12” that will add to the b term “7”. The only way to get a leading term of x2 is when you multiply x by x. The factor pair of 12 that adds to 7 would be 3 and 4. (x + 3) (x+4)  \nPercent Increase or Decrease  \n􀮺􀯠􀯢􀯨􀯡􀯧 􀯢􀯙 􀯖ℎ􀯔􀯡􀯚􀯘  \n( ) x 100  \n􀯈􀯥􀯜􀯚􀯜􀯡􀯔􀯟  \nArithmetic Sequences:  \nRadicals:  \nMultiplying Radicals: Mutliply the coefficients of the radicals, muliply the radicands or the expressions under the radical sign and simplify.  \nDividing by a radical: When you divide by a radical, you must rationalize the denominator, by multiplying the expression by radical 7 over radical 7.  \n2 times radical seven =  2 radical seven  \nradical seven times radical seven = 7  \nAdd or Subtracting Radicals, can only be done when theradicand or the number under the radical is the same number.  \nTriangle Inequality Theorem: a + b > c > b – a  \nwhere a = smallest side, b= medium side, c=largest side of a triangle  \nA tangent to a circle is s a line in the plane of the circle that intersects the circle in exactly one point.  \n*If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency (forms a 90 degree \u003C)  \nA measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.  \nMotion Problems:  \ndistance = rate x time  \nEx. A passenger train and a freight train leave at 10:30 AM from stations that are 405 miles apart and travel toward each other. The rate of the passenger train is 45 miles per hour faster than that of the freight train. If they pass each other at 1:30 PM, how fast was the passenger train travelling? Set up this chart:  \nRate Time Distance  \n3x + 135 + 3x = 405 x = 45, passenger train travels at 90mph.  \nConsecutive Integer Problems:  \nLet the x= 1st consecutive integer x + 1= 2ndconsecutive integer  \nx + 2= 3rd consecutive integer If it says consecutive odd/even integers Set up your legend as: x, x +2, x+4 etc  \nCombined Rate Problems:  \nAngelica can mow one lawn in 30 minutes. Lawrence can mow the same lawn in 40 minutes. If they mow the lawn together, how long will it take them to complete the task?  \nAngelica’s rate is 1 lawn .  \n30min  \nLawrence’s rate is 1 lawn .  \n40min  \nSince they are working together, add their rates and then create a proportion.  \n1 lawn + 1 lawn = 1 lawn  \n30min 40 min x minutes  \nSolve by getting a common denominator and then cross  \n\n| Investment Problems: Principle x Rate = Interest Income |\n| --- |\n| Solve Coin Problems: with the Substitution Method of Simultaneous Equations. A postal clerk sold 40 stamps for $5.40. Some were ten cent stamps and others were fifteen cent stamps. Set up your equations. Let x= the \\# of 15 cent stamps and Let y= \\# of 10 cent stamps, therefore x + y = 40 and the second equation attaches value; 15x + 10y = 540 (use whole numbers) |\n| Solving Simultaneous Equations: (Systems of Equations)\u003Cbr>1) Addition or Subtraction (Elimination): Add or Subtract both equations in order to cancel out a variable. Solve for the variable that’s left and then substitute to find the other.\u003Cbr>2) Substitution Method: Solve one of the equations for one variable, and substitute it into the other equation. |\n| Permutation and Combination\u003Cbr>\u003Cbr>A permutation is an ordered arrangement of Distinct objects in a sequence.\u003Cbr>A combination is an unordered collection of unique elements. 2 lis","cbCaid2ENDImgwVt","https://ap.wps.com/l/cbCaid2ENDImgwVt","pdf",530471,"English","# Factor Completely\n## Greatest Common Factor and Difference of Two Perfect Squares\n## Factoring Trinomials and Percents\n\n# Arithmetic, Radicals, and Sequences\n## Multiplying and Dividing Radicals\n## Adding/Subtracting Like Radicals\n## Arithmetic Sequences\n\n# Geometry and Trigonometry Basics\n## Triangle Inequality Theorem\n## Tangent to a Circle and Exterior Angles\n## Triangle and Polygon Angle Relationships\n## Slope, Distance, Midpoint\n## Special Right Triangles and Trig Ratios\n\n# Algebra Tools and Word Problems\n## Motion Problems\n## Consecutive Integer and Combined Rate Problems\n## Investment and Coin Problems\n## Simultaneous Equations (Elimination/Substitution)\n## Permutation and Combination","[{\"question\":\"How do you factor out the greatest common factor (GCF) on this sheet?\",\"answer\":\"Identify a common factor present in every term, then factor it out to create an equivalent expression. The remaining terms stay inside parentheses as a simplified polynomial.\"},{\"question\":\"What are the rules for multiplying and dividing radicals here?\",\"answer\":\"For multiplication, multiply the coefficients and the radicands under the radical signs, then simplify. For division, rationalize the denominator by multiplying by an appropriate form of the radical.\"},{\"question\":\"Which formulas and steps are provided for rate and work problems?\",\"answer\":\"Use distance = rate × time for motion. For combined work, add the individual rates and set up a proportion using the time variable, then solve with a common denominator and cross-multiplication.\"}]","SHSAT Math Reference Sheet - quick study guide | PDF"]