[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-266410-105":59,"doc-detail-266410-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","the-ultimate-digital-sat-math-cheat-sheet-algebra-functions-quick-guide","The Ultimate Digital SAT Math Cheat Sheet - Algebra & Functions Quick Guide","","Digital SAT Math cheat sheet compiling high-yield formulas and decision rules across algebra, linear models, inequalities, quadratics, and key exponent/radical/function transformations. Covers slope-intercept and standard forms, line systems and solution conditions, inequality graphing with absolute value and compound logic, and interpreting intercepts, rate of change, constraints, residuals, and correlation without causation. Includes quadratic representations, factoring and discriminant real-root checks, completing the square, and exponent/radical/function rule shortcuts for rapid equation solving and model selection.",{"@graph":69,"@context":122},[70,84,105],{"@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/the-ultimate-digital-sat-math-cheat-sheet-algebra-functions-quick-guide/266410/",{"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/the-ultimate-digital-sat-math-cheat-sheet-algebra-functions-quick-guide/266410.png","ImageObject",300,407,{"name":92,"@type":93},"Xiajie","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":56},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find slope and intercept in different linear equation forms?","Question",{"text":112,"@type":113},"Use slope-intercept form y=mx+b where m is slope and b is the y-intercept. In standard form Ax+By=C, slope is −A/B and intercepts are x-int=C/A and y-int=C/B.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the fastest way to determine the number of solutions for a system of linear equations?",{"text":117,"@type":113},"For parallel lines (same slope, different y-intercepts) there are no solutions; for the same line there are infinite solutions; when slopes differ the lines intersect at exactly one solution. For word problems, define variables, write two equations, then solve.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you decide how many real roots a quadratic has using the discriminant?",{"text":121,"@type":113},"Compute b²−4ac: if it’s greater than 0 there are 2 real roots; if it equals 0 there is 1 repeated root; if less than 0 there are 0 real roots (complex). This also helps answer how many x-intercepts exist.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},266410,1789407127,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":56,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":81},8814010472675,"https://avatar.qwps.com/avatar/WGlhamll","[The Ultimate Digital SAT Math Cheat Sheet](The Ultimate Digital SAT Math Cheat Sheet www.albert.io)[ www.albert.io](The Ultimate Digital SAT Math Cheat Sheet www.albert.io)  \n\n| Linear Equations & Inequalities (Algebra 35%) |\n| --- |\n| Slope-Intercept & Standard Form |\n| y = mx + b: m = slope (rise/run) , b = y-int. To graph → plot b, use m to find 2nd pt.\u003Cbr>Standard form: Ax + By = C. Slope = −A/B. x-int = C/A, y-int = C/B.\u003Cbr>Slope formula: m = (y₂ − y₁)/(x₂ − x₁) . Undefined when x₁ = x₂(vertical line) .\u003Cbr>Parallel lines: same slope, diff. y-int. Perpendicular: slopes areneg. reciprocals (m₁ · m₂ = −1) .\u003Cbr>Point-slope form: y − y₁ = m(x − x₁) . Use when given slope + 1 point. Convert to slope-int for final answer.\u003Cbr>Horizontal line: y = k (slope 0) . Vertical line: x = k (undefined slope) . Know the difference.\u003Cbr>Systems of Linear Equations |\n| Substitution: isolate 1 var → plug into other eq. Elimination: multiply to match coeffs → add/subtract. |\n| \\# Solutions Condition Graph |\n| One Diff. slopes Lines cross |\n| None Same slope, diff b Parallel |\n| Infinite Same line (a=kb) Overlap |\n| System word problems: define vars → write 2 eqs → solve. Total eq + value eq pattern common.\u003Cbr>Inequalities & Absolute Value |\n| Flip inequality sign when ×/÷ by neg. number. |x| \u003C a → −a \u003C x \u003C a. |x| > a → x \u003C −a or x > a.\u003Cbr>Compound inequalities: \"and\" = overlap (intersection) , \"or\" = union. Graph on \\# line to visualize.\u003Cbr>System of inequalities: graph each → solution = shaded overlap region. Test a point to check which side to shade. |\n| \u003Cbr>⚠ Trap: \"at most\" = ≤ , \"at least\" = ≥ , \"fewer than\" = \u003C , \"more than\" = > . Read inequality words carefully.\u003Cbr>✓ For systems w/ no solution: set slopes equal & show y-ints differ. Saves time vs. full solve. |\n\n\n| Linear Functions & Graphs |\n| --- |\n| Interpreting Linear Models |\n| Slope = rate of change. In context: \"for each additional [x-unit],[y] changes by m [y-units] .\"\u003Cbr>y-intercept = initial value (when x = 0) . In context: \"when [x] is 0 , [y] is b.\"\u003Cbr>x-intercept: set y = 0 → solve. In context: \"[y] reaches 0 when [x]= value.\"\u003Cbr>Building Equations from Context |\n| Fixed cost + variable cost pattern: y = (rate)(x) + (start) . E.g. , $50 + $12/hr → y = 12x + 50.\u003Cbr>Two points given → find slope first → plug one pt into y = mx + b → solve for b.\u003Cbr>Table of values → check constant Δy/Δx. If constant → linear; write eq. from any row.\u003Cbr>Domain, Range & Constraints |\n| Real-world constraints: x ≥ 0 (can't have neg. items) , y ≥ 0 (can't have neg. cost) . Domain/range match context.\u003Cbr>Discrete vs. continuous: \\# of people = integers only.\u003Cbr>Time/distance = continuous (any value) .\u003Cbr>Scatterplots & Line of Best Fit |\n| Line of best fit ≈ trend. Use eq. to predict (interpolate inside data, extrapolate outside) . Extrapolation = less reliable.\u003Cbr>Residual = actual − predicted. Pos. residual → model underestimates. Neg. → overestimates.\u003Cbr>r (correlation coeff.): −1 ≤ r ≤ 1. Closer to ±1 → stronger linear relationship. r = 0 → no linear trend.\u003Cbr>Non-linear patterns: if residual plot shows curve → linear model is wrong. Try quadratic or exponential. |\n| ✓ When asked \"what does the slope represent?\", always answer in context w/ units: \"per [x-unit], [y] changes by [m] .\" |\n| ⚠ Correlation ≠ causation. Even r = 0.99 doesn't prove X causes Y —could be confounding variable. |\n\n\n| Quadratics & Polynomials (Adv. Math 35%) |\n| --- |\n| Three Forms of Quadratics |\n|  |\n| Form Equation Reveals |\n| Standard ax² + bx + c y-int = c, opens ↑(a>0)/↓(a\u003C0) |\n| Vertex a(x−h)² + k Vertex (h, k) , axis x=h |\n| Factored a(x−r₁)(x−r₂) Roots r₁ , r₂ (x-ints) |\n| Vertex from standard: x = −b/(2a) , plug back for y. Axis of\u003Cbr>symmetry: x = −b/(2a) .\u003Cbr>Solving Quadratics |\n| Factoring: find two \\#s that multiply to ac & add to b. Zero\u003Cbr>product: if ab = 0 → a = 0 or b = 0.\u003Cbr>Quadratic formula: x = (−b ± √(b²−4ac)) / 2a. Discriminant = b²−4ac. Sum & product of roots: For ax2+bx+c=0 , the sum of the roots is −b/a ","cbCaiol3EsAxXfbX","https://ap.wps.com/l/cbCaiol3EsAxXfbX","pdf",202305,"English","# Linear Equations & Inequalities (Algebra 35%)\n## Slope-Intercept & Standard Form\n## Systems of Linear Equations\n## Inequalities & Absolute Value\n# Linear Functions & Graphs\n## Interpreting Linear Models\n## Building Equations from Context\n## Domain, Range & Constraints\n## Scatterplots & Line of Best Fit\n# Quadratics & Polynomials (Adv. Math 35%)\n## Three Forms of Quadratics\n## Solving Quadratics\n# Advanced Math: Exponents, Radicals & Functions\n## Exponent Rules\n## Radicals\n## Function Notation & Transformations","[{\"question\":\"How do you find slope and intercept in different linear equation forms?\",\"answer\":\"Use slope-intercept form y=mx+b where m is slope and b is the y-intercept. In standard form Ax+By=C, slope is −A/B and intercepts are x-int=C/A and y-int=C/B.\"},{\"question\":\"What is the fastest way to determine the number of solutions for a system of linear equations?\",\"answer\":\"For parallel lines (same slope, different y-intercepts) there are no solutions; for the same line there are infinite solutions; when slopes differ the lines intersect at exactly one solution. For word problems, define variables, write two equations, then solve.\"},{\"question\":\"How do you decide how many real roots a quadratic has using the discriminant?\",\"answer\":\"Compute b²−4ac: if it’s greater than 0 there are 2 real roots; if it equals 0 there is 1 repeated root; if less than 0 there are 0 real roots (complex). This also helps answer how many x-intercepts exist.\"}]","The Ultimate Digital SAT Math Cheat Sheet - Algebra & Functions Quick Guide | PDF"]