[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207784-en":3,"doc-seo-207784-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207784,1374402524268,"Berry Peter","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",4,"Exam","GCSE MATHS - COMPLETE FORMULA SHEET - Free resource for practising key formulas","GCSE MATHS COMPLETE FORMULA SHEET compiles essential formulas across five maths strands and both tiers (Foundation & Higher, plus Higher-only items) covering number, algebra, ratio, rates of change, geometry and statistics. It provides quick reference rules for fractions, percentages, interest, surds, standard form, indices, sequences and simultaneous equations, alongside core ratio and proportionality methods such as speed, density, pressure and area relationships. Includes exam-board coverage and supports practice with instant AI feedback.","GCSE MATHS  \nCOMPLETE FORMULA SHEET  \nAll 5 Strands · Foundation & Higher · AQA, Edexcel & OCR  \nNUMBER ALGEBRA RATIO & RATES GEOMETRY STATISTICS  \n90+  \nFORMULAS  \n5  \nSTRANDS  \nBoth  \nTIERS  \n3  \nEXAM BOARDS  \nFree  \nRESOURCE  \nF & H  = Foundation & Higher  \n Higher  = Higher tier only  \n[gcsemathsai.co.uk](gcsemathsai.co.uk)  \nPractise every formula with instant AI feedback—completely free  \n[gcsemathsai.co.uk](gcsemathsai.co.uk) GCSE MATHS — COMPLETE FORMULA SHEET Page 2  \n\n| NUMBER |  |  |\n| --- | --- | --- |\n| Fractions—\u003Cbr>Adding/Subtracting\u003Cbr>| Find common denominator, then add/subtract numerators | \u003Cbr>F & H |\n| \u003Cbr>Fractions—Multiplying | a/b x c/d = ac / bd | \u003Cbr>F & H |\n| \u003Cbr>Fractions—Dividing | a/b ÷ c/d = a/b x d/c = ad / bc | \u003Cbr>F & H |\n| \u003Cbr>Percentage of an Amount | % of amount = (percentage ÷ 100) x amount | \u003Cbr>F & H |\n| \u003Cbr>Percentage Change | % change = (change ÷ original) x 100 | \u003Cbr>F & H |\n| \u003Cbr>Percentage\u003Cbr>Increase/Decrease | new value = original x (1 + r/100)\u003Cbr>decrease: use 1-r/100 | \u003Cbr>F & H |\n| \u003Cbr>Reverse Percentage | original = final amount ÷ (1 ± r/100) | \u003Cbr>F & H |\n| \u003Cbr>Simple Interest | Interest = (P x R x T) / 100\u003Cbr>P = principal, R = rate, T = time | \u003Cbr>F & H |\n\n| Prime Factorisation | Write as product of primes, e.g.  F & H  60 = 2^2 x 3 x 5 |  |\n| --- | --- | --- |\n| Index Law—Multiply | a^m x a^n = a^(m+n) | \u003Cbr>F & H |\n| Index Law—Divide | a^m ÷ a^n = a^(m-n) | \u003Cbr>F & H |\n| Index Law—Power of Power | (a^m)^n = a^(m x n) | \u003Cbr>F & H |\n| Index Law—Zero Power | a^0 = 1 (for any a ≠ 0) | \u003Cbr>F & H |\n| Negative Index | a^(-n) = 1 / a^n | \u003Cbr>F & H |\n| Fractional Index | a^(1/n) = nth root of a\u003Cbr>a^(m/n) = (nth root of a)^m | \u003Cbr>Higher |\n| Standard Form | A x 10^n where 1 ≤ A \u003C 10 | \u003Cbr>F & H |\n| Surd—Simplify | sqrt(ab) = sqrt(a) x sqrt(b) | \u003Cbr>Higher |\n| Surd—Rationalise Denominator | a / sqrt(b) = (a x sqrt(b)) / b | \u003Cbr>Higher |\n\nFree [resource | gcsemathsai.co.uk | Practise every formula with](resource | gcsemathsai.co.uk | Practise every formula with) instant AI feedback F&H = Foundation & Higher H = Higher only  \n[gcsemathsai.co.uk](gcsemathsai.co.uk) GCSE MATHS — COMPLETE FORMULA SHEET Page 3  \n\n| NUMBER |  |  |  |\n| --- | --- | --- | --- |\n|  | Surd—Difference of Squares | (sqrt(a) + sqrt(b))(sqrt(a) -sqrt(b)) = a-b | \u003Cbr>Higher |\n| \u003Cbr>Upper & Lower Bounds |  | UB = value + 0.5 x precision\u003Cbr>LB = value-0.5 x precision | \u003Cbr>Higher |\n|  | Bounds—Max/Min Results | max(a+b) = UB(a) + UB(b); minmax((aa/b-b)LB(Ba)(B- (Ub)B(b) | \u003Cbr>Higher |\n\n\n| ALGEBRA |  |  |\n| --- | --- | --- |\n| Expanding—Single Bracket | a(b + c) = ab + ac | \u003Cbr>F & H |\n| Expanding—Double Brackets | (a+b)(c+d) = ac + ad + bc + bd | \u003Cbr>F & H |\n| Difference of Two Squares | a^2-b^2 = (a+b)(a-b) | \u003Cbr>F & H |\n| Perfect Square | (a+b)^2 = a^2 + 2ab + b^2\u003Cbr>(a-b)^2 = a^2-2ab + b^2 | \u003Cbr>F & H |\n| Gradient of a Line | m = (y2-y1) / (x2-x1) | \u003Cbr>F & H |\n| Equation of a Straight Line | y = mx + c\u003Cbr>m = gradient, c = y-intercept | \u003Cbr>F & H |\n| Perpendicular Lines | m1 x m2 = -1 (gradients multiply to-1) | \u003Cbr>Higher |\n| Nth Term—Linear Sequence | nth term = a + (n-1)d = dn + (a-d)\u003Cbr>d = common difference, a = 1st term | \u003Cbr>F & H |\n| Nth Term—Quadratic Sequence | nth term = an^2 + bn + c\u003Cbr>a = 2nd difference ÷ 2 | \u003Cbr>Higher |\n| Quadratic Formula | x = (-b ± sqrt(b^2-4ac)) / 2a\u003Cbr>for ax^2 + bx + c = 0 | \u003Cbr>F & H |\n| Completing the Square | ax^2 + bx + c = a(x + b/2a)^2-(b/2a)^2 + c | \u003Cbr>Higher |\n| Discriminant | b^2-4ac > 0 two real roots\u003Cbr>= 0 one root; \u003C 0 no real roots | \u003Cbr>Higher |\n| Algebraic Fractions | Same rules as numeric fractions—factorise first | \u003Cbr>Higher |\n| Simultaneous—Elimination | Multiply to match coefficients, then add or subtract | \u003Cbr>F & H |\n| Simultaneous—Substitution | Rearrange one equation, substitute into the other | \u003Cbr>F & H |\n| Direct Proportion | y = kx (y proportional to x)\u003Cbr>find k using given values | \u003Cbr>F & H |\n| Inverse Proportion | y = k/x (y inversely propor","cbCaicE7DVaKl493","https://ap.wps.com/l/cbCaicE7DVaKl493","pdf",48407,1,7,"English","en",105,"# Number\n## Fractions, percentages and interest\n## Indices, surds and standard form\n# Algebra\n## Expanding, quadratics and sequences\n## Graphs, transformations and algebraic proof\n# Ratio, proportion & rates of change\n## Sharing, unitary method and speed/density/pressure\n# Geometry\n## Bounds and core geometric relationships\n# Statistics\n## Probability and interpretation","[{\"question\":\"What topics are included in the GCSE Maths complete formula sheet?\",\"answer\":\"It covers number, algebra, ratio/proportion/rates of change, geometry and statistics, with formulas for both Foundation \\u0026 Higher and Higher-only where applicable.\"},{\"question\":\"How does the sheet distinguish between Foundation \\u0026 Higher and Higher tier?\",\"answer\":\"It labels formulas with “F \\u0026 H” for Foundation \\u0026 Higher and “Higher” for items that apply to the Higher tier only.\"},{\"question\":\"How can learners practise using this resource?\",\"answer\":\"The resource promotes practising every formula with instant AI feedback via the linked site.\"}]","GCSE MATHS - COMPLETE FORMULA SHEET - Free resource for practising key formulas | 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