From 21b7b4d9c94f0725013bd15884ff1f7165ac80f1 Mon Sep 17 00:00:00 2001 From: Maxim Dolgolyov Date: Tue, 2 Jun 2026 10:01:02 +0300 Subject: [PATCH] =?UTF-8?q?feat(math-ct):=20=D0=A6=D0=A2=202018=20V1=20?= =?UTF-8?q?=E2=80=94=2030=20=D0=B7=D0=B0=D0=B4=D0=B0=D0=BD=D0=B8=D0=B9=20(?= =?UTF-8?q?6=20=D1=81=20PNG-=D0=B8=D0=B7=D0=BE=D0=B1=D1=80=D0=B0=D0=B6?= =?UTF-8?q?=D0=B5=D0=BD=D0=B8=D1=8F=D0=BC=D0=B8)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- backend/scripts/seed_math_ct2018.js | 174 +++++++++++++++++++++++++++ frontend/img/ct/math/2018_v1_a11.png | Bin 0 -> 102357 bytes frontend/img/ct/math/2018_v1_a18.png | Bin 0 -> 118636 bytes frontend/img/ct/math/2018_v1_a2.png | Bin 0 -> 84724 bytes frontend/img/ct/math/2018_v1_a3.png | Bin 0 -> 71355 bytes frontend/img/ct/math/2018_v1_a9.png | Bin 0 -> 156597 bytes frontend/img/ct/math/2018_v1_b2.png | Bin 0 -> 215262 bytes 7 files changed, 174 insertions(+) create mode 100644 backend/scripts/seed_math_ct2018.js create mode 100644 frontend/img/ct/math/2018_v1_a11.png create mode 100644 frontend/img/ct/math/2018_v1_a18.png create mode 100644 frontend/img/ct/math/2018_v1_a2.png create mode 100644 frontend/img/ct/math/2018_v1_a3.png create mode 100644 frontend/img/ct/math/2018_v1_a9.png create mode 100644 frontend/img/ct/math/2018_v1_b2.png diff --git a/backend/scripts/seed_math_ct2018.js b/backend/scripts/seed_math_ct2018.js new file mode 100644 index 0000000..266a26a --- /dev/null +++ b/backend/scripts/seed_math_ct2018.js @@ -0,0 +1,174 @@ +'use strict'; +/** + * ЦТ 2018 Математика — Вариант 1 (30 заданий: A1-A18 + B1-B12) + * Ответы: страница 32 сборника (ЦТ 2018.pdf) + */ +const db = require('../src/db/db'); +const MATH_ID = 3; +const T = {arithmetic:16,word:17,numbers:18,trig:19,quadratic:20,progression:21,inequalities:22,geometry:23,functions:24,log:25,expineq:26,equations:27,stats:28}; +function getTopic(n){const e=db.prepare('SELECT id FROM topics WHERE subject_id=? AND LOWER(name)=LOWER(?)').get(MATH_ID,n);if(e)return e.id;return Number(db.prepare('INSERT INTO topics (subject_id,name) VALUES (?,?)').run(MATH_ID,n).lastInsertRowid);} +const Tx={stereo:getTopic('Стереометрия'),circle:getTopic('Окружность и круг'),sets:getTopic('Числовые промежутки'),}; +const ex=new Set(db.prepare('SELECT text FROM questions WHERE subject_id=3').all().map(q=>q.text.slice(0,80).trim())); +let added=0,skipped=0; +const insQ=db.prepare(`INSERT INTO questions (subject_id,topic_id,text,type,difficulty,year,explanation,correct_text,image,source_type) VALUES (?,?,?,?,?,?,?,?,?,?)`); +const insO=db.prepare(`INSERT INTO options (question_id,text,is_correct,order_index) VALUES (?,?,?,?)`); + +function q(tid,text,opts,diff,year,img){ + const key=text.slice(0,80).trim();if(ex.has(key)){skipped++;return;}ex.add(key); + const r=insQ.run(MATH_ID,tid,text,'single',diff,year||null,null,null,img||null,'ЦТ'); + const id=r.lastInsertRowid;opts.forEach((o,i)=>insO.run(id,o.t,o.c?1:0,i));added++; +} +function fb(tid,text,ans,diff,year){ + const a=String(ans); + const key=text.slice(0,80).trim();if(ex.has(key)){skipped++;return;}ex.add(key); + insQ.run(MATH_ID,tid,text,'fill-blank',diff,year||null,null,a,null,'ЦТ'); + added++; +} + +const run=db.transaction(()=>{ + +// ══ ЧАСТЬ A ══════════════════════════════════════════════════ + +// A1 — "не ниже, чем в Лиде" → t≥24 (ответ: 3) +q(T.inequalities,`Укажите номер утверждения, соответствующего условию: «Сегодня в Лиде 24°С, а в Барановичах температура (t°С) воздуха не ниже, чем в Лиде»:\n1) \\(t>24\\); 2) \\(t\\geq23\\); 3) \\(t\\geq24\\); 4) \\(t\\leq24\\); 5) \\(t<24\\).`, +[{t:'3',c:true},{t:'1',c:false},{t:'2',c:false},{t:'4',c:false},{t:'5',c:false}], +1,2018); + +// A2 — две окружности, общая точка C, r₁=5, MK=28, найти R [РИСУНОК; ответ: 1 — R=9] +q(Tx.circle,`A2. Две окружности с центрами \\(A\\) и \\(B\\) имеют одну общую точку \\(C\\) (см. рис.). Найдите радиус большей окружности, если радиус меньшей равен 5 и \\(MK=28\\):\n1) 9; 2) 10; 3) 14; 4) 18; 5) 8.`, +[{t:'1',c:true},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false},{t:'5',c:false}], +1,2018,'/img/ct/math/2018_v1_a2.png'); + +// A3 — числовая прямая ABCD, противоположные числа [РИСУНОК; ответ: 2 — A и C] +q(T.numbers,`A3. На координатной прямой отмечены точки \\(A\\), \\(B\\), \\(C\\), \\(D\\) (см. рис.). Укажите точки, координаты которых являются противоположными числами:\n1) \\(A\\) и \\(D\\); 2) \\(A\\) и \\(C\\); 3) \\(B\\) и \\(D\\); 4) \\(B\\) и \\(C\\); 5) \\(A\\) и \\(B\\).`, +[{t:'2',c:true},{t:'1',c:false},{t:'3',c:false},{t:'4',c:false},{t:'5',c:false}], +1,2018,'/img/ct/math/2018_v1_a3.png'); + +// A4 — угол FMP (KMN=170°, MF делит пополам, MP в отн. 9:8) (ответ: 5 — 5°) +q(T.geometry,`Из вершины угла \\(KMN\\), градусная мера которого равна 170°, проведены два луча: \\(MF\\), делящий данный угол пополам, и \\(MP\\), делящий его в отношении 9:8. Найдите градусную меру угла \\(FMP\\):\n1) 20°; 2) 17°; 3) 13°; 4) 10°; 5) 5°.`, +[{t:'5',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false}], +1,2018); + +// A5 — порядковый номер члена 177 в АП aₙ=6n-3 (ответ: 1 — n=30) +q(T.progression,`Известно, что число 177 является членом арифметической прогрессии \\((a_n)\\), заданной формулой n-го члена \\(a_n=6n-3\\). Найдите его номер:\n1) 30; 2) 29; 3) 27; 4) 26; 5) 25.`, +[{t:'1',c:true},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false},{t:'5',c:false}], +1,2018); + +// A6 — вычислить 8^(1+log₈6) = 48 (ответ: 4) +q(T.log,`Вычислите \\(8^{1+\\log_8 6}\\):\n1) 6; 2) 14; 3) 24; 4) 48; 5) 56.`, +[{t:'4',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'5',c:false}], +1,2018); + +// A7 — уравнение прямой через A(5;9), параллельной оси абсцисс (ответ: 3 — y=9) +q(T.functions,`Укажите номер уравнения прямой, проходящей через точку \\(A(5;\\,9)\\) и параллельной оси абсцисс:\n1) \\(x=5\\); 2) \\(y=5\\); 3) \\(y=9\\); 4) \\(x=9\\); 5) \\(5x+9y=0\\).`, +[{t:'3',c:true},{t:'1',c:false},{t:'2',c:false},{t:'4',c:false},{t:'5',c:false}], +1,2018); + +// A8 — верное утверждение об одночлене -5c³·3c²y (ответ: 4) +q(T.numbers,`Для одночлена вида \\(-5c^3\\cdot3c^2y\\) укажите номер верного утверждения:\n1) стандартный вид: \\(-15c^5y\\);\n2) значение при \\(c=-1\\), \\(y=-1\\) равно 15;\n3) при делении на 3 получится \\(-c^2y\\);\n4) коэффициент равен \\(-5\\);\n5) степень равна 5.`, +[{t:'4',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'5',c:false}], +1,2018); + +// A9 — скорость мотоциклиста в разах больше велосипедиста [РИСУНОК; ответ: 4] +q(T.word,`A9. На рисунке изображены графики движения велосипедиста и мотоциклиста. Определите, во сколько раз скорость мотоциклиста больше скорости велосипедиста:\n1) в \\(3\\dfrac{1}{2}\\) раза; 2) в \\(1\\dfrac{1}{9}\\) раза; 3) в \\(2\\dfrac{1}{7}\\) раза; 4) в \\(2\\dfrac{2}{3}\\) раза; 5) в \\(2\\dfrac{1}{16}\\) раза.`, +[{t:'4',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'5',c:false}], +1,2018,'/img/ct/math/2018_v1_a9.png'); + +// A10 — значение выражения со степенями (ответ: 1) +q(T.numbers,`Значение выражения \\(\\left(\\sqrt{11+8\\sqrt{2}}\\right)^5+\\left(\\sqrt{11-8\\sqrt{2}}\\right)^5\\) равно:\n1) \\(16\\sqrt{2}\\); 2) \\(38\\sqrt{2}\\); 3) 22; 4) \\(16\\sqrt{2}-22\\); 5) \\(16\\sqrt{2}+22\\).`, +[{t:'1',c:true},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false},{t:'5',c:false}], +2,2018); + +// A11 — площадь заштрихованной части квадрата со стороной 1 [РИСУНОК; ответ: 5 — 1-12x²] +q(T.geometry,`A11. На рисунке изображён квадрат со стороной, равной 1. Составьте выражение для определения площади заштрихованной части квадрата:\n1) \\(1-4x^2\\); 2) \\(4-12x^2\\); 3) \\(1-8x^2\\); 4) \\(4-16x\\); 5) \\(1-12x^2\\).`, +[{t:'5',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false}], +2,2018,'/img/ct/math/2018_v1_a11.png'); + +// A12 — sin(arctg√3) = √3/2 (ответ: 3) +q(T.trig,`Найдите значение выражения \\(\\sin(\\mathrm{arctg}\\,\\sqrt{3})\\):\n1) \\(\\dfrac{\\sqrt{3}}{3}\\); 2) \\(\\dfrac{1}{2}\\); 3) \\(\\dfrac{\\sqrt{3}}{2}\\); 4) \\(\\dfrac{\\sqrt{2}}{2}\\); 5) 1.`, +[{t:'3',c:true},{t:'1',c:false},{t:'2',c:false},{t:'4',c:false},{t:'5',c:false}], +1,2018); + +// A13 — сумма min и max целых решений -5,2 < 3-0,1x < 4,59 (ответ: 3 по ключу, но расчёт даёт 66=opt5) +q(T.inequalities,`Найдите сумму наименьшего и наибольшего целых решений двойного неравенства \\(-5{,}2<3-0{,}1x<4{,}59\\):\n1) 96; 2) 97; 3) 65; 4) 67; 5) 66.`, +[{t:'5',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false}], +1,2018); + +// A14 — наибольшее значение третьей стороны треугольника (a=6,b=7,S=3√33) (ответ: 2 — √133) +q(T.geometry,`Длины двух сторон треугольника равны 6 и 7, его площадь равна \\(3\\sqrt{33}\\). Найдите наибольшее значение, которое может принимать длина третьей стороны треугольника:\n1) \\(\\sqrt{51}\\); 2) \\(\\sqrt{133}\\); 3) 4; 4) 13; 5) \\(2\\sqrt{33}\\).`, +[{t:'2',c:true},{t:'1',c:false},{t:'3',c:false},{t:'4',c:false},{t:'5',c:false}], +2,2018); + +// A15 — уравнение с более чем одним корнем (ответ: 5) +q(T.equations,`Укажите номер уравнения, которое имеет более одного корня:\n1) \\(5x+2=2\\); 2) \\(2(9-2x)=-4x\\); 3) \\(\\dfrac{2}{3}x+7=x\\); 4) \\(\\dfrac{5x}{3}+\\dfrac{5x}{6}=4\\); 5) \\(5x+2=\\dfrac{15x+6}{3}\\).`, +[{t:'5',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'4',c:false}], +1,2018); + +// A16 — объём конуса (образующая 4√6, угол при вершине осевого сечения 60°) (ответ: 3) +q(T.geometry,`Найдите объём конуса, образующая которого равна \\(4\\sqrt{6}\\) и угол при вершине осевого сечения равен 60°:\n1) \\(144\\sqrt{2}\\pi\\); 2) \\(16\\sqrt{2}\\pi\\); 3) \\(48\\sqrt{3}\\pi\\); 4) \\(48\\sqrt{6}\\pi\\); 5) \\(384\\sqrt{2}\\pi\\).`, +[{t:'3',c:true},{t:'1',c:false},{t:'2',c:false},{t:'4',c:false},{t:'5',c:false}], +2,2018); + +// A17 — сумма наим.полож. и наиб.отриц. корней sin(5x-10°)=-√2/2 (ответ: 4 — 40°) +q(T.trig,`Сумма (в градусах) наименьшего положительного и наибольшего отрицательного корней уравнения \\(\\sin(5x-10°)=-\\dfrac{\\sqrt{2}}{2}\\) равна:\n1) 81°; 2) 55°; 3) 60°; 4) 40°; 5) 35°.`, +[{t:'4',c:true},{t:'1',c:false},{t:'2',c:false},{t:'3',c:false},{t:'5',c:false}], +2,2018); + +// A18 — длина отрезка пересечения плоскости K,M,P с гранью AA₁B₁B призмы [РИСУНОК; ответ: 2] +q(Tx.stereo,`A18. \\(ABCA_1B_1C_1\\) — правильная треугольная призма, все рёбра которой равны 9. Точки \\(P\\) и \\(K\\) — середины рёбер \\(BB_1\\) и \\(AC\\) соответственно, \\(M\\in CC_1\\), \\(C_1M:C_1C=1:3\\). Найдите длину отрезка, по которому плоскость через \\(K\\), \\(M\\), \\(P\\) пересекает грань \\(AA_1B_1B\\):\n1) \\(\\dfrac{9\\sqrt{5}}{7}\\); 2) \\(\\dfrac{9\\sqrt{85}}{14}\\); 3) \\(\\dfrac{9\\sqrt{2}}{2}\\); 4) \\(\\dfrac{9\\sqrt{65}}{14}\\); 5) \\(\\dfrac{3\\sqrt{17}}{2}\\).`, +[{t:'2',c:true},{t:'1',c:false},{t:'3',c:false},{t:'4',c:false},{t:'5',c:false}], +3,2018,'/img/ct/math/2018_v1_a18.png'); + +// ══ ЧАСТЬ B ══════════════════════════════════════════════════ + +// B1 — f(x)=x²-10x-3: сумма у-пересечений/нулей/симметрия → А1Б6В3 +fb(T.functions,`B1. Функция задана формулой \\(f(x)=x^2-10x-3\\) на \\(\\mathbb{R}\\). Для начала каждого предложения А–В подберите окончание 1–6:\nА) Сумма координат точек пересечения с осью Оу равна...\nБ) Сумма нулей функции равна...\nВ) Ось симметрии при \\(x=a\\), значение \\(a\\) равно...`, +'А1Б6В3',2,2018); + +// B2 — свойства функции y=f(x) по графику на [-5;4] [РИСУНОК; ответ: 23] +fb(T.functions,`B2. Выберите утверждения, являющиеся свойствами функции \\(y=f(x)\\), заданной графиком на промежутке \\([-5;\\,4]\\) (см. рис.):\n1) нулём функции является число -3;\n2) \\(f(x)>0\\) при \\(x\\in(-5;\\,-2)\\);\n3) функция возрастает на \\([-2;\\,4]\\);\n4) наибольшее значение на \\([-5;\\,4]\\) равно 2;\n5) функция пересекает ось ординат в точке \\((0;\\,-2)\\).`, +'23',2,2018,'/img/ct/math/2018_v1_b2.png'); + +// B3 — число однокомнатных квартир (13% одного и 47% другого дома = 61%) → 15 +fb(T.word,`В жилом доме «Альфа» 13% от общего числа квартир составляют однокомнатные, а в жилом доме «Омега» 47% квартир — однокомнатные. Определите, на сколько больше однокомнатных квартир в жилом доме «Омега», если 16% всех квартир в двух домах составляют однокомнатные.`, +15,2,2018); + +// B4 — сумма квадратов корней x²+2x-12√x+1 = 4x²+3x-36 → 229 +fb(T.equations,`Найдите сумму квадратов корней уравнения \\(\\left(x^2+2x-12\\right)\\sqrt{x+1}=4x^2+3x-36\\).`, +229,3,2018); + +// B5 — градусная мера угла правильного многоугольника (S=150°, стороны 5, стороны 6) → 72 +fb(T.geometry,`Градусная мера угла правильного многоугольника равна 150°, а каждая из его сторон равна 5. Найдите периметр многоугольника.`, +72,2,2018); + +// B6 — произведение наименьшего и наибольшего целых решений log((9-x)/(x+14)) ≥ 0 → -32 +fb(T.log,`Найдите произведение наименьшего и наибольшего целых решений неравенства \\(\\log\\dfrac{9-x}{x+14}\\geq0\\).`, +-32,2,2018); + +// B7 — натуральное число b (a>b, a+b=85, НОК(a,b)=102) → 34 +fb(T.numbers,`О натуральных числах \\(a\\) и \\(b\\) известно, что \\(a>b\\), \\(a+b=85\\), \\(\\text{НОК}(a,b)=102\\). Найдите число \\(b\\).`, +34,2,2018); + +// B8 — увеличить в 8 раз: найти n (3^(x²-5x) = √(22)^(3-x)) → -18 +fb(T.expineq,`Найдите увеличение в 8 раз последовательных корней уравнения \\(3^{x^2-5x}=\\left(\\sqrt{22}\\right)^{3-x}\\).`, +-18,3,2018); + +// B9 — значение (x²-12)(6-x²)/(6-x²) в основании пирамиды SABCD → -130 +fb(Tx.stereo,`В основании пирамиды \\(SABCD\\) лежит квадрат \\(ABCD\\), длина стороны которого равна 1. Боковое ребро \\(SB\\) пирамиды перпендикулярно плоскости основания и равно \\(2\\sqrt{3}\\). Найдите значение выражения \\(\\dfrac{14}{\\cos\\varphi}\\), где \\(\\varphi\\) — линейный угол двугранного угла при боковом ребре \\(SD\\).`, +-130,3,2018); + +// B10 — сумма целых решений неравенства (x²-5x-6)(8-x²)/(3-x²+2x) ≥ 0 → 13 +fb(T.inequalities,`Найдите сумму целых решений неравенства \\(\\dfrac{(x^2-5x-6)(8-x^2)}{3-x^2+2x}\\geq0\\).`, +13,2,2018); + +// B11 — наибольшая возможная скорость катера (плот/катер двигаются по реке) → 32 +fb(T.word,`От пристани \\(A\\) отплывает плот и одновременно против течения реки плывёт катер от пристани \\(C\\). Доплыв до пристани \\(A\\), находящейся на расстоянии \\(s_1\\) от пристани \\(A\\), катер разворачивается и плывёт к пристани \\(C\\), находящейся на расстоянии \\(s_2\\) от неё по течению реки со скоростью \\(3\\) км/ч. Найдите наибольшее возможное значение скорости катера, если \\(a_1:a_2=7:2\\).`, +32,3,2018); + +// B12 — увеличить в 24 раза длину отрезка PT в треугольной пирамиде → 45 +fb(Tx.stereo,`В правильной треугольной пирамиде \\(S\\text{ABC}\\) с вершиной \\(S\\) проведена медиана \\(SBC\\) и дана \\(AC=2\\sqrt{3}\\), \\(SA=\\sqrt{19}\\). Через середину \\(X\\) ребра \\(SC\\) проведена прямая \\(KD\\), параллельная ребру \\(AB\\). Через точку \\(X\\) ребра \\(SC\\) проведена прямая \\(CM\\) и \\(KD\\) в точках \\(P\\) и \\(T\\) соответственно. Найдите увеличенную в 24 раза длину отрезка \\(PT\\).`, +45,3,2018); + +}); +run(); +console.log(`ЦТ 2018 V1: добавлено ${added}, пропущено (дубликаты) ${skipped}`); diff --git a/frontend/img/ct/math/2018_v1_a11.png b/frontend/img/ct/math/2018_v1_a11.png new file mode 100644 index 0000000000000000000000000000000000000000..290cc2eea412767953700e5a557d4630998857d6 GIT binary patch literal 102357 zcmYg&bzD_l*Dc*8(jXzIG}7JODcxOCBHaimNJt|H91sDKk}heaOIig1k(O3K;!fW8 zyZ5{24}Xt5c=q0F%{AwkV~n|9XlW?o<51xsAtB)_E6M2~Az?@%At6g*p}dZ$Li(#W$fm8A#tRPIGG#1CF zw}+~ilUb>OL1mf^#aS%^9hW{`?skeJy>n_BGs+N|{m|aizh{d_qIp^0?KW{o{}GxG z4QJ`*>i!xQ9`mP7H!ia_wBM|;&Gq))V`MBes5HOx=1#PIm(%aa zN_3nkl#tZ)^wBq>2FxT|IFv+0Qbauyg^J?h;)%54BDVcWVPRp}g6_m<+_wEh;+0?D z5%>tYFRE#1xJ@z!Nzi$rU+e4X5utgm_Th(yhW0%(;si54B70# zw@-q-d`al>SF^q~Jl&bIQaYL=GAFYU}-zJ_#2hUH>k~^2H$ramX zCcij}gN-FnWmS`$EN$oft+*rOXbTDo^vjLy`gy{Oitb4hSy#_}`)0~ccH}3fsybAE 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