commit 725b571c63d6c65276f2bfde81c1cf0fa9edb8f1
parent c239a3998e2a80e0694dcc0fef868ff878c11454
Author: fen123456 <fenwthompson@gmail.com>
Date: Sat, 8 Aug 2026 17:28:39 +0100
nicer quadratics
Diffstat:
4 files changed, 73 insertions(+), 37 deletions(-)
diff --git a/TODO.md b/TODO.md
@@ -1,9 +1,16 @@
-# General
+# Fixes
- Use KaTeX_Math font outside MathML
# Questions
- Improve existing questions
- - Negative b toggle
+ - Negative c toggle (DOTS?)
- Add more questions
- Add graphing questions
+ - Find all roots of this quintic (or something) polynomial (repeated root knowledge)
+ - Transformations of shapes and graphs (curves)
- Drop-down for finer controls
+- tricky parallel lines / internal angles etc questions
+
+# Other stuff
+- minesweeper / youtube video.
+- crosswords
diff --git a/src/components/questions/QuadraticEquationQuestion.jsx b/src/components/questions/QuadraticEquationQuestion.jsx
@@ -1,40 +1,43 @@
import Question from '../Question.jsx';
-import { getRandomInt, getRandomBoolean, getRandomChoice, formatNumber } from '../../scripts/utils.js';
+import { getRandomInt, getRandomBoolean, getRandomChoice, formatCoefficient, getHCF } from '../../scripts/utils.js';
function formatQuadraticExpression(a, b, c) {
- const fa = formatNumber(a, {showPlus: false, showOne: false, showZero: false, suffix: 'x^2'});
- const fb = formatNumber(b, {showPlus: true, showOne: false, showZero: false, suffix: 'x'});
- const fc = formatNumber(c, {showPlus: true, showOne: true, showZero: false});
+ const fa = formatCoefficient(a, { showPlus: false, showOne: false, showZero: false, suffix: 'x^2' });
+ const fb = formatCoefficient(b, { showPlus: true, showOne: false, showZero: false, suffix: 'x' });
+ const fc = formatCoefficient(c, { showPlus: true, showOne: true, showZero: false });
return `${fa} ${fb} ${fc}`;
}
-function formatRoots(root1, root2) {
- const froot2 = formatNumber(root2, {showPlus: false, showOne: true, showZero: true});
- if (root1 == root2) { return `x = ${froot2}`; }
- if (Math.abs(root1) == root2) { return `x = plus.minus ${root2}`; }
- const froot1 = formatNumber(root1, {showPlus: false, showOne: true, showZero: true});
- return `x = ${froot1} "or" x = ${froot2}`;
+function formatFraction(num, denom) {
+ const hcf = getHCF(Math.abs(num), Math.abs(denom))
+ num = num / hcf
+ denom = denom / hcf
+ if (denom == 1) { return `${num}`; }
+ return `frac(${num}, ${denom})`
}
-function formatFactor(root) {
- if (root == 0) { return "x"; }
- const froot = formatNumber(root, {showPlus: true, showOne: true, showZero: false});
- return `(x${froot})`;
+function formatRoots(l, m, n, o) {
+ if (m / l == o / n) { return `x = ${formatFraction(-m, l)}`; }
+ if (-m / l == o / n) { return `x = plus.minus ${formatFraction(Math.abs(-m), l)}`; }
+
+ return `x = ${formatFraction(-m, l)} "or" x = ${formatFraction(-o, n)}`;
}
-function sortFactors(root1, root2) {
- if (root1 > 0 && root2 < 0) { return -1; }
- if (root1 < 0 && root2 > 0) { return +1; }
- return Math.abs(root1) - Math.abs(root2);
+function formatFactor(x_coeff, const_coeff) {
+ if (const_coeff == 0) { return "x"; }
+ const fx_coeff = formatCoefficient(x_coeff, { showPlus: false, showOne: false, showZero: false, suffix: 'x'})
+ const fconst_coeff = formatCoefficient(const_coeff, { showPlus: true, showOne: true, showZero: false })
+ return `(${fx_coeff}${fconst_coeff})`;
}
-function formatFactors(root1, root2, a) {
- const fa = formatNumber(a, {showPlus: false, showOne: false, showZero: false});
- [root1, root2] = [root1, root2].sort(sortFactors);
- const froot2 = formatFactor(root2);
- if (root1 == root2) { return `${fa}${froot2}^2`; }
- const froot1 = formatFactor(root1);
- return `${fa}${froot1}${froot2}`;
+function formatFactors(l, m, n, o) {
+ // const fa = formatCoefficient(a, {showPlus: false, showOne: false, showZero: false});
+ // [root1, root2] = [root1, root2].sort(sortFactors);
+ // const froot2 = formatFactor(root2);
+ // if (root1 == root2) { return `${fa}${froot2}^2`; }
+ // const froot1 = formatFactor(root1);
+ // return `${fa}${froot1}${froot2}`;
+ return `${formatFactor(l, m)}${formatFactor(n, o)}`
}
function getRandomRoots(seed) {
@@ -44,25 +47,44 @@ function getRandomRoots(seed) {
].sort((a, b) => a - b);
}
-export default function QuadraticEquationQuestion({ seed, showAnswer, aPlurality, framing }) {
+export default function QuadraticEquationQuestion({ seed, showAnswer, aPlurality, framing, cSigns }) {
+ // (lx + m)(nx + o)
+
const aChoices = Array();
aPlurality.includes("a=1") && aChoices.push(1);
aPlurality.includes("a>1") && aChoices.push(2, 3);
- const a = getRandomChoice(aChoices, seed);
+ let l = getRandomChoice(aChoices, seed);
+ let n = getRandomChoice(aChoices, seed + .1);
const factoriseChoices = Array();
framing.includes("Solve") && factoriseChoices.push(false);
framing.includes("Factorise") && factoriseChoices.push(true);
- const factorise = getRandomChoice(factoriseChoices, seed + .1);
+ const factorise = getRandomChoice(factoriseChoices, seed + .2);
+
+ const cSignChoices = Array();
+ cSigns.includes("Positive") && cSignChoices.push(1)
+ cSigns.includes("Negative") && cSignChoices.push(-1)
+
+ const mSign = getRandomChoice([-1, 1], seed + .3)
+ const cSign = getRandomChoice(cSignChoices, seed + .4)
+
+ let m = getRandomInt(1, 9, seed + .5) * mSign
+ let o = getRandomInt(1, 9, seed + .6) * mSign * cSign
- const [root1, root2] = getRandomRoots(seed + .2);
+ if (-m/l > -o/n) {
+ [l, m, n, o] = [n, o, l, m]
+ }
- const b = a * -(root1 + root2);
- const c = a * root1 * root2;
+ // lnx^2 + (lo + nm)x + mo
+ const a = l * n
+ const b = (l * o) + (n * m)
+ const c = m * o
const quadratic = formatQuadraticExpression(a, b, c);
const question = factorise ? `"Factorise" ${quadratic}` : `${quadratic} = 0`;
- const answer = factorise ? formatFactors(root1, root2, a) : formatRoots(root1, root2);
+
+ const answer = factorise ? formatFactors(l, m, n, o) : formatRoots(l, m, n, o);
return <Question question={question} answer={answer} showAnswer={showAnswer} />;
-}
+
+}
+\ No newline at end of file
diff --git a/src/data/questions/gcse/quadratic-equations.js b/src/data/questions/gcse/quadratic-equations.js
@@ -12,13 +12,18 @@ export const data = {
legend: 'Coefficient a',
type: MultipleSelection,
values: ["a=1", "a>1"],
+ }, {
+ id: 'cSigns',
+ legend: 'Coefficient c',
+ type: MultipleSelection,
+ values: ["Positive", "Negative"]
}],
questionLists: [{
id: 0,
n: 10,
questions: [{
type: QuadraticEquationQuestion,
- variables: { aPlurality: 'aPlurality', framing: 'framing' },
+ variables: { aPlurality: 'aPlurality', framing: 'framing', cSigns: 'cSigns' },
}]
}]
}
diff --git a/src/scripts/utils.js b/src/scripts/utils.js
@@ -16,10 +16,11 @@ export function getRandomNumber(seed) {
}
export function getHCF(a, b) {
+ if (a == 1 && b == 1) { return 1 }
return b == 0 ? a : getHCF(b, a % b);
}
-export function formatNumber(x, parameters = {showPlus: false, showOne: true, showZero: true, suffix: ''}) {
+export function formatCoefficient(x, parameters = {showPlus: false, showOne: true, showZero: true, suffix: ''}) {
if (!parameters.showZero && x == 0) { return ''; }
const plus = parameters.showPlus ? '+' : '';
const sign = x < 0 ? '-' : plus;
