Quest for Knowledge: Math Mountains Game

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<div class="feedback no"> <strong>Hint:</strong> Subtract 5 from both sides to get $2x=10$, then divide by 2. </div>

A fallen sign reads: “Distribute before you combine.” **Solve:** $3(2x - 4) = 18$ <div class="choices"> <<linkreplace "x = 5">> <<wrong>> <div class="feedback no">Check distribution: $3(2x-4)=6x-12$.</div> <div class="nav-row"><<link "Try again">><<goto "ALG Q2">><</link>></div> <</linkreplace>> <<linkreplace "x = 5 (Correct)">> <<givexp 12>> <div class="feedback ok"><strong>Correct!</strong> $6x-12=18 \Rightarrow 6x=30 \Rightarrow x=5$. +12 XP.</div> <div class="nav-row"> <<link "Onward to Geometry Gorge">><<goto "Geometry Gorge (Intro)">><</link>> <<link "Back to Start">><<goto "Start">><</link>> </div> <</linkreplace>> </div>

A weathered rope bridge sways above a chasm labeled "Systems of Equations." **Solve the system:** $ 2x + y = 7 $ $ x - y = 1 $ <div class="choices"> <<linkreplace "x = 8/3, y = 5/3">> <<wrong>> <div class="feedback no">Try solving one equation for a variable and substituting into the other.</div> <div class="nav-row"><<link "Try again">><<goto "ALG Q3">><</link>></div> <</linkreplace>> <<linkreplace "x = 4, y = -1">> <<givexp 14>><<addfragment "Systems">> <div class="feedback ok"><strong>Correct!</strong> Adding the equations quickly eliminates $y$. +14 XP, Fragment: <em>Systems</em>.</div> <div class="nav-row"> <<link "Next Algebra challenge">><<goto "ALG Q4">><</link>> <<link "Return to Cliffs hub">><<goto "Algebraic Cliffs">><</link>> </div> <</linkreplace>> </div>

Higher on the ridge, runes glow around a quadratic. **Find the roots:** $ x^2 - 6x + 5 = 0 $ <div class="choices"> <<linkreplace "x = 1 and x = 5">> <<givexp 16>><<set $doneAlgebra = true>> <div class="feedback ok"><strong>Correct!</strong> $(x-1)(x-5)$ gives roots at 1 and 5. +16 XP.</div> <div class="nav-row"> <<link "View Path Summary">><<goto "Path Summary">><</link>> <<link "More Algebra practice">><<goto "Algebraic Cliffs">><</link>> </div> <</linkreplace>> <<linkreplace "x = 2 and x = 3">> <<wrong>> <div class="feedback no">Check: $(x-2)(x-3) = x^2 - 5x + 6$, not our quadratic.</div> <div class="nav-row"><<link "Try again">><<goto "ALG Q4">><</link>></div> <</linkreplace>> </div>

You approach a narrow ledge with carvings: “Undo operations in reverse.” **Solve:** $2x + 5 = 15$ <div class="choices"> /* Wrong choice with hint logic */ <<linkreplace "x = 3">> <<set $skillInsight = $skillInsight ?? true>>  <<wrong>> <<if $skillInsight>><<include "ALG Q1 Hint">><<else>> <div class="feedback no">Try isolating $x$ by undoing operations in reverse.</div><</if>> <div class="nav-row"> <<link "Try again">><<goto "Algebraic Cliffs">><</link>> </div> <</linkreplace>> /* Correct choice */ <<linkreplace "x = 5">> <<givexp 10>><<addfragment "Algebra">> <div class="feedback ok"><strong>Correct!</strong> Subtract 5, then divide by 2. +10 XP, Fragment: <em>Algebra</em>.</div> <div class="nav-row"> <<link "Continue up the Cliffs">><<goto "ALG Q2">><</link>> </div> <</linkreplace>> </div>

A glowing graph shows $f(x) = 3x^2$. **Find $f'(x)$.** <div class="choices"> <<linkreplace "f'(x) = 6x">> <<givexp 10>><<addfragment "Derivatives">> <div class="feedback ok"><strong>Correct!</strong> Power rule: bring down the 2 and multiply the coefficient. +10 XP, Fragment: <em>Derivatives</em>.</div> <div class="nav-row"> <<link "Next Calculus challenge">><<goto "CALC Q2">><</link>> <<link "Back to Calculus hub">><<goto "Calculus Crater (Intro)">><</link>> </div> <</linkreplace>> <<linkreplace "f'(x) = 3x">> <<wrong>> <div class="feedback no">You missed the factor of 2 from the exponent.</div> <div class="nav-row"><<link "Try again">><<goto "CALC Q1">><</link>></div> <</linkreplace>> </div>

An inscription reads: "Total change from 0 to 2." You see $f(x) = 4x$. **Compute $ \int_{0}^{2} 4x \, dx $.** <div class="choices"> <<linkreplace "8">> <<givexp 14>><<set $doneCalculus = true>> <div class="feedback ok"><strong>Correct!</strong> The antiderivative is $2x^2$, so $2(2^2) - 2(0^2) = 8$. +14 XP.</div> <div class="nav-row"> <<link "View Path Summary">><<goto "Path Summary">><</link>> <<link "Back to Calculus Crater">><<goto "Calculus Crater (Intro)">><</link>> </div> <</linkreplace>> <<linkreplace "16">> <<wrong>> <div class="feedback no">Remember to plug in the bounds after finding the antiderivative $2x^2$.</div> <div class="nav-row"><<link "Try again">><<goto "CALC Q2">><</link>></div> <</linkreplace>> </div>

The air crackles with changing rates. Here, slopes and accumulated areas decide your fate. <div class="choices"> <<link "Derivative Ridge">><<goto "CALC Q1">><</link>> <<link "Area Basin">><<goto "CALC Q2">><</link>> <<link "Back to Start">><<goto "Start">><</link>> </div>

A quick warm-up. Solve: **If $ f(x)=2x+7 $, what is $ f(4) $?** <div class="choices"> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Close! Compute $2 \cdot 4 + 7$.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 16">> <<wrong>> <div class="feedback no">That’s $2\cdot4=8$, don’t forget the +7.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Recheck your arithmetic and parentheses.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Try once more.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Keep at it.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">One more think step.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Compute carefully.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Almost!</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Rethink.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15">> <<wrong>> <div class="feedback no">Try computing step by step.</div> <div class="nav-row"> <<link "Try again">><<goto "Daily Challenge">><</link>> </div> <</linkreplace>> <<linkreplace "f(4) = 15 (Correct)">> <<givexp 5>><<addfragment "Functions">> <div class="feedback ok"><strong>Correct!</strong> $2\cdot4+7=15$. +5 XP, Fragment: <em>Functions</em>.</div> <div class="nav-row"> <<link "Back to Start">><<goto "Start">><</link>> </div> <</linkreplace>> </div>

At Angle Arch, three rays meet. The measures are $40^\circ$, $50^\circ$, and $90^\circ$. **What kind of triangle do these angles form?** <div class="choices"> <<linkreplace "Acute triangle">> <<wrong>> <div class="feedback no">An acute triangle has all angles less than $90^\circ$.</div> <div class="nav-row"><<link "Try again">><<goto "GEO Q1">><</link>></div> <</linkreplace>> <<linkreplace "Right triangle">> <<givexp 10>><<addfragment "Geometry">> <div class="feedback ok"><strong>Correct!</strong> One angle is $90^\circ$, so it’s a right triangle. +10 XP, Fragment: <em>Geometry</em>.</div> <div class="nav-row"> <<link "Next Geometry challenge">><<goto "GEO Q2">><</link>> <<link "Return to Gorge hub">><<goto "Geometry Gorge (Intro)">><</link>> </div> <</linkreplace>> </div>

A stone tablet shows a base and height: $b = 10$ units, $h = 6$ units. **What is the area of the triangle?** <div class="choices"> <<linkreplace "A = 60">> <<wrong>> <div class="feedback no">That’s the area of a rectangle with those dimensions. A triangle is half that.</div> <div class="nav-row"><<link "Try again">><<goto "GEO Q2">><</link>></div> <</linkreplace>> <<linkreplace "A = 30">> <<givexp 12>><<set $doneGeometry = true>> <div class="feedback ok"><strong>Correct!</strong> $A = \\tfrac12 bh = \\tfrac12 (10)(6) = 30$. +12 XP.</div> <div class="nav-row"> <<link "View Path Summary">><<goto "Path Summary">><</link>> <<link "Back to Geometry Gorge">><<goto "Geometry Gorge (Intro)">><</link>> </div> <</linkreplace>> </div>

Mist curls over jagged shapes. Signs point toward arches, caverns, and terraces of triangles and circles. <div class="choices"> <<link "Angle Arch">><<goto "GEO Q1">><</link>> <<link "Triangle Terrace">><<goto "GEO Q2">><</link>> <<link "Back to Start">><<goto "Start">><</link>> </div>

- Click answers to receive instant feedback. - Correct choices award **XP** and sometimes a **Fragment**. - Hints appear automatically if you’ve earned the **Insight** skill. <div class="nav-row"> <<link "Back">><<goto "Start">><</link>> </div>

# Path Summary You pause to catch your breath and review your climb so far. <div class="card"> <h3>Progress Overview</h3> <p><strong>Total XP:</strong> <<print $xp>></p> <p> <strong>Knowledge Fragments:</strong> <<if $fragments.length == 0>> None collected yet. Each world hides at least one Fragment of Power. <<else>> <<for _i, _frag range $fragments>> <span class="tag-chip"><<print _frag>></span> <</for>> <</if>> </p> </div> <div class="card"> <h3>Worlds Completed</h3> <ul> <li> <<if $doneAlgebra>> ✅ Algebraic Cliffs cleared <<else>> ⛰️ Algebraic Cliffs — still climbing <</if>> </li> <li> <<if $doneGeometry>> ✅ Geometry Gorge cleared <<else>> 📐 Geometry Gorge — puzzles remain <</if>> </li> <li> <<if $doneCalculus>> ✅ Calculus Crater cleared <<else>> ∫ Calculus Crater — challenges ahead <</if>> </li> </ul> </div> <div class="card"> <h3>Where next?</h3> <p>Choose your next destination.</p> <div class="nav-row"> <<link "Return to Base Camp">><<goto "Start">><</link>> <<link "Algebraic Cliffs">><<goto "Algebraic Cliffs">><</link>> <<link "Geometry Gorge">><<goto "Geometry Gorge (Intro)">><</link>> <<link "Calculus Crater">><<goto "Calculus Crater (Intro)">><</link>> </div> </div>

# Math Mountains Welcome, climber! Your path winds through Algebraic Cliffs, Geometry Gorge, and Calculus Crater. Solve challenges to gain **XP** and collect **Knowledge Fragments**. When you’re ready, choose a route. <div class="choices"> <<link "Algebraic Cliffs">><<goto "Algebraic Cliffs">><</link>> <<link "Geometry Gorge">><<goto "Geometry Gorge (Intro)">><</link>> <<link "Calculus Crater">><<goto "Calculus Crater (Intro)">><</link>> <<link "Daily Challenge">><<goto "Daily Challenge">><</link>> <<link "How to Play">><<goto "How to Play">><</link>> <<link "View Path Summary">><<goto "Path Summary">><</link>> </div> <div class="card"> <strong>Tip:</strong> Press <span class="kbd">L</span> to toggle Light/Dark mode. Your choice is saved. </div>

By: Cyrus Saleem

SugarCube 2

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