{"slug":"act-formula-sheet","tier":1,"subject":"act","title":"ACT Math Formula Sheet","description":"The ACT gives you ZERO formulas. This program has the full set — geometry, trig, sequences, probability, and logs.","files":[{"filename":"ACTMATH.py","content":"def p(s):print(s)\ndef w():input(\"...\")\ndef o1():\n p(\"=GEOMETRY=\")\n p(\"CIRCLE:\")\n p(\"A=pi*r^2\")\n p(\"C=2*pi*r\")\n w()\n p(\"TRIANGLE:\")\n p(\"A=bh/2\")\n p(\"P=a+b+c\")\n w()\n p(\"TRAPEZOID:\")\n p(\"A=h(b1+b2)/2\")\n p(\"CYLINDER:\")\n p(\"V=pi*r^2*h\")\n w()\ndef o2():\n p(\"=TRIG=\")\n p(\"SOHCAHTOA:\")\n p(\"sin=opp/hyp\")\n p(\"cos=adj/hyp\")\n p(\"tan=opp/adj\")\n w()\n p(\"LAW SINES:\")\n p(\"a/sinA=\")\n p(\"b/sinB=\")\n p(\"c/sinC\")\n w()\n p(\"LAW COS:\")\n p(\"c2=a2+b2\")\n p(\"-2ab*cosC\")\n w()\ndef o3():\n p(\"=SEQ/SERIES=\")\n p(\"ARITH nth:\")\n p(\"an=a1+(n-1)d\")\n p(\"SUM n terms:\")\n p(\"S=n(a1+an)/2\")\n w()\n p(\"GEOM nth:\")\n p(\"an=a1*r^(n-1)\")\n p(\"SUM geom:\")\n p(\"S=a1(1-r^n)\")\n p(\"/(1-r)\")\n w()\ndef o4():\n p(\"=PROBABILITY=\")\n p(\"P(A)=favor/\")\n p(\"total\")\n w()\n p(\"P(A and B)=\")\n p(\"P(A)*P(B)\")\n p(\"(indep)\")\n w()\n p(\"P(A or B)=\")\n p(\"P(A)+P(B)-\")\n p(\"P(A and B)\")\n w()\ndef o5():\n p(\"=LOGS=\")\n p(\"log_b(x)=y\")\n p(\"=> b^y=x\")\n w()\n p(\"log(mn)=\")\n p(\"log m+log n\")\n p(\"log(m/n)=\")\n p(\"log m-log n\")\n w()\n p(\"log(m^n)=\")\n p(\"n*log m\")\n p(\"CHANGE BASE:\")\n p(\"log_b(x)=\")\n p(\"log(x)/log(b)\")\n w()\ndef menu():\n while True:\n  p(\"=ACT MATH=\")\n  p(\"1:GEOMETRY\")\n  p(\"2:TRIG\")\n  p(\"3:SEQUENCES\")\n  p(\"4:PROB\")\n  p(\"5:LOGS\")\n  p(\"0:EXIT\")\n  c=input(\"?>\")\n  if c==\"1\":o1()\n  elif c==\"2\":o2()\n  elif c==\"3\":o3()\n  elif c==\"4\":o4()\n  elif c==\"5\":o5()\n  elif c==\"0\":break\nmenu()"}],"testCases":[{"id":"geometry","inputs":["1","","","","0"],"expectedContains":["A=pi*r^2","C=2*pi*r"]},{"id":"trig","inputs":["2","","","","0"],"expectedContains":["SOHCAHTOA","sin=opp/hyp"]}],"usage":"The ACT is the test where you're on your own for formulas — they give you nothing. This program bundles the 15-20 formulas that actually appear on the ACT Math section, organized by topic.\n\nLaunch `ACTMATH` from `prgm`. Open the category matching your current question:\n\n- `1:GEOMETRY` — circle, triangle, trapezoid, cylinder (the four shapes ACT loves)\n- `2:TRIG` — SOHCAHTOA, Law of Sines, Law of Cosines\n- `3:SEQUENCES` — arithmetic + geometric nth-term and sum formulas\n- `4:PROB` — basic probability + and/or rules\n- `5:LOGS` — log definition, product/quotient/power rules, change-of-base\n\nPure reference — no prompts. Flip through between problems.","example":{"problem":"ACT question: In a triangle, sides a=5, b=7, and angle C between them is 60°. Find side c.","walkthrough":"This is a Law of Cosines setup.\n\n1. Run `ACTMATH`, pick `2:TRIG`.\n2. Page through to: `c2=a2+b2-2ab*cosC`.\n3. Plug in: c² = 25 + 49 − 2(5)(7)(0.5) = 74 − 35 = 39.\n4. c = √39 ≈ **6.24**. ✓\n\nACT wants you to nail this in under 90 seconds. Having the formula on-screen saves the scratch-work of rederiving it."}}