{"slug":"sat-formula-sheet","tier":1,"subject":"sat","title":"SAT Math Formula Sheet","description":"The formulas the SAT does NOT give you — quadratic formula, exponent rules, distance, midpoint, linear forms.","files":[{"filename":"SATMATH.py","content":"def p(s):print(s)\ndef w():input(\"...\")\ndef o1():\n p(\"=QUADRATIC=\")\n p(\"ax2+bx+c=0\")\n p(\"x=(-b+/-\")\n p(\"sqrt(b2-4ac))\")\n p(\"/(2a)\")\n w()\n p(\"DISC=b2-4ac\")\n p(\">0: 2 real\")\n p(\"=0: 1 real\")\n p(\"<0: 2 imag\")\n w()\ndef o2():\n p(\"=EXPONENTS=\")\n p(\"x^a*x^b=\")\n p(\"x^(a+b)\")\n p(\"x^a/x^b=\")\n p(\"x^(a-b)\")\n w()\n p(\"(x^a)^b=\")\n p(\"x^(ab)\")\n p(\"x^(-a)=\")\n p(\"1/x^a\")\n w()\n p(\"x^(1/n)=\")\n p(\"nth root x\")\n p(\"x^0=1 (x!=0)\")\n w()\ndef o3():\n p(\"=LINES=\")\n p(\"SLOPE-INT:\")\n p(\"y=mx+b\")\n p(\"POINT-SL:\")\n p(\"y-y1=m(x-x1)\")\n w()\n p(\"STANDARD:\")\n p(\"Ax+By=C\")\n p(\"m=(y2-y1)\")\n p(\"/(x2-x1)\")\n w()\ndef o4():\n p(\"=DIST MID=\")\n p(\"d=sqrt(\")\n p(\"(x2-x1)^2+\")\n p(\"(y2-y1)^2)\")\n w()\n p(\"MID=(\")\n p(\"(x1+x2)/2,\")\n p(\"(y1+y2)/2)\")\n w()\ndef o5():\n p(\"=SYSTEM HINT=\")\n p(\"SUB: solve\")\n p(\"1 for 1 var\")\n p(\"sub in other\")\n w()\n p(\"ELIM: mult\")\n p(\"eqs to match\")\n p(\"coefs, add\")\n w()\ndef menu():\n while True:\n  p(\"=SAT MATH=\")\n  p(\"1:QUADRATIC\")\n  p(\"2:EXPONENTS\")\n  p(\"3:LINES\")\n  p(\"4:DIST/MID\")\n  p(\"5:SYSTEMS\")\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":"quad-formula","inputs":["1","","","0"],"expectedContains":["ax2+bx+c=0","x=(-b+/-"]},{"id":"exp-rules","inputs":["2","","","","0"],"expectedContains":["x^a*x^b=","x^(a+b)"]}],"usage":"The SAT gives you a small formula strip at the start of each Math section — circles, triangles, basic volume. Everything else (quadratic formula, exponent rules, line equations, distance/midpoint) you have to know cold. This program keeps all of it one menu away on the calculator.\n\nLaunch `SATMATH` from `prgm`. Pick the category you need:\n\n- `1:QUADRATIC` — the formula + discriminant interpretation\n- `2:EXPONENTS` — the 6 exponent rules\n- `3:LINES` — slope-intercept, point-slope, standard form, slope formula\n- `4:DIST/MID` — distance and midpoint between two points\n- `5:SYSTEMS` — substitution vs elimination procedure\n\nEach page prints 5-8 lines paginated with `...` presses. Zero inputs — pure reference.","example":{"problem":"SAT Math: Solve 2x² − 5x − 3 = 0.","walkthrough":"You need the quadratic formula but blanked.\n\n1. Run `SATMATH`, pick `1:QUADRATIC`.\n2. Screen shows: `x=(-b+/- sqrt(b2-4ac))/(2a)`.\n3. Apply with a=2, b=−5, c=−3:\n   - Discriminant: (−5)² − 4(2)(−3) = 25 + 24 = 49\n   - x = (5 ± 7) / 4 → **x = 3 or x = −½**. ✓\n\nThe discriminant page also tells you that since it was positive, you'd expect two real solutions — quick sanity check before you spend 90 seconds solving."}}