{"slug":"sat-no-calc-tricks","tier":1,"subject":"sat","title":"SAT No-Calculator Tricks","description":"Shortcuts tuned for the SAT Math no-calculator section — fast factoring, fraction ops, percent hacks, and sign-analysis.","files":[{"filename":"SATNOCAL.py","content":"def p(s):print(s)\ndef w():input(\"...\")\ndef o1():\n p(\"=FAST FACT=\")\n p(\"ax2+bx+c\")\n p(\"find m,n:\")\n p(\"m*n=a*c\")\n p(\"m+n=b\")\n w()\n p(\"Then split:\")\n p(\"ax2+mx+nx+c\")\n p(\"factor by\")\n p(\"grouping\")\n w()\ndef o2():\n p(\"=FRACTIONS=\")\n p(\"a/b + c/d=\")\n p(\"(ad+bc)/bd\")\n w()\n p(\"DIV by frac:\")\n p(\"flip + mult\")\n p(\"a/b / c/d=\")\n p(\"ad/bc\")\n w()\ndef o3():\n p(\"=PERCENTS=\")\n p(\"x% of y=\")\n p(\"xy/100\")\n w()\n p(\"INC by x%:\")\n p(\"*(1+x/100)\")\n p(\"DEC by x%:\")\n p(\"*(1-x/100)\")\n w()\n p(\"% CHANGE:\")\n p(\"(new-old)\")\n p(\"/old *100\")\n w()\ndef o4():\n p(\"=SIGN ANAL=\")\n p(\"(x-a)(x-b)>0\")\n p(\"test regions:\")\n p(\"x<a: both -\")\n p(\"a<x<b: mixed\")\n p(\"x>b: both +\")\n w()\ndef o5():\n p(\"=COMMON CUBES=\")\n p(\"1,8,27,64\")\n p(\"125,216,343\")\n p(\"SQUARES:\")\n p(\"1,4,9,16,25\")\n p(\"36,49,64,81\")\n p(\"100,121,144\")\n w()\ndef menu():\n while True:\n  p(\"=NO-CALC=\")\n  p(\"1:FACTORING\")\n  p(\"2:FRACTIONS\")\n  p(\"3:PERCENTS\")\n  p(\"4:SIGN ANAL\")\n  p(\"5:NUM TABLES\")\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":"factoring","inputs":["1","","","0"],"expectedContains":["ax2+bx+c","m*n=a*c"]},{"id":"percents","inputs":["3","","","","0"],"expectedContains":["x% of y=","xy/100"]}],"usage":"The no-calc section of the SAT Math is where most students lose points. You're not allowed to reach for the calculator, so you need these patterns in your head — this program keeps them a tap away before you start the section.\n\nLaunch `SATNOCAL` from `prgm`. Skim your weak areas before the section starts:\n\n- `1:FACTORING` — the AC method for quadratics where a≠1\n- `2:FRACTIONS` — add/divide fraction formulas\n- `3:PERCENTS` — x% of y, increase/decrease, percent change\n- `4:SIGN ANAL` — how to test regions for product-of-factors inequalities\n- `5:NUM TABLES` — first 7 cubes and 12 squares (memory aid)\n\nEvery page is pure reference — no inputs. Read, close, take the test.","example":{"problem":"SAT no-calc: What is 15% of 80?","walkthrough":"1. Run `SATNOCAL`, pick `3:PERCENTS`.\n2. Screen shows: `x% of y = xy/100`.\n3. Apply: (15 × 80) / 100 = 1200 / 100 = **12**. ✓\n\nFaster mental math once the formula is in front of you. SAT rewards this — most no-calc questions are ≤ 60 seconds with the right pattern."}}