Tier 1 · sat

SAT Math Formula Sheet

The formulas the SAT does NOT give you — quadratic formula, exponent rules, distance, midpoint, linear forms.

Files (1)

SATMATH.py1134 bytes

def p(s):print(s)
def w():input("...")
def o1():
 p("=QUADRATIC=")
 p("ax2+bx+c=0")
 p("x=(-b+/-")
 p("sqrt(b2-4ac))")
 p("/(2a)")
 w()
 p("DISC=b2-4ac")
 p(">0: 2 real")
 p("=0: 1 real")
 p("<0: 2 imag")
 w()
def o2():
 p("=EXPONENTS=")
 p("x^a*x^b=")
 p("x^(a+b)")
 p("x^a/x^b=")
 p("x^(a-b)")
 w()
 p("(x^a)^b=")
 p("x^(ab)")
 p("x^(-a)=")
 p("1/x^a")
 w()
 p("x^(1/n)=")
 p("nth root x")
 p("x^0=1 (x!=0)")
 w()
def o3():
 p("=LINES=")
 p("SLOPE-INT:")
 p("y=mx+b")
 p("POINT-SL:")
 p("y-y1=m(x-x1)")
 w()
 p("STANDARD:")
 p("Ax+By=C")
 p("m=(y2-y1)")
 p("/(x2-x1)")
 w()
def o4():
 p("=DIST MID=")
 p("d=sqrt(")
 p("(x2-x1)^2+")
 p("(y2-y1)^2)")
 w()
 p("MID=(")
 p("(x1+x2)/2,")
 p("(y1+y2)/2)")
 w()
def o5():
 p("=SYSTEM HINT=")
 p("SUB: solve")
 p("1 for 1 var")
 p("sub in other")
 w()
 p("ELIM: mult")
 p("eqs to match")
 p("coefs, add")
 w()
def menu():
 while True:
  p("=SAT MATH=")
  p("1:QUADRATIC")
  p("2:EXPONENTS")
  p("3:LINES")
  p("4:DIST/MID")
  p("5:SYSTEMS")
  p("0:EXIT")
  c=input("?>")
  if c=="1":o1()
  elif c=="2":o2()
  elif c=="3":o3()
  elif c=="4":o4()
  elif c=="5":o5()
  elif c=="0":break
menu()

How to use it

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.

Launch SATMATH from prgm. Pick the category you need:

1:QUADRATIC — the formula + discriminant interpretation
2:EXPONENTS — the 6 exponent rules
3:LINES — slope-intercept, point-slope, standard form, slope formula
4:DIST/MID — distance and midpoint between two points
5:SYSTEMS — substitution vs elimination procedure

Each page prints 5-8 lines paginated with ... presses. Zero inputs — pure reference.

Example problem

SAT Math: Solve 2x² − 5x − 3 = 0.

You need the quadratic formula but blanked.

Run SATMATH, pick 1:QUADRATIC.
Screen shows: x=(-b+/- sqrt(b2-4ac))/(2a).
Apply with a=2, b=−5, c=−3:
- Discriminant: (−5)² − 4(2)(−3) = 25 + 24 = 49
- x = (5 ± 7) / 4 → x = 3 or x = −½. ✓

The 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.

TI-84 Plus CE — try before committingoff

TI-84 Plus CE




  (calculator off)

  Press ON to start.

Test cases (2)

ID	Inputs	Expected contains
quad-formula	1, , , 0	ax2+bx+c=0, x=(-b+/-
exp-rules	2, , , , 0	x^a*x^b=, x^(a+b)