8 categories, 26 formulas total. Designed for grades 9–10 curriculum

# MathPhys 9-10 - NumWorks
# Created by Pärle Laigna - https://parle.laigna.com
# Arrows:select OK:choose Back:back
from kandinsky import fill_rect as F,draw_string as D
from ion import keydown as K
from time import sleep as Z
from math import pi,sqrt,sin,cos,tan,asin,acos,atan,degrees,radians
SW,SH=320,222
BK=(0,)*3;WH=(255,)*3
BL=(50,110,230);TL=(0,190,190)
YL=(220,200,60);DG=(120,)*3

okv=1 if K(4)or K(52) else 0

def okd():
 return K(4)or K(52)

def okp():
 global okv
 d=okd()
 if d and not okv:
  okv=1
  return True
 if not d:okv=0
 return False

def wup():
 while okd():Z(0.02)
 Z(0.12)

def menu(title,items,sub=False):
 sel=0;n=len(items)
 while True:
  F(0,0,SW,SH,BK)
  D(title,SW//2-len(title)*5,6,TL,BK)
  F(0,24,SW,2,(40,)*3)
  for i in range(n):
   y=34+i*22
   if i==sel:
    F(8,y,SW-16,20,BL)
    D("> "+items[i],14,y+2,WH,BL)
   else:
    D("  "+items[i],14,y+2,DG,BK)
  if sub:D("Back=return",100,SH-16,(60,)*3,BK)
  else:D("Back=quit",115,SH-16,(60,)*3,BK)
  while True:
   if K(1):sel=(sel-1)%n;Z(0.15);break
   if K(2):sel=(sel+1)%n;Z(0.15);break
   if okp():wup();return sel
   if K(17):return-1
   Z(0.04)

def inp(prompt):
 try:return float(input(prompt))
 except:return None

def show(lines):
 F(0,0,SW,SH,BK)
 D("RESULT",130,6,TL,BK)
 F(0,24,SW,2,(40,)*3)
 for i,ln in enumerate(lines):
  c=YL if i==len(lines)-1 else WH
  D(str(ln),14,34+i*20,c,BK)
 D("OK=back",130,SH-16,DG,BK)
 while True:
  if okp()or K(17):wup();return
  Z(0.04)

# === ALGEBRA ===
def f_quad():
 a=inp("a: ");b=inp("b: ");c=inp("c: ")
 if a and a!=0 and b is not None and c is not None:
  disc=b*b-4*a*c
  r=["ax^2 + bx + c = 0",
   "a="+str(a)+" b="+str(b)+" c="+str(c),
   "D = b^2-4ac = "+str(round(disc,6))]
  if disc>0:
   x1=(-b+sqrt(disc))/(2*a)
   x2=(-b-sqrt(disc))/(2*a)
   r+=["x1 = "+str(round(x1,6)),
    "x2 = "+str(round(x2,6))]
  elif disc==0:
   x1=-b/(2*a)
   r+=["x = "+str(round(x1,6))+" (double)"]
  else:
   re=-b/(2*a);im=sqrt(-disc)/(2*a)
   r+=["x1 = "+str(round(re,4))+"+"+str(round(im,4))+"i",
    "x2 = "+str(round(re,4))+"-"+str(round(im,4))+"i"]
  show(r)

def f_slope():
 x1=inp("x1: ");y1=inp("y1: ")
 x2=inp("x2: ");y2=inp("y2: ")
 if x1 is not None and y1 is not None and x2 is not None and y2 is not None:
  r=["Points: ("+str(x1)+","+str(y1)+") ("+str(x2)+","+str(y2)+")"]
  if x2!=x1:
   m=(y2-y1)/(x2-x1)
   b=y1-m*x1
   d=sqrt((x2-x1)**2+(y2-y1)**2)
   r+=["Slope m = "+str(round(m,6)),
    "y-int b = "+str(round(b,6)),
    "y = "+str(round(m,4))+"x + "+str(round(b,4)),
    "Distance = "+str(round(d,6))]
  else:r+=["Vertical line (x="+str(x1)+")"]
  show(r)

def f_prop():
 c=menu("Proportions",
  ["a/b = c/d  (find d)",
   "a/b = c/d  (find c)"],True)
 if c==0:
  a=inp("a: ");b=inp("b: ");cv=inp("c: ")
  if a and b and cv is not None and a!=0:
   show(["a/b = c/d","a="+str(a)+" b="+str(b)+" c="+str(cv),
    "d = b*c/a","d = "+str(round(b*cv/a,6))])
 elif c==1:
  a=inp("a: ");b=inp("b: ");d=inp("d: ")
  if a and b and d is not None and b!=0:
   show(["a/b = c/d","a="+str(a)+" b="+str(b)+" d="+str(d),
    "c = a*d/b","c = "+str(round(a*d/b,6))])

# === TRIGONOMETRY ===
def f_trig():
 c=menu("Trigonometry",
  ["sin/cos/tan (angle->ratio)",
   "arcsin/cos/tan (ratio->angle)",
   "Right triangle solver"],True)
 if c==0:
  a=inp("Angle (degrees): ")
  if a is not None:
   r=radians(a)
   show(["Angle = "+str(a)+" deg",
    "sin = "+str(round(sin(r),8)),
    "cos = "+str(round(cos(r),8)),
    "tan = "+str(round(tan(r),8))if abs(cos(r))>1e-10 else "tan = undefined"])
 elif c==1:
  v=inp("Ratio value: ")
  if v is not None:
   r=["Value = "+str(v)]
   if-1<=v<=1:
    r+=["arcsin = "+str(round(degrees(asin(v)),6))+" deg",
     "arccos = "+str(round(degrees(acos(v)),6))+" deg"]
   else:r+=["arcsin/arccos: |v| must be <=1"]
   r+=["arctan = "+str(round(degrees(atan(v)),6))+" deg"]
   show(r)
 elif c==2:
  print("\n"*5+"Right triangle: know 2 sides")
  a=inp("Side a (or 0=unknown): ")
  b=inp("Side b (or 0=unknown): ")
  c2=inp("Hypotenuse c (or 0=unknown): ")
  if a is not None and b is not None and c2 is not None:
   r=["Right triangle solver"]
   if a and b and not c2:
    c2=sqrt(a*a+b*b)
    r+=["c = "+str(round(c2,6))]
   elif a and c2 and not b:
    if c2>a:b=sqrt(c2*c2-a*a);r+=["b = "+str(round(b,6))]
   elif b and c2 and not a:
    if c2>b:a=sqrt(c2*c2-b*b);r+=["a = "+str(round(a,6))]
   if a and c2 and c2!=0:
    A=degrees(asin(a/c2))
    r+=["Angle A = "+str(round(A,4))+" deg",
     "Angle B = "+str(round(90-A,4))+" deg"]
   show(r)

# === MECHANICS ===
def f_force():
 c=menu("Force (F=ma)",
  ["F = m x a  (find force)",
   "m = F / a  (find mass)",
   "a = F / m  (find accel)"],True)
 if c==0:
  m=inp("Mass (kg): ");a=inp("Accel (m/s2): ")
  if m and a is not None:
   show(["F = m x a","m="+str(m)+" a="+str(a),
    "F = "+str(round(m*a,6))+" N"])
 elif c==1:
  f=inp("Force (N): ");a=inp("Accel (m/s2): ")
  if f is not None and a and a!=0:
   show(["m = F / a","F="+str(f)+" a="+str(a),
    "m = "+str(round(f/a,6))+" kg"])
 elif c==2:
  f=inp("Force (N): ");m=inp("Mass (kg): ")
  if f is not None and m and m!=0:
   show(["a = F / m","F="+str(f)+" m="+str(m),
    "a = "+str(round(f/m,6))+" m/s2"])

def f_energy():
 c=menu("Energy & Work",
  ["Ek = 1/2 mv^2 (kinetic)",
   "Ep = mgh (potential)",
   "W = F x d (work)",
   "P = W / t (power)"],True)
 if c==0:
  m=inp("Mass (kg): ");v=inp("Speed (m/s): ")
  if m and v is not None:
   show(["Kinetic energy","m="+str(m)+" v="+str(v),
    "Ek = 0.5 x m x v^2",
    "Ek = "+str(round(0.5*m*v*v,4))+" J"])
 elif c==1:
  m=inp("Mass (kg): ");h=inp("Height (m): ")
  if m and h is not None:
   g=9.81
   show(["Potential energy (g=9.81)",
    "m="+str(m)+" h="+str(h),
    "Ep = m x g x h",
    "Ep = "+str(round(m*g*h,4))+" J"])
 elif c==2:
  f=inp("Force (N): ");d=inp("Distance (m): ")
  if f is not None and d is not None:
   show(["Work","F="+str(f)+" d="+str(d),
    "W = F x d","W = "+str(round(f*d,4))+" J"])
 elif c==3:
  w=inp("Work (J): ");t=inp("Time (s): ")
  if w is not None and t and t!=0:
   show(["Power","W="+str(w)+" t="+str(t),
    "P = W / t","P = "+str(round(w/t,4))+" W"])

# === ELECTRICITY ===
def f_ohm():
 c=menu("Ohm's law + Power",
  ["V = I x R  (voltage)",
   "I = V / R  (current)",
   "R = V / I  (resistance)",
   "P = V x I  (power)",
   "P = I^2 x R",
   "P = V^2 / R"],True)
 vals=[(("Current I (A): ","Resistance R (ohm): "),lambda i,r:("V = I x R","V = "+str(round(i*r,6))+" V")),
  (("Voltage V (V): ","Resistance R (ohm): "),lambda v,r:("I = V / R","I = "+str(round(v/r,6))+" A")),
  (("Voltage V (V): ","Current I (A): "),lambda v,i:("R = V / I","R = "+str(round(v/i,6))+" ohm")),
  (("Voltage V (V): ","Current I (A): "),lambda v,i:("P = V x I","P = "+str(round(v*i,6))+" W")),
  (("Current I (A): ","Resistance R (ohm): "),lambda i,r:("P = I^2 x R","P = "+str(round(i*i*r,6))+" W")),
  (("Voltage V (V): ","Resistance R (ohm): "),lambda v,r:("P = V^2 / R","P = "+str(round(v*v/r,6))+" W"))]
 if 0<=c<6:
  pr,fn=vals[c]
  a=inp(pr[0]);b=inp(pr[1])
  if a is not None and b is not None and b!=0:
   f,r=fn(a,b)
   show([f,"= "+str(a)+", "+str(b),r])

# === KINEMATICS ===
def f_kinem():
 c=menu("Kinematics",
  ["v = v0 + at",
   "d = v0*t + 1/2*a*t^2",
   "v^2 = v0^2 + 2ad",
   "d = (v0+v)/2 * t"],True)
 if c==0:
  v0=inp("v0 (m/s): ");a=inp("a (m/s2): ");t=inp("t (s): ")
  if v0 is not None and a is not None and t is not None:
   show(["v = v0 + a*t",
    "v0="+str(v0)+" a="+str(a)+" t="+str(t),
    "v = "+str(round(v0+a*t,6))+" m/s"])
 elif c==1:
  v0=inp("v0 (m/s): ");a=inp("a (m/s2): ");t=inp("t (s): ")
  if v0 is not None and a is not None and t is not None:
   d=v0*t+0.5*a*t*t
   show(["d = v0*t + 0.5*a*t^2",
    "v0="+str(v0)+" a="+str(a)+" t="+str(t),
    "d = "+str(round(d,6))+" m"])
 elif c==2:
  v0=inp("v0 (m/s): ");a=inp("a (m/s2): ");d=inp("d (m): ")
  if v0 is not None and a is not None and d is not None:
   v2=v0*v0+2*a*d
   if v2>=0:
    show(["v^2 = v0^2 + 2ad",
     "v0="+str(v0)+" a="+str(a)+" d="+str(d),
     "v^2 = "+str(round(v2,4)),
     "v = "+str(round(sqrt(v2),6))+" m/s"])
   else:
    show(["v^2 = v0^2 + 2ad",
     "v^2 = "+str(round(v2,4)),
     "Object stops before d"])
 elif c==3:
  v0=inp("v0 (m/s): ");v=inp("v (m/s): ");t=inp("t (s): ")
  if v0 is not None and v is not None and t is not None:
   show(["d = (v0+v)/2 * t",
    "v0="+str(v0)+" v="+str(v)+" t="+str(t),
    "d = "+str(round((v0+v)/2*t,6))+" m"])

CATS=["Algebra - Quadratic",
 "Algebra - Slope & Line",
 "Algebra - Proportions",
 "Trigonometry",
 "Force (F=ma)",
 "Energy & Work & Power",
 "Electricity (Ohm's law)",
 "Kinematics (motion)"]
FNS=[f_quad,f_slope,f_prop,f_trig,
 f_force,f_energy,f_ohm,f_kinem]
def run():
 while True:
  c=menu("MathPhys 9-10",CATS)
  if c<0:return
  while True:
   FNS[c]()
   break
run()