def polynomial_function_find_negative():
max_coeff_abs = 144
min_degree = 2
max_degree = 5
degree = randint(min_degree, max_degree)
coeffs = around(random.rand(6) * (max_coeff_abs * 2)) - max_coeff_abs
x = symbols('x')
# f(x)
expr = 0
# f(-x)
neg_expr = 0
# arange is half open; it doesn't include the top value, so we add 1
for i in arange(degree - 1) + 1:
coeff = Rational(coeffs[int(i)])
power = Rational(degree - i)
expr += coeff * (x)**power
neg_expr += coeff * (-x)**power
question = fmath("f(x) = " + latex(expr))
answer = fmath("f(-x) = " + latex(neg_expr))
return create_full_text_problem([question], [answer])
def geom_parabola_given_v_aos_p_find_eq_and_lr(
env: Environment = Environment.prod):
problem_instruction = f"Find the equation of a parabola, and find the two points that define the latus rectum."
a = choice([randint(-5, 0), randint(1, 6)])
a_abs = abs(a)
axis = choice([Axis.x, Axis.y])
d = -a
shift = (0, 0) if bool(getrandbits(1)) else (randint(-5, 6),
randint(-5, 6))
shifted_d = d + (shift[0] if axis == Axis.x else shift[1])
d_str = f"x={shifted_d}" if axis == Axis.x else f"y={shifted_d}"
problem_text = f"Directrix the line {fmath(d_str, env)}; vertex at {fmath(str(shift), env)}"
expr = f_expr_str_parabola(a, shift[0], shift[1], axis)
solution_text = fmath(expr, env)
problem = create_full_text_problem([problem_instruction, problem_text],
[solution_text])
if env.is_debug():
debug_info = [{'a_abs': a_abs}, {"d": d}]
return DebugProblemWrapper(debug_info, problem)
return problem
def geom_parabola_given_f_v_find_eq_and_lr(
env: Environment = Environment.prod):
problem_instruction = f"Find the equation of a parabola, and find the two points that define the latus rectum."
a = choice([randint(-5, 0), randint(1, 6)])
a_abs = abs(a)
axis = choice([Axis.x, Axis.y])
f = (0, a) if axis == Axis.y else (a, 0)
shift = (0, 0) if bool(getrandbits(1)) else (randint(-5, 6),
randint(-5, 6))
shifted_f = tuple(map(sum, zip(f, shift)))
problem_text = f"Focus at {fmath(str(shifted_f), env)}; vertex at {fmath(str(shift), env)}"
expr = f_expr_str_parabola(a, shift[0], shift[1], axis)
# lr_abs = 4*
solution_text = fmath(expr, env)
problem = create_full_text_problem([problem_instruction, problem_text],
[solution_text])
if env.is_debug():
debug_info = [{'a_abs': a_abs}, {"f": f}]
return DebugProblemWrapper(debug_info, problem)
return problem
def compound_interest_discrete_find_effective_roi():
compounding_choices = {1: "annually", 4: "quarterly", 12: "monthly", 356: "daily"}
n_choices = list(compounding_choices.keys())
n = choice(n_choices)
r = randint(1, 15) / 100
r_str = rf"{int(r*100)}\%"
r_e = ((1 + r / n) ** (n)) - 1
r_e_str = rf"{round(r_e*100,3)}\%"
problem_instruction = "Find the effective return on investment for this investment (round to 3 decimal points):"
problem_text = rf"For {fmath(r_str)} compounded {compounding_choices[n]}"
solution_text = fmath(r_e_str)
content = [
Widget(TextWidgetOptions(problem_instruction)),
Widget(TextWidgetOptions(problem_text)),
]
solution = Widget(TextWidgetOptions(solution_text))
return Problem(content, [solution])
def quadratic_function_find_vertex_intercept_form():
# We may want to include fractions for more difficult problems in the future
min_c = 1
max_c = 6
min_n = 1
max_n = 30
min_a = 1
max_a = 5
c = randint(min_c, max_c)
n = randint(min_n, max_n)
a = randint(min_a, max_a)
c = -c if rand() < 0.5 else c
x = symbols('x')
expr = a * (x + c)**2
# Expand into standard form
expr = expand(expr)
# Remove c^2
expr = expr - a * c**2
# Add n
expr = expr + n
eval_expr = a * (x + c)**2 + n - (a * (c**2))
problem_content = fmath(latex(expr) + ' = 0')
problem_solution = fmath(latex(eval_expr) + ' = 0')
return create_full_text_problem([problem_content], [problem_solution])
def compound_interest_continuous_find_effective_roi():
r = randint(1, 15) / 100
r_str = rf"{int(r*100)}\%"
r_e = (e ** r) - 1
r_e_str = rf"{round(r_e*100,3)}\%"
problem_instruction = "Find the effective return on investment for this investment (round to 3 decimal points):"
problem_text = rf"For {fmath(r_str)} compounded continuously"
solution_text = fmath(r_e_str)
content = [
Widget(TextWidgetOptions(problem_instruction)),
Widget(TextWidgetOptions(problem_text)),
]
solution = Widget(TextWidgetOptions(solution_text))
return Problem(content, [solution])