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 compound_interest_compare_discrete_vs_discrete():
n_1, n_2 = sample(compounding_n_choices, 2)
# The way this works is that we come up with an interest rate for the highest compounding rate
# then we come up with an interest rate that is some amount higher for the lower compounding rate
# this way it's not dead easy to tell which is the better deal--and that's the point
base_rate = randint(1, 15) / 100
higher_rate = base_rate + choice(linspace(0.1, 0.3, 9)) / 100
# The lower interest rate with the higher compounding rate should be fractional as
# often as the other interest rate
if bool(getrandbits(1)):
old_base_rate = base_rate
base_rate -= higher_rate - base_rate
higher_rate = old_base_rate
if n_1 > n_2:
r_1 = base_rate
r_2 = higher_rate
else:
r_1 = higher_rate
r_2 = base_rate
r_e_1 = f_effective_rate_of_interest_discrete(r_1, n_1)
r_e_2 = f_effective_rate_of_interest_discrete(r_1, n_1)
r_n_description_1 = f"{fmath(fper(r_1,))} compounded {compounding_choices[n_1]}"
r_n_description_2 = f"{fmath(fper(r_2,))} compounded {compounding_choices[n_2]}"
solution_description = r_n_description_1 if r_e_1 > r_e_2 else r_n_description_2
problem_instruction = "Which of the following is a better investment?"
description_set = [r_n_description_1, r_n_description_2]
# Randomize the order
if bool(getrandbits(1)):
description_set = description_set.reverse()
problem_text = f"{r_n_description_1} or {r_n_description_2}"
solution_text = solution_description
return create_full_text_problem(
[problem_instruction, problem_text], [solution_text]
)
def compound_interest_continuous_find_effective_roi():
r = randint(1, 15) / 100
r_e = f_effective_rate_of_interest_continuous(r)
problem_instruction = "Find the effective return on investment for this investment (round to 3 decimal points):"
problem_text = f"For {fmath(fper(r))} compounded continuously"
solution_text = fmath(fper(r_e))
return create_full_text_problem(
[problem_instruction, problem_text], [solution_text]
)
def compound_interest_discrete_find_effective_roi():
n = choice(compounding_n_choices)
r = randint(1, 15) / 100
r_e = f_effective_rate_of_interest_discrete(r, n)
problem_instruction = "Find the effective return on investment for this investment (round to 3 decimal points):"
problem_text = f"For {fmath(fper(r))} compounded {compounding_choices[n]}"
solution_text = fmath(fper(r_e))
return create_full_text_problem(
[problem_instruction, problem_text], [solution_text]
)
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_instruction = "Find vertex "
problem_expr = fmath(latex(expr) + ' = 0')
problem_solution = fmath(latex(eval_expr) + ' = 0')
return create_full_text_problem([problem_expr], [problem_solution])
def compound_interest_continuous_find_p():
a = 50 * randint(1, 21)
t = randint(1, 3) + choice([0, 0.5])
r = randint(1, 15) / 100
p = round(f_present_value_continuous(a, r, t), 2)
plural_end = "s" if t != 1 else ""
problem_instruction = "Find the present value of this investment:"
problem_text = f"To get {fmath(fcur(a))} after {fmath(ffrac(t))} year{plural_end} at {fmath(fper(r))} compounded continuously"
solution_text = fmath(fcur(p))
return create_full_text_problem(
[problem_instruction, problem_text], [solution_text]
)
def compound_interest_discrete_find_p():
a = 50 * randint(1, 21)
n = choice(compounding_n_choices)
t = randint(1, 3) + choice([0, 0.5])
r = randint(1, 15) / 100
p = round(f_present_value_discrete(a, r, n, t), 2)
year_word = fplural("year", "years", t)
problem_instruction = "Find the present value of this investment:"
problem_text = f"To get {fmath(fcur(a))} after {fmath(ffrac(t))} {year_word} at {fmath(fper(r))} compounded {compounding_choices[n]}"
solution_text = fmath(fcur(p))
return create_full_text_problem(
[problem_instruction, problem_text], [solution_text]
)
def compound_interest_discrete_find_a():
p = 50 * randint(1, 21)
n = choice(compounding_n_choices)
t = randint(1, 3) + choice([0, 0.5])
r = randint(1, 15) / 100
a = f_compound_interest_discrete(p, r, n, t)
year_word = fplural("year", "years", t)
problem_instruction = "Find the amount that results from this following investment:"
problem_text = f"{fmath(fcur(p))} invested at {fmath(fcur(r))} compounded {compounding_choices[n]} after a period of {fmath(ffrac(t))} {year_word}"
solution_text = fmath(fcur(a))
return create_full_text_problem(
[problem_instruction, problem_text], [solution_text]
)
def sum_consecutive_integers(integer_count: bool = None, max_initial_integer: int = 50) -> Problem:
if integer_count is not None and integer_count < 2:
raise ValueError('parameter integer_count on sum_consecutive_integers must be greater than or equal to 2')
integer_count = integer_count if integer_count is not None else Random().randint(3, 5)
base_integer = Random().randrange(0, max_initial_integer)
final_integer = 0
for i in range(integer_count):
final_integer += base_integer + i
nth_integer_to_find = Random().randint(1, integer_count)
ordinal_number = ford(nth_integer_to_find)
question_label = f"The number {fmath(final_integer)} is the sum of {fmath(integer_count)} consecutive integers. What is the {ordinal_number}?"
solution_integer = base_integer + (nth_integer_to_find - 1)
solution = fmath(solution_integer)
return create_full_text_problem([question_label], [solution])