R/Derivatives.R
In dtkaplan/drillr: Simple drill question generator
Defines functions
D_quiz
D_structure
Test_images
Sinusoids
Powers
Exponentials
Polynomials
Documented in
Polynomials
#' First derivatives
#'
#' @export
Polynomials <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$\\partial_x\\,f(x) \\equiv 0$$" , "two", "$$f(x) \\equiv b$$",
"$$\\partial_x\\,f(x) \\equiv 0$$" , "two", "$$f(x) \\equiv a$$",
"$$\\partial_x\\,f(x) \\equiv 0$$" , "two", "$$f(x) \\equiv a + b$$",
"$$\\partial_x\\,f(x) \\equiv b$$" , "two", "$$f(x) \\equiv a + b x$$",
"$$\\partial_x\\,f(x) \\equiv a$$" , "two", "$$f(x) \\equiv a x + b$$",
"$$\\partial_x\\,f(x) \\equiv 2bx$$", "two", "$$f(x) \\equiv a + b x^2$$",
"$$\\partial_x\\,f(x) \\equiv 2ax$$", "two", "$$f(x) \\equiv a x^2 + b$$",
"$$\\partial_x\\,f(x) \\equiv b + 2 c x$$", "two", "$$f(x) \\equiv a + b x + c x^2$$",
"$$\\partial_x\\,f(x) \\equiv b + c x$$", "two", "$$f(x) \\equiv a + b x + c x^2 / 2$$",
"$$\\partial_x\\,f(x) \\equiv 2b + 2c x$$", "two", "$$f(x) \\equiv a + 2b x + c x^2$$",
"$$\\partial_x\\,f(x) \\equiv 2b + cx$$", "two", "$$f(x) \\equiv a + 2b x + c x^2/2$$",
"$$\\partial_x\\,f(x) \\equiv a + b$$", "two", "$$f(x) \\equiv a x + b x$$",
"$$\\partial_x\\,f(x) \\equiv ax + bx$$", "two", "$$f(x) \\equiv a x^2/2 + b x^2/2$$",
"$$\\partial_x\\,f(x) \\equiv b + 2cx + 3dx^2$$", "three", "$$f(x) \\equiv a + b x + c x^2 + d x^3$$",
"$$\\partial_x\\,f(x) \\equiv a+b + 2cx + dx^2$$", "three", "$$f(x) \\equiv ax+bx+cx^2+dx^3/3$$",
"$$\\partial_x\\,f(x) \\equiv bx + 2 c x + 2dx^2$$", "three", "$$f(x) \\equiv a +bx^2/2 + c x^2 + 2 d x^3/3$$",
"$$\\partial_x\\,f(x) \\equiv 2ax + b + 3cx^2$$", "three", "$$f(x) \\equiv a x^2 + b x + c x^3 + d$$",
"$$\\partial_x\\,f(x) \\equiv a + 3cx^2 - 2dx$$", "three", "$$f(x) \\equiv ax + b + cx^3 - dx^2$$",
"$$\\partial_x\\,f(x) \\equiv ax^2 + b + 4cx +16dx^3$$","three", "$$f(x) \\equiv ax^3/3 + bx + 2cx^2 + 4dx^4$$",
"$$\\partial_x\\,f(x) \\equiv 4dx^3 $$", "three", "$$f(x) \\equiv 4b + dx^4$$",
"$$\\partial_x\\,f(x) \\equiv c + 2cx$$", "three", "$$f(x) \\equiv cx + cx^2$$",
"$$\\partial_x\\,f(x) \\equiv d $$", "three", "$$f(x) \\equiv cx + cx^2$$",
"$$\\partial_x\\,f(x) \\equiv 2cbx $$", "three", "$$f(x) \\equiv c(a + bx^2)$$") %>%
mutate(id = "polynomials",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Exponentials <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$d_t\\, f(t) \\equiv k \\exp(kt )$$", "exponential", "$$f(t) \\equiv \\exp(kt)$$",
"$$d_t\\, f(t) \\equiv -k \\exp(-kt )$$", "exponential", "$$f(t) \\equiv \\exp(-kt )$$",
"$$d_t\\, f(t) \\equiv k\\exp(-kt )$$", "exponential", "$$f(t) \\equiv -\\exp(-kt )$$",
"$$d_t\\, f(t) \\equiv - \\exp( kt)$$", "exponential", "$$f(t) \\equiv -\\exp( kt)$$",
"$$d_t\\, f(t) \\equiv \\exp( t)$$", "exponential", "$$f(t) \\equiv \\exp( t)$$",
"$$d_t\\, f(t) \\equiv k \\exp( t)$$", "exponential", "$$f(t) \\equiv k \\exp(t )$$",
"$$d_t\\, f(t) \\equiv -k \\exp( t)$$", "exponential", "$$f(t) \\equiv -k \\exp(t)$$",
"$$d_t\\, f(t) \\equiv -k \\exp(-t )$$", "exponential", "$$f(t) \\equiv k\\exp(-t )$$",
"$$d_t\\, f(t) \\equiv k \\exp(-t )$$", "exponential", "$$f(t) \\equiv -k \\exp(-t )$$",
"$$d_t\\, f(t) \\equiv (1/k) \\exp(t/k)$$", "exponential", "$$f(t) \\equiv \\exp(t/k )$$",
"$$d_t\\, f(t) \\equiv (1/k^2)\\exp(t/k^2 )$$", "exponential", "$$f(t) \\equiv \\exp(t/k^2 )$$",
"$$d_t\\, f(t) \\equiv -(1/k)\\exp(-t/k )$$", "exponential", "$$f(t) \\equiv \\exp(-t/k )$$",
"$$d_t\\, f(t) \\equiv (1/k) \\exp(-t/k )$$", "exponential", "$$f(t) \\equiv -\\exp(-t/k )$$",
) %>%
mutate(id = "exponentials",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Powers <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$d_t\\, f(t) \\equiv 3 x^2$$", "powers", "$$f(t) \\equiv x^3$$",
"$$d_t\\, f(t) \\equiv -3 x^{-4}$$", "powers", "$$f(t) \\equiv x^{-3}$$",
"$$d_t\\, f(t) \\equiv 2 x^{1}$$", "powers", "$$f(t) \\equiv x^2$$",
"$$d_t\\, f(t) \\equiv 2 x^1$$", "powers", "$$f(t) \\equiv x^{-2}$$",
"$$d_t\\, f(t) \\equiv -1 x^{-2}$$", "powers", "$$f(t) \\equiv x^1$$",
"$$d_t\\, f(t) \\equiv \\ln(x)$$", "powers", "$$f(t) \\equiv x^{-1} $$",
"$$d_t\\, f(t) \\equiv 0$$", "powers", "$$f(t) \\equiv x^0$$",
"$$d_t\\, f(t) \\equiv 2 x^2$$", "powers", "$$f(t) \\equiv 2 x^3 / 3$$",
"$$d_t\\, f(t) \\equiv 3 x$$", "powers", "$$f(t) \\equiv 3 x^2 /2$$",
"$$d_t\\, f(t) \\equiv 0.5 x^{-0.5}$$", "powers", "$$f(t) \\equiv \\sqrt{x}$$",
"$$d_t\\, f(t) \\equiv 1.5 x^{0.5}$$", "powers", "$$f(t) \\equiv x^{1.5} $$",
"$$d_t\\, f(t) \\equiv x^{-2.5} $$", "powers", "$$f(t) \\equiv x^{-1.5}/1.5 $$",
"$$d_t\\, f(t) \\equiv x^{1.5}$$", "powers", "$$f(t) \\equiv x^{2.5}/2.5$$",
"$$d_t\\, f(t) \\equiv 5 x^{-3.5}$$", "powers", "$$f(t) \\equiv -2 x^{-2.5}$$",
) %>%
mutate(id = "powers",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Sinusoids <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$d_t\\, f(t) \\equiv a\\sin(at)$$", "trig", "$$f(t) \\equiv \\sin(at)$$",
"$$d_t\\, f(t) \\equiv a\\cos(t)$$", "trig", "$$f(t) \\equiv \\sin(t)$$",
"$$d_t\\, f(t) \\equiv -a\\sin(at)$$", "trig", "$$f(t) \\equiv \\cos(at)$$",
"$$d_t\\, f(t) \\equiv a\\sin(t)$$", "trig", "$$f(t) \\equiv a \\cos(t)$$",
"$$d_t\\, f(t) \\equiv a\\cos(t)$$", "trig", "$$f(t) \\equiv a \\sin(t)$$",
"$$d_t\\, f(t) \\equiv -a^2 \\sin(at)$$", "trig", "$$f(t) \\equiv -a \\sin(at)$$",
"$$d_t\\, f(t) \\equiv -a\\sin(t)$$", "trig", "$$f(t) \\equiv -a \\cos(t)$$",
"$$d_t\\, f(t) \\equiv -a\\cos(at)$$", "trig", "$$f(t) \\equiv -\\sin(at)$$",
"$$d_t\\, f(t) \\equiv - \\sin(-t)$$", "trig", "$$f(t) \\equiv -\\cos(-t)$$",
"$$d_t\\, f(t) \\equiv \\sin(-t)$$", "trig", "$$f(t) \\equiv \\cos(-t)$$",
"$$d_t\\, f(t) \\equiv - \\cos(-t)$$", "trig", "$$f(t) \\equiv \\sin(-t)$$",
) %>%
mutate(id = "trig",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Test_images <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"<img src='https://upload.wikimedia.org/wikipedia/commons/8/83/Sir_Isaac_Newton_%281643-1727%29.jpg' width = 200>", "", "Leibniz",
"Abraham Lincoln", "", "<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Gilbert_Stuart_Williamstown_Portrait_of_George_Washington.jpg/440px-Gilbert_Stuart_Williamstown_Portrait_of_George_Washington.jpg' width=200>",
"<img src='https://image.shutterstock.com/image-photo/no-limits-message-on-asphalt-260nw-198889661.jpg' width=200>", "", "Math 141Z"
) %>%
mutate(id = "images",
direction = direction,
forward = "Which matches?",
backward = "Which matches backward?")
}
#' @export
D_structure <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"0", "all","$$\\partial_x \\exp(t)$$",
"0", "all","$$\\partial_t \\ln(x)$$",
"0", "all", "$$\\partial_x 7$$",
"1", "all", "$$\\partial_x x$$",
"1", "all", "$$\\partial_y y x^3$$",
"1", "all", "$$\\partial_x \\exp(x) \\sin(\\omega t)$$",
"fundamental", "all", "$$\\partial_x 7x$$",
"fundamental", "all", "$$\\partial_y x \\exp(y)$$",
"fundamental", "all","$$\\partial_t \\exp(t)$$",
"fundamental", "all", "$$\\partial_x \\exp(t) \\sin(x)$$",
"fundamental", "all","$$\\partial_t \\sin(t)$$",
"fundamental", "all","$$\\partial_x x^n (n\\neq 0)",
"fundamental", "all","$$\\partial_x \\ln(x)$$",
"fundamental", "all", "$$\\partial_x \\mbox{sigmoid}(x, center, width)$$",
"scaled fundamental", "all", "$$\\partial_t \\exp(kt)$$",
"scaled fundamental", "all", "$$\\partial_t \\sin(2\\pi t/P)$$",
"scaled fundamental", "all", "$$\\partial_x \\mbox{sigmoid}(4 x, center, width)$$",
"scaled fundamental", "all", "$$\\partial_t \\sin(\\omega t)$$",
"product", "all", "$$\\partial_x \\exp(x) \\sin(ax)$$",
"product", "all", "$$\\partial_t \\sin(\\omega t)\\cos(\\alpha t)$$",
"product", "all", "$$\\partial_x x^3 \\sin(k x)$$",
"product", "all", "$$\\partial_x sin(\\omega x) \\ln(x)$$",
"product", "all", "$$\\partial_x x \\exp(x)$$",
"product", "all", "$$\\partial_x (x^2 + 1) \\exp(kx)$$",
"product", "all", "$$\\partial_t x \\cos(t) \\sin(\\omega t)$$",
"quotient", "all", "$$\\partial_x sin(x)/cos(x)$$",
"chain", "all", "$$\\partial_x \\sin(x^2)$$",
"chain", "all", "$$\\partial_x \\ln(x^2 + x)$$",
"linear combination", "all", "$$\\partial_x (x + 3)$$",
"linear combination", "all", "$$\\partial_x (a_0 + a_1 x + a_2 x^2)$$",
"linear combination", "all", "$$\\partial_x (2 x^2 - sin(\\omega x))$$",
"$$g(x) \\partial_x f(x) + f(x) \\partial_x g(x)$$", "rule", "$$\\partial_x \\left[f(x) g(x)\\right]$$",
"$$g(x) \\partial_x f(x) + \\partial_x g(x)$$", "rule", "$$\\partial_x \\left[f(x) + g(x)\\right]$$",
"$$g(x) f'(g(x)) g'(x)$$", "rule", "$$\\partial_x f(g(x))$$",
"$$g(x) a f'(a g(x)) g'(a x)$$", "rule", "$$\\partial_x f(a g(x))$$",
"$$g(x) g'(f(x)) f'(x)$$", "rule", "$$\\partial_x g(f(x))$$",
"$$g(x) a f'(a x)$$", "rule", "$$\\partial_x f(a x + b) $$",
"$$g(x) a \\partial_x f(x) + b \\partial_x g(x)$$", "rule", "$$\\partial_x \\left[a f(x) + b g(x)\\right]$$",
"$$g(x) b \\partial_x f(x) + a \\partial_x g(x)$$", "rule", "$\\partial_x \\left[b f(x) + a g(x)\\right]$$",
) %>%
mutate(id = "structure",
direction = direction,
forward = "Which structure matches the function?",
backward = "Which function matches the structure?")
}
#' @export
#' @export
D_quiz <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$7 \\cos(x) - 2/x$$", "quizx1",
"$$\\partial_x \\left[ 7 \\sin(x) - 2 \\ln(x)\\right]$$",
"$$7 \\cos(7x) - 1/x$$", "quizx1",
"$$\\partial_x \\left[ \\sin(7 x) - \\ln(2 x)\\right]$$",
"$$7 \\cos(7x) - 1/x $$", "quizx1", "$$\\partial_x \\left[ \\sin(7 x) - \\ln(x/2)\\right]$$",
"$$7 \\cos(x) - 2/x $$", "quizx1", "$$\\partial_x \\left[7 \\sin(x) - 2 \\ln(x/2)\\right]$$",
"$$-4 \\sqrt{6} / x^5$$", "quizx2", "$$\\partial_x \\left[ \\sqrt{6} / x^4 \\right]$$",
"$$4 \\sqrt{6} / x^5$$", "quizx2", "$$\\partial_x \\left[ - \\sqrt{6} / x^4 \\right]$$",
"$$4 \\sqrt{6} / x^4$$", "quizx2", "$$\\partial_x \\left[ -(4/3) \\sqrt{6} / x^3\\right]$$",
"$$4 \\sqrt{6} / x^6$$", "quizx2",
"$$\\partial_x \\left[ -(4/5) \\sqrt{6} / x^5\\right]$$",
"$$\\log(4)\\log(3) 4^x$$" , "quizx3", "$$\\partial_x \\log(3) 4^x$$",
"$$\\log(4)\\log(3) 3^x$$", "quizx3", "$$\\partial_x \\log(4) 3^x$$",
"$$3 \\log(4) x^2$$", "quizx3", "$$\\partial_x \\log(4) x^3$$",
"$$4 \\log(3) x^3$$", "quizx3", "$$\\partial_x \\log(3) x^4$$",
"$$- 75 \\sin(x)$$", "quizx4", "$$\\partial_x \\left[75 \\cos(x) \\right]$$",
"$$75 \\cos(x)$$", "quizx4", "$$\\partial_x \\left[75 \\sin(x) \\right]$$",
"$$75 \\sin(x)$$", "quizx4", "$$\\partial_x \\left[- 75 \\cos(x)\\right]$$",
"$$-75 \\cos(x)$$", "quizx4", "$$\\partial_x \\left[- 75 \\sin(x)\\right]$$",
"$$- 75 \\sin(75 x)$$", "quizx4", "$$\\partial_x \\left[\\cos(75 x) \\right]$$",
"$$75 \\cos(75 x)$$", "quizx4", "$$\\partial_x \\left[\\sin(75 x) \\right]$$",
"$$75 \\sin(75 x)$$", "quizx4", "$$\\partial_x \\left[-\\cos(75 x)\\right]$$",
"$$-75 \\cos(75 x)$$", "quizx4", "$$\\partial_x \\left[-\\sin(75 x)\\right]$$",
"$$2 - (1/9)/x^2 $$", "quizx5", "$$\\partial_x\\left[2 x + 1/(9x)\\right]$$",
"$$2 + (1/9)/x^2 $$", "quizx5", "$$\\partial_x\\left[2 x - 1/(9x)\\right]$$",
"$$2x$$", "quizx5", "$$\\partial_x\\left[x^2 + 1/(9k)\\right]$$",
"$$2x + 9 $$", "quizx5", "$$\\partial_x\\left[x^2 + 9x\\right]$$",
"$$\\log(2) 2^x - (1/9)/x^2$$", "quizx5", "$$\\partial_x\\left[2^x + 1/(9x)\\right]$$",
"$$\\log(2) 2^x + (1/9)/x^2$$", "quizx5", "$$\\partial_x\\left[2^x - 1/(9x)\\right]$$",
"$$2x - (1/81)/x^2$$", "quizx5", "$$\\partial_x\\left[x^2 + 1/(81 x)\\right]$$",
"$$2x - (1/3)/x^{3} $$", "quizx5", "$$\\partial_x\\left[2 x + 1/(3x)^2\\right]$$",
) %>%
mutate(id = "quiz_practice",
direction = direction,
forward = "Which is the derivative of the function?",
backward = "Which is an anti-derivative of the function?")
}
dtkaplan/drillr documentation built on Jan. 1, 2021, 12:08 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Defines functions D_quiz D_structure Test_images Sinusoids Powers Exponentials Polynomials
Documented in Polynomials
#' First derivatives
#'
#' @export
Polynomials <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$\\partial_x\\,f(x) \\equiv 0$$" , "two", "$$f(x) \\equiv b$$",
"$$\\partial_x\\,f(x) \\equiv 0$$" , "two", "$$f(x) \\equiv a$$",
"$$\\partial_x\\,f(x) \\equiv 0$$" , "two", "$$f(x) \\equiv a + b$$",
"$$\\partial_x\\,f(x) \\equiv b$$" , "two", "$$f(x) \\equiv a + b x$$",
"$$\\partial_x\\,f(x) \\equiv a$$" , "two", "$$f(x) \\equiv a x + b$$",
"$$\\partial_x\\,f(x) \\equiv 2bx$$", "two", "$$f(x) \\equiv a + b x^2$$",
"$$\\partial_x\\,f(x) \\equiv 2ax$$", "two", "$$f(x) \\equiv a x^2 + b$$",
"$$\\partial_x\\,f(x) \\equiv b + 2 c x$$", "two", "$$f(x) \\equiv a + b x + c x^2$$",
"$$\\partial_x\\,f(x) \\equiv b + c x$$", "two", "$$f(x) \\equiv a + b x + c x^2 / 2$$",
"$$\\partial_x\\,f(x) \\equiv 2b + 2c x$$", "two", "$$f(x) \\equiv a + 2b x + c x^2$$",
"$$\\partial_x\\,f(x) \\equiv 2b + cx$$", "two", "$$f(x) \\equiv a + 2b x + c x^2/2$$",
"$$\\partial_x\\,f(x) \\equiv a + b$$", "two", "$$f(x) \\equiv a x + b x$$",
"$$\\partial_x\\,f(x) \\equiv ax + bx$$", "two", "$$f(x) \\equiv a x^2/2 + b x^2/2$$",
"$$\\partial_x\\,f(x) \\equiv b + 2cx + 3dx^2$$", "three", "$$f(x) \\equiv a + b x + c x^2 + d x^3$$",
"$$\\partial_x\\,f(x) \\equiv a+b + 2cx + dx^2$$", "three", "$$f(x) \\equiv ax+bx+cx^2+dx^3/3$$",
"$$\\partial_x\\,f(x) \\equiv bx + 2 c x + 2dx^2$$", "three", "$$f(x) \\equiv a +bx^2/2 + c x^2 + 2 d x^3/3$$",
"$$\\partial_x\\,f(x) \\equiv 2ax + b + 3cx^2$$", "three", "$$f(x) \\equiv a x^2 + b x + c x^3 + d$$",
"$$\\partial_x\\,f(x) \\equiv a + 3cx^2 - 2dx$$", "three", "$$f(x) \\equiv ax + b + cx^3 - dx^2$$",
"$$\\partial_x\\,f(x) \\equiv ax^2 + b + 4cx +16dx^3$$","three", "$$f(x) \\equiv ax^3/3 + bx + 2cx^2 + 4dx^4$$",
"$$\\partial_x\\,f(x) \\equiv 4dx^3 $$", "three", "$$f(x) \\equiv 4b + dx^4$$",
"$$\\partial_x\\,f(x) \\equiv c + 2cx$$", "three", "$$f(x) \\equiv cx + cx^2$$",
"$$\\partial_x\\,f(x) \\equiv d $$", "three", "$$f(x) \\equiv cx + cx^2$$",
"$$\\partial_x\\,f(x) \\equiv 2cbx $$", "three", "$$f(x) \\equiv c(a + bx^2)$$") %>%
mutate(id = "polynomials",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Exponentials <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$d_t\\, f(t) \\equiv k \\exp(kt )$$", "exponential", "$$f(t) \\equiv \\exp(kt)$$",
"$$d_t\\, f(t) \\equiv -k \\exp(-kt )$$", "exponential", "$$f(t) \\equiv \\exp(-kt )$$",
"$$d_t\\, f(t) \\equiv k\\exp(-kt )$$", "exponential", "$$f(t) \\equiv -\\exp(-kt )$$",
"$$d_t\\, f(t) \\equiv - \\exp( kt)$$", "exponential", "$$f(t) \\equiv -\\exp( kt)$$",
"$$d_t\\, f(t) \\equiv \\exp( t)$$", "exponential", "$$f(t) \\equiv \\exp( t)$$",
"$$d_t\\, f(t) \\equiv k \\exp( t)$$", "exponential", "$$f(t) \\equiv k \\exp(t )$$",
"$$d_t\\, f(t) \\equiv -k \\exp( t)$$", "exponential", "$$f(t) \\equiv -k \\exp(t)$$",
"$$d_t\\, f(t) \\equiv -k \\exp(-t )$$", "exponential", "$$f(t) \\equiv k\\exp(-t )$$",
"$$d_t\\, f(t) \\equiv k \\exp(-t )$$", "exponential", "$$f(t) \\equiv -k \\exp(-t )$$",
"$$d_t\\, f(t) \\equiv (1/k) \\exp(t/k)$$", "exponential", "$$f(t) \\equiv \\exp(t/k )$$",
"$$d_t\\, f(t) \\equiv (1/k^2)\\exp(t/k^2 )$$", "exponential", "$$f(t) \\equiv \\exp(t/k^2 )$$",
"$$d_t\\, f(t) \\equiv -(1/k)\\exp(-t/k )$$", "exponential", "$$f(t) \\equiv \\exp(-t/k )$$",
"$$d_t\\, f(t) \\equiv (1/k) \\exp(-t/k )$$", "exponential", "$$f(t) \\equiv -\\exp(-t/k )$$",
) %>%
mutate(id = "exponentials",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Powers <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$d_t\\, f(t) \\equiv 3 x^2$$", "powers", "$$f(t) \\equiv x^3$$",
"$$d_t\\, f(t) \\equiv -3 x^{-4}$$", "powers", "$$f(t) \\equiv x^{-3}$$",
"$$d_t\\, f(t) \\equiv 2 x^{1}$$", "powers", "$$f(t) \\equiv x^2$$",
"$$d_t\\, f(t) \\equiv 2 x^1$$", "powers", "$$f(t) \\equiv x^{-2}$$",
"$$d_t\\, f(t) \\equiv -1 x^{-2}$$", "powers", "$$f(t) \\equiv x^1$$",
"$$d_t\\, f(t) \\equiv \\ln(x)$$", "powers", "$$f(t) \\equiv x^{-1} $$",
"$$d_t\\, f(t) \\equiv 0$$", "powers", "$$f(t) \\equiv x^0$$",
"$$d_t\\, f(t) \\equiv 2 x^2$$", "powers", "$$f(t) \\equiv 2 x^3 / 3$$",
"$$d_t\\, f(t) \\equiv 3 x$$", "powers", "$$f(t) \\equiv 3 x^2 /2$$",
"$$d_t\\, f(t) \\equiv 0.5 x^{-0.5}$$", "powers", "$$f(t) \\equiv \\sqrt{x}$$",
"$$d_t\\, f(t) \\equiv 1.5 x^{0.5}$$", "powers", "$$f(t) \\equiv x^{1.5} $$",
"$$d_t\\, f(t) \\equiv x^{-2.5} $$", "powers", "$$f(t) \\equiv x^{-1.5}/1.5 $$",
"$$d_t\\, f(t) \\equiv x^{1.5}$$", "powers", "$$f(t) \\equiv x^{2.5}/2.5$$",
"$$d_t\\, f(t) \\equiv 5 x^{-3.5}$$", "powers", "$$f(t) \\equiv -2 x^{-2.5}$$",
) %>%
mutate(id = "powers",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Sinusoids <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$d_t\\, f(t) \\equiv a\\sin(at)$$", "trig", "$$f(t) \\equiv \\sin(at)$$",
"$$d_t\\, f(t) \\equiv a\\cos(t)$$", "trig", "$$f(t) \\equiv \\sin(t)$$",
"$$d_t\\, f(t) \\equiv -a\\sin(at)$$", "trig", "$$f(t) \\equiv \\cos(at)$$",
"$$d_t\\, f(t) \\equiv a\\sin(t)$$", "trig", "$$f(t) \\equiv a \\cos(t)$$",
"$$d_t\\, f(t) \\equiv a\\cos(t)$$", "trig", "$$f(t) \\equiv a \\sin(t)$$",
"$$d_t\\, f(t) \\equiv -a^2 \\sin(at)$$", "trig", "$$f(t) \\equiv -a \\sin(at)$$",
"$$d_t\\, f(t) \\equiv -a\\sin(t)$$", "trig", "$$f(t) \\equiv -a \\cos(t)$$",
"$$d_t\\, f(t) \\equiv -a\\cos(at)$$", "trig", "$$f(t) \\equiv -\\sin(at)$$",
"$$d_t\\, f(t) \\equiv - \\sin(-t)$$", "trig", "$$f(t) \\equiv -\\cos(-t)$$",
"$$d_t\\, f(t) \\equiv \\sin(-t)$$", "trig", "$$f(t) \\equiv \\cos(-t)$$",
"$$d_t\\, f(t) \\equiv - \\cos(-t)$$", "trig", "$$f(t) \\equiv \\sin(-t)$$",
) %>%
mutate(id = "trig",
direction = direction,
forward = "Select the derivative",
backward = "Select the anti-derivative")
}
#' @export
Test_images <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"<img src='https://upload.wikimedia.org/wikipedia/commons/8/83/Sir_Isaac_Newton_%281643-1727%29.jpg' width = 200>", "", "Leibniz",
"Abraham Lincoln", "", "<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Gilbert_Stuart_Williamstown_Portrait_of_George_Washington.jpg/440px-Gilbert_Stuart_Williamstown_Portrait_of_George_Washington.jpg' width=200>",
"<img src='https://image.shutterstock.com/image-photo/no-limits-message-on-asphalt-260nw-198889661.jpg' width=200>", "", "Math 141Z"
) %>%
mutate(id = "images",
direction = direction,
forward = "Which matches?",
backward = "Which matches backward?")
}
#' @export
D_structure <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"0", "all","$$\\partial_x \\exp(t)$$",
"0", "all","$$\\partial_t \\ln(x)$$",
"0", "all", "$$\\partial_x 7$$",
"1", "all", "$$\\partial_x x$$",
"1", "all", "$$\\partial_y y x^3$$",
"1", "all", "$$\\partial_x \\exp(x) \\sin(\\omega t)$$",
"fundamental", "all", "$$\\partial_x 7x$$",
"fundamental", "all", "$$\\partial_y x \\exp(y)$$",
"fundamental", "all","$$\\partial_t \\exp(t)$$",
"fundamental", "all", "$$\\partial_x \\exp(t) \\sin(x)$$",
"fundamental", "all","$$\\partial_t \\sin(t)$$",
"fundamental", "all","$$\\partial_x x^n (n\\neq 0)",
"fundamental", "all","$$\\partial_x \\ln(x)$$",
"fundamental", "all", "$$\\partial_x \\mbox{sigmoid}(x, center, width)$$",
"scaled fundamental", "all", "$$\\partial_t \\exp(kt)$$",
"scaled fundamental", "all", "$$\\partial_t \\sin(2\\pi t/P)$$",
"scaled fundamental", "all", "$$\\partial_x \\mbox{sigmoid}(4 x, center, width)$$",
"scaled fundamental", "all", "$$\\partial_t \\sin(\\omega t)$$",
"product", "all", "$$\\partial_x \\exp(x) \\sin(ax)$$",
"product", "all", "$$\\partial_t \\sin(\\omega t)\\cos(\\alpha t)$$",
"product", "all", "$$\\partial_x x^3 \\sin(k x)$$",
"product", "all", "$$\\partial_x sin(\\omega x) \\ln(x)$$",
"product", "all", "$$\\partial_x x \\exp(x)$$",
"product", "all", "$$\\partial_x (x^2 + 1) \\exp(kx)$$",
"product", "all", "$$\\partial_t x \\cos(t) \\sin(\\omega t)$$",
"quotient", "all", "$$\\partial_x sin(x)/cos(x)$$",
"chain", "all", "$$\\partial_x \\sin(x^2)$$",
"chain", "all", "$$\\partial_x \\ln(x^2 + x)$$",
"linear combination", "all", "$$\\partial_x (x + 3)$$",
"linear combination", "all", "$$\\partial_x (a_0 + a_1 x + a_2 x^2)$$",
"linear combination", "all", "$$\\partial_x (2 x^2 - sin(\\omega x))$$",
"$$g(x) \\partial_x f(x) + f(x) \\partial_x g(x)$$", "rule", "$$\\partial_x \\left[f(x) g(x)\\right]$$",
"$$g(x) \\partial_x f(x) + \\partial_x g(x)$$", "rule", "$$\\partial_x \\left[f(x) + g(x)\\right]$$",
"$$g(x) f'(g(x)) g'(x)$$", "rule", "$$\\partial_x f(g(x))$$",
"$$g(x) a f'(a g(x)) g'(a x)$$", "rule", "$$\\partial_x f(a g(x))$$",
"$$g(x) g'(f(x)) f'(x)$$", "rule", "$$\\partial_x g(f(x))$$",
"$$g(x) a f'(a x)$$", "rule", "$$\\partial_x f(a x + b) $$",
"$$g(x) a \\partial_x f(x) + b \\partial_x g(x)$$", "rule", "$$\\partial_x \\left[a f(x) + b g(x)\\right]$$",
"$$g(x) b \\partial_x f(x) + a \\partial_x g(x)$$", "rule", "$\\partial_x \\left[b f(x) + a g(x)\\right]$$",
) %>%
mutate(id = "structure",
direction = direction,
forward = "Which structure matches the function?",
backward = "Which function matches the structure?")
}
#' @export
#' @export
D_quiz <- function(direction = c("forward", "both", "backward")) {
direction <- match.arg(direction)
tibble::tribble(
~ answer, ~ group, ~ question,
"$$7 \\cos(x) - 2/x$$", "quizx1",
"$$\\partial_x \\left[ 7 \\sin(x) - 2 \\ln(x)\\right]$$",
"$$7 \\cos(7x) - 1/x$$", "quizx1",
"$$\\partial_x \\left[ \\sin(7 x) - \\ln(2 x)\\right]$$",
"$$7 \\cos(7x) - 1/x $$", "quizx1", "$$\\partial_x \\left[ \\sin(7 x) - \\ln(x/2)\\right]$$",
"$$7 \\cos(x) - 2/x $$", "quizx1", "$$\\partial_x \\left[7 \\sin(x) - 2 \\ln(x/2)\\right]$$",
"$$-4 \\sqrt{6} / x^5$$", "quizx2", "$$\\partial_x \\left[ \\sqrt{6} / x^4 \\right]$$",
"$$4 \\sqrt{6} / x^5$$", "quizx2", "$$\\partial_x \\left[ - \\sqrt{6} / x^4 \\right]$$",
"$$4 \\sqrt{6} / x^4$$", "quizx2", "$$\\partial_x \\left[ -(4/3) \\sqrt{6} / x^3\\right]$$",
"$$4 \\sqrt{6} / x^6$$", "quizx2",
"$$\\partial_x \\left[ -(4/5) \\sqrt{6} / x^5\\right]$$",
"$$\\log(4)\\log(3) 4^x$$" , "quizx3", "$$\\partial_x \\log(3) 4^x$$",
"$$\\log(4)\\log(3) 3^x$$", "quizx3", "$$\\partial_x \\log(4) 3^x$$",
"$$3 \\log(4) x^2$$", "quizx3", "$$\\partial_x \\log(4) x^3$$",
"$$4 \\log(3) x^3$$", "quizx3", "$$\\partial_x \\log(3) x^4$$",
"$$- 75 \\sin(x)$$", "quizx4", "$$\\partial_x \\left[75 \\cos(x) \\right]$$",
"$$75 \\cos(x)$$", "quizx4", "$$\\partial_x \\left[75 \\sin(x) \\right]$$",
"$$75 \\sin(x)$$", "quizx4", "$$\\partial_x \\left[- 75 \\cos(x)\\right]$$",
"$$-75 \\cos(x)$$", "quizx4", "$$\\partial_x \\left[- 75 \\sin(x)\\right]$$",
"$$- 75 \\sin(75 x)$$", "quizx4", "$$\\partial_x \\left[\\cos(75 x) \\right]$$",
"$$75 \\cos(75 x)$$", "quizx4", "$$\\partial_x \\left[\\sin(75 x) \\right]$$",
"$$75 \\sin(75 x)$$", "quizx4", "$$\\partial_x \\left[-\\cos(75 x)\\right]$$",
"$$-75 \\cos(75 x)$$", "quizx4", "$$\\partial_x \\left[-\\sin(75 x)\\right]$$",
"$$2 - (1/9)/x^2 $$", "quizx5", "$$\\partial_x\\left[2 x + 1/(9x)\\right]$$",
"$$2 + (1/9)/x^2 $$", "quizx5", "$$\\partial_x\\left[2 x - 1/(9x)\\right]$$",
"$$2x$$", "quizx5", "$$\\partial_x\\left[x^2 + 1/(9k)\\right]$$",
"$$2x + 9 $$", "quizx5", "$$\\partial_x\\left[x^2 + 9x\\right]$$",
"$$\\log(2) 2^x - (1/9)/x^2$$", "quizx5", "$$\\partial_x\\left[2^x + 1/(9x)\\right]$$",
"$$\\log(2) 2^x + (1/9)/x^2$$", "quizx5", "$$\\partial_x\\left[2^x - 1/(9x)\\right]$$",
"$$2x - (1/81)/x^2$$", "quizx5", "$$\\partial_x\\left[x^2 + 1/(81 x)\\right]$$",
"$$2x - (1/3)/x^{3} $$", "quizx5", "$$\\partial_x\\left[2 x + 1/(3x)^2\\right]$$",
) %>%
mutate(id = "quiz_practice",
direction = direction,
forward = "Which is the derivative of the function?",
backward = "Which is an anti-derivative of the function?")
}
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.