Mathematical Modeling - ACT Math
Card 1 of 30
Given $A=50(1.1)^t$, what is $A$ when $t=0$?
Given $A=50(1.1)^t$, what is $A$ when $t=0$?
Tap to reveal answer
$50$. Initial value when exponent equals zero.
$50$. Initial value when exponent equals zero.
← Didn't Know|Knew It →
Calculate the volume of a sphere with radius 2.
Calculate the volume of a sphere with radius 2.
Tap to reveal answer
Volume = $\frac{32}{3}\pi$. Sphere volume: $\frac{4}{3}\pi(2^3) = \frac{32}{3}\pi$.
Volume = $\frac{32}{3}\pi$. Sphere volume: $\frac{4}{3}\pi(2^3) = \frac{32}{3}\pi$.
← Didn't Know|Knew It →
Identify the formula for the circumference of a circle.
Identify the formula for the circumference of a circle.
Tap to reveal answer
Circumference = $2\pi r$. Perimeter formula where $r$ is the radius.
Circumference = $2\pi r$. Perimeter formula where $r$ is the radius.
← Didn't Know|Knew It →
Identify the best model type when the change in $y$ is a constant amount per unit increase in $x$.
Identify the best model type when the change in $y$ is a constant amount per unit increase in $x$.
Tap to reveal answer
Linear model. Constant rate of change indicates linear relationship.
Linear model. Constant rate of change indicates linear relationship.
← Didn't Know|Knew It →
State the formula for the circumference of a circle.
State the formula for the circumference of a circle.
Tap to reveal answer
Circumference = $2 \pi r$. Multiply radius by $2\pi$ for circle's perimeter.
Circumference = $2 \pi r$. Multiply radius by $2\pi$ for circle's perimeter.
← Didn't Know|Knew It →
What is the formula for the surface area of a sphere?
What is the formula for the surface area of a sphere?
Tap to reveal answer
Surface Area = $4\pi r^2$. Four $\pi$ times radius squared.
Surface Area = $4\pi r^2$. Four $\pi$ times radius squared.
← Didn't Know|Knew It →
What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
Tap to reveal answer
$a^2 + b^2 = c^2$. Sum of squares of legs equals hypotenuse squared.
$a^2 + b^2 = c^2$. Sum of squares of legs equals hypotenuse squared.
← Didn't Know|Knew It →
State the quadratic formula.
State the quadratic formula.
Tap to reveal answer
$x = \frac{-b , \text{±} , \text{√}(b^2 - 4ac)}{2a}$. Solves $ax^2 + bx + c = 0$ for any quadratic.
$x = \frac{-b , \text{±} , \text{√}(b^2 - 4ac)}{2a}$. Solves $ax^2 + bx + c = 0$ for any quadratic.
← Didn't Know|Knew It →
Calculate the volume of a cylinder with radius 3 and height 5.
Calculate the volume of a cylinder with radius 3 and height 5.
Tap to reveal answer
Volume = $45\text{π}$. Cylinder volume: $\text{π}(3^2)(5) = 45\text{π}$.
Volume = $45\text{π}$. Cylinder volume: $\text{π}(3^2)(5) = 45\text{π}$.
← Didn't Know|Knew It →
What is the formula for the perimeter of a rectangle?
What is the formula for the perimeter of a rectangle?
Tap to reveal answer
Perimeter = $2(\text{length} + \text{width})$. Sum of all four sides of rectangle.
Perimeter = $2(\text{length} + \text{width})$. Sum of all four sides of rectangle.
← Didn't Know|Knew It →
Calculate the volume of a sphere with radius 2.
Calculate the volume of a sphere with radius 2.
Tap to reveal answer
Volume = $\frac{32}{3}\text{π}$. Sphere volume: $\frac{4}{3}\text{π}(2^3) = \frac{32}{3}\text{π}$.
Volume = $\frac{32}{3}\text{π}$. Sphere volume: $\frac{4}{3}\text{π}(2^3) = \frac{32}{3}\text{π}$.
← Didn't Know|Knew It →
What is the formula for the volume of a cylinder?
What is the formula for the volume of a cylinder?
Tap to reveal answer
Volume = $\text{πr}^2 \times \text{height}$. Base area times height for cylinder volume.
Volume = $\text{πr}^2 \times \text{height}$. Base area times height for cylinder volume.
← Didn't Know|Knew It →
Find the surface area of a cube with side length 4.
Find the surface area of a cube with side length 4.
Tap to reveal answer
Surface Area = 96. Cube surface area: $6s^2 = 6(16) = 96$.
Surface Area = 96. Cube surface area: $6s^2 = 6(16) = 96$.
← Didn't Know|Knew It →
Determine the equation of a line with slope 3 and y-intercept 5.
Determine the equation of a line with slope 3 and y-intercept 5.
Tap to reveal answer
$y = 3x + 5$. Slope-intercept form with $m=3$, $b=5$.
$y = 3x + 5$. Slope-intercept form with $m=3$, $b=5$.
← Didn't Know|Knew It →
Determine the equation of a line parallel to $y=2x+3$.
Determine the equation of a line parallel to $y=2x+3$.
Tap to reveal answer
$y = 2x + c$. Parallel lines have identical slopes.
$y = 2x + c$. Parallel lines have identical slopes.
← Didn't Know|Knew It →
Find the circumference of a circle with diameter 10.
Find the circumference of a circle with diameter 10.
Tap to reveal answer
Circumference = $10\text{π}$. Circumference equals π times diameter.
Circumference = $10\text{π}$. Circumference equals π times diameter.
← Didn't Know|Knew It →
Calculate the slope for points (2,3) and (4,7).
Calculate the slope for points (2,3) and (4,7).
Tap to reveal answer
Slope = 2. Apply slope formula: $\frac{7-3}{4-2} = 2$.
Slope = 2. Apply slope formula: $\frac{7-3}{4-2} = 2$.
← Didn't Know|Knew It →
What is the formula for compound interest?
What is the formula for compound interest?
Tap to reveal answer
$A = P(1 + \frac{r}{n})^{nt}$. Principal grows with rate $r$, compounded $n$ times.
$A = P(1 + \frac{r}{n})^{nt}$. Principal grows with rate $r$, compounded $n$ times.
← Didn't Know|Knew It →
Find the area of a circle with radius 4.
Find the area of a circle with radius 4.
Tap to reveal answer
Area = $16\text{π}$. Use $A = \text{π}r^2$ with $r = 4$.
Area = $16\text{π}$. Use $A = \text{π}r^2$ with $r = 4$.
← Didn't Know|Knew It →
Identify the vertex form of a quadratic equation.
Identify the vertex form of a quadratic equation.
Tap to reveal answer
$y = a(x-h)^2 + k$. Parabola with vertex at $(h,k)$.
$y = a(x-h)^2 + k$. Parabola with vertex at $(h,k)$.
← Didn't Know|Knew It →
State the midpoint formula for two points.
State the midpoint formula for two points.
Tap to reveal answer
$\text{Midpoint} = \bigg(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\bigg)$. Average the x-coordinates and y-coordinates.
$\text{Midpoint} = \bigg(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\bigg)$. Average the x-coordinates and y-coordinates.
← Didn't Know|Knew It →
What is the formula for the area of a parallelogram?
What is the formula for the area of a parallelogram?
Tap to reveal answer
Area = $\text{base} \times \text{height}$. Same as rectangle when sides are perpendicular.
Area = $\text{base} \times \text{height}$. Same as rectangle when sides are perpendicular.
← Didn't Know|Knew It →
What is the area of a triangle with base 6 and height 4?
What is the area of a triangle with base 6 and height 4?
Tap to reveal answer
Area = 12. Triangle area: $\frac{1}{2}(6)(4) = 12$.
Area = 12. Triangle area: $\frac{1}{2}(6)(4) = 12$.
← Didn't Know|Knew It →
Identify the formula for converting Celsius to Fahrenheit.
Identify the formula for converting Celsius to Fahrenheit.
Tap to reveal answer
$F = \frac{9}{5}C + 32$. Multiply by $\frac{9}{5}$ then add 32 degrees.
$F = \frac{9}{5}C + 32$. Multiply by $\frac{9}{5}$ then add 32 degrees.
← Didn't Know|Knew It →
Identify the formula for the slope of a line given two points.
Identify the formula for the slope of a line given two points.
Tap to reveal answer
Slope = $\frac{y_2 - y_1}{x_2 - x_1}$. Rise over run between two coordinate points.
Slope = $\frac{y_2 - y_1}{x_2 - x_1}$. Rise over run between two coordinate points.
← Didn't Know|Knew It →
What is the volume of a cube with side length 5?
What is the volume of a cube with side length 5?
Tap to reveal answer
Volume = 125. Cube volume is $s^3 = 5^3 = 125$.
Volume = 125. Cube volume is $s^3 = 5^3 = 125$.
← Didn't Know|Knew It →
What is the formula for the area of a rectangle?
What is the formula for the area of a rectangle?
Tap to reveal answer
Area = $\text{length} \times \text{width}$. Multiply the two perpendicular dimensions.
Area = $\text{length} \times \text{width}$. Multiply the two perpendicular dimensions.
← Didn't Know|Knew It →
Find the area of a rectangle with length 7 and width 3.
Find the area of a rectangle with length 7 and width 3.
Tap to reveal answer
Area = 21. Rectangle area: $7 \times 3 = 21$.
Area = 21. Rectangle area: $7 \times 3 = 21$.
← Didn't Know|Knew It →
Calculate the Fahrenheit for 25°C.
Calculate the Fahrenheit for 25°C.
Tap to reveal answer
$F = 77$. Apply conversion: $\frac{9}{5}(25) + 32 = 77$.
$F = 77$. Apply conversion: $\frac{9}{5}(25) + 32 = 77$.
← Didn't Know|Knew It →
What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
Tap to reveal answer
Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Base times height divided by 2 gives triangle area.
Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Base times height divided by 2 gives triangle area.
← Didn't Know|Knew It →