☁️ • Module 9 : Finance, Growth Patterns & Symmetry Flashcards
This lesson covers income tax, interest, exponential growth, quadratic and reciprocal graphs, symmetry in 2D, 3D, and circles, as well as histograms and cumulative frequency.
What is income tax?
A tax on earnings, usually calculated as a percentage of income above a certain threshold.
What is the formula for simple interest?
I = P x r x t,
Where I = interest, P = principal, r = rate (as a decimal), and t = time.
How is compound interest calculated?
A = P(1 + r)ᵗ,
Where A = final amount, P = principal, r = rate per period, and t = number of periods.
What is depreciation?
A decrease in the value of an asset over time, often calculated using the formula for compound decay.
A = P(1-r)ᵗ
What is exponential growth?
When a quantity increases by a fixed percentage over equal time intervals, following the formula;
A = P(1+r)ᵗ
What is a parabola’s vertex?
The highest or lowest point of a quadratic graph, found using x= -(b)/2a
What is a reciprocal function?
A function of the form y=k/x, where k is a constant, creating a hyperbola with asymptotes.
What is a line fo symmetry in 2D shapes?
A line that divides a shape into two mirror-image halves.
What are the asymptotes of a reciprocal graph?
Asymptotes = Vertical and horizontal lines the graph approaches but never touches, usually x=0 and y=0 for y=k/x
How do you find the turning points of a quadratic function?
By completing the square or using the formula x=-(b)/2a, then substituting into the equation for y.
How can you determine the number of roots of a quadratic equation?
Using the discriminant; b²-4ac.
If positive → 2 roots,
zero → 1 root,
negative → no real roots.
What is rotational symmetry?
When a shape looks the same after a rotation of less than 360°.
The order is the number of times it matches itself.
How do you find the symmetry planes of a 3D shape?
Identify imaginary planes that divide the shape into two mirror-image halves (ex. A cube has 9 symmetry planes).
What is the symmetry of a circle?
A circle has infinite lines of symmetry and a rotational symmetry of infinite order.
What is a tangent to a circle?
A straight line that touches a circle at exactly one point, perpendicular to the radius at that point.
How is a histogram different from a bar chart?
A histogram represents continuous data with no gaps between bars, and bar heights show frequency density, not just frequency.
How do you find the median from a cumulative frequency curve?
Locate the total frequency, divide by 2, and find the corresponding value on the x-axis.
What is an arc of a circle?
A portion of the circumference of a circle, defined by two points on the circle.
What is a sector of a circle?
A region enclosed by two radii and an arc,
Like a “pizza slice” of the circle.
What is a segment of a circle?
A region bounded by a chord and an arc, dividing the circle into a larger major segment and a smaller minor segment.
