Things to Remember ( Math ) Notes | Knowt (2024)

Positive Lead coefficient & even degree = both ends going up

Positive Lead coefficient & odd degree = left end going down and right end going up

Negative Lead coefficient & odd degree = left end going up & right end going down

Negative Lead coefficient & even degree = both ends going down

Standard Quadratic Equation = ( y = ax²+bx+c , where c is the y intercept )

Vertex Quadratic Equation = ( y = a(x-h)² + k , where the vertex is (h,k) )

Factored Quadratic Equation = ( y = a ( x - R1 ) ( x - R2 ) , where R1 and R2 are roots )

Quadratic Formula = (-b±√(b²-4ac))/(2a)

Discriminant Formula = b² -4ac

• Positive discriminant = 2 different real solutions

• Negative discriminant = no real solutions

• discriminant is 0 = repeated real number solution

Standard form of linear function = Ay + Bx = C

In systems of equations a single x or y value = one solution ( intersect at one point )

In systems of equations an untrue statement ( like 5 = 9 ) = zero solutions ( parallel lines )

In systems of equations two values that always equal each other ( like 3x = 6x - 3x ) = infinite solutions ( same line )

Square of a sum is ( a + b )² = ( a + b ) ( a + b ) = a² + 2ab + b²

Square of a different is ( a - b )² = ( a - b ) ( a - b ) = a² - 2ab + b²

Standard form slope = if Ax + By = C then -A/B is the slope

Midpoint formula of ( x1, y1) and ( x2, y2 ) = ( (x1 + x2 ) / 2 ) , ( y2 + y2 ) / 2 )

Distance formula between (x1 , y1 ) and ( x2, y2 ) = sqrt ( ( x2 - x1 ) ² + ( y2 - y1 ) ² )

How to find the vertex of any parabola

• when y = ax² + bx + c , h of ( h , k ) = (-b/2a)

• Then substitute a into the main equation again to find the y value of the vertex ( k )

The midpoint of 2 zeroes ( in a quadratic ) is x-value of a vertex

Circle equation : ( x-h )² + ( y-k )² = r², where ( h, k ) is the center point

Central angles are proportional to the arc length they intersect

• central angle degree / 360 degrees = arc length in radians / 2pi * r

Degrees to radians = degree * pi / 180

Radians to Degrees = 180 / pi * radians

for an arc on a circle with a central angle of theta

• Length of arc = theta times r

central angle measure / total measure of an angle in circle = sector area / total circle area

For any sector in a circle with a central angle of theta

• Area = ½ * theta * r²

(f o g)(x) = f(g(x))

(f * g ) ( x ) = f g(x) = f(x) g(x)

(f/g) ( x ) = f(x)/g(x)

mode = most common term in a set of terms

median = the middle number

mean = the average of the data set ( sum of terms divided by number of terms )

Sum of 2 cubes : a³ + b³ = ( a + b ) ( a² - ab + b² )

Difference of 2 cubes : a³ - b³ = ( a - b ) ( a² + ab + b² )

Speed = distance / time

Time = distance / speed

Parallel lines have the same slope

The magnitude ( how steep the line is ) of a slope is always positive = absolute value of slope

Perpendicular lines have opposite reciprocal slope

Sub in 0 for y to find the x intercept(s)

Sub in 0 for x to find the y intercept

Vertical asymptote = vertical line ( x = ? )

Horizontal asymptote = horizontal line ( y = ? )

If functions are symmetrical across y axis = even function

if f(-x) = f(x) then the function is an even function ( even degree )

if f(-x) = -f(x) then the function is an odd function ( odd degree )

To shift a graph up, ADD a constant outside the x

To shift a graph down, subtract a constant outside the x

To shift a graph to the left, ADD a constant inside the x

Frequency = number of times a value occurs in a data set

positive correlation = distribution of data points in a scatter plot show a positive slope

Normal distribution : Mean = median

Outlier = a data point that differs significantly from the other values in a set

Large outlier : mean > median

Small outlier : mean < median

outliers mainly impact the mean and have no effect on median

Standard deviation = measure of the amount of variability in a set of data. Measure of how far the individual data points are from the mean of the data

High standard deviation = spread out over a wide range of values

low standard deviation = data points are clustered around mean

Margin of Error = how far off the mean in a sample is compared to the true mean in a larger population ( like error bars )

The larger the standard the deviation the larger the margin of error

The larger the sample size the smaller the margin of error

Confidence interval = range of values within which true population mean is likely to fall with a given level of confidence ( ex: on average he gets 6 hours of sleep ± 1 hours. Confidence interval = 5-7 hours )

larger the standard deviation the larger the confidence interval

larger the sample size the smaller the confidence interval

To calculate the mean of combined data, add together the total sum of both sets of data and divide by the total number of values