SDSU MATH PLACEMENT ASSESSMENT FORMULAS
WITH COMPLETE SOLUTIONS 100% 2023/2024
vertex
-b/2a
domain and range
(-∞ ,∞)
and brackets for numbers for sure or equal to [ , ]
parentheses for < or > or infinity
end behavior
odd: different- positive: falls left, rises right; negative: rises left, falls right
even: same- positive: rises x2; negative: falls x2
polynomial division
answer+ (remainder/divison)
quadratic formula
-b±[√b²-4ac]/2a
Vertical asymptote of a rational function
occurs at x value which makes denominator 0, y=(ax+b)/(cx+d)
horizontal asymptote rules for rational functions
n= degree of numerator
m= degree of denominator
1. if n<m asymptote y=o
2. if n=m y= dividing coeff of n/m
3. if n>m there is no asymptote
polynomials and rational inequalities
1. solve for f(x)=0 to get x values at 0
2. locate values on a number line
3.Choose one representative number, called a test value, within each interval and evaluate f at that
number.
4. Write the solution set, selecting the interval or intervals that satisfy the given inequality
5. plug in those values to the original equation and check for truth
rational number inequalities on number line
numerator zero: circle based on inequality (closed or open)
denominator zero: always an open circle
exponential functions
f(x)=a(b)^x,
, logarithmic function
log: y= log(base)x
exponential: b^y=x
log for e
log(base e)x=lnx
log rules
product: log (mn) = log(m) + log(n)
quotient: log (m/n) = log(m) - log(n)
power: log (m^n) = nlog(m)
exponential log equations to solve for x
1. match bases when its like 2^2x=8 = 8 is 2^3
2. common logs, natural logs, power rules. - have log on both sides and divide there
3. use the property: logbx= # equals to b^#=x, divide out coefficients then change number with the
property
change of base property
evaluate log with any base (log(a)b = log b/ log a)
measuring angle in a circle using radians
theta= side/radius
degrees to radians
multiply by pi/180
radians to degrees
multiply by 180/pi
length of a circular arc
s=r(theta)
angular speed
w=theta/t
linear speed
v=s/t or v=rw
how many radians per revolution
2pi
sin, cos, tan
SOH CAH TOA
WITH COMPLETE SOLUTIONS 100% 2023/2024
vertex
-b/2a
domain and range
(-∞ ,∞)
and brackets for numbers for sure or equal to [ , ]
parentheses for < or > or infinity
end behavior
odd: different- positive: falls left, rises right; negative: rises left, falls right
even: same- positive: rises x2; negative: falls x2
polynomial division
answer+ (remainder/divison)
quadratic formula
-b±[√b²-4ac]/2a
Vertical asymptote of a rational function
occurs at x value which makes denominator 0, y=(ax+b)/(cx+d)
horizontal asymptote rules for rational functions
n= degree of numerator
m= degree of denominator
1. if n<m asymptote y=o
2. if n=m y= dividing coeff of n/m
3. if n>m there is no asymptote
polynomials and rational inequalities
1. solve for f(x)=0 to get x values at 0
2. locate values on a number line
3.Choose one representative number, called a test value, within each interval and evaluate f at that
number.
4. Write the solution set, selecting the interval or intervals that satisfy the given inequality
5. plug in those values to the original equation and check for truth
rational number inequalities on number line
numerator zero: circle based on inequality (closed or open)
denominator zero: always an open circle
exponential functions
f(x)=a(b)^x,
, logarithmic function
log: y= log(base)x
exponential: b^y=x
log for e
log(base e)x=lnx
log rules
product: log (mn) = log(m) + log(n)
quotient: log (m/n) = log(m) - log(n)
power: log (m^n) = nlog(m)
exponential log equations to solve for x
1. match bases when its like 2^2x=8 = 8 is 2^3
2. common logs, natural logs, power rules. - have log on both sides and divide there
3. use the property: logbx= # equals to b^#=x, divide out coefficients then change number with the
property
change of base property
evaluate log with any base (log(a)b = log b/ log a)
measuring angle in a circle using radians
theta= side/radius
degrees to radians
multiply by pi/180
radians to degrees
multiply by 180/pi
length of a circular arc
s=r(theta)
angular speed
w=theta/t
linear speed
v=s/t or v=rw
how many radians per revolution
2pi
sin, cos, tan
SOH CAH TOA
