SDSU MATH PLACEMENT ASSESSMENT FORMULAS WITH COMPLETE SOLUTIONS 100% 2023/2024

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 sin= y/1 cos= x/1 tan: y/x csc, sec, cot csc: 1/sin sec: 1/cos cot: x/y QI QII QIII QIV which are positive for which trig f QI= all trig are positive QII= only sin is positive Qiii= only tan is positive QIV= only cos is positive s | a -----, all students take classes t | c Pythagorean Identities sin^2x+cos^2x=1 1+tan^2x=sec^2x 1+cot^2x=csc^2x periodic functions sin(t+2pin)=sint same with cos, tan, etc because 2pi is a revolution right triangle trigonometry SOH CAH TOA trigonometric function complements sin(theta)= cos(90-theta) cos(theta)=sin(90-theta) tan(theta)=cot(90-theta) csc=sec, sec=csc, cot=tan... trigonometric functions of any angle sin=y/r cos=x/r tan=y/x √ x^2+y^2= r step 1. determine quadrant step 2: find two sides of triangle step 3: find missing side