SDSU Math Lacement Assessment
Formulas Exam-Graded A
vertex - ANSWER--b/2a
domain and range - ANSWER-(-∞ ,∞)
and brackets for numbers for sure or equal to [ , ]
parentheses for < or > or infinity
end behavior - ANSWER-odd: different- positive: falls left, rises right; negative: rises left,
falls right
even: same- positive: rises x2; negative: falls x2
polynomial division - ANSWER-answer+ (remainder/divison)
quadratic formula - ANSWER--b±[√b²-4ac]/2a
Vertical asymptote of a rational function - ANSWER-occurs at x value which makes
denominator 0, y=(ax+b)/(cx+d)
horizontal asymptote rules for rational functions - ANSWER-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 - ANSWER-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
secant and cosecant graphs - ANSWER-y=secx
x|y
-pi/2 | undefined
0 | -1
, pi/2 | undefined
pi | 1
3pi/2 | undefined
va= bx-c=-pi/2
y=cscx
x|y
0 | undefined
pi/2 | -1
pi | undefined
3pi/2 | 1
2pi | undefined
bx-c=0
Sum and Difference Formulas - ANSWER-sin (x + y) = sin x cos y + cos x sin y
sin (x- y) = sin x cos y - cos x sin y
cos (x + y) = cos x cos y - sin x sin y
cos (x - y) = cos x cos y + sin x sin y
tan (x + y ) = (tan x + tan y)/(1 - tan x tan y)
tan (x - y) = (tan x - tan y)/(1 + tan x tan y)
Double Angle Formulas - ANSWER-sin(2x)=2sin(x)cos(x)
cos(2x)=cos^2-sin^2
=1-2sin^2
=2cos^2-1
tan(2x)=2tanx/1-tan^2
Half Angle Formulas - ANSWER-sin x/2 = + or - √(1 - cos x)/2
cos x/2 = + or - √1 + cos x)/2
tan x/2 = (1 - cos x)/(sin x) or (sin x)/(1 + cos x)
Power-Reducing Formulas - ANSWER-sin^2 x = (1 - cos 2x)/(2)
cos^2 x = (1 + cos 2x)/2
tan^2 x = (1 - cos 2x)/(1 + cos 2x)
Product to Sum Formulas - ANSWER-sinx sin y = 1/2 [cos(x - y) - cos(x + y)]
cosx cos y = 1/2 [cos(x - y) + cos(x + y)]
sinx cos y = 1/2 [sin(x + y) + sin(x - y)]
cos x sin y = 1/2 [sin(x + y) - sin(x - y)]
Formulas Exam-Graded A
vertex - ANSWER--b/2a
domain and range - ANSWER-(-∞ ,∞)
and brackets for numbers for sure or equal to [ , ]
parentheses for < or > or infinity
end behavior - ANSWER-odd: different- positive: falls left, rises right; negative: rises left,
falls right
even: same- positive: rises x2; negative: falls x2
polynomial division - ANSWER-answer+ (remainder/divison)
quadratic formula - ANSWER--b±[√b²-4ac]/2a
Vertical asymptote of a rational function - ANSWER-occurs at x value which makes
denominator 0, y=(ax+b)/(cx+d)
horizontal asymptote rules for rational functions - ANSWER-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 - ANSWER-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
secant and cosecant graphs - ANSWER-y=secx
x|y
-pi/2 | undefined
0 | -1
, pi/2 | undefined
pi | 1
3pi/2 | undefined
va= bx-c=-pi/2
y=cscx
x|y
0 | undefined
pi/2 | -1
pi | undefined
3pi/2 | 1
2pi | undefined
bx-c=0
Sum and Difference Formulas - ANSWER-sin (x + y) = sin x cos y + cos x sin y
sin (x- y) = sin x cos y - cos x sin y
cos (x + y) = cos x cos y - sin x sin y
cos (x - y) = cos x cos y + sin x sin y
tan (x + y ) = (tan x + tan y)/(1 - tan x tan y)
tan (x - y) = (tan x - tan y)/(1 + tan x tan y)
Double Angle Formulas - ANSWER-sin(2x)=2sin(x)cos(x)
cos(2x)=cos^2-sin^2
=1-2sin^2
=2cos^2-1
tan(2x)=2tanx/1-tan^2
Half Angle Formulas - ANSWER-sin x/2 = + or - √(1 - cos x)/2
cos x/2 = + or - √1 + cos x)/2
tan x/2 = (1 - cos x)/(sin x) or (sin x)/(1 + cos x)
Power-Reducing Formulas - ANSWER-sin^2 x = (1 - cos 2x)/(2)
cos^2 x = (1 + cos 2x)/2
tan^2 x = (1 - cos 2x)/(1 + cos 2x)
Product to Sum Formulas - ANSWER-sinx sin y = 1/2 [cos(x - y) - cos(x + y)]
cosx cos y = 1/2 [cos(x - y) + cos(x + y)]
sinx cos y = 1/2 [sin(x + y) + sin(x - y)]
cos x sin y = 1/2 [sin(x + y) - sin(x - y)]
