MATH PLACEMENT EXAMS SCRIPT 2025/2026 QUESTIONS
WITH ANSWERS TAGGED A+
✔✔BOTU - ✔✔there is no horizontal asymptote, find slant asymptote (Bigger On Top
Undefined)
✔✔How do you find the slant asymptote? - ✔✔Divide the ENTIRE numerator by the
ENTIRE denominator, the slant asymptote is the quotient, ignore the remainder (might
include division with variables raised to exponents)
✔✔How do you find the vertical asymptote? - ✔✔Set the denominator equal to 0
✔✔sin - ✔✔csc
✔✔cos - ✔✔sec
✔✔tan - ✔✔cot
✔✔Can a graph have more than one local maximum or minimum? - ✔✔yes
✔✔volume - ✔✔cubed
✔✔area - ✔✔squared
✔✔perimeter/ length - ✔✔no power
✔✔How do you find the vertex of a parabola? - ✔✔take the derivative (slope) and set it
equal to 0
✔✔d/dx (x^a) - ✔✔ax^a-1
✔✔antiderivative (x^a) - ✔✔(x^a+1)/a+1
✔✔circumference - ✔✔2πr
✔✔area of a circle - ✔✔πr²
✔✔Translate this equation to the right 3 and up 4:
f(x)=1/2x^2 - ✔✔(1/2(x-3)^2)+4
✔✔If a question asks for all real zeroes should you include imaginary numbers? - ✔✔no
, ✔✔In the functions (f + g)(x), (f-g)(1), (f・g)(x), (f/g)(2) etc. is the x or the coefficient in
the second parentheses being multiplied by the solution of f and g? - ✔✔No, x is the
input for the combined functions (just like it would be in single functions like f(x))
✔✔y=af(x) - ✔✔multiply y coordinate by a
✔✔y=f(ax) - ✔✔divide x coordinate by a
✔✔to find x intercept - ✔✔set f(x) equal to 0
✔✔to find y intercept - ✔✔find f(0)
✔✔What are inverse functions. - ✔✔Functions that switch the input and output
✔✔How do you find the inverse function of an equation? - ✔✔Solve for x then swap the
variables of the new solved equation
✔✔What should you always do first - ✔✔Cancel/ simplify/ factor
✔✔When a problem says that one variable varies inversely with another variable what
do you need to know/ find? - ✔✔the constant k
✔✔Direct variation - ✔✔y=kx (ratio remains constant (y/x stays the same))
✔✔Inverse variation - ✔✔y=k/x (product remains constant (yx stays the same))
✔✔Joint variation - ✔✔y=kzx (y varies jointly with x and z (y/xz stays the same))
✔✔When doing polynomial long division, which terms do you use - ✔✔The leading
coefficients
✔✔What do you normally confuse the least common multiple with? - ✔✔The greatest
common factor (the least common multiple IS NOT the greatest common factor)
✔✔How do you find the least common multiple? - ✔✔Find the smallest whole number
that both expressions divide evenly into. Then use the variables with the highest power
✔✔What is the least common multiple of 25u^3v^4 and 10w^2u^5v^6 -
✔✔50u^5w^2v^6
✔✔y < 9 - ✔✔make a graph that shows where this equation is true
WITH ANSWERS TAGGED A+
✔✔BOTU - ✔✔there is no horizontal asymptote, find slant asymptote (Bigger On Top
Undefined)
✔✔How do you find the slant asymptote? - ✔✔Divide the ENTIRE numerator by the
ENTIRE denominator, the slant asymptote is the quotient, ignore the remainder (might
include division with variables raised to exponents)
✔✔How do you find the vertical asymptote? - ✔✔Set the denominator equal to 0
✔✔sin - ✔✔csc
✔✔cos - ✔✔sec
✔✔tan - ✔✔cot
✔✔Can a graph have more than one local maximum or minimum? - ✔✔yes
✔✔volume - ✔✔cubed
✔✔area - ✔✔squared
✔✔perimeter/ length - ✔✔no power
✔✔How do you find the vertex of a parabola? - ✔✔take the derivative (slope) and set it
equal to 0
✔✔d/dx (x^a) - ✔✔ax^a-1
✔✔antiderivative (x^a) - ✔✔(x^a+1)/a+1
✔✔circumference - ✔✔2πr
✔✔area of a circle - ✔✔πr²
✔✔Translate this equation to the right 3 and up 4:
f(x)=1/2x^2 - ✔✔(1/2(x-3)^2)+4
✔✔If a question asks for all real zeroes should you include imaginary numbers? - ✔✔no
, ✔✔In the functions (f + g)(x), (f-g)(1), (f・g)(x), (f/g)(2) etc. is the x or the coefficient in
the second parentheses being multiplied by the solution of f and g? - ✔✔No, x is the
input for the combined functions (just like it would be in single functions like f(x))
✔✔y=af(x) - ✔✔multiply y coordinate by a
✔✔y=f(ax) - ✔✔divide x coordinate by a
✔✔to find x intercept - ✔✔set f(x) equal to 0
✔✔to find y intercept - ✔✔find f(0)
✔✔What are inverse functions. - ✔✔Functions that switch the input and output
✔✔How do you find the inverse function of an equation? - ✔✔Solve for x then swap the
variables of the new solved equation
✔✔What should you always do first - ✔✔Cancel/ simplify/ factor
✔✔When a problem says that one variable varies inversely with another variable what
do you need to know/ find? - ✔✔the constant k
✔✔Direct variation - ✔✔y=kx (ratio remains constant (y/x stays the same))
✔✔Inverse variation - ✔✔y=k/x (product remains constant (yx stays the same))
✔✔Joint variation - ✔✔y=kzx (y varies jointly with x and z (y/xz stays the same))
✔✔When doing polynomial long division, which terms do you use - ✔✔The leading
coefficients
✔✔What do you normally confuse the least common multiple with? - ✔✔The greatest
common factor (the least common multiple IS NOT the greatest common factor)
✔✔How do you find the least common multiple? - ✔✔Find the smallest whole number
that both expressions divide evenly into. Then use the variables with the highest power
✔✔What is the least common multiple of 25u^3v^4 and 10w^2u^5v^6 -
✔✔50u^5w^2v^6
✔✔y < 9 - ✔✔make a graph that shows where this equation is true
