MATHNASIUM JOB ASSESSMENT MAIN EXAM 2025/2026
QUESTIONS WITH ANSWERS GRADED A+
✔✔What are the characteristics of a polynomial? - ✔✔1. No negative exponents
2. No fraction exponents
3. The leading coefficient is the coefficient with the highest degree
✔✔How does multiplicity shape a graph? - ✔✔cross = multiplicity of 1
bounce = multiplicity that is even
twist = multiplicity that is odd
✔✔How is end behavior determined? - ✔✔1. Degree
2. Leading Coefficient
Odd Degree > L.C. is + > down-up
Odd Degree > L.C. is - > up-down
Even Degree > L.C. is + > up-up
Even Degree > L.C. is - > down-down
✔✔How does an oblique asymptote occur? - ✔✔When there is no Horizontal Asymptote
✔✔How do you find Arc length? - ✔✔s = radians x radius
✔✔What are the trig identities? - ✔✔
✔✔How do you find the magnitude of a vector? - ✔✔Distance formula
✔✔What are the standard unit vectors? - ✔✔i = <1, 0>
j = <0, 1>
✔✔How do you find the angle between a vector? - ✔✔* Remember inverse cosine
when plugging into the calculator
✔✔How do you find the unit vector? - ✔✔(component vector) / (magnitude)
✔✔Polar > Rectangular - ✔✔x = r x cosine x theta
y = r x sine x theta
✔✔Rectangular > Polar - ✔✔x^2 + y^2 = r^2
theta = inverse tangent (y/x)
✔✔50!/48! = ? - ✔✔2450
, ✔✔A solution containing 30% juice is mixed with a solution containing 10% juice to
make 100 gallons of solution that makes 12% juice.How much of the 30% solution was
used? - ✔✔10 gallons
✔✔7 runners in a race, how many different orderings of 1st, 2nd, and 3rd place can
there be? - ✔✔210
✔✔What is the formula for arithmetic sequence? - ✔✔an=a1+(n-1)d
✔✔i^63 = ? - ✔✔-i
✔✔Combination Formula - ✔✔nCr = n!/r!(n-r)!
Use when order doesn't matter
✔✔Permutation formula - ✔✔nPr = n!/(n-r)!
Use when order matters
✔✔ How do you find the perimeter and area of a rectangle? - ✔✔P = 2l + 2w
P = 2 (l + w)
A = lw
✔✔How do you find the area of a parallelogram? - ✔✔A = bh
✔✔How do you find the circumference and area of a circle? - ✔✔C = 2 x pi x r
C = pi x d
A = pi x r^2
✔✔What is the Pythagorean Theorem? - ✔✔a^2 + b^2 = c^2
✔✔How do you find the area of a triangle? - ✔✔A = (1/2)bh
✔✔How do you find the area of a trapezoid? - ✔✔A = (1/2)h (b1 + b2)
✔✔How do you find the volume and surface area of a rectangular solid? - ✔✔V = lwh
SA = 2lw + 2lh + hw
✔✔How do you find the volume of a cylinder? - ✔✔V = pi x r^2 x h
✔✔How do you find the volume of a cone? - ✔✔V = (1/3) x pi x r^2 xh
✔✔How do you find the volume of a square pyramid? - ✔✔V = (1/3) x (area of base) x
height
QUESTIONS WITH ANSWERS GRADED A+
✔✔What are the characteristics of a polynomial? - ✔✔1. No negative exponents
2. No fraction exponents
3. The leading coefficient is the coefficient with the highest degree
✔✔How does multiplicity shape a graph? - ✔✔cross = multiplicity of 1
bounce = multiplicity that is even
twist = multiplicity that is odd
✔✔How is end behavior determined? - ✔✔1. Degree
2. Leading Coefficient
Odd Degree > L.C. is + > down-up
Odd Degree > L.C. is - > up-down
Even Degree > L.C. is + > up-up
Even Degree > L.C. is - > down-down
✔✔How does an oblique asymptote occur? - ✔✔When there is no Horizontal Asymptote
✔✔How do you find Arc length? - ✔✔s = radians x radius
✔✔What are the trig identities? - ✔✔
✔✔How do you find the magnitude of a vector? - ✔✔Distance formula
✔✔What are the standard unit vectors? - ✔✔i = <1, 0>
j = <0, 1>
✔✔How do you find the angle between a vector? - ✔✔* Remember inverse cosine
when plugging into the calculator
✔✔How do you find the unit vector? - ✔✔(component vector) / (magnitude)
✔✔Polar > Rectangular - ✔✔x = r x cosine x theta
y = r x sine x theta
✔✔Rectangular > Polar - ✔✔x^2 + y^2 = r^2
theta = inverse tangent (y/x)
✔✔50!/48! = ? - ✔✔2450
, ✔✔A solution containing 30% juice is mixed with a solution containing 10% juice to
make 100 gallons of solution that makes 12% juice.How much of the 30% solution was
used? - ✔✔10 gallons
✔✔7 runners in a race, how many different orderings of 1st, 2nd, and 3rd place can
there be? - ✔✔210
✔✔What is the formula for arithmetic sequence? - ✔✔an=a1+(n-1)d
✔✔i^63 = ? - ✔✔-i
✔✔Combination Formula - ✔✔nCr = n!/r!(n-r)!
Use when order doesn't matter
✔✔Permutation formula - ✔✔nPr = n!/(n-r)!
Use when order matters
✔✔ How do you find the perimeter and area of a rectangle? - ✔✔P = 2l + 2w
P = 2 (l + w)
A = lw
✔✔How do you find the area of a parallelogram? - ✔✔A = bh
✔✔How do you find the circumference and area of a circle? - ✔✔C = 2 x pi x r
C = pi x d
A = pi x r^2
✔✔What is the Pythagorean Theorem? - ✔✔a^2 + b^2 = c^2
✔✔How do you find the area of a triangle? - ✔✔A = (1/2)bh
✔✔How do you find the area of a trapezoid? - ✔✔A = (1/2)h (b1 + b2)
✔✔How do you find the volume and surface area of a rectangular solid? - ✔✔V = lwh
SA = 2lw + 2lh + hw
✔✔How do you find the volume of a cylinder? - ✔✔V = pi x r^2 x h
✔✔How do you find the volume of a cone? - ✔✔V = (1/3) x pi x r^2 xh
✔✔How do you find the volume of a square pyramid? - ✔✔V = (1/3) x (area of base) x
height
