Mathnasium Job Assessment

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

How do you find the volume of a sphere?

V = (4/3) x pi x r^3

How many liters are in 1 quart?

1 quart = 0.95 liters

How many centimeters are there in an inch?

1 inch = 2.54 centimeters

How many kilograms are in a pound?

1 pound = 0.45 kilograms

How do you convert Celsius to Fahrenheit?

F = (9/5)C + 32

How do you convert Fahrenheit to Celsius?

C = (5/9) x (F - 32)

How do you find the distance between two points?

How do you find slope?

How many feet are in one mile?

1 mile = 5,280 feet

How many feet are in one yard?

1 yard = 3 feet

How many inches are in one foot?

1 foot = 12 inches

How many pounds are in one ton?

1 ton = 2,000 pounds

How many ounces are in one pound?

1 pound = 16 ounces

How many quarts are in one gallon?

1 gallon = 4 quarts

How many pints are in one quart?

1 quart = 2 pints

How many cups are in one pint?

1 pint = 2 cups

How many fluid ounces are in one cup?

1 cup = 8 fluid ounces

How many days are in one year?

1 year = 365 days

How many hours are in a day?

1 day = 24 hours

How many minutes are in an hour?

1 hour = 60 minutes

How many seconds are in a minute?

1 minute = 60 seconds

What is the quadratic formula?

How do you calculate the degrees of a polygon?

Angle degree = 180 (n-2) *n = number of sides

How do you solve a 30-60-90 triangle?

How do you solve a 45-45-90 triangle?

What does "i" equal?

sqrt of -1

What does "i^2" equal?

-1

What is GCF?

GCF is the greatest factor that divides two numbers.

What is LCM?

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

What is a relation?

A correspondence between 2 variables.

What is a function?

A relation such that for each x-value in the domain, there is exactly one corresponding y-value.

When do vertical asymptotes occur?

A factor in the denominator only equals zero.

When do holes occur?

A factor in the numerator and the denominator equal zero.

What is the acronym for horizontal asymptotes?

Bottom heavy

y = O

S ame degree, divide the leading coefficient

Top heavy

O

N No HA

How do you classify polynomials by degree?

0-constant

1-linear

2-quadratic

3-cubic

4- quartic

5- quintic

How do you classify polynomials by the number of terms?

1-monomial

2-binomial

3-trinomial

4-quadnomial

5-polynomial

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?

a1 + 4d = an

i^63 = ?

-i