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Math Questions and Answers: A Comprehensive Guide to Key Concepts and Formulas, Exams of Mathematics

A.T. Still University of Health Sciences (ATSU)Mathematics

A comprehensive list of essential math questions and answers, covering a wide range of topics from basic arithmetic to advanced geometry and trigonometry. It serves as a valuable resource for students seeking to reinforce their understanding of fundamental concepts and formulas. Clear explanations and concise answers, making it an effective tool for self-study and exam preparation.

Typology: Exams

2024/2025

Available from 02/16/2025

DrShirley
DrShirley 🇺🇸

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(4)

4.6K documents

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Math Questions
What is the order of operations? -
✅Parentheses, exponents, multiplication, division, addition, subtraction
What are natural numbers? -
✅All whole numbers except for 0
How to determine if a number is prime -
✅Approximate a square root, then try to divide the number by all prime numbers below the
approximated root
What are relatively prime numbers? -
✅The greatest common factor is 1, but the numbers are not necessarily prime.
Formula for calculation exponential growth -
✅final amount = original amount x (1+growth rate)^number of changes
Supplementary angles add up to -
✅180°
Complimentary angles add up to -
✅90°
What is the triangle inequality rule? -
✅The length of a side of a triangle is less than the sum of and greater than the difference of the
other two sides.
Scalene triangle -
✅No equal sides and no equal angles
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Math Questions

What is the order of operations? - ✅Parentheses, exponents, multiplication, division, addition, subtraction What are natural numbers? - ✅All whole numbers except for 0 How to determine if a number is prime - ✅Approximate a square root, then try to divide the number by all prime numbers below the approximated root What are relatively prime numbers? - ✅The greatest common factor is 1, but the numbers are not necessarily prime. Formula for calculation exponential growth - ✅final amount = original amount x (1+growth rate)^number of changes Supplementary angles add up to - ✅ 180 ° Complimentary angles add up to - ✅ 90 ° What is the triangle inequality rule? - ✅The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides. Scalene triangle - ✅No equal sides and no equal angles

Isosceles Triangles - ✅Two sides and two angle are equal 30-60-90 triangle - ✅Hypotenuse is 2x, short side is x, long side is x√ 3 45-45-90 triangle - ✅Hypotenuse is x√2, and the sides are x. What is the sum of the interior angles for a polygon with n sides? - ✅(n-2) Formula for the area of a trapezoid - ✅A = ((s₁ + s₂)h) / 2 How can you determine the arc degree or central angle of an inscribed angle? - ✅Multiply the inscribed angle by 2 Formula for arc length - ✅Arc length equals = (degree of the arc / 360)(circumference) Formula for the area of a sector - ✅A = (degree of the arc / 360)(area of a circle) Formula for the diagonal length of a rectangular prism - ✅d = √(l²+w²+h²) Formula for the diagonal length of a cube - ✅d= s√ 3 Formula for the volume of a cone -

✅(x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center of the ellipse, the length of the horizontal axis is 2a, the length of the vertical axis is 2b, if a>b, the horizontal axis is the major axis. Standard form for a hyperbola that opens to the sides - ✅(x-h)²/a² - (y-k)²/b² = 1 Standard form for a hyperbola that opens vertically - ✅(y-k)²/a² - (x-h)²/b² = 1 Two vectors are perpendicular if - ✅Their dot product = 0 How to find the distance between two points in 3d plane? - ✅Square the differences between each coordinate, then square root the sum What is the form of a polar coordinate? - ✅(r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis How can multiple polar coordinates be made? - ✅Adding or subtracting 180 to θ and reversing the sign of r. What are the conversion equations for polar coordinates to normal coordinates? - ✅x=rcosθ y=rsinθ Where is tangent positive/negative? - ✅Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4 Pythagorean Identities - ✅sin²x+cos²x = 1

sec²x = 1+tan²x csc²x = 1+cot²x Double Angle Formulas - ✅sin2x= 2sinxcosx cos2x = cos²x − sin²x = 2cos²x − 1 = 1 − sin²x Sum of 2 Angles Formulas - ✅sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)] Difference between 2 Angles formulas - ✅sin(a-b) = sin(a)cos(b) - sin(b)cos(a) cos(a-b) = cos(a)cos(b) + sin(a)sin(b) tan(a-b) = [tan(a) - tan(b)] / [1+tan(a)tan(b)] Law of Cosines - ✅c² = a² + b² - 2abcos(C) If a function is of the nth degree, what is the maximum number of extreme bumps it can have? - ✅n- Define an even function. - ✅f(x) = f(-x) Define an odd function. - ✅f(x) = -f(-x) How many ways can n elements be ordered? - ✅n!