Mathematics Concepts Overview

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Questions and Answers

What is the formula for calculating simple interest?

  • I = prt (correct)
  • PC = (New Value - Old Value) / Old Value x 100
  • Mean = Sum of all Data Points / Number of Data Points
  • d = rt

In the Distance, Rate, and Time formula, if the rate is given in miles per hour, the time must be in minutes.

False (B)

What does PEMDAS stand for?

Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

The formula for calculating the percent change is: PC = (New Value - Old Value) / ______ x 100.

<p>Old Value</p> Signup and view all the answers

Match the following statistical terms with their definitions:

<p>Mean = The value in the middle of the data set Range = The value in the data set that occurs the most often Mode = The difference between the maximum and minimum values in a data set Median = The average of all values in a data set</p> Signup and view all the answers

What is the area of a circle with a radius of 5 centimeters?

<p>$25Ï€$ square centimeters (B)</p> Signup and view all the answers

There are 3600 seconds in one hour.

<p>True (A)</p> Signup and view all the answers

What is the sum of the interior angles of a hexagon?

<p>720 degrees</p> Signup and view all the answers

The perimeter of a circle is also known as its ______.

<p>circumference</p> Signup and view all the answers

Match the following units of measurement with their corresponding values:

<p>1 mile = 5280 feet 1 yard = 36 inches 1 pound = 16 ounces 1 gallon = 4 quarts</p> Signup and view all the answers

Which of the following linear units is the largest?

<p>Mile (A)</p> Signup and view all the answers

To convert from a smaller unit to a larger unit, you should multiply.

<p>False (B)</p> Signup and view all the answers

What is the formula for the circumference of a circle in terms of its diameter?

<p>C = πd</p> Signup and view all the answers

A polygon with 7 sides is called a ______ or ______.

<p>heptagon</p> Signup and view all the answers

How many minutes are there in a day?

<p>1440 (C)</p> Signup and view all the answers

The product of any number and zero is always zero.

<p>True (A)</p> Signup and view all the answers

What is the result of dividing any non-zero number by zero?

<p>Undefined (A)</p> Signup and view all the answers

Calculate the perimeter of a square with a side length of 5 units.

<p>20 units</p> Signup and view all the answers

The area of a rectangle is calculated by multiplying its ______ and ______.

<p>length, width</p> Signup and view all the answers

Match the following quadrilaterals with their corresponding formulas for area:

<p>Square = A = s^2 Rectangle = A = lw Parallelogram = A = bh</p> Signup and view all the answers

Which of the following statements about quadrilaterals is TRUE?

<p>All quadrilaterals have at least one pair of parallel sides. (A)</p> Signup and view all the answers

The formula for finding the perimeter of any quadrilateral is P = 2l + 2w.

<p>False (B)</p> Signup and view all the answers

What is the area of a parallelogram with a base of 8 units and a height of 6 units?

<p>48 square units</p> Signup and view all the answers

Which of the following is the correct formula for finding the slope of a line given two points?

<p>$m = \frac{y_2 - y_1}{x_2 - x_1}$ (C)</p> Signup and view all the answers

To find the y-intercept of a line given its slope and a point on the line, substitute the slope and the point's coordinates into the slope-intercept form (y = mx + b) and solve for b.

<p>True (A)</p> Signup and view all the answers

What is the point-slope form of a linear equation?

<p>y - y<sub>1</sub> = m(x - x<sub>1</sub>)</p> Signup and view all the answers

The equation of a line that passes through the point (2, 3) and has a slope of -1 is ______.

<p>y - 3 = -1(x - 2)</p> Signup and view all the answers

Match the following terms with their corresponding mathematical representations:

<p>Slope = m Y-intercept = b Slope-intercept form = y = mx + b Point-slope form = y - y<sub>1</sub> = m(x - x<sub>1</sub>)</p> Signup and view all the answers

What is the surface area formula for a cylinder?

<p>2Ï€r^2 + 2Ï€rh (C)</p> Signup and view all the answers

The volume of a sphere is calculated using the formula V = (4/3)Ï€r^2.

<p>False (B)</p> Signup and view all the answers

What is the formula for the perimeter of a trapezoid?

<p>P = a + b1 + c + b2</p> Signup and view all the answers

The volume of a rectangular pyramid is given by ______.

<p>V = (1/3)abh</p> Signup and view all the answers

Which formula represents the volume of a cone?

<p>V = (1/3)Ï€r^2h (B)</p> Signup and view all the answers

The area of a rectangle can be calculated using the formula A = l + w.

<p>False (B)</p> Signup and view all the answers

What is the surface area formula for a cube?

<p>SA = 6a^2</p> Signup and view all the answers

Match the following solids with their corresponding volume formula:

<p>Cube = a^3 Cylinder = πr^2h Sphere = (4/3)πr^3 Rectangular Solid = l x w x h</p> Signup and view all the answers

Which of the following is a correct combination of like terms?

<p>2x and 6x (A)</p> Signup and view all the answers

Subtracting polynomials requires the same process as adding polynomials.

<p>False (B)</p> Signup and view all the answers

How many different lunch combinations can be made with 3 sandwiches, 3 sides, and 2 drinks?

<p>18</p> Signup and view all the answers

The process of combining like terms is used when __________ polynomials.

<p>adding</p> Signup and view all the answers

Match the following types of terms with their categories:

<p>2x = Like terms 6y = Not like terms -5x = Like terms 8xy2 = Not like terms</p> Signup and view all the answers

When subtracting the polynomials (3x2 – 8x + 7) - (2x2 - 6x + 12), what is the first step?

<p>Distribute the negative sign (C)</p> Signup and view all the answers

The total number of combinations for two events can be found using the formula m + n.

<p>False (B)</p> Signup and view all the answers

What is the total number of lunch options for Sarah at the deli with 3 soups, 3 salads, and 6 sandwiches?

<p>54</p> Signup and view all the answers

Flashcards

Multiplication by One

The product of one and any number is the number itself. Example: 7 x 1 = 7

Zero Times Any Number

Zero multiplied by any number equals zero. Example: 0 x 2 = 0

Zero Divided by Nonzero

Zero divided by any nonzero number is zero. Example: 0 ÷ 3 = 0

Dividing by Zero

Dividing a number by zero is undefined. Example: 5 ÷ 0 = undefined

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Square Area Formula

The area of a square is calculated as A = s², where s is the side length.

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Rectangle Area Formula

The area of a rectangle is calculated as A = lw, where l is length and w is width.

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Parallelogram Area Formula

The area of a parallelogram is calculated as A = bh, where b is the base and h is the height.

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Quadrilateral Perimeter

The perimeter of any quadrilateral is found by adding all its sides together.

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Simple Interest Formula

Formula to calculate interest: I = prt, where I is interest, p is principal, r is rate, and t is time.

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Principal (p)

The initial amount of money invested or loaned.

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Distance Formula

Formula to calculate distance: d = rt, where d is distance, r is rate, and t is time.

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Percent Change (PC)

Calculation of change in value represented as a percentage: PC = (New Value - Old Value) / Old Value x 100.

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Order of Operations

Rules for the sequence of mathematical operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

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Mean

Average of a set of numbers: Mean = Sum of all Data Points / Number of Data Points.

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Median

Middle value in a sorted data set.

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Mode

The value that appears most frequently in a data set.

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Circumference

The perimeter or boundary line of a circle.

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Area of a Circle

The space contained within a circle, calculated by A = πr².

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Diameter

The distance across a circle through its center, equal to twice the radius.

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Convert Units

The process of changing from one unit of measurement to another.

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Pint

A unit of volume equal to 2 cups.

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Triangle

A polygon with 3 sides and 180 degrees sum of interior angles.

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Hexagon

A polygon with 6 sides and 720 degrees sum of interior angles.

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Fluid Ounce

A unit of measurement for volume often used in cooking.

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Sum of Interior Angles

Calculated by the formula S = 180(n - 2) for polygons.

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Trapezoid Perimeter

The perimeter of a trapezoid is the sum of its four sides: P = a + b1 + c + b2.

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Trapezoid Area

The area of a trapezoid is calculated as A = (b1 + b2) ∙ h / 2.

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Cube Volume

Volume for a cube is given by V = a^3, where 'a' is the length of a side.

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Cube Surface Area

Surface area for a cube is SA = 6a^2.

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Rectangular Solid Volume

For a rectangular solid, volume is V = l × w × h.

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Cylinder Volume

The volume of a cylinder is given by V = πr^2 h.

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Sphere Volume

Volume of a sphere is V = (4/3)Ï€r^3.

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Cone Volume

The volume of a cone is V = (1/3)Ï€r^2 h.

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Like Terms

Terms in algebra that have the same variable and exponent.

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Not Like Terms

Terms in algebra that have different variables or exponents.

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Adding Polynomials

Combining like terms from two polynomial expressions.

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Subtracting Polynomials

Rewrite subtraction as addition by distributing the negative sign.

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Fundamental Counting Principle

A method to find the total number of ways events can occur.

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Event M Ways

The number of ways event M can occur in the Fundamental Counting Principle.

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Event N Ways

The number of ways event N can occur in the Fundamental Counting Principle.

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Combinations

Different possible outcomes from multiple events or choices.

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Slope (m)

The steepness of a line, calculated as rise over run.

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Y-intercept (b)

The point where the line crosses the y-axis.

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Point-slope equation

y - y1 = m(x - x1); defines a line given a point and slope.

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Slope formula

m = (y2 - y1) / (x2 - x1); calculates the slope between two points.

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Writing equations of lines

Use slope and y-intercept or points to write line equations.

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Study Notes

Fundamental Counting Principle

  • The Fundamental Counting Principle is a method to quickly determine the total number of ways different events can occur.
  • If event M can occur m ways and event N can occur n ways, the total number of ways these events can occur is m × n.

Angle Types and Special Angle Pairs

  • Acute Angle: An angle measuring less than 90 degrees.
  • Right Angle: An angle measuring exactly 90 degrees.
  • Obtuse Angle: An angle measuring greater than 90 degrees but less than 180 degrees.
  • Straight Angle: An angle measuring exactly 180 degrees.
  • Complementary Angles: Two angles that add up to 90 degrees.
  • Supplementary Angles: Two angles that add up to 180 degrees.

Properties of Radicals

  • √a² = a
  • √(a√b) = a√(b)
  • √(ab) = √a · √b
  • √(a/b) = √a / √b
  • √(a²) = |a| (Note the absolute value)

Factoring Guide

  • Difference of Two Squares: a² - b² = (a - b)(a + b)
  • Sum of Two Cubes: a³ + b³ = (a + b)(a² - ab + b²)
  • Difference of Two Cubes: a³ - b³ = (a - b)(a² + ab + b²)
  • Leading coefficient 1: Factor based on finding two numbers that multiply to the constant term and add up to the linear term.
  • Leading coefficient not 1: Employ trial and error or the AC-Method to factor.
  • Three terms: Often trial and error is the most pragmatic method if the leading coefficient isn't 1.

Factorials

  • n! = n × (n - 1) × (n - 2) × ... × 1
  • Special Cases: 0! = 1, 1! = 1, etc.

Prime Numbers and Divisibility Rules

  • Divisibility by 2: If the last digit is even (0, 2, 4, 6, or 8).
  • Divisibility by 3: If the sum of the digits is divisible by 3.
  • Divisibility by 4: If the last two digits are divisible by 4.
  • Divisibility by 5: If the last digit is 0 or 5.
  • Divisibility by 6: If the number is divisible by both 2 and 3.
  • Divisibility by 9: If the sum of the digits is divisible by 9.
  • Divisibility by 10: If the last digit is 0.

Reciprocals

  • The reciprocal of a fraction a/b is b/a.
  • The reciprocal of a whole number n is 1/n.
  • The reciprocal of a mixed number is found by converting it to an improper fraction first.

Adding and Subtracting Polynomials

  • Combine like terms when adding polynomials.
  • Distribute the negative sign to each term in the second polynomial when subtracting and then combine like terms.

Combined Work Rates

  • Formula for combined rates: (time A) + (time B) = 1 (time together)
  • Find the common denominator to solve for time together

Converting Celsius to Fahrenheit and vice versa

  • Conversion formulas: F = (9/5)C + 32, C = (5/9)(F - 32).

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