Intro to ss ppt
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A spreadsheet is a grid of rows and columns used to enter text, numbers, and calculation results. It allows users to easily perform calculations like adding numbers and monetary amounts. Spreadsheets become more powerful as their formulas can reference cell values, allowing users to calculate results by changing input values. Examples of spreadsheet uses include gradebooks for school, budgets for personal finances, and inventory tracking for business.
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Tafe presentation1
The student is expected to add, subtract, multiply, and divide decimals and whole numbers to solve problems. Specific skills include:
- Adding and subtracting whole numbers and decimals by lining up the decimals
- Multiplying whole numbers by starting with the last digit of the second number
- Dividing decimals by placing the larger number in the "house" and including any remainder to the side
The document provides rules and examples for performing each operation on decimals and whole numbers.
Tafe presentation
The student is expected to add, subtract, multiply, and divide decimals and whole numbers to solve meaningful problems. When adding decimals, the decimals must be lined up. When subtracting decimals, the small number is subtracted from the large number and the decimals must be lined up. For multiplication, the last digit of the second number is used first. For division, the large number goes inside the "house" and any remainder is written on the side.
Graphs
The document discusses different ways to represent graphs in a computer's memory. Graphs can be represented using either an adjacency matrix or linked lists. An adjacency matrix uses an n x n matrix to represent a graph with n vertices, where entries mark connections between vertices. Linked list representation connects each vertex to its neighbors through pointers. Both directed and undirected graphs as well as weighted graphs can be modeled with these approaches.
Second Period Math Applications
1. The document provides objectives and instructions for various math concepts including the order of operations, transposing equations, squares and square roots, scientific notation, SI prefixes, trigonometry, the Pythagorean theorem, phasors, and ratios.
2. It explains how to apply the order of operations (BEDMAS) to evaluate expressions and how to transpose terms in equations by applying the same operations to both sides.
3. Examples are provided for calculating the square of numbers, taking square roots, converting between standard and scientific notation, and using SI prefixes to modify units of measurement.
Closure properties of numbers
The document discusses the closure property of real numbers. It explains that when you perform addition or multiplication on real numbers, the result will always be another real number. This is an important property because it means equations involving only addition and multiplication are guaranteed to have a real number solution. The closure property ensures operations like adding costs in a shopping basket will always yield a real number total.
Significant numbers in calculations fall 2014
This document discusses significant figures and calculations in science. It explains that calculated answers can only be as precise as the least precise measurement. When adding or subtracting numbers, the answer should have the same number of decimal places as the measurement with the fewest places. When multiplying or dividing, the answer must reflect the precision of the least precise tool by rounding or adding zeros. The document provides examples of calculations and their correctly rounded answers.
Indirect measurement
The document provides examples and explanations of using indirect measurement to find unknown heights or lengths. It gives two examples of setting up proportions using corresponding sides of similar triangles to calculate heights that cannot be measured directly. The examples find the height of a tree using a 6 foot person and 7 foot shadow, and the height of a rocket using a 4 foot model rocket and its 3 foot shadow. It explains that indirect measurement, also called using similar figures and proportions, allows calculating heights by setting up and solving proportions.
Lesson5.1 complexnumbers
This document provides an introduction to complex numbers. It defines the imaginary number i and shows that i raised to even powers is 1 and raised to odd powers alternates between i and -i. Complex numbers combine real and imaginary parts in the form a + bi. The document demonstrates operations like addition, subtraction, multiplication and division on complex numbers. It warns that the properties of radicals do not directly apply when combining real and imaginary parts, and instead those expressions should be written using i. The final sections demonstrate working with complex numbers on a calculator.
Recommended
Tafe presentation1
The student is expected to add, subtract, multiply, and divide decimals and whole numbers to solve problems. Specific skills include:
- Adding and subtracting whole numbers and decimals by lining up the decimals
- Multiplying whole numbers by starting with the last digit of the second number
- Dividing decimals by placing the larger number in the "house" and including any remainder to the side
The document provides rules and examples for performing each operation on decimals and whole numbers.
Tafe presentation
The student is expected to add, subtract, multiply, and divide decimals and whole numbers to solve meaningful problems. When adding decimals, the decimals must be lined up. When subtracting decimals, the small number is subtracted from the large number and the decimals must be lined up. For multiplication, the last digit of the second number is used first. For division, the large number goes inside the "house" and any remainder is written on the side.
Graphs
The document discusses different ways to represent graphs in a computer's memory. Graphs can be represented using either an adjacency matrix or linked lists. An adjacency matrix uses an n x n matrix to represent a graph with n vertices, where entries mark connections between vertices. Linked list representation connects each vertex to its neighbors through pointers. Both directed and undirected graphs as well as weighted graphs can be modeled with these approaches.
Second Period Math Applications
1. The document provides objectives and instructions for various math concepts including the order of operations, transposing equations, squares and square roots, scientific notation, SI prefixes, trigonometry, the Pythagorean theorem, phasors, and ratios.
2. It explains how to apply the order of operations (BEDMAS) to evaluate expressions and how to transpose terms in equations by applying the same operations to both sides.
3. Examples are provided for calculating the square of numbers, taking square roots, converting between standard and scientific notation, and using SI prefixes to modify units of measurement.
Closure properties of numbers
The document discusses the closure property of real numbers. It explains that when you perform addition or multiplication on real numbers, the result will always be another real number. This is an important property because it means equations involving only addition and multiplication are guaranteed to have a real number solution. The closure property ensures operations like adding costs in a shopping basket will always yield a real number total.
Significant numbers in calculations fall 2014
This document discusses significant figures and calculations in science. It explains that calculated answers can only be as precise as the least precise measurement. When adding or subtracting numbers, the answer should have the same number of decimal places as the measurement with the fewest places. When multiplying or dividing, the answer must reflect the precision of the least precise tool by rounding or adding zeros. The document provides examples of calculations and their correctly rounded answers.
Indirect measurement
The document provides examples and explanations of using indirect measurement to find unknown heights or lengths. It gives two examples of setting up proportions using corresponding sides of similar triangles to calculate heights that cannot be measured directly. The examples find the height of a tree using a 6 foot person and 7 foot shadow, and the height of a rocket using a 4 foot model rocket and its 3 foot shadow. It explains that indirect measurement, also called using similar figures and proportions, allows calculating heights by setting up and solving proportions.
Lesson5.1 complexnumbers
This document provides an introduction to complex numbers. It defines the imaginary number i and shows that i raised to even powers is 1 and raised to odd powers alternates between i and -i. Complex numbers combine real and imaginary parts in the form a + bi. The document demonstrates operations like addition, subtraction, multiplication and division on complex numbers. It warns that the properties of radicals do not directly apply when combining real and imaginary parts, and instead those expressions should be written using i. The final sections demonstrate working with complex numbers on a calculator.
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This document provides examples of using indirect measurement to solve for unknown distances. It begins with an example of using similar triangles to find the length of side EG of triangle EFG given the lengths of sides AB, AC, and EF of similar triangle ABC. It then gives another example using similar triangles formed by a building, its shadow, and a tree and its shadow to calculate the height of the tree. Finally, it provides two practice problems asking the reader to use indirect measurement to solve for the width of a river and the height of a tree.
Chapter5.6
The document provides examples of using proportions to solve problems involving similar triangles formed by objects and their shadows. It includes two examples: 1) Finding the length of one side of a similar triangle where the other sides are given. The length is found to be 12 feet. 2) Finding the height of a tree using the height and shadow length of a building and the shadow length of the tree. The height of the tree is found to be 14 feet. It also includes a practice problem to check understanding.
Unit .2
This document introduces several topics related to the Cartesian coordinate system including the Cartesian plane, absolute value, distance formulas, midpoint formulas, and equations of circles. It provides examples and explanations of each concept. Key points covered are the four quadrants of the Cartesian plane, the definition and properties of absolute value, formulas for finding the distance between two points and the midpoint of a line segment using coordinates, and the standard form equation of a circle given its center and radius.
4. lesson 3 addition of whole numbers
This document discusses addition of whole numbers. It defines addition as bringing two or more numbers together to make a new total sum. The addends are the numbers being added and the plus sign is the addition symbol. When adding, digits are added from right to left and carrying is used when the sum is greater than 9. Word problems can be solved using the ESA method which stands for writing the Equation, finding the Solution, and stating the Answer. Key words that indicate addition is needed include add, altogether, both, more than, in all, plus, sum, total, combined, and join.
Measurements and sig figs
Precision refers to the reproducibility of measurements while accuracy refers to how close a measurement is to the true value. All measurements must include units and use the metric system of grams, meters, and liters. Temperature is measured in Celsius with the formula to convert to Fahrenheit. When taking measurements, always estimate one digit past the last readable digit to show uncertainty. Significant figures indicate the number of digits that are certain in a measurement based on rules like nonzero integers and captive zeros counting as significant. Mathematical operations follow rules where addition and subtraction take the least precise measurement's decimal places as significant figures and multiplication and division take the least precise measurement's significant figures. Scientific notation allows easy conversion between decimal and exponential forms while maintaining the same value.
D.e.v
The document provides step-by-step instructions for solving 4 math problems:
1) Finding the maximum water volume of a plastic water bottle given the plastic area.
2) Isolating variables, long division, and factoring to simplify a quadratic equation in order to graph it and find the domain.
3) Factoring and solving for zero to find the values of x that satisfy a polynomial equation.
4) The steps for completing the square to derive the quadratic formula.
Solving Equations
This document provides an overview of equations in one variable, including:
- Defining equations and expressions, and distinguishing between the two
- Identifying linear equations and determining if a number is a solution
- Explaining properties of equality like addition, subtraction, multiplication, and division
- Outlining the steps to solve linear equations in one variable
- Describing types of linear equations like conditional, identity, and contradiction
Square roots
The document discusses square roots including:
1. Defining square roots and the radical symbol, and that the square root of a number can be positive or negative.
2. Explaining that the principal square root is always positive and how to identify squares of integers from 1 to 20.
3. Giving examples of simplifying square root expressions and identifying numbers as rational or irrational.
4. Discussing estimating square roots by finding what two consecutive integers a square root lies between.
5. Providing a word problem about finding the length of a wire supporting a tower using a square root formula.
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The document contains notes from a math lesson on linear equations and their graphs. It includes examples of writing linear equations in standard form and slope-intercept form, finding x- and y-intercepts, and making tables of values to graph linear equations. Key terms defined are linear equation, standard form, x-intercept, y-intercept, and various methods for graphing linear equations like finding intercepts and making tables. Sample problems are worked through as examples.
Lecture
This document provides an overview of numerical analysis and number systems. It discusses:
1. Assessment criteria for the course including exams, assignments, and participation.
2. An introduction to numbers, digits, and different number systems like binary, octal, decimal, and hexadecimal.
3. Methods for converting between number systems including decimal to other bases, other bases to decimal, and shortcuts for binary, octal, and hexadecimal conversions.
Comparing and ordering integers
The document introduces integers, absolute value, and comparing and ordering integers. It provides definitions for integers, opposites, and absolute value. Examples are given for finding absolute value, comparing integers using <, =, >, and ordering integers from least to greatest. Quick practice problems with answers are included for comparing and ordering integers.
Ratios and proportions
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The document provides information about absolute values and the real number system. It includes:
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- Examples of absolute value and how it measures the distance from zero, including that operations inside the absolute value signs must be done first before taking the absolute value.
- Class work assignments on opposites and absolute values problems from pages 17-18 including a mixed review.
Adding without Regrouping
This document discusses adding numbers without regrouping. It explains that adding numbers means combining two sets to form a new set. It provides examples of adding two-digit and three-digit numbers step-by-step without regrouping. The steps are to add the ones, tens, and hundreds places separately. Practice problems are included for the reader to try adding numbers without regrouping.
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The document summarizes key terms and concepts for adding integers in 8th grade algebra, including that a zero pair results when a positive and negative number with the same value are added together, making their sum equal to zero. It can then be removed from the equation. Whether the integers have the same or different signs determines if you add or take the difference of their absolute values, and the sign of the result follows the larger absolute value. Some example problems are assigned from the textbook for students to work through.
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This document outlines lessons on opposite quantities combining to make zero. It includes:
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- Instructions for a "Do Now" activity involving a Venn diagram
- Explanations and examples of addition of positive and negative numbers, absolute value, and the additive inverse property
- Rules for an integer card game to practice adding and discarding positive and negative numbers
- An example of representing a negative number as a temperature change
- A prompt for students to write a money-based word problem representing the expression 200 + (-200)
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This document discusses vectors and their components, magnitude, direction, and addition. It provides examples of calculating the magnitude and component form of vectors. It also explains how to add vectors using the parallelogram method by drawing a parallelogram and finding the diagonal vector sum, or the component method by finding the horizontal and vertical components and adding them. Vector addition is important in physics for the law of conservation of momentum.
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1) Provides tips for subtracting numbers with many trailing zeros such as 1,000 - 258 by breaking it into steps or subtracting from 999 and adding 1 back.
2) Explains a method for easily multiplying numbers by 250 or other multiples of 10 by multiplying by 1000 and dividing by 4.
3) Discusses mental math tricks like knowing that 11 multiplied by any two-digit number involves adding the digits in pairs and how memorizing things like squares and fractions can speed up calculations.
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The course project involves solving two counting problems using a computer program. Problem 1 asks students to write a program to count the number of positive integer solutions to an equation with multiple variables summing to a given total. Problem 2 uses the principle of inclusion-exclusion to count the number of integers below a threshold that are not divisible by three given numbers. Students are provided templates to guide their programming solutions and are asked to test their programs on sample cases.
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The document provides lesson content on addition and subtraction of whole numbers. It includes examples and explanations of key concepts like finding the sum, carrying, borrowing, properties of addition/subtraction, and word problems. Practice problems are provided at the end to solve applications using the whole number operations and problem-solving process covered in the lesson.
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The document discusses various functions and concepts related to spreadsheets, including columns, rows, simple formulas, complex formulas, SUM and AVERAGE functions, inserting rows and columns, charting, cell protection, IF formulas, relative and absolute referencing. Spreadsheets allow users to store, calculate, and analyze numerical data using formulas and functions, and can automatically recalculate results when data changes. Charts can be created to visually represent spreadsheet data to make it easier to understand trends and relationships.
ppt math6 qt3-wk3.pptx
The document provides instructions on subtracting integers. It explains:
1) To subtract integers, transform the subtraction into addition by keeping the first number and changing the second number's sign.
2) Examples are provided of subtracting integers with different signs and the same sign.
3) A multi-step word problem is worked out as an example of subtracting integers.
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The document provides examples of using proportions to solve problems involving similar triangles formed by objects and their shadows. It includes two examples: 1) Finding the length of one side of a similar triangle where the other sides are given. The length is found to be 12 feet. 2) Finding the height of a tree using the height and shadow length of a building and the shadow length of the tree. The height of the tree is found to be 14 feet. It also includes a practice problem to check understanding.
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This document discusses addition of whole numbers. It defines addition as bringing two or more numbers together to make a new total sum. The addends are the numbers being added and the plus sign is the addition symbol. When adding, digits are added from right to left and carrying is used when the sum is greater than 9. Word problems can be solved using the ESA method which stands for writing the Equation, finding the Solution, and stating the Answer. Key words that indicate addition is needed include add, altogether, both, more than, in all, plus, sum, total, combined, and join.
Measurements and sig figs
Precision refers to the reproducibility of measurements while accuracy refers to how close a measurement is to the true value. All measurements must include units and use the metric system of grams, meters, and liters. Temperature is measured in Celsius with the formula to convert to Fahrenheit. When taking measurements, always estimate one digit past the last readable digit to show uncertainty. Significant figures indicate the number of digits that are certain in a measurement based on rules like nonzero integers and captive zeros counting as significant. Mathematical operations follow rules where addition and subtraction take the least precise measurement's decimal places as significant figures and multiplication and division take the least precise measurement's significant figures. Scientific notation allows easy conversion between decimal and exponential forms while maintaining the same value.
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The document provides step-by-step instructions for solving 4 math problems:
1) Finding the maximum water volume of a plastic water bottle given the plastic area.
2) Isolating variables, long division, and factoring to simplify a quadratic equation in order to graph it and find the domain.
3) Factoring and solving for zero to find the values of x that satisfy a polynomial equation.
4) The steps for completing the square to derive the quadratic formula.
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This document provides an overview of equations in one variable, including:
- Defining equations and expressions, and distinguishing between the two
- Identifying linear equations and determining if a number is a solution
- Explaining properties of equality like addition, subtraction, multiplication, and division
- Outlining the steps to solve linear equations in one variable
- Describing types of linear equations like conditional, identity, and contradiction
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The document discusses square roots including:
1. Defining square roots and the radical symbol, and that the square root of a number can be positive or negative.
2. Explaining that the principal square root is always positive and how to identify squares of integers from 1 to 20.
3. Giving examples of simplifying square root expressions and identifying numbers as rational or irrational.
4. Discussing estimating square roots by finding what two consecutive integers a square root lies between.
5. Providing a word problem about finding the length of a wire supporting a tower using a square root formula.
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The document contains notes from a math lesson on linear equations and their graphs. It includes examples of writing linear equations in standard form and slope-intercept form, finding x- and y-intercepts, and making tables of values to graph linear equations. Key terms defined are linear equation, standard form, x-intercept, y-intercept, and various methods for graphing linear equations like finding intercepts and making tables. Sample problems are worked through as examples.
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3. Methods for converting between number systems including decimal to other bases, other bases to decimal, and shortcuts for binary, octal, and hexadecimal conversions.
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The document introduces integers, absolute value, and comparing and ordering integers. It provides definitions for integers, opposites, and absolute value. Examples are given for finding absolute value, comparing integers using <, =, >, and ordering integers from least to greatest. Quick practice problems with answers are included for comparing and ordering integers.
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This document discusses ratios, proportions, rates, and unit rates. It provides examples and explanations of each concept. Ratios compare two quantities and can be expressed as fractions or "to". Proportions are when two ratios are equal. Rates compare quantities with different units, like dollars per kilogram. Unit rates have a denominator of 1. Real-world applications and quizzes are provided to help understand and test knowledge of these mathematical concepts.
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The document provides information about absolute values and the real number system. It includes:
- Definitions of rational numbers, integers, whole numbers, natural numbers, and irrational numbers.
- Examples of absolute value and how it measures the distance from zero, including that operations inside the absolute value signs must be done first before taking the absolute value.
- Class work assignments on opposites and absolute values problems from pages 17-18 including a mixed review.
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This document discusses adding numbers without regrouping. It explains that adding numbers means combining two sets to form a new set. It provides examples of adding two-digit and three-digit numbers step-by-step without regrouping. The steps are to add the ones, tens, and hundreds places separately. Practice problems are included for the reader to try adding numbers without regrouping.
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This document outlines lessons on opposite quantities combining to make zero. It includes:
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- Instructions for a "Do Now" activity involving a Venn diagram
- Explanations and examples of addition of positive and negative numbers, absolute value, and the additive inverse property
- Rules for an integer card game to practice adding and discarding positive and negative numbers
- An example of representing a negative number as a temperature change
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This document discusses vectors and their components, magnitude, direction, and addition. It provides examples of calculating the magnitude and component form of vectors. It also explains how to add vectors using the parallelogram method by drawing a parallelogram and finding the diagonal vector sum, or the component method by finding the horizontal and vertical components and adding them. Vector addition is important in physics for the law of conservation of momentum.
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2) Explains a method for easily multiplying numbers by 250 or other multiples of 10 by multiplying by 1000 and dividing by 4.
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MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below for special IP instructions. This is mandatory.
Remember that the standard form for the quadratic function equation is
y
=
f
(
x
) =
ax
2
+
bx
+
c
and the vertex form is
y
=
f
(
x
) =
a
(
x
–
h
)
2
+
k
, where (
h
,
k
) are the coordinates of the vertex of this quadratic function’s graph.
You will use
P
(
x
) = −0.2
x
2
+
bx
–
c
where (−0.2
x
2
+
bx
) represents the business’ variable profit and
c
is the business’s fixed costs.
So,
P
(
x
) is the store’s total annual profit (in $1,000) based on the number of items sold,
x
.
1. Choose a value between 100 and 200 for
b
. That value does not have to be a whole number.
2. Think about and list what the fixed costs might represent for your fictitious business (be creative). Start by choosing a fixed cost,
c
, between $5,000 and $10,000, according to the first letter of your last name from the values listed in the following chart:
If your last name begins with the letter
Choose a fixed cost between
A–E
$5,000–$5,700
F–I
$5,800–$6,400
J–L
$6,500–$7,100
M–O
$7,200–$7,800
P–R
$7,800–$8,500
S–T
$8,600–$9,200
U–Z
$9,300–$10,000
4.Replace
b
and
c
with your chosen values in Parts 1 and 2 in
P
(
x
) = −0.2
x
2
+
bx
−
c
. This is your quadratic profit model function. State that quadratic profit model functions equation.
5. Next, choose 5 values of
x
(number of items sold) between 500 and 1,000. Think about the general characteristics of quadratic function graphs (parabolas) to help you with choosing these 5 values of
x
.
6. Plug these 5 values into your model for
P
(
x
), and evaluate the annual business profit given those sales volumes. (Be sure to show all of your work for these calculations.)
7. Use the 5 ordered pairs of numbers from 5 and 6 and Excel or another graphing utility to graph your quadratic profit model, and insert the graph into your Word answer document. The graph of the quadratic function is called a
parabola
.
8. What is the vertex of the quadratic function graph? (Show your work details, or explain how you found the vertex.)
9. What is the equation of the line of symmetry? Explain how you found this equation.
10. Write the vertex form for your quadratic profit function.
11. Is there a maximum profit for your business? If so, how many items must be sold to produce the maximum profit, and what is that maximum profit? If your quadratic profit function has a maximum, show your work or explain how the maximum profit figure was obtained.
12. How would knowing the number of items sold that produces the maximum profit help you to run your business more effectively.
13. Analyze the results of these profit cal.
2 simple regression
This document discusses using simple linear regression to describe relationships between variables in data. It explains that regression finds the linear equation that best describes how a dependent variable (y) changes with an independent variable (x). The equation is the line that minimizes the sum of the squared residuals (deviations from the observed data points). Examples are given of regression analyses conducted to estimate the cost of computer networks based on number of computers, estimate real estate values based on house size, and forecast housing starts based on mortgage rates.
Similar to Intro to ss ppt (20)
MATH133 UNIT 2 Quadratic Equations Individual Project Assignm.docx
MATH133 UNIT 2 Quadratic Equations Individual Project Assignm.docx
Intro to ss ppt
- 2. A grid of rows and columns in which you enter text, numbers, and the results of calculations; the main purpose of a spreadsheet is to solve problems that involve numbers A grid is a pattern of regularly spaced horizontal and vertical lines Horizontal Vertical
- 3. Add these numbers: 2 5 3 The answer is 10. That was easy!
- 4. Add the following amounts of money: $25.00 $19.25 $77.77 $94.89 The answer is $216.91. This one is a bit more difficult, but you can still do it easily!
- 5. Solve the following equation: A1 + A2 + A3 – A4 (If A1 = 5, A2 = 9, A3 = 4, and A4 = 5) The answer is 13. This one took more time since you had to “plug” in the values.
- 6. Using the previous equation, let’s make some changes: A1 + A2 + A3 – A4 If A1 = 5, A2 = 9, A3 = 4, and A4 = 5, then the answer is 13. What if I change the value of A2 to 12? The answer is 16. What if I change the operation between A1 and A2? Instead of addition, now it should be multiplication. The answer is 59. Now it is getting more difficult!
- 7. These are a few uses for spreadsheets: Gradebook Budget Inventory
- 11. The main purpose of a spreadsheet is to solve problems that involve numbers. Identify one use for a spreadsheet in each of the following categories: 1. Business 2. Personal 3. School