Q1 MATH 4 WEEK 3 DAY 1-MULTIPLICATION.pptx
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Module 4 quadratic functions
This module discusses quadratic functions and their application to solving word problems. Students will learn to 1) recall steps to solve word problems, 2) translate problems to symbolic expressions, and 3) apply quadratic equations. Examples provided cover number, geometry, and motion problems. Students must first translate word problems into equations before solving. Key steps include identifying unknowns, writing the equation, solving, and checking solutions. Practice problems are provided to help students apply the concepts.
Module 4 Homework Assignment 1Module 4 Homework Assignment 1.docx
Module 4 Homework Assignment 1
Module 4 Homework Assignment 1
MAT 110: Beginning Algebra
Daniel S. Bernardez
Ms. Carrie Dugan
August 16, 2013
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.
1.
Find the greatest common factor. 4, 6, 12.
2.
Factor. 24x3 + 30x2
3.
Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n4
4.
Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y
5.
The GCF of 15y + 20 is 5. The GCF of 15y + 21 is 3. Find the GCF of the product (15y + 20)(15y + 21).
6.
The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x.
7.
Factor the trinomial completely. x2 + 8x – 9
8.
Factor the trinomial completely. 2x2 + 16x + 32
9.
Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__)
10.
State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x – 10)
11.
Factor completely. x2 + 11x + 28
12.
Factor completely. 15x2 + 23x + 4
13.
Factor completely. 6z3 – 27z2 + 12z
14.
The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2 – 19h + 24. Write this polynomial in factored form.
15.
Find a positive value for k for which the polynomial can be factored.
x2 – kx + 29
16.
Factor completely.
9x2 + 4
17.
Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 36
18.
Factor completely. 25x2 + 40xy + 16y2
19.
Factor.
s2(t – u) – 9t2(t – u)
20.
State which method should be applied as the first step for factoring the polynomial. 6x3 + 9x
21.
State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 10
22.
Solve the quadratic equation. 5x2 + 17x = –6
23.
Solve the quadratic equation.
3x(2x – 15) = –84
24.
The sum of an integer and its square is 30. Find the integer.
25.
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?
26.
Write in simplest form.
8
14
9
27
x
x
27.
Write in simplest form.
2
2
– 6+ 8
16
xx
x
-
28.
Write the expression in simplest form.
4 – 8 + 32
4 – 2 + 8
zyzy
yzzy
-
-
29.
The area of the rectangle is represented by 5x2 + 19x + 12. What is the length?
5x + 4
30.
Multiply.
3
8
98
2
x
x
×
31.
Multiply.
2
3127
– 54
xx
xxx
-
×
-
32.
Divide.
26515
2112
xx
--
¸
33.
Divide.
(
)
22
2
2
4
+ 2
6– 12
xy
xxy
xxy
-
¸
34.
Perform the indicated operations.
22
22
– 9368
4 – 244 – 36 + 5 – 6
xxxx
xxxxx
-
××
35.
Find the area of the rectangle shown.
36.
Subtract. Express your ...
Miscellaneous examples of binary , quinary and octonary numbers (2)
This document provides examples for converting between binary, quinary (base 5), octal (base 8) and decimal number systems. It shows how to convert numbers between these number bases by first converting to decimal, then from decimal to the target base. Tricks and tables are also introduced to directly convert between binary and octal without using decimal. Sample conversions include 324(5) to binary, 345(8) to binary, 1011001(2) to quinary, and others between various number bases.
Solving quadratics by completing the square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Additional examples demonstrate applying these steps to solve quadratic equations algebraically.
Solving Quadratics by Completing the Square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Another example problem is worked through to demonstrate the process. Practice problems are provided for the reader to try on their own.
Factoring Trinomials
1. The document discusses various methods for factoring trinomials, including using algebra tiles and looking for pairs of numbers that multiply to the constant term and add to the coefficient of the middle term.
2. It provides examples of factoring different types of trinomials step-by-step, including those with and without leading coefficients.
3. Some trinomials cannot be factored, like those where the pairs of numbers do not add up to the middle coefficient, making the expression prime.
alam moba sino nagsabi? na crush ko siya
This document provides examples and practice problems for multiplying numbers up to three digits by numbers up to two digits without regrouping. It begins with sample word problems and step-by-step worked examples using both the short and long multiplication methods. The remainder of the document consists of exercises for students to complete, including multiplying various 3-digit by 2-digit numbers, word problems involving multiplication, and questions about the costs of items based on given prices.
Box multiplication copy
The document describes the box or grid multiplication method for multiplying multi-digit numbers. It involves expanding the numbers, drawing a grid with the place values, placing the numbers in the grid, multiplying the numbers in each column and adding the results. Two examples are shown of multiplying a 2-digit by 2-digit number and a 3-digit by 2-digit number using this method.
Recommended
Module 4 quadratic functions
This module discusses quadratic functions and their application to solving word problems. Students will learn to 1) recall steps to solve word problems, 2) translate problems to symbolic expressions, and 3) apply quadratic equations. Examples provided cover number, geometry, and motion problems. Students must first translate word problems into equations before solving. Key steps include identifying unknowns, writing the equation, solving, and checking solutions. Practice problems are provided to help students apply the concepts.
Module 4 Homework Assignment 1Module 4 Homework Assignment 1.docx
Module 4 Homework Assignment 1
Module 4 Homework Assignment 1
MAT 110: Beginning Algebra
Daniel S. Bernardez
Ms. Carrie Dugan
August 16, 2013
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.
1.
Find the greatest common factor. 4, 6, 12.
2.
Factor. 24x3 + 30x2
3.
Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n4
4.
Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y
5.
The GCF of 15y + 20 is 5. The GCF of 15y + 21 is 3. Find the GCF of the product (15y + 20)(15y + 21).
6.
The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x.
7.
Factor the trinomial completely. x2 + 8x – 9
8.
Factor the trinomial completely. 2x2 + 16x + 32
9.
Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__)
10.
State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x – 10)
11.
Factor completely. x2 + 11x + 28
12.
Factor completely. 15x2 + 23x + 4
13.
Factor completely. 6z3 – 27z2 + 12z
14.
The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2 – 19h + 24. Write this polynomial in factored form.
15.
Find a positive value for k for which the polynomial can be factored.
x2 – kx + 29
16.
Factor completely.
9x2 + 4
17.
Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 36
18.
Factor completely. 25x2 + 40xy + 16y2
19.
Factor.
s2(t – u) – 9t2(t – u)
20.
State which method should be applied as the first step for factoring the polynomial. 6x3 + 9x
21.
State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 10
22.
Solve the quadratic equation. 5x2 + 17x = –6
23.
Solve the quadratic equation.
3x(2x – 15) = –84
24.
The sum of an integer and its square is 30. Find the integer.
25.
If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?
26.
Write in simplest form.
8
14
9
27
x
x
27.
Write in simplest form.
2
2
– 6+ 8
16
xx
x
-
28.
Write the expression in simplest form.
4 – 8 + 32
4 – 2 + 8
zyzy
yzzy
-
-
29.
The area of the rectangle is represented by 5x2 + 19x + 12. What is the length?
5x + 4
30.
Multiply.
3
8
98
2
x
x
×
31.
Multiply.
2
3127
– 54
xx
xxx
-
×
-
32.
Divide.
26515
2112
xx
--
¸
33.
Divide.
(
)
22
2
2
4
+ 2
6– 12
xy
xxy
xxy
-
¸
34.
Perform the indicated operations.
22
22
– 9368
4 – 244 – 36 + 5 – 6
xxxx
xxxxx
-
××
35.
Find the area of the rectangle shown.
36.
Subtract. Express your ...
Miscellaneous examples of binary , quinary and octonary numbers (2)
This document provides examples for converting between binary, quinary (base 5), octal (base 8) and decimal number systems. It shows how to convert numbers between these number bases by first converting to decimal, then from decimal to the target base. Tricks and tables are also introduced to directly convert between binary and octal without using decimal. Sample conversions include 324(5) to binary, 345(8) to binary, 1011001(2) to quinary, and others between various number bases.
Solving quadratics by completing the square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Additional examples demonstrate applying these steps to solve quadratic equations algebraically.
Solving Quadratics by Completing the Square
The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and how to find the missing constant term to create them. The steps for solving a quadratic equation by completing the square are described: 1) move all terms to the left side, 2) find and add the "completing the square" term, 3) factor into a perfect square trinomial, 4) take the square root of each side, 5) solve the resulting equations. Another example problem is worked through to demonstrate the process. Practice problems are provided for the reader to try on their own.
Factoring Trinomials
1. The document discusses various methods for factoring trinomials, including using algebra tiles and looking for pairs of numbers that multiply to the constant term and add to the coefficient of the middle term.
2. It provides examples of factoring different types of trinomials step-by-step, including those with and without leading coefficients.
3. Some trinomials cannot be factored, like those where the pairs of numbers do not add up to the middle coefficient, making the expression prime.
alam moba sino nagsabi? na crush ko siya
This document provides examples and practice problems for multiplying numbers up to three digits by numbers up to two digits without regrouping. It begins with sample word problems and step-by-step worked examples using both the short and long multiplication methods. The remainder of the document consists of exercises for students to complete, including multiplying various 3-digit by 2-digit numbers, word problems involving multiplication, and questions about the costs of items based on given prices.
Box multiplication copy
The document describes the box or grid multiplication method for multiplying multi-digit numbers. It involves expanding the numbers, drawing a grid with the place values, placing the numbers in the grid, multiplying the numbers in each column and adding the results. Two examples are shown of multiplying a 2-digit by 2-digit number and a 3-digit by 2-digit number using this method.
Bvco u1 a2_jogf
This document contains an activity on complex numbers and functions of a complex variable. The activity includes two problems. The first problem involves calculating the modulus of complex expressions. Various steps are shown to solve the expressions, including using binomial theorem to expand powers of complex numbers. The second problem expresses vectors representing complex numbers in the form a + ib. Steps are outlined to calculate the components from the vector properties like length and angle. Graphical representations of the complex numbers are also provided.
Math Short Tricks ( english)
The document discusses methods for finding squares, cubes, remainders, and day of the week for a given date using shortcuts and patterns. It provides examples of finding the square of numbers ending in 1-9 and multiplying multi-digit numbers where the tens digit is the same. It also includes a table to add to the month number to determine the day of the week and shows how to find the remainder when dividing a large multiplication expression by 7 by multiplying the remainders individually.
Vedic maths 2
The document provides several methods from Vedic mathematics for operations like squaring, multiplying, dividing, finding squares and square roots of numbers. Some key techniques discussed are:
1) A quick way to square numbers ending in 5 by splitting the answer into two parts and using the formula of multiplying the first number by one more than itself.
2) A method for multiplying where the first and last digits add to 10 by multiplying the first digit by the next number and combining with the product of the last digits.
3) Finding squares of numbers between 50-60 by adding the last digit to 25 and squaring the last digit.
4) Various sutras and techniques like vertically and crosswise,
Chapter1.9
The document provides examples of translating word problems into two-step equations and solving them. It includes examples such as "17 less than the quotient of a number x and 2 is 21" translated to (x/2) - 17 = 21 and solved. Consumer math word problems are also presented, like one about a person buying a DVD player and DVDs with a total cost. The document concludes with a lesson quiz with similar translation and solving exercises.
3a. multiplication, division
This document provides instructions for multiplication and division without a calculator. It begins by emphasizing the importance of knowing multiplication tables. It then demonstrates several methods for multiplication, including the traditional method, grid method, and lattice method. It also shows how to use bus stop division to divide numbers without a calculator. Examples are provided for each method.
Chithra
This document provides an overview of different methods for solving quadratic equations: factorisation, completing the square, and the quadratic formula. It includes examples of solving quadratic equations using each method. Factorisation involves finding two binomial factors whose product is the quadratic expression. Completing the square transforms the equation into a perfect square plus an extra term, allowing it to be factorised. The quadratic formula provides the general solution for any quadratic equation in the form ax^2 + bx + c = 0.
Vedic Mathematics 16 sutras with example problems
1. Ramanujan was an extraordinary Indian mathematician who made significant contributions to mathematics despite facing challenges as he was largely self-taught.
2. The document then provides an overview of Ramanujan's achievements and contributions to areas like infinite series, number theory, and modular forms.
3. It also gives a brief introduction to Vedic mathematics, which originated in ancient India, discussing key concepts like the 16 sutras (mathematical formulas) and how its principles can be applied to different areas of mathematics.
Ejercicios algebra.
Ejercicios de algebra con pasos y una breve descripción del tema
como sumas y restas de polinomios, división sintética, entre otras.
Descripción de cada uno de los ejercicios propuestos.
Polynomial math
1) The document discusses various methods for manipulating and solving algebraic expressions, including adding, subtracting, and factoring polynomials.
2) Factoring techniques include grouping like terms, using the difference of squares formula, and recognizing perfect square trinomials.
3) The quadratic formula is introduced as a way to solve quadratic equations of the form ax2 + bx + c = 0.
Quadratic functions and their application
Quadratic functions have several real-life applications and can be used to model mathematical problems. To solve problems involving quadratic functions, identify given information, represent the problem as a function, and consider the maximum or minimum property to solve for the final answer. Examples provided demonstrate solving for unknown variables in quadratic equations derived from word problems about rectangles, consecutive numbers, and the dimensions of a tennis table.
factorization
This document discusses various methods for factoring polynomials, including:
1) Factoring trinomials by finding two numbers that multiply to the constant term and add to the middle coefficient.
2) The "box method" for factoring trinomials where the leading coefficient is not 1, which involves arranging terms in a 2x2 grid.
3) Factoring the difference of two squares using the formula (a + b)(a - b).
Number Sense Book
1. Number sense involves memorizing rules and practicing them quickly under time limits. The first steps are memorizing perfect squares and cubes.
2. The document provides explanations and rules for multiplying different combinations of single-digit, double-digit, and fraction numbers.
3. It also covers rules for operations involving bases, percentages, reciprocals, decimals, and conversions between units.
Quadratic functions and their application
Quadratic functions have several real-life applications and can be used to model mathematical problems. To solve problems involving quadratic functions, identify given information, represent the problem as a function, and consider the maximum or minimum property to solve for the final answer. Examples provided demonstrate solving for unknown variables in quadratic equations derived from word problems about rectangles, consecutive numbers, and dimensions of a tennis table.
3 lesson 3 problems involving maximum and minimum points
1) This document discusses problems involving finding the maximum or minimum values of quadratic functions by determining their vertices. It also contains 5 word problems about finding maximum or minimum values given certain constraints.
2) The problems ask about finding the dimensions of the largest rectangular pen that can be made with 64m of fence, the minimum product of two numbers that differ by 5, the maximum product of two numbers that add to 26, the minimum product of two numbers that differ by 9, and the dimensions that yield the maximum area of a rectangular stained-glass window with a perimeter of 220cm.
3) The document provides quadratic functions and constraints for several problems about finding maximum/minimum values and the dimensions or numbers that produce them.
5. multiplying 2 to 4 digit numbers by 1-to 2-digit
1) The document provides instructions and examples for multiplying 2-4 digit numbers by 1-2 digit numbers without regrouping. It includes step-by-step worked examples and exercises.
2) Students are asked to solve word problems that require multiplying numbers with 2-4 digits by 1-2 digits to find totals, lengths, or amounts spent.
3) The assignment asks students to solve 5 word problems that require multiplying given amounts, lengths, or prices to determine totals, lengths, or amounts spent.
sim-140907230908-phpapp01.pptx
This document provides an overview of solving quadratic equations by factoring. It discusses identifying quadratic equations, rewriting them in standard form, factoring trinomials in the form x^2 + bx + c, and determining roots. Several examples of factoring trinomials and solving quadratic equations are shown. Activities include identifying quadratic equations, rewriting equations in standard form, factoring trinomials, and solving equations by factoring. The document provides resources for further learning about quadratic equations and factoring.
Guide to binomial and trnomial
The document provides steps for multiplying a binomial and a trinomial:
1) Write the terms of each expression in a table and multiply corresponding terms.
2) Write the products in order from highest to lowest exponent.
3) Combine like terms by adding coefficients with the same exponents from lowest to highest.
Solving digit problems
The document provides examples of solving digit problems by assigning variables to represent unknown digits, forming equations based on the information provided, and solving the equations to find the original numbers. It also provides exercises for the user to practice solving additional digit problems.
Week 9-Quadratic Function.pptx
1. The document provides examples of determining the equation of a quadratic function from tables of values, graphs, and zeros.
2. It gives step-by-step solutions for finding the quadratic equation from various representations, such as using the table of values to find the coefficients a, b, and c in the standard form y = ax^2 + bx + c.
3. The objectives are for students to be able to derive the quadratic equation from different representations and participate actively in virtual class discussions.
Tema 1 Repaso productos notables
1. The document provides a review of notable algebraic products, including definitions, rules, and examples of:
- The square of the sum of two quantities
- The square of the difference of two quantities
- The product of the sum and difference of two quantities
- The cube of the sum of a binomial
- The cube of the difference of a binomial
- The product of two binomials with a common term
2. Students are provided with practice problems applying these notable product rules and asked to identify which rule each problem falls under.
3. Links are provided for an online quiz and practice test for students to evaluate their understanding of the material.
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
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Bvco u1 a2_jogf
This document contains an activity on complex numbers and functions of a complex variable. The activity includes two problems. The first problem involves calculating the modulus of complex expressions. Various steps are shown to solve the expressions, including using binomial theorem to expand powers of complex numbers. The second problem expresses vectors representing complex numbers in the form a + ib. Steps are outlined to calculate the components from the vector properties like length and angle. Graphical representations of the complex numbers are also provided.
Math Short Tricks ( english)
The document discusses methods for finding squares, cubes, remainders, and day of the week for a given date using shortcuts and patterns. It provides examples of finding the square of numbers ending in 1-9 and multiplying multi-digit numbers where the tens digit is the same. It also includes a table to add to the month number to determine the day of the week and shows how to find the remainder when dividing a large multiplication expression by 7 by multiplying the remainders individually.
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The document provides several methods from Vedic mathematics for operations like squaring, multiplying, dividing, finding squares and square roots of numbers. Some key techniques discussed are:
1) A quick way to square numbers ending in 5 by splitting the answer into two parts and using the formula of multiplying the first number by one more than itself.
2) A method for multiplying where the first and last digits add to 10 by multiplying the first digit by the next number and combining with the product of the last digits.
3) Finding squares of numbers between 50-60 by adding the last digit to 25 and squaring the last digit.
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The document provides examples of translating word problems into two-step equations and solving them. It includes examples such as "17 less than the quotient of a number x and 2 is 21" translated to (x/2) - 17 = 21 and solved. Consumer math word problems are also presented, like one about a person buying a DVD player and DVDs with a total cost. The document concludes with a lesson quiz with similar translation and solving exercises.
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This document provides instructions for multiplication and division without a calculator. It begins by emphasizing the importance of knowing multiplication tables. It then demonstrates several methods for multiplication, including the traditional method, grid method, and lattice method. It also shows how to use bus stop division to divide numbers without a calculator. Examples are provided for each method.
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This document provides an overview of different methods for solving quadratic equations: factorisation, completing the square, and the quadratic formula. It includes examples of solving quadratic equations using each method. Factorisation involves finding two binomial factors whose product is the quadratic expression. Completing the square transforms the equation into a perfect square plus an extra term, allowing it to be factorised. The quadratic formula provides the general solution for any quadratic equation in the form ax^2 + bx + c = 0.
Vedic Mathematics 16 sutras with example problems
1. Ramanujan was an extraordinary Indian mathematician who made significant contributions to mathematics despite facing challenges as he was largely self-taught.
2. The document then provides an overview of Ramanujan's achievements and contributions to areas like infinite series, number theory, and modular forms.
3. It also gives a brief introduction to Vedic mathematics, which originated in ancient India, discussing key concepts like the 16 sutras (mathematical formulas) and how its principles can be applied to different areas of mathematics.
Ejercicios algebra.
Ejercicios de algebra con pasos y una breve descripción del tema
como sumas y restas de polinomios, división sintética, entre otras.
Descripción de cada uno de los ejercicios propuestos.
Polynomial math
1) The document discusses various methods for manipulating and solving algebraic expressions, including adding, subtracting, and factoring polynomials.
2) Factoring techniques include grouping like terms, using the difference of squares formula, and recognizing perfect square trinomials.
3) The quadratic formula is introduced as a way to solve quadratic equations of the form ax2 + bx + c = 0.
Quadratic functions and their application
Quadratic functions have several real-life applications and can be used to model mathematical problems. To solve problems involving quadratic functions, identify given information, represent the problem as a function, and consider the maximum or minimum property to solve for the final answer. Examples provided demonstrate solving for unknown variables in quadratic equations derived from word problems about rectangles, consecutive numbers, and the dimensions of a tennis table.
factorization
This document discusses various methods for factoring polynomials, including:
1) Factoring trinomials by finding two numbers that multiply to the constant term and add to the middle coefficient.
2) The "box method" for factoring trinomials where the leading coefficient is not 1, which involves arranging terms in a 2x2 grid.
3) Factoring the difference of two squares using the formula (a + b)(a - b).
Number Sense Book
1. Number sense involves memorizing rules and practicing them quickly under time limits. The first steps are memorizing perfect squares and cubes.
2. The document provides explanations and rules for multiplying different combinations of single-digit, double-digit, and fraction numbers.
3. It also covers rules for operations involving bases, percentages, reciprocals, decimals, and conversions between units.
Quadratic functions and their application
Quadratic functions have several real-life applications and can be used to model mathematical problems. To solve problems involving quadratic functions, identify given information, represent the problem as a function, and consider the maximum or minimum property to solve for the final answer. Examples provided demonstrate solving for unknown variables in quadratic equations derived from word problems about rectangles, consecutive numbers, and dimensions of a tennis table.
3 lesson 3 problems involving maximum and minimum points
1) This document discusses problems involving finding the maximum or minimum values of quadratic functions by determining their vertices. It also contains 5 word problems about finding maximum or minimum values given certain constraints.
2) The problems ask about finding the dimensions of the largest rectangular pen that can be made with 64m of fence, the minimum product of two numbers that differ by 5, the maximum product of two numbers that add to 26, the minimum product of two numbers that differ by 9, and the dimensions that yield the maximum area of a rectangular stained-glass window with a perimeter of 220cm.
3) The document provides quadratic functions and constraints for several problems about finding maximum/minimum values and the dimensions or numbers that produce them.
5. multiplying 2 to 4 digit numbers by 1-to 2-digit
1) The document provides instructions and examples for multiplying 2-4 digit numbers by 1-2 digit numbers without regrouping. It includes step-by-step worked examples and exercises.
2) Students are asked to solve word problems that require multiplying numbers with 2-4 digits by 1-2 digits to find totals, lengths, or amounts spent.
3) The assignment asks students to solve 5 word problems that require multiplying given amounts, lengths, or prices to determine totals, lengths, or amounts spent.
sim-140907230908-phpapp01.pptx
This document provides an overview of solving quadratic equations by factoring. It discusses identifying quadratic equations, rewriting them in standard form, factoring trinomials in the form x^2 + bx + c, and determining roots. Several examples of factoring trinomials and solving quadratic equations are shown. Activities include identifying quadratic equations, rewriting equations in standard form, factoring trinomials, and solving equations by factoring. The document provides resources for further learning about quadratic equations and factoring.
Guide to binomial and trnomial
The document provides steps for multiplying a binomial and a trinomial:
1) Write the terms of each expression in a table and multiply corresponding terms.
2) Write the products in order from highest to lowest exponent.
3) Combine like terms by adding coefficients with the same exponents from lowest to highest.
Solving digit problems
The document provides examples of solving digit problems by assigning variables to represent unknown digits, forming equations based on the information provided, and solving the equations to find the original numbers. It also provides exercises for the user to practice solving additional digit problems.
Week 9-Quadratic Function.pptx
1. The document provides examples of determining the equation of a quadratic function from tables of values, graphs, and zeros.
2. It gives step-by-step solutions for finding the quadratic equation from various representations, such as using the table of values to find the coefficients a, b, and c in the standard form y = ax^2 + bx + c.
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2. Students are provided with practice problems applying these notable product rules and asked to identify which rule each problem falls under.
3. Links are provided for an online quiz and practice test for students to evaluate their understanding of the material.
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Q1 MATH 4 WEEK 3 DAY 1-MULTIPLICATION.pptx
- 1. Multiplication W E E K 3 D A Y 1 Multiplies numbers up to three digits by numbers up to two digits without regrouping.
- 2. SAMPLE PROBLEM Rosalina Mantuano, dressmaker for 45 years, began sewing dozens of colorful masks using scrap fabric and gave it away for free to her neighbors. All in all, she gave 12 boxes with 214 pcs of face masks in each box. How many pieces of face masks did she share with her neighbors?
- 3. 214 214 214 214 214 214 214 214 214 214 214 214 12 boxes and each boxes has 214 face masks 214 x 12 = N
- 4. LONG METHOD STEP 1: Write the multiplicand and multiplier in expanded form. 214 = 200 + 10 + 4 12 = 10 + 2
- 5. LONG METHOD STEP 2: Multiply the digit in the ones place by the multiplicand, Then multiply the digit in tens place in the multiplicand 214 = (200 + 10 + 4) 10 214 = (200 + 10 + 4) 2 12 = 10 + 2
- 6. LONG METHOD STEP 2: 214 = (200 + 10 + 4) 10 214 = (200 + 10 + 4) 2 = (200x10) + (10x10) + (4x10) = (200x2) + (10x2) + (4x2)
- 7. LONG METHOD STEP 2: = (200x10) + (10x10) + (4x10) = (200x2) + (10x2) + (4x2)
- 8. LONG METHOD STEP 3: Add all the products. = (200x10) + (10x10) + (4x10) = (200x2) + (10x2) + (4x2) = 2000 + 100 + 40 = 400 + 20 +8
- 9. LONG METHOD STEP 3: Add all the products. = 2000 + 100 + 40 = 400 + 20 +8 = 2140 = 428
- 10. LONG METHOD STEP 3: Add all the products. 2 140 + 428 2 568 204 x 12 2 568
- 11. SHORT METHOD Th O T H 2 1 4 2 1 X 8 2 4 4 1 2 8 6 5 2 +
- 12. LONG METHOD 302 x 23 = N
- 13. LONG METHOD STEP 1: Write the multiplicand and multiplier in expanded form. 302 = 300 + 2 23 = 20 + 3
- 14. LONG METHOD STEP 2: Multiply the digit in the ones place by the multiplicand, Then multiply the digit in tens place in the multiplicand 302 = (300+2) 20 302 = (300+2) 3 23 = 20 + 3
- 15. LONG METHOD STEP 2: 302 = (300 + 2) 20 302 = (300 + 2) 3 = (300x20) + (2x20) = (300x3) + (2x3)
- 16. LONG METHOD STEP 2: = (300x20) + (2x20) = (300x3) + (2x3)
- 17. LONG METHOD STEP 3: Add all the products. = (300x20) + (2x20) = (300x3) + (2x3) = 6000 + 40 = 900 +6
- 18. LONG METHOD STEP 3: Add all the products. = 6000 + 40 = 900 +6 = 6 040 = 906
- 19. LONG METHOD STEP 3: Add all the products. 6 040 + 906 6 946 302 X 23 6 646
- 20. SHORT METHOD Th O T H 3 0 2 3 2 X 6 0 9 4 0 6 6 4 9 6 +