The document contains notes from January 17, 2012 about solving various math word problems:
1) A word problem about a son's age that can be solved two different ways.
2) A word problem about two unknown numbers with relationships between their sums, parts and wholes.
3) A word problem about students cleaning a garbage-filled lot, working for different periods of time in different group sizes.
The document contains calculations to determine the height of geometric shapes given other measurements. For a prism with a volume of 60 cm3, width of 3 cm, and length of 4 cm, the height is calculated as 5 cm. For a cylinder with an area of 175.84 cm2 and radius of 4 cm, the height is calculated as 8 cm.
This document contains an answer key for a math worksheet on quadratic functions. It includes:
1) Graphing quadratic equations and finding vertices, zeros, and y-intercepts.
2) Solving quadratic equations by factoring.
3) Identifying true statements about the discriminant and solutions of quadratic equations.
4) Solving quadratic equations using the quadratic formula.
5) Writing the equation for a situation where a hockey player's salary is a quadratic function of his goals.
6) Analyzing the graph of a quadratic equation.
7) Writing the equation for a situation where the sum and product of two numbers is given.
8) Setting up and
This document is an untitled notebook from December 15, 2011 that contains time stamps ranging from 10:51 AM to 11:48 AM, with various intervals of time between each entry. There are a total of 3 pages documented.
1. This document contains 11 multi-part math problems involving systems of equations and inequalities. The problems cover topics such as solving systems graphically, algebraically, and determining if ordered pairs are solutions. They also involve word problems about ages, expenses, and splitting amounts into parts.
2. Key steps addressed include setting up tables of values, identifying line types, finding the solution set intersection, using substitution or elimination methods, stating yes or no for ordered pairs, and drawing graphs of solution sets for systems of inequalities.
3. The problems progress from simpler systems to more complex ones involving multiple equations or inequalities, requiring skills like algebraic manipulation, graphical analysis, and translating word problems into mathematical systems.
1. The solution to the system of equations y=2x and x/5 is (0,0).
2. The solutions to the systems of equations x+y=5 and 3x+2y-14=0 are (3,2) and the solutions to x=3 and y=6.5 are (3,6.5).
3. The system of equations representing spending $164 on books costing $15 each or $17 each can be expressed as a system of first degree equations in two variables.
1) The document discusses solving systems of equations and inequalities. It contains 13 problems involving setting up, graphing and solving systems of linear and nonlinear equations and inequalities.
2) The problems cover a range of techniques for solving systems, including substitution, elimination, graphing, and applying constraints to identify variable values that satisfy simultaneous relationships.
3) The document provides practice with setting up and solving different types of systems, as well as interpreting solutions in the context of word problems about rates, prices, ages and coin values.
The document contains 14 problems involving systems of equations and inequalities. Problem 1 asks for the solution of a system of equations as an ordered pair. Problem 2 asks to determine the solution set of another system of equations. Problem 3 asks to express a word problem as a system of two equations.
This document contains 11 problems involving quadratic functions and equations. The problems cover graphing quadratic functions, solving quadratic equations by factoring and using the quadratic formula, identifying properties of quadratic functions, modeling real-world word problems with quadratic equations, and applying the Pythagorean theorem and properties of parabolas.
1. The document contains the answer key to a math test on quadratic functions.
2. It includes graphing quadratic equations, solving by factoring, identifying properties, using the quadratic formula, modeling real world situations, and applying the Pythagorean theorem and properties of parabolas.
3. Several questions involve finding the vertex, x-intercepts, maximum/minimum values, and distance or drop measures for quadratic equations describing real world motions or sales situations.
This document provides 10 problems involving quadratic functions and equations: (1) graphing quadratic equations; (2) solving quadratic equations by factoring; (3) identifying true statements about quadratic equations; (4) solving quadratic equations using the quadratic formula; (5) writing an equation to model profit from bracelet sales; (6) writing an equation for the sum of squares of two consecutive even numbers; (7) analyzing a graph of a quadratic function; (8) solving for measurements of a rhombus given information about its diagonals and area; (9) solving for the number of students in a classroom given information about class time and changes in time per student; (10) solving application problems involving the height
This document contains:
1) A key for a quadratic functions test with graphing and solving problems.
2) The test asks students to graph and solve quadratic equations, identify true statements about discriminants and solutions, and solve word problems involving quadratic models.
3) The key provides the full worked out solutions and answers to all problems on the test.
This document contains 10 problems related to quadratic functions and equations. The problems cover topics such as: 1) graphing quadratic functions, 2) solving quadratic equations by factoring and using the quadratic formula, 3) identifying properties of quadratic functions from their graphs or equations, and 4) modeling real-world situations using quadratic equations. The goal is to demonstrate understanding of key concepts for quadratic functions and practice applying various techniques for solving quadratic equations.
This document contains 10 word problems involving quadratic functions. Each problem provides relationships between two or more numbers and asks the reader to determine the specific values of those numbers based on the given information. The problems cover a variety of quadratic equation scenarios including differences, sums, products, and consecutive numbers.
The document provides 10 examples of word problems involving quadratic equations. For each problem it defines the variables, sets up the quadratic equation, solves for the zeros, and states the answer.
This document contains 11 problems involving quadratic functions and equations. The problems cover graphing quadratic functions, solving quadratic equations by factoring and using the quadratic formula, identifying properties of quadratic functions, modeling real-world word problems with quadratic equations, and applying the Pythagorean theorem and properties of parabolas.
The document contains an answer key for a mathematics assignment on quadratic functions. It includes:
1) Graphing quadratic equations and identifying vertex, zeros, and y-intercept.
2) Solving quadratic equations by factoring.
3) Identifying true statements about quadratic functions.
4) Solving quadratic equations using the quadratic formula.
5) Setting up and solving an optimization word problem involving quadratic sales based on number of items sold.
6) Answering true/false questions based on a graph of a quadratic function.
7) Writing the quadratic equation for an age relationship problem.
8) Setting up the Pythagorean theorem to solve for side lengths of
This document provides 10 problems involving quadratic functions and equations: (1) graphing quadratic equations; (2) solving quadratic equations by factoring; (3) identifying true statements about quadratic equations; (4) solving quadratic equations using the quadratic formula; (5) writing an equation to model profit from bracelet sales; (6) writing an equation for the sum of squares of two consecutive even numbers; (7) analyzing a graph of a quadratic function; (8) finding measurements of diagonals of a rhombus using its area; (9) determining the number of students in a classroom using time per student; (10) analyzing the height of a hot air balloon over time.
This document contains 10 problems related to quadratic functions and equations. The problems cover topics such as: 1) graphing quadratic functions, 2) solving quadratic equations by factoring and using the quadratic formula, 3) identifying properties of quadratic functions from their graphs or equations, and 4) modeling real-world situations using quadratic equations. The goal is to demonstrate understanding of key concepts for quadratic functions and practice applying various techniques for solving quadratic equations.
This document contains the answer key for a math test on quadratic functions. It includes:
1) Graphing quadratic equations and finding vertices, zeros, and y-intercepts.
2) Solving quadratic equations by factoring.
3) Using the quadratic formula to solve equations.
4) Questions about salaries as a function of goals scored, the areas of trapezoids, and the maximum height of a tennis ball thrown in the air.
This document contains an answer key for a quiz on quadratic functions. It includes:
1) Graphing quadratic equations and identifying vertex, zeros, axis of symmetry, and y-intercept.
2) Solving quadratic equations by factoring.
3) Identifying true statements about the discriminant and solutions of a quadratic equation.
4) Solving quadratic equations using the quadratic formula and identifying the discriminant and solutions.
5) Writing the equation for a situation involving profit from selling bracelets with discounts.
6) Writing the equation for a situation involving the sum of squares of consecutive even numbers.
7) Analyzing the graph of a quadratic equation to identify the vertex,
1. This document contains 11 multi-part math problems involving systems of equations and inequalities. The problems cover topics such as solving systems graphically, algebraically, and determining if ordered pairs are solutions. They also involve word problems about ages, expenses, and splitting amounts into parts.
2. Key steps addressed include setting up tables of values, identifying line types, finding the solution set intersection, using substitution or elimination methods, stating yes or no for ordered pairs, and drawing graphs of solution sets for systems of inequalities.
3. The problems progress from simpler systems to more complex ones involving multiple equations or inequalities, requiring skills like algebraic manipulation, graphical analysis, and translating word problems into mathematical systems.
1. The solution to the system of equations y=2x and x/5 is (0,0).
2. The solutions to the systems of equations x+y=5 and 3x+2y-14=0 are (3,2) and the solutions to x=3 and y=6.5 are (3,6.5).
3. The system of equations representing spending $164 on books costing $15 each or $17 each can be expressed as a system of first degree equations in two variables.
1) The document discusses solving systems of equations and inequalities. It contains 13 problems involving setting up, graphing and solving systems of linear and nonlinear equations and inequalities.
2) The problems cover a range of techniques for solving systems, including substitution, elimination, graphing, and applying constraints to identify variable values that satisfy simultaneous relationships.
3) The document provides practice with setting up and solving different types of systems, as well as interpreting solutions in the context of word problems about rates, prices, ages and coin values.
The document contains 14 problems involving systems of equations and inequalities. Problem 1 asks for the solution of a system of equations as an ordered pair. Problem 2 asks to determine the solution set of another system of equations. Problem 3 asks to express a word problem as a system of two equations.
This document contains 11 problems involving quadratic functions and equations. The problems cover graphing quadratic functions, solving quadratic equations by factoring and using the quadratic formula, identifying properties of quadratic functions, modeling real-world word problems with quadratic equations, and applying the Pythagorean theorem and properties of parabolas.
1. The document contains the answer key to a math test on quadratic functions.
2. It includes graphing quadratic equations, solving by factoring, identifying properties, using the quadratic formula, modeling real world situations, and applying the Pythagorean theorem and properties of parabolas.
3. Several questions involve finding the vertex, x-intercepts, maximum/minimum values, and distance or drop measures for quadratic equations describing real world motions or sales situations.
This document provides 10 problems involving quadratic functions and equations: (1) graphing quadratic equations; (2) solving quadratic equations by factoring; (3) identifying true statements about quadratic equations; (4) solving quadratic equations using the quadratic formula; (5) writing an equation to model profit from bracelet sales; (6) writing an equation for the sum of squares of two consecutive even numbers; (7) analyzing a graph of a quadratic function; (8) solving for measurements of a rhombus given information about its diagonals and area; (9) solving for the number of students in a classroom given information about class time and changes in time per student; (10) solving application problems involving the height
This document contains:
1) A key for a quadratic functions test with graphing and solving problems.
2) The test asks students to graph and solve quadratic equations, identify true statements about discriminants and solutions, and solve word problems involving quadratic models.
3) The key provides the full worked out solutions and answers to all problems on the test.
This document contains 10 problems related to quadratic functions and equations. The problems cover topics such as: 1) graphing quadratic functions, 2) solving quadratic equations by factoring and using the quadratic formula, 3) identifying properties of quadratic functions from their graphs or equations, and 4) modeling real-world situations using quadratic equations. The goal is to demonstrate understanding of key concepts for quadratic functions and practice applying various techniques for solving quadratic equations.
This document contains 10 word problems involving quadratic functions. Each problem provides relationships between two or more numbers and asks the reader to determine the specific values of those numbers based on the given information. The problems cover a variety of quadratic equation scenarios including differences, sums, products, and consecutive numbers.
The document provides 10 examples of word problems involving quadratic equations. For each problem it defines the variables, sets up the quadratic equation, solves for the zeros, and states the answer.
This document contains 11 problems involving quadratic functions and equations. The problems cover graphing quadratic functions, solving quadratic equations by factoring and using the quadratic formula, identifying properties of quadratic functions, modeling real-world word problems with quadratic equations, and applying the Pythagorean theorem and properties of parabolas.
The document contains an answer key for a mathematics assignment on quadratic functions. It includes:
1) Graphing quadratic equations and identifying vertex, zeros, and y-intercept.
2) Solving quadratic equations by factoring.
3) Identifying true statements about quadratic functions.
4) Solving quadratic equations using the quadratic formula.
5) Setting up and solving an optimization word problem involving quadratic sales based on number of items sold.
6) Answering true/false questions based on a graph of a quadratic function.
7) Writing the quadratic equation for an age relationship problem.
8) Setting up the Pythagorean theorem to solve for side lengths of
This document provides 10 problems involving quadratic functions and equations: (1) graphing quadratic equations; (2) solving quadratic equations by factoring; (3) identifying true statements about quadratic equations; (4) solving quadratic equations using the quadratic formula; (5) writing an equation to model profit from bracelet sales; (6) writing an equation for the sum of squares of two consecutive even numbers; (7) analyzing a graph of a quadratic function; (8) finding measurements of diagonals of a rhombus using its area; (9) determining the number of students in a classroom using time per student; (10) analyzing the height of a hot air balloon over time.
This document contains 10 problems related to quadratic functions and equations. The problems cover topics such as: 1) graphing quadratic functions, 2) solving quadratic equations by factoring and using the quadratic formula, 3) identifying properties of quadratic functions from their graphs or equations, and 4) modeling real-world situations using quadratic equations. The goal is to demonstrate understanding of key concepts for quadratic functions and practice applying various techniques for solving quadratic equations.
This document contains the answer key for a math test on quadratic functions. It includes:
1) Graphing quadratic equations and finding vertices, zeros, and y-intercepts.
2) Solving quadratic equations by factoring.
3) Using the quadratic formula to solve equations.
4) Questions about salaries as a function of goals scored, the areas of trapezoids, and the maximum height of a tennis ball thrown in the air.
This document contains an answer key for a quiz on quadratic functions. It includes:
1) Graphing quadratic equations and identifying vertex, zeros, axis of symmetry, and y-intercept.
2) Solving quadratic equations by factoring.
3) Identifying true statements about the discriminant and solutions of a quadratic equation.
4) Solving quadratic equations using the quadratic formula and identifying the discriminant and solutions.
5) Writing the equation for a situation involving profit from selling bracelets with discounts.
6) Writing the equation for a situation involving the sum of squares of consecutive even numbers.
7) Analyzing the graph of a quadratic equation to identify the vertex,