September 10 2014
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This document provides information and examples about algebra rules and concepts including: - Assigning variables to unknown quantities, such as assigning 'm' to the person who weighs the least. - Identifying like terms in algebraic expressions as terms that contain the same variables raised to the same power, even if the coefficients are different. - Providing formulas for perimeter and area of squares and triangles. - Examples of translating word problems into algebraic expressions and equations, and simplifying expressions by combining like terms. - A review of topics to be covered on Test #1, including simplifying expressions, solving simple one- and two-step equations, and translating sentences into algebraic representations.
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1.
List all the factors of 88.
2.
List all the prime numbers between 25 and 60.
3.
Find the GCF for 16 and 17.
4.
Find the LCM for 13 and 39.
5.
Write the fraction in simplest form.
6.
Multiply. Be sure to simplify the product.
7.
Divide.
Write the result in simplest form.
8.
Add.
9.
Perform the indicated operation.
Write the result in simplest form.
–
10.
Perform the indicated operation. Write the result in simplest form.
÷
11.
Find the decimal equivalent of
rounded to the hundredths place.
12.
Write 0.12 as a fraction and simplify.
13.
Perform the indicated operation.
8.50 – 1.72
14.
Divide.
15.
Write 255% as a decimal.
16.
Write 0.037 as a percent.
17.
Evaluate.
56 ÷ 7 – 28 ÷ 7
18.
Evaluate.
9
·
4
2
19.
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20.
Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
21.
Identify the property that is illustrated by the following statement.
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22.
Identify the property that is illustrated by the following statement.
(6 · 13)
·
10 = 6 · (13 · 10)
23.
Identify the property that is illustrated by the following statement.
10
·
(3 + 11) = 10
·
3 + 10
·
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24.
Use the distributive property to remove the parentheses in the following expression.
Then simplify your result where possible.
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25.
Add.
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Write the following phrase using symbols: 2 times the sum of
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Write the following phrase using symbols.
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times the Area of the base (
A
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h
)
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Evaluate
if
x
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y
=
, and
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=
.
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If the current temperature is 59°F, what is the Celsius temperature?
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If the circumference of a circle whose radius is
r
is given by
C
= 2
πr
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π
≈ 3.14, find the circumference when
r
= 15 meters (m).
40.
Combine like terms: 9
v
+ 6
w
+ 4
v
41.
A rectangle has sides of 3
x
– 4 and 7
x
+ 10.
Provide a simplified expression for its perimeter.
42.
Subtract 4
ab
3
from the sum of 10
ab
3
and 2
ab
3
.
43.
Use the distributive property to remove the parentheses, then simplify by combining like terms: 7(4
s
– 5) + 9
44.
Multiply: 8
u
6
·
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List all the factors of 88.
2.
List all the prime numbers between 25 and 60.
3.
Find the GCF for 16 and 17.
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Find the LCM for 13 and 39.
5.
Write the fraction in simplest form.
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Multiply. Be sure to simplify the product.
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Divide.
Write the result in simplest form.
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Perform the indicated operation. Write the result in simplest form.
÷
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Write 255% as a decimal.
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Write 0.037 as a percent.
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18.
Evaluate.
9
·
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Write the following phrase using symbols: 2 times the sum of
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Write the following phrase using symbols.
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Write the following geometric expression using the given symbols.
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A
) times the height(
h
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37.
Evaluate
if
x
= 12,
y
=
, and
z
=
.
38.
A formula that relates Fahrenheit and Celsius temperature is
.
If the current temperature is 59°F, what is the Celsius temperature?
39.
If the circumference of a circle whose radius is
r
is given by
C
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πr
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π
≈ 3.14, find the circumference when
r
= 15 meters (m).
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Combine like terms: 9
v
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w
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v
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A rectangle has sides of 3
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x
+ 10.
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42.
Subtract 4
ab
3
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ab
3
and 2
ab
3
.
43.
Use the distributive property to remove the parentheses, then simplify by combining like terms: 7(4
s
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Multiply: 8
u
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Jovie earns 125 pesos per hour for tutoring. She earns 250 pesos for 2 hours and 375 pesos for 3 hours. Her earnings vary directly with the number of hours tutored, according to the equation E=125t, where E is earnings in pesos and t is time in hours.
Equations problems
This document provides examples for solving word problems by translating English phrases into mathematical expressions. It discusses key phrases like "more than", "less than", and "times" and how they relate to addition, subtraction, and multiplication. Several geometry and consecutive number word problems are worked out step-by-step. The document emphasizes setting up variables clearly before solving and checking that the answer makes sense in the original context.
Mathprize2016solutions
The document contains solutions to 11 math problems from a math competition. The solutions provide explanations and work shown to arrive at the answers. The greatest possible sum of distances from a point P to the three sides of a triangle is 4. The probability that a sequence of random button picks will have at least 3 picks and the third pick be the M button is 1/12. The least possible value of ABCD - AB x CD, where ABCD is a 4-digit positive integer and AB and CD are 2-digit positive integers, is 109.
Logarithm
1. The document defines logarithmic functions and their relationship to exponential functions. Logarithmic functions are the inverse of exponential functions with the same base.
2. Methods for determining the logarithm of a number are presented, including using a logarithm table to find the logarithm of numbers that are not perfect powers of their base.
3. The laws of logarithms are proved using properties of exponents, including laws such as log(ab) = log(a) + log(b) and log(a/b) = log(a) - log(b). Examples of applying the laws of logarithms to equations are provided.
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1.2 simplifying expressions and order of operations
1.2 simplifying expressions and order of operations
Beginning Algebra1.List all the factors of 88.2..docx
Beginning Algebra1.List all the factors of 88.2..docx
presentation_class-7_maths_simple_equation_1594721868_387804-converted.pptx
presentation_class-7_maths_simple_equation_1594721868_387804-converted.pptx
More from khyps13
August 23, 2016
The document provides classwork and practice problems related to algebraic expressions and one-step equations. New vocabulary terms introduced are coefficient and like terms. Examples are given of adding and subtracting like terms. There are also practice problems for translating expressions, solving one-step equations, and word problems involving algebraic relationships between variables.
August 22, 2016
This document provides instructions and examples for students on organizing their math notebooks. It includes examples of how to categorize different math concepts like properties, formulas, and vocabulary in the resource section. It also provides warm-up problems covering large and small numbers. Students are instructed to complete homework assignment 1.1 by the due date of August 23, 2016. They are also given examples of translating expressions and equations.
August 19, 2016
This document contains a math lesson on large and small numbers, number relationships, and problem solving. It includes warm-up questions about numbers greater than or less than a trillion, billions, and millions. It also has questions about the width of a human hair, distance from Earth to the Sun, and how fast a hummingbird flaps its wings. The document provides answers to the warm-up questions and has an end of week review on number operations and translating word problems into algebraic equations. It concludes with an example of solving a multi-step word problem algebraically to find the individual weights of Mike, Bob, and Don.
August 18, 2016
This document contains reminders for school supplies needed by Monday, an overview of the 5 essential understandings of algebra, and 5 fraction practice questions. The 5 essential understandings are: 1) Algebra is a method for solving math problems, not the problems themselves. 2) Mathematics uses symbols as shortcuts. 3) Algebra rules come from natural number rules. 4) Algebra examines patterns and relationships between numbers. 5) Look for equality and use it to your advantage when solving problems. Mastering multiplication tables is also emphasized.
Aug 17, 2016
The document outlines the daily routine and learning process for a math class. It includes:
1. A warm-up with 4-5 review or new problems to introduce topics for the day. Class work is to be completed during class time and any unfinished work should be done outside of class.
2. New concepts are introduced through demonstration by the teacher, then practiced together through examples before students work independently.
3. Additional learning resources like online math sites are provided to support studying outside of class, since class time is limited to 60 minutes per day.
4. A short practice test is included covering translating expressions, order of operations, and fractions to gauge readiness.
Ultimate guide to systems of equations
i) The document discusses various methods for solving systems of linear equations, including graphing, substitution, elimination, and cross-multiplication.
ii) It also addresses solving systems that can be reduced to linear equations, such as transforming non-linear equations using substitution.
iii) Examples are provided to illustrate each method for deriving the solution of a system of equations.
March 29, 2016
The document provides examples for solving systems of equations through various methods like elimination, substitution, and word problems. It demonstrates setting up systems as equations based on information provided, choosing an elimination method by adding or multiplying equations, isolating variables, substituting values, and checking solutions. Word problems are converted to systems of equations and then solved to find unknown variable values.
March 28, 2016
The document provides information about assignments and tests for today and upcoming dates. It includes notes about 4th quarter grade trackers, make-up tests during lunch, systems of equations lessons for some periods today and tomorrow, and distributing worksheets. The document also contains math content on solving systems of equations by graphing, substitution, and elimination.
March 31, 2016
The document discusses reviewing Khan Academy topics on systems of equations and solving 3x3 systems. It includes examples of solving systems of equations by elimination, addition, and substitution. Students will review methods, complete assignments, and take a five question quiz on solving systems of equations.
March 30, 2016
The document provides instructions for practicing Khan Academy topics on systems of equations word problems. It also reminds the student to make progress on homework 4.1-4.2 which is due on Friday for full credit. Examples are given for solving systems of equations by substitution and word problems involving jeans/shirts and movie tickets.
March 21, 2016
This document provides information about upcoming tests, review material, and math concepts to be covered in class. It includes:
- Details on making up remaining tests and reviewing for the final exam
- The 5 most missed questions from the last test
- Vocabulary and terms related to systems of equations to be covered
- Sample word problems and equations involving ratios, rates, percents, and lines to work on for the next class
April 5, 2016
The document provides examples and steps for solving systems of inequalities and linear equations. It discusses graphing a single inequality, the steps for graphing systems of inequalities, and provides an example of solving a two-variable linear system of inequalities. Sample problems include determining the number of hours until costs are the same for two plumbing companies and graphing the inequality y < 5x + 1.
April 4, 2016
This document contains a daily agenda and warm-up problems for math class including:
1) Solving systems of equations by graphing, substitution, and elimination. Example problems include solving for costs of flowers and costs of different internet providers over time.
2) Review of fractions, inequalities, and solving multi-step equations.
3) An example of solving a 3x3 system of equations by eliminating a variable and substituting values.
4) Warm-up questions ask students to write and solve systems of equations modeling real-world scenarios like costs of soccer equipment and costs of fitness clubs over time.
April 6, 2016
The document provides a review of topics related to solving systems of equations and inequalities including:
1) There are two methods for solving systems - elimination or substitution. An example problem is worked through using elimination.
2) When graphing systems of inequalities, each line must be drawn and labeled as above, below, or dashed before moving to the next line.
3) Word problems can be modeled with systems and solved, such as determining the number of chickens and pigs given the total number of legs.
April 1, 2016
This document contains examples of solving systems of equations word problems. It begins with a warm-up problem about a math test worth a total of 63 points made up of 2-point and 3-point problems. Then it provides steps for solving systems of equations, including labeling variables, writing equations, solving, and checking. Finally, it applies these steps to two word problems, one about movie tickets and one about flowers for Valentine's Day.
February 17 2015
The document provides instruction on calculating and interpreting slope. It defines slope as the ratio of rise over run between two points on a line. It gives the formula for calculating slope as the change in y over the change in x between two points. Several examples are worked out step-by-step to demonstrate calculating slope from graphs and point pairs. Key concepts covered include identifying horizontal and vertical lines that have slopes of 0 and undefined respectively.
February 18 2016
The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between
February 16 2016
The document provides information about an upcoming test on coordinate planes and linear functions. It includes:
- A review of topics to be covered on the test like functions, ordered pairs, slope of a line, and standard form of a line.
- Examples of problems about domain and range, graphing lines, finding intercepts, and interpreting graphs.
- Instructions to have materials like graph paper and a calculator ready for working through sample problems.
- A reminder that attempting all problems is better than leaving them blank on the test.
February 9 2016
The document outlines an agenda for a math class that includes a warm-up on missed test questions, learning about functions and their domains and ranges, using the vertical line test to determine if a relation is a function, and interpreting graphs. It provides examples of mapping relations to check if they are functions and using the vertical line test. Students are given practice problems to determine if relations are functions and to graph relations and use the vertical line test.
February 10 2016
This document provides instruction on determining the domain and range of functions, identifying functions using mapping and the vertical line test, and interpreting graphs. It includes examples of determining domain and range for various functions defined by equations. Warm-up questions are provided to have students plot points and draw lines from equations. Students are reminded that their class work CW 3.4 is due for full credit.
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September 10 2014
- 2. Algebra Rules: When solving for unknown quantities, always assign the variable to the smallest quantity. (Smallest may be lightest, least expensive, shortest, etc. depending on the type of value. Bob weighs 10 more pounds than Mike. Don weighs 15 more pounds than Bob. The sum of their weight is 440 pounds. How much does each weigh? Who weighs the least? We’ll use ‘m’ as the variable. Now, the key part of our solution: For the other two, what are their weights relative to Mike’s weight? Bob is... m + 10 Don is... m + 10(Bob) + 15, or m + 25 Putting them all together, we have... m + (m + 10) + (m + 25) = 440 3m + 35 = 440 3m = 405 Mike = 135, Bob = 145, Don = 160
- 3. 1. Coefficient: 2. Like Terms: Vocabulary: In algebraic expressions & equations, like terms are terms that contain the same variables raised to the same power. Only the coefficients of like terms can be different. Examples include: 7x x -2x (1/3)xy2 -2y2x 6xy2
- 4. Vocabulary: Write the expression or equation. Then, identify the number of: a) terms What are the: b) like terms, c) coefficients, & d) constants 1. 3 + 7x + 3x + x No. of Terms? Like Terms? Coefficients? Constants? 2. 2a + 5c – a + 6a 3. 7x – 3y + 3z - 2 Are these expressions or equations?
- 5. Formulas: 1. Perimeter of a Square: 2. Area of a Square: 3. Perimeter of a Triangle: = Side + Side+ Side 4. Area of a Triangle: = ½ base x height or, ½ (base x height) P = 4S The area of a square is actually the same as the area of a rectangle: LxW However, since the lengths of the sides are the same, you are multiplying a number by itself. So, the formula for the area of a square is: A S2
- 6. Warm-Up: 1. Translate & Solve: The difference between a number and four. The sum of three times a number and eight. Four less than the product of four and a number is nine. The quotient of a number and eight is one and five-tenths. Three times the quantity of a number decreased by three is nine. 2. Simplify the Expression: a2 + a + a2 2x + 3y – 5x + 2y 5(a – 2b) – 3(a – 2b)
- 10. And finally…
- 11. Test #1 Topics: 1. Simplifying Expressions --Key Concept: Combining Like Terms 2. Solving Simple Equations (1 or 2 step) --Key Concepts: a.) Variable replaced by value which make the sentence true. b.) Isolate the variable (get the variable by itself) on one side of the equation by correctly using the rules. 3. Translating Sentences into Expressions or Equations --Key Concepts: sum, difference, product, quotient, less than, the quantity of.