Ms. amrhein
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The 4th grade math class document outlines lessons over 3 days that cover triangle problems, using the value of unknowns, and the commutative property. On day 1, the class broke down a triangle problem into steps and identified all prime numbers less than 20. On day 2, the class practiced solving equations for unknown values using the guess and check method. On day 3, students solved equations and identified which problem demonstrated the commutative property of addition.
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This document provides a review with answers for a 1st period class at Colegio San Patricio for the 2010-2011 school year. It covers topics like working with real numbers, adding and subtracting polynomials, drawing and classifying angles, ratios, rates, proportions, and scale factors. There are 22 problems in total across these topics with step-by-step workings shown to arrive at the answers.
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This document provides a review with answers for a 1st period class at Colegio San Patricio for the 2010-2011 school year. It contains 22 questions across 4 sections: 1) working with real numbers, 2) adding and subtracting polynomials, 3) drawing and classifying angles, and 4) ratios, rates, proportions and scale factors. The questions range from performing basic arithmetic operations to solving multi-step word problems involving percentages, taxes, ratios, and scale drawings.
9.8
The document discusses factoring polynomials using the difference of squares pattern and perfect square trinomial pattern. It provides examples of factoring expressions involving these patterns, including solving polynomial equations. The examples illustrate factoring expressions with variables and evaluating expressions to solve vertical motion problems.
Answers for first period review
This math review document provides answers and explanations for various math problems involving converting between number systems, identifying patterns and rules, calculating areas and perimeters of shapes, working with expressions and equations, and evaluating expressions. It includes converting between Egyptian, Chinese, and Mayan numerals; matching number sequences to their rules; finding areas and perimeters of rectangles and triangles; calculating interest; writing algebraic expressions; and evaluating expressions with variables.
Factoring pst
The document provides instructions on factoring polynomials using perfect square trinomials. It begins with examples of multiplying perfect square binomials and identifies the pattern. Students are shown how to determine if a trinomial is a perfect square and factor it using the formula. The document concludes with examples of factoring various polynomials using perfect square trinomials.
The solution-of-problem
1. The document presents problems involving number theory, algebra, geometry, and probability. For number theory, it provides exercises and solutions involving sums of powers and nearest integers. For algebra, it solves systems of equations and determines values based on relationships between variables. For geometry, it calculates areas and volumes. For probability, it determines probabilities of events occurring based on arrangements and selections from sets.
The solution of problem
1. The document presents problems involving number theory, algebra, geometry, and probability. For number theory, it provides exercises and solutions involving sums of powers and finding the nearest integer of a difference. For algebra, it solves systems of equations and determines values based on given equations. For geometry, it calculates areas and volumes. For probability, it finds probabilities of arrangements and outcomes of dice rolls and ball draws.
Summer Task - MATHS - Yr 12 preparation
1. The document provides 13 mathematics questions covering topics such as: simplifying expressions, solving quadratic equations, working with cylinders and areas, and proving identities. Students must show their working and attempt all questions.
2. The questions involve skills like factorizing, using the quadratic formula, eliminating variables, finding minimum points on graphs, and proving statements about odd numbers. Working is required for full marks.
3. Students must complete the questions for homework and bring their work to the next mathematics lesson.
Taller matemáticas empresariales.
The document provides 18 math equations involving variables like x, y, m, r, a, and c. The equations include operations like addition, subtraction, multiplication, exponents, and grouping terms using parentheses. For example, one equation is (x-2y)2 + 2(x-2y)(z-3r) + (z-3r)2, another is 4m10 + 4m7 - m4 - m8 - 1. The document presents the equations without context or explanation of the variables.
Taller matemáticas empresariales
The document provides 18 math equations involving variables like x, y, m, r, a, and c. The equations include operations like addition, subtraction, multiplication, exponents, and grouping terms using parentheses. They range in complexity from single term equations like x2 to longer equations combining multiple terms like 21r2 + 38rs - 5s2.
Đề Thi HK2 Toán 6 - THCS Trung Mỹ Tây 1
1) The document contains a math test for 6th grade students with 6 questions testing various math skills like calculations, solving equations, and geometry.
2) Question 1 involves calculations like fractions, percentages, and order of operations. Question 2 asks students to solve equations for variable x.
3) Question 3 asks about the total weight of fruits in a plate given the individual weights. It tests word problems.
4) The last few questions involve more geometry, like finding missing angles and determining if a ray is a bisector.
Review exercises
1. The document contains 42 multiple choice questions about factorizing algebraic expressions and evaluating expressions.
2. The questions cover topics like factorizing quadratic expressions, common factors of expressions, evaluating expressions involving exponents and fractions, and identifying factors of expressions.
3. The multiple choice options provide the possible factored forms or simplified expressions for evaluating each question.
Factoring perfect-square-trinomials
To factor perfect square trinomials:
1. Get the square root of the first and last terms.
2. List down the square root as the sum or difference of two terms.
3. Factor the expression into the form (term 1 ± term 2)2.
Colour in Mathematics
The document discusses how colour can be used in mathematics to add clarity. It provides examples of how colour highlights which terms are associated with signs in algebra examples. Colour can also emphasise the order of operations. Further examples show how colour aids understanding of topics like factorisation, composite functions, inequalities, coordinate geometry, binomial expansion, completing the square, circle geometry, integration, and decision mathematics algorithms. Worked solutions with colour coding are also suggested to help students understand steps at their own pace.
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Ms. amrhein
- 1. 4th Grade Math Class
- 2. Day 1 Triangle Problem Day 2 Value of Unknown Day 3 Commutative Problem
- 3. Day 1 20 1. Breakdown 10 2 2. All Prime Numbers 5 X 2 X 2 = 20 3. “Guess and Check”
- 4. 16 24 8 2 4 6 4 2 2 2 2 3 2 2 2 2 2
- 5. 1) 15 2) 32 3) 20 5 3 8 4 2 10 4 2 2 2 2 2 5 2 2 2 2 2
- 6. Find the Value How many more M&M’s do you need to have 11 M&M’s. 5 + b = 11 -5 -5 b = 6 5 + 6 = 11
- 7. 1. Equation 7+ A = 9 -7 -7 2. Subtract from both sides A= 2 3. Value 7 + 2 = 9
- 8. 1. Equation b - 3 = 10 2. Add number + 3 + 3 3. Value b = 13
- 9. 1) m – 6 = 0 2) 10 + f = 30 3) z – 4 = 7 +6 +6 -10 - 10 +4 +4 m = 6 f = 20 z = 11
- 10. 1) 12 2) 7 + b = 10 3) w - 6 = 13 -7 -7 +6 +6 3 4 b = 3 w = 19 3 2 2
- 12. Example: t + s = s +t *Notice the same units
- 13. 13 = 6 + 3 + 4 9+2=2+9 (7 + 2) + 4 = 7 + (4 + 2) Which problem shows the commutative property?
- 14. 13 = 6 + 3 + 4 No! (7 + 2) + 4 = 7 + (4 + 2) No! 9+2=2+9 Yes!!!
- 15. 1) 14 2) b + 3 = 4 3) Commutative -3 -3 Problem 7 2 b= 1
- 16. 1) 100 2) 20 + j = 55 10 10 -20 -20 5 2 2 5 j = 35
Editor's Notes
- Yes billy?..6! Good job! That’s right!....In terms of an equation. We start with 5 m&ms and trying to figure out what the other number we need in order to have 11 m&ms.