Part 1 Algebra Simplify
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The document contains 10 algebra simplification questions with multiple choice answers. It tests skills in simplifying expressions involving exponents, multiplication, division, addition and subtraction of variables.
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2) Factoring the square of a binomial expression.
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4) Factoring a perfect square trinomial.
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6) Factoring a trinomial that is a perfect square by addition and subtraction.
7) Factoring quadratic trinomials in the form x^2 + bx + c.
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This document provides examples of factorizing polynomial expressions in various forms:
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1) An example of a hyperbola with center (3, -1), x-radius of 4, y-radius of 2, and vertices of (7, -1) and (-1, -1).
2) Steps for completing the square to put a quadratic equation into standard form for a hyperbola, including an example starting with 4y^2 - 9x^2 - 18x - 16y = 29.
3) An example of graphing a parabola given by the equation x = -y^2 + 2y + 15, identifying
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2) It explains how to factor square trinomials of the form x^2 + bx + c by finding two factors of c that sum to b.
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The document provides instructions for an individual activity where students must follow 16 directions within 2 minutes to complete tasks like writing their name, drawing shapes, and tapping their desk. It asks what implications the activity might have if directions are not followed properly. The second part of the document provides examples of factoring polynomials using greatest common factor and common monomial factoring methods. It includes practice problems for students to determine the greatest common factor, quotient, and factored form. The document emphasizes following directions and learning different factoring techniques.
Strategic intervention materials on mathematics 2.0
This document provides teaching materials on solving quadratic equations by factoring for a mathematics class. It includes an overview of quadratic equations and their standard form. It then outlines least mastered skills and activities to practice identifying quadratic equations, rewriting them in standard form, factoring trinomials, and determining roots. Example problems and solutions are provided to demonstrate factoring trinomials and using factoring to solve quadratic equations. A practice problem asks students to solve a word problem involving a quadratic equation. Key terms and concepts are bolded. References for further reading are listed at the end.
Units 1 3 review
1. The document provides an overview of the curriculum for 6th grade math including topics, pacing, and vocabulary for three units: Expressions and Equations, Solving Equations and Inequalities, and Decimals.
2. Key topics include exponents, order of operations, variables and expressions, translating between words and math, equations and solutions, adding/subtracting/multiplying/dividing decimals.
3. Each unit lists the corresponding textbook chapters and New York State Common Core Learning Standards addressed. Common assessments are also included.
C2 st lecture 6 handout
The document discusses integration, which is the reverse process of differentiation. It provides formulas for integrating polynomial expressions like xn and axn and explains how to find the constant of integration C. Examples are given for integrating expressions and finding the area under a curve by integrating between limits of integration.
THE BINOMIAL THEOREM
THE BINOMIAL THEOREM shows how to calculate a power of a binomial –
(x+ y)n -- without actually multiplying out.
For example, if we actually multiplied out the 4th power of (x + y) --
(x + y)4 = (x + y) (x + y) (x + y) (x + y)
-- then on collecting like terms we would find:
(x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 . . . . . (1)
Section 4.5 graphing linear equations
The document summarizes how to graph linear equations. It discusses:
1) The standard form of a linear equation is Ax + By = C, where A and B are integers with greatest common factor of 1.
2) Linear equations can also be written in y-intercept form as y = mx + b, where y has a coefficient of +1.
3) Examples are given of converting between standard and y-intercept form.
4) The document shows how to graph linear equations by plotting points in a table using the equation to relate x and y values.
Pembahasan Soal Matematika Kelas 10 Semester 1
This document provides the answers to a mathematics exam for 10th grade students. It includes multiple choice questions with explanations and word problems with step-by-step solutions. The topics covered include algebra, logarithms, quadratic equations, and inequalities.
November 23, 2015
The document discusses solving equations involving variables. It provides examples of solving equations by changing signs of terms to isolate the variable. It also discusses factoring expressions, solving formulas for variables, and additive and multiplicative inverses. Key steps shown include changing all signs when changing one sign, using the lowest common multiple to solve equations, and isolating the variable in a formula by dividing both sides by the coefficient of the variable term.
Binomial
The document discusses binomial coefficients and the binomial theorem. It provides examples of expanding binomial expressions using Pascal's triangle and the binomial coefficient formula. The key points are:
1) Binomial coefficients describe the coefficients that arise when expanding binomial expressions using the binomial theorem.
2) Pascal's triangle provides a visual representation of the binomial coefficients.
3) The binomial theorem can be used to expand binomial expressions in terms of binomial coefficients and write individual terms.
0.3 Factoring Polynomials
This document provides an overview of various techniques for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF);
2) Factoring by grouping terms with a common factor;
3) Factoring perfect square trinomials where the first and last terms are perfect squares;
4) Factoring trinomials using techniques like the reverse box method or grouping.
Perfect square of Binomials
1. The square of a binomial (a + b) is a trinomial with terms a2, 2ab, and b2.
2. To square a binomial, square each term and multiply the unlike terms by 2.
3. Examples are provided of squaring binomials like (x + 6)2 = x2 + 12x + 36 and factoring trinomials into perfect square forms like (x - 2)2.
Similar to Part 1 Algebra Simplify (20)
Rewriting Linear Equation from standard form to slope intercept form
Rewriting Linear Equation from standard form to slope intercept form
Strategic intervention materials on mathematics 2.0
Strategic intervention materials on mathematics 2.0
Part 1 Algebra Simplify
- 1. Algebra Simplification Ten quick questions
- 2. 1 b: y4 d: 4 + y a: 4y c: y 4 Which of the following is equivalent to: y + y + y + y
- 3. 2 b: y4 d: 4 + y a: 4y c: y 4 Which of the following is equivalent to: y × y × y × y
- 4. 3 b: y15 d: y 8 a: 8y c: y 15 Which of the following is equivalent to: y 3 × y 5
- 5. 4 b: y 4 d: 4y a: 8y c: y 3 Which of the following is equivalent to: y 6 ÷ y 2
- 6. 5 b: 6x 3 y 3 d: 5 + x + y a: 6xy c: 5xy Simplify the following expression: xy + 2xy + 3xy
- 7. 6 b: 16xy d: 6x + 4y a: 6x + 10y c: 10xy Simplify the following expression: 4x + 7y + 2x - 3y
- 8. 7 b: 2x 2 + 3x a: 8x 2 + 3x Simplify the following expression: 5x 2 + 2x - 3x 2 - x c: 2x 2 + x d: 8x 2 + x
- 9. 8 b: 7m + 11 a: m - 11 Simplify the following expression: 4m - 5 + 3m - 6 c: m + 11 d: 7m - 11
- 10. 9 b: 8mn d: 8m + n a: 2m + 6n c: 12mn Simplify the following expression, if possible: 2m + 6n
- 11. 10 b: 8mn d: 9mn a: 2m × 6n c: 12mn Simplify the following expression: 2m × n × 6
- 12. Answers
- 13. 1 b: y4 d: 4 + y a: 4y c: y 4 Which of the following is equivalent to: y + y + y + y
- 14. 2 b: y4 d: 4 + y a: 4y c: y 4 Which of the following is equivalent to: y × y × y × y
- 15. 3 b: y15 d: y 8 a: 8y c: y 15 Which of the following is equivalent to: y 3 × y 5
- 16. 4 b: y 4 d: 4y a: 8y c: y 3 Which of the following is equivalent to: y 6 ÷ y 2
- 17. 5 b: 6x 3 y 3 d: 5 + x + y a: 6xy c: 5xy Simplify the following expression: xy + 2xy + 3xy
- 18. 6 b: 16xy d: 6x + 4y a: 6x + 10y c: 10xy Simplify the following expression: 4x + 7y + 2x - 3y
- 19. 7 b: 2x 2 + 3x a: 8x 2 + 3x Simplify the following expression: 5x 2 + 2x - 3x 2 - x c: 2x 2 + x d: 8x 2 + x
- 20. 8 b: 7m + 11 a: m - 11 Simplify the following expression: 4m - 5 + 3m - 6 c: m + 11 d: 7m - 11
- 21. 9 b: 8mn d: 8m + n a: 2m + 6n c: 12mn Simplify the following expression, if possible: 2m + 6n
- 22. 10 b: 8mn d: 9mn a: 2m × 6n c: 12mn Simplify the following expression: 2m × n × 6