Strategic intervention material
40
HOME Click to proceed Activi ty 1 Activi ty 2 Activi ty 3 Assessmen t 1 Assessmen t 2 Enrichmen t Reference s Answer Key
Transcript of Strategic intervention material
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Click to proceedActivity 1
Activity 2
Activity 3
Assessment 1
Assessment 2
Enrichment
References
Answer Key
STRATEGIC INTERVENTION
MATERIAL
Prepared by: REORINA C. MINAO T-I
Don Carlos National High SchoolSinanguyan, Don Carlos, Bukidnon
STRATEGIC INTERVENTION
MATERIAL(Computer-Based)
G9-MathematicsSolving Quadratic Equation by Completing the Square
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STRATEGIC INTERVENTION
MATERIAL
Solving Quadratic Equation by Completing the Square
Least Mastered Competency* Solving Quadratic Equation by Completing a Square
Sub Tasks:*Identifying quadratic equation*Determining a perfect square trinomial*Expressing Perfect Square trinomial as a square of a binomial*Solving quadratic equation by completing the square.
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GUIDE CARD A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following form;
In the equation, is the quadratic term, is the linear term, and is the constant term.
Example:
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Activity 1. Quadratic or Not
Determine the given expression as quadratic or not. Write Q if it quadratic and NQ if it is not.__________1. __________2. __________3. =0__________4. __________5.
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On Quadratic EquationA quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following form;
In the equation, is the quadratic term, is the linear term, and is the constant term.
Why do you think a must not be equal to zero?
Example:
Why do you think a must not be equal to zero? ans
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πππ+ππ+π=πSubstituting in the equation
will yield a linear equation. So must not be equal to zero
illustration
The derived equation is in first degree
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Activity 2: Am I a Perfect Square Trinomial or Not?
Determine each of the following whether it is a perfect square trinomial or not. Write PST if it is a perfect square trinomial and NPST if it is not._________1. _________2. _________3. _________4. _________5.
How do you describe a
perfect square trinomial?
How do you describe a
perfect square trinomial?
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Perfect Square TrinomialFirst and last terms are perfect square.Middle term is twice the product of the square
root of the first and last terms.Example:
first and last term
(perfect squares)
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Activity 3. Transform Me!Express each of the given trinomial as a square of a binomial.1. ___________2. ___________3. ___________4. ___________5.
How to transform a PST to a square of
a binomial?
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Simply get the square root of the first term, copy the sign of the middle term,
and get the square root of the third term.
Then square the given binomial.
Activity 3. Answers
1.
2.
3.
4.
5.
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How to solve QE using completing the square method?
Another method of solving quadratic equation is by completing the square. This method involves transforming the quadratic equation into the form where
What are the steps in solving QE by completing the
square?
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Steps in solving QE by completing the square
1. Divide both sides of the equation by a then simplify.2. Write the equation such that the terms with variables are on
the left side of the equation and the constant term is on the right side.
3. Add the square of one-half of the coefficient of x on both sides of the resulting equation.
4. Express the perfect square trinomial on the left side of the equation as a square of a binomial.
What happens to the left side of the equation? ans
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The left side of the equation becomes
a perfect square trinomial
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Steps in solving QE by completing the square: Contβ¦
5. Solve the resulting QE by extracting the square root. Add the square of one-half of the coefficient of x on both sides of the resulting equation.6. Solve the resulting linear equation.7. Check the solution obtained against the original equation.
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Example: Solve the quadratic equation by completing the square.
Solution: Divide both sides of the equation by 2 then simplify. =
Add 5 to both sides of the equation, then simplify.
Add to both sides of the equation the square of one-half
of 4.=4.
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Express as a square of a binomial.
Solve by extracting the square root.
Solve the resulting linear equations.
Check the solutions obtained against the original equation
For For :
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Answer :
has two solutions: x = 1 and x = -5
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Assessment Card 1This Might Be Easy
Direction: Factor the following and Select the correct answer.
π¨ . (πβπ )π
π© . (π+π )π
πͺ . (π+π )π
ππβπππ+ππ ππ+πππ+ππ
A.
π© . (π+ππ )π
C.
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π¨ . (π+π )π
π© . (π+π )π
πͺ . (πβ π )π
A.
π© . (π π+π )π
C.
π¨ . (πβπππ )π
π© . (π+πππ )π
πͺ . (πβπ π )π
π¨ . (π π+π )π
π© . (π π+π )π
πͺ . (ππ βπ )π
π+π π+ππ πβππ π+ππππ
π ππ βπππ+ππ π ππ βπ π+π
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Assessment Card 2Reveal My Secret !
Direction: Solve the following Quadratic equation by completing the square
ππ+ππ+ππ=πππ+ππ+π=πππ+ππ+ππ=ππ ππβππ π=βππ
solutions
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1. 2.
Therefore, the solutions are -3 and -4
Therefore, the solutions are -1 and -5
Click for 3 and 4 solution
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3. 4.
Therefore, the solutions are -3 and -5
Therefore, the solutions are 7 and 1
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Enrichment CardThink Deeper !An open box is to be constructed from a square piece of metal sheet by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?
Solution
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Use the figure as a guide. Let x be the length of a side of the square piece of metal. The box will have a height of 1 foot and its square base will have x-2 as the length of a side. The volume of the box is therefore
Length x width x height
Since the volume of the box is to be 4 cubic feet,
or11
x
x-2 Discard the solution because length cannot be zero.
Therefore, the sheet metal should be 4 feet by 4 feet
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Answer key
Activity 1. Quadratic or Not
1. NQ2. Q3. Q4. NQ5. NQ
Activity 2: Am I a Perfect Square Trinomial or Not?
1. NPST2. PST3. NPST4. NPST5. NPST
Activity 3. Transform Me!
Assessment Card 1
1. A2. C3. B4. C5. C6. A
Assessment Card 2
1. -3 and -42. -1 and -53. -3 and -54. 7 and 1
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Oh no! Iβm not Quadratic
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Ouch! It hurts! Iβm not a perfect
Square trinomial
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1-2
Oopps ! Iβm DefinitelyWrong!
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3-6
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SORRY! YOU ARE WRONG AGAIN
1-2 3-6
Nice try! But I am not the answer
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1-2 3-6
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Amazing! Youβre Right!Iβm Quadratic
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Yipee! Iβm QuadraticHOME
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You Got Me!!Iβm Perfect Square Trinomial
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EXCELLENT!HOME
1-2 3-6
AMAZING! Youβre Correct
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1-2 3-6
FANTASTIC! Youβre right again
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1-2 3-6
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&
Job well done!
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Reference Card
Learnerβs Material-Mathematics IX, First Edition pp. 35-45.
Alferez, Duro et al. MSA ADVANCED ALGEBRA. MSA Publishing House. Quezon city, Philppines, 2012 pp. 58-63.
http://www.themathpage.com/alg/perfect-square-trinomial.htm
http://mathbitsnotebook.com/Algebra1/Factoring/FCPerfSqTri.html
http://www.onemathematicalcat.org/algebra_book/online_problems/word_problems_perfect_squares.htm
