excel to the rescue...how to use excel in high-school math

Excel to the rescue…usage of Excel in high-school math (3 examples)Meni PoratE-mail: [email protected]: Meniporat.blogspot.com Facebook fan page: http://www.Facebook.com/meni.porat

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"אקסל" לתלמידי חטיבת הביניים- המשוואה הריבועית:

1. Excel for Junior high schoolThe Quadratic Equation

2. Excel for high schoolProbability: Binomial Distribution

3. Higher Level Math using ExcelMatrices: Solving A System Of N Equations With N Variables

3 Examples:

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The general formula of a quadratic equation

Excel for Junior high schoolThe Quadratic Equation

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The 2 solutions of a quadratic equation

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The first Solution Formula of the Equation

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The second Solution Formula of the Equation

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The Δ (Discriminant) of the Equation

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• Solution of the equation: -X2+6X-5=0 Δ is positive: the equation has 2 solutions

This Equation has 2 solutions

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-1X2 + 6x -5 = 0

The coefficients of the Equation in cells: E2, F2, G2

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Calculating Δ in cell H2Δ = b2 – 4ac = 62 – 4*(-1)*(-5) = 36-20=16

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Defining the formula in cell H2 using Excel's Name Manager10




The general formula for finding the 1st root of a quadratic equation: algebraic (above) and Excel (below)

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“No Solution” message (when Δ is negative)

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Equation’s Solutions: X 1 =1, X 2 =5

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14

Excel for high schoolProbability – Binomial Distribution

Binomial Probability Distribution

n – Number of attemptsk – Number of success resultsP – Probability

In order to use the formula, 3 conditions must be met:1) Successive trials are independent2) Boolean result in each trial: yes/no, success/failure3) Constant probability: Each trial has the same probability


• Example # 1: Non-cumulative Probability (an exact number of successes)

Probability of marksmanship is: 0.33if a soldier shoots at the target 5 times, what is the probability of the

soldier’s hitting the target exactly three times?

Solution when: n = 5, k = 3, p = 0.33

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• Example # 1: Non-cumulative Probability (an exact number of successes)

Solution in Excel: the BINOMDIST function: n = 5, k = 3, p = 0.33

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Example # 2: Cumulative Probability (at least number of successes)

Probability of marksmanship is: 0.33if a soldier shoots at the target 5 times, what is the probability of the

soldier’s hitting the target at least three times (i.e. 3, 4 or 5 times)?

Solution when: n = 5, k = 3, p = 0.33

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Example # 2: Cumulative Probability (at least number of successes)

=BINOMDIST(3,5,0.33,0) + BINOMDIST(4,5,0.33,0) + BINOMDIST(5,5,0.33,0)

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Example # 3: Cumulative Probability (no more than x successes)Probability of marksmanship is: 0.33if a soldier shoots at the target 5 times, what is the probability of the

soldier’s hitting the target no more than three times (i.e. 0, 1, 2 or 3 times)?

Solution when: n = 5, k <= 3, p = 0.3319



Example # 3: Cumulative Probability (no more than x successes)

=BINOMDIST(3,5,0.33, 1) n = 5, k <= 3, p = 0.33

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A system of 2 Equations with 2 Variables4 Solution methods:1. Elimination2. Substitution3. Graphical4. Excel

The Special Program for the gifted High School StudentMatrices: Solving a System of N Equations with N Variables

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Method # 1: Elimination

Elimination Method: Finding X

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Method # 1: Elimination

Elimination Method: Finding Y

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Method # 2: Substitution

Step 1: “extracting” X from the second Equation

Step 2: replacing X by (3 – Y) in the first Equation

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Method # 2: Substitution

Step3: Finding Y Step 4: Finding X

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Method # 3: Graphical

The Intersection of the two Lines is the Solution

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Method # 4: Excel

1. The Equations system can be expressed as a multiplication of matrices:coefficient matrix * variable matrix(vector) = constant matrix (vector)

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Method # 4: Excel

2. The variable vector expressed as the multiplication of the coefficientmatrix with the constant matrix

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Method # 4: Excel

A. The coefficient matrix B. the Values Vectoris in cells A7:B8 is in cells G7:G8

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Method # 4: Excel

C. Calculating the inverse matrix (in cells D7:E8) using the MINVERSEarray formula

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Method # 4: Excel

D. The MMULT array formula (in cells E13:E14) – finally suppliesus with the Equation’s solutions.

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I’d be glad to answer yourquestions….

Meni PoratE-Mail: [email protected]: Meniporat.blogspot.com Facebook Fan Page: http://www.Facebook.com/meni.porat

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