ARITHMOGONS BENGT ÅHLANDER ARITHMOGONS. A WAY TO VARIATE THE EDUCATION AND PERHAPS SHOW THE STUDENTS THE BENEFITS OF CAS ARITHMOGONS.

Slides:

Advertisements

Similar presentations

Factoring the Sum or the Difference of Two Cubes. Subtitle: Know the CARD!!!

Advertisements

Grid Topic IIII I I I Calculations Fractions 2222 Scientific Notation 11 % Calculations Circle Geometry

Algebra Recap Solve the following equations (i) 3x + 7 = x (ii) 3x + 1 = 5x – 13 (iii) 3(5x – 2) = 4(3x + 6) (iv) 3(2x + 1) = 2x + 11 (v) 2(x + 2)

Table of Contents Example 1: Solve 3x = 0. Quadratic Equation: Solving by the square root method This method can be used if the quadratic equation.

Precalculus January 17, Solving equations algebraically Solve.

EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

Percentages L.O. to understand percentages as a fraction of 100.

EXAMPLE 1 Identify direct variation equations

Section 1.3 Problem Solving 1. Steps to world problem solving process 1.Understand the Problem 2.Devise a plan 3.Carry out the plan 4.Look back 5.MAKE.

Over Lesson 8–4 A.A B.B C.C D.D 5-Minute Check 1 (2c – 9)(c – 4) Factor 2c 2 – 17c + 36, if possible.

8.5 – Factoring Differences of Squares. Recall: Recall: Product of a Sum & a Difference.

Arcs and Angles Continued

Triangle Angle Sum. Properties of triangles Triangles have three sides and three angles Triangles are named according to their vertices The sum of the.

Factoring GCF and Binomials

Miss Battaglia AP Calculus. If u and v are functions of x and have continuous derivatives, then.

Rules of Fractions Investigation. What do you understand from this statement? What can we say about this? What do we need to know first? What should we.

A hands on approach to completing the square Completing the Square with Algebra Tiles.

Properties of Exponents Part 2 Foundations of Algebra.

1.4 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for.

Warm Up. What is the area & circumference of a circle?

Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression

Factoring and Solving Polynomial Equations (Day 1)

Algebra 10.3 Special Products of Polynomials. Multiply. We can find a shortcut. (x + y) (x – y) x² - xy + - y2y2 = x² - y 2 Shortcut: Square the first.

Algebra 1 Quiz Equations: Quadratic…FOIL? Click Here To Begin.

Order Of Operations Fractions Absolute Value Algebraic Expression Algebraic Equations Real Numbers.

1 §3.2 Some Differentiation Formulas The student will learn about derivatives of constants, the product rule,notation, of constants, powers,of constants,

The easy way to divide! Partial Quotients 72 ÷ 4 = 472 we know 10 x we know 8 x We highlight the times table we are using. We circle.

You evaluated and simplified algebraic expressions. (Lesson 1–2)

Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions = – 3737 n

PROGRESSION IN NUMBER AND ALGEBRA. Objectives The objectives vary depending on which attainment target(s) are relative to the learning objectives of your.

4.6 Model Direct Variation

Review of Matrix Operations Vector: a sequence of elements (the order is important) e.g., x = (2, 1) denotes a vector length = sqrt(2*2+1*1) orientation.

Math 409/409G History of Mathematics

Special Factoring. Difference of Squares General Formula: (x) 2 – (y) 2 = (x + y)(x – y)

Warm Up. 4.3 Solve by Factoring Find this in your notes!

Equations of Circles.

Pythagorean Theorem Proof 8th Math Presented by Mr. Laws

TARGET FRACTION GAME. Let’s practice together. 1)What is our target fraction? 2)Roll all 4 dice only once. 3)Find the best 2 fractions using the numbers.

Problem Solving 1. Steps to world problem solving process 1. Understand the Problem 2. Devise a plan 3. Carry out the plan 4. Look back 5. MAKE SURE YOU.

Writing a direct variation equation. write a direct variation problem when y = 20 and x = 10 y = kx 20 = k·10 k = 2 y = 2x.

Multiplying Polynomials “Two Special Cases”. Special Products: Square of a binomial (a+b) 2 = a 2 +ab+ab+b 2 = a 2 +2ab+b 2 (a-b) 2 =a 2 -ab-ab+b 2 =a.

Factor completely EXAMPLE 4 Factor the polynomial completely. a.a. n 2 – + 2n –1 SOLUTION a.a. The terms of the polynomial have no common monomial factor.

Patterns and Algebra 1 Investigation: 1.Select a pattern made using dot pattern cards. 2.Describe the pattern. 3.Record the pattern. 4.Circle the.

You have 10 seconds to answer the following question…….

Lesson 9.3 Find Special Products of Polynomials

Warm Up Check the solution to these problems; are they correct? If not, correct them. 3 – x = -17; x = -20 x/5 = 6; x = 30.

Topic I II Calculations 1 Fractions 2

Lecture 3 0f 8 Topic 5: VECTORS 5.3 Scalar Product.

Multiple Regression.

National 5 By Topic 2014 onwards

Notes Over 10.3 Multiply binomials by using F O I L.

r = The correlation between price and calories is 0. 79

6.4 Factoring and Solving Polynomial Equations

Quadratic Patterns.

Equation Review Given in class 10/4/13.

The numbers 3,6,and 9 have been placed to guide you.

National 5 By Topic 2014 onwards

,. . ' ;; '.. I I tI I t : /..: /.. ' : ····t I 'h I.;.; '..'.. I ' :".:".

Least-Squares Regression

Objective: To know the equations of simple straight lines.

Credit Past Papers by Topic

Equation Review.

SECTION 8-4 – MULTIPLYING SPECIAL CASES

Credit Past Papers by Topic

Algebra I Solving Equations (1, 2, multi-step)

Unit 5: Geometric and Algebraic Connections

A STAAR REVIEW CIRCUIT A # 1-16 M. N. O. P..

BETONLINEBETONLINE A·+A·+

Objective: To know the equations of simple straight lines.

Presentation transcript:

ARITHMOGONS BENGT ÅHLANDER ARITHMOGONS

A WAY TO VARIATE THE EDUCATION AND PERHAPS SHOW THE STUDENTS THE BENEFITS OF CAS ARITHMOGONS

Arithmogons addition 4+8=? 8+3=? 3+4=?

Arithmogons addition 8+10 =? 10+6 =? 6+8 =?

Arithmogons addition Try to find the numbers! Is there a pattern? ? ?

Arithmogons addition Sum of the squares = Sum of the circles =

Arithmogons addition

Arithmogons addition (a+b)+(b+c)+(a+c)=2*(a+b+c) a c b a +bb + c a + c

Arithmogons addition and algebra 6aa 3a 9a4a 7a ? ? 2b + 2 b b + 6 3b+82b+6 3b+2 ? ? ?

Arithmogons addition and algebra 2b + 2 b b + 6 3b+82b+6 3b+2

Arithmogons addition and partial fractions

Arithmogons addition fractions TI Nspire CAS

Make a straight line beetwen the dots and decide the equation of the lines.

Chainrule at derivation of two factors