Math Competition - Problem # 6

MATHEMATICS PROBLEM SOLVING COMPETITION

SEMESTER 2, 2007-8

THREE WEEK PROBLEM #6

TWENTY FOUR

Create the number 24 by using only a 1, 3, 4 and 6.

The only operations symbols you may use are those

for addition, subtraction, multiplication and division.

You may use parentheses.

In how many different ways can you get 24?

You must show your all your working.

********************************************

Due Date: Friday, April 18, 2008

**********************************************************

Remember:

* Your entry must clearly show your name, school name, mathematics class code, teacher’s

name and date of submission

* All steps must be clearly shown.

* The most accurate and best presented entry will win the prize.

* Your mathematics teacher will give you credit for your entry and you will also receive a

certificate for participating.

**************************************************************************************

MPSC THREE WEEK PROBLEM #6, 2007-8 Tom Frossinakis (AUSSIE) March 30, 2008

Aims week of 3/31:

Aim 38: How can we find the vertex of a parabola?
hw: pg 501 1-4, 8, 12, 18

Aim 39: How can we model using parabolas?
hw: pg 502 22,24,30,32,36, 37

Aim 40: How can find x intercepts; review factoring
hw: pg 511 2-12 even

Aim 41: more on parabolas
hw: study for test

Aim 42: Chapter Test on Quadratics
Given an equation ---> sketch a graph
Given a graph ---> write an equation
Given an equation ---> find the vertex (max / min)
Factor
Solve word problems (find vertex (h,k))
hw: none

Quadratic Equations

Try it yourself:

http://hotmath.com/util/hm_flash_movie.html?movie=/
learning_activities/interactivities/translating_scaling.swf&
return_to=undefined&title=Transforming%20Functions

Graphing Form and Standard Form As you have worked with quadratic functions, equations, and expressions you have regularly seen two forms. One is known as graphing (or vertex) form, the other is known as standard form.

A quadratic equation in GRAPHING or VERTEX FORM looks like:

Y = a(x–h)² + k.

- the vertex is (h,k) and the axis of symmetry is the line x=h.
- the parabola opens up when a is positive and opens down when a is negative.
- if |a| > 1, the graph will be narrower than the graph of y = x²

- if |a| <1, the graph will be wider than the graph of y = x^ 2

For example, the equation Y = 3(x–1)² – 5 is in graphing form where a = 3, h = 1, and k = –5.

The following quadratic equation represents the same parabola as y = 3(x – 1)² – 5, but it is written in what is generally called standard form. For y = 3x² – 6x – 2, a = 3, b = –6, and c = –2.

A quadratic equation in STANDARD FORM is written as y = ax² + bx + c.

The vertex of a parabola locates its position on the axes. The vertex serves as LOCATOR POINT for a parabola. The other shapes we will be investigating in this course also have locator points. These points have different names but the same purpose for each different type of graph.

Aims week of 3/24:

Aim 33: What are identity and inverse matrices?
hw: pg 427 2,4,6

Aim 34: How can you use inverse matrices to solve matrix equations?
hw: pg 427 14,16,18,37,40

Aim 35: continuation solving matrix equations.
hw: none

Aim 36: Investigation into quadratic functions
hw: pg 490 22,24,26,33

Aim 37: What are the standard and graphing form of a quadratic equation?
hw: none

Aims week of 3/17:

Aim 29: How do we use matrices for a geometric transformation?
hw: pg 413 2,8,10,11,16, 18

Aim 30: What is a square matrix and it's determinant?
hw: pg 430 - 431 2-18 even

Aim 31: Review linear systems & matrices
hw: study for test

Aim 32: Chapter 3 test

Friday - No School!

Matrix Defintions

Introduction to Matrices:
Matrices are simply tables of numbers, but the rise of modern computing has made them increasingly important in science, economics, computer science, and mathematics. Matrices have their own notation and form, and their own unique arithmetic which you’ll need to become familiar with before proceeding further. Once you understand the mechanics, the computations are straightforward, and your calculator can even do them for you! Matrices have many applications, and we’ll see how they tie together with systems of equations later in this unit.

A MATRIX is a rectangular array of numbers or algebraic expressions enclosed in square brackets. (Some math texts use parentheses instead.) Usually, a matrix is denoted by a capital letter. The plural of matrix is matrices. Each matrix has ROWS and COLUMNS. In mathematics we are very precise: rows are horizontal, and columns are vertical. If matrix M has 2 rows and 3 columns, we say the dimensions of M are 2 3, or M is a 2 by 3 matrix. m2,1 is the ENTRY in the second row and first column of matrix M; in general, mr, c is the entry in the rth row and cth column.

Two matrices can be added only if they have the same dimensions.

We can multiply matrices of any size as long as they "fit " right. You get the entries of the product matrix by finding "sums of products " of rows of the first matrix with columns of the second. Here is a more formal description:

To get the r,c entry of the product matrix, multiply the corresponding entries in the r^th row of the first matrix and the c^th column of the second matrix and add the products.

Aims week of 3/10:

Aim 24: Review - Solving Linear Systems
hw: finish worksheet

Aim 25: What is a matrix (matrice)?
hw: pg 392 2,3,6,10,14,16,18,20

Aim 26: How do we add and subtract matrices?
hw: pg 399 2,4,6,32,34,36

Aim 27: How do we multiply and divide matrices?
hw: pg 406 2,4,8,14,21,26,28

Aim 28: More on Matrix operations
hw: none

Math Competition - 3 Week Problem #5

MATHEMATICS PROBLEM SOLVING COMPETITION

SEMESTER 2, 2007-8

THREE WEEK PROBLEM #5

TRAIN IN TUNNEL

How long will it take a two-mile long train

traveling at 12 miles per hour to travel completely

through a mile-long tunnel?

You must show your reasoning.

********************************************

Due Date: Friday, March 28, 2008

**********************************************************

Remember:

* Your entry must clearly show your name, school name, mathematics class code, teacher’s

name and date of submission

* All steps must be clearly shown.

* The most accurate and best presented entry will win the prize.

* Your mathematics teacher will give you credit for your entry and you will also receive a

certificate for participating.

**************************************************************************************

MPSC THREE WEEK PROBLEM #5, 2007-8 Tom Frossinakis (AUSSIE) March 4, 2008

Math Competition - Semester Problem

MATHEMATICS PROBLEM SOLVING COMPETITION

SEMESTER 2, 2007-8

SEMESTER PROBLEM #2

FORTY

Using four different whole numbers and any number of mathematical operations, write expressions for all the whole numbers from 0 to 40.

The same set of the four different numbers must be

used for each of the numbers from 0 to 40.

Examples: 24 + 8 + 5+ 3 = 40; 24 –5 + 8/2 = 23

All working must be clearly shown.

*****************************************

Due Date: Friday, May 30, 2008 (or sooner)

*******************************************************

Remember:

* Your entry must clearly show your name, school’s name, mathematics class code,

teacher’s name and date of submission.

* All steps must be clearly shown.

* The most accurate and best presented entry will win the prize.

* Your mathematics teacher will give you credit for your entry and you will also receive

a certificate for participating.

**************************************************************

MPSC SEMESTER PROBLEM #2, 2007-8 (FORTY) Tom Frossinakis (AUSSIE) March 4, 2008

Aims week of 3/3:

Aim 19: More on Absolute Value
hw: pg 368 35 , finish worksheet

Aim 20: How do we graph 2 dimensional absolute value functions?
hw: pg 372 13, 15, 18, 20

Aim 21: Review Chap 2
hw: pg 387 1-4,6,8,10 Due Friday

Aim 22: Test: What have learned in Chapter 2?
hw: none

Aim 23: What are linear systems?
hw: none