Download EOC Review Information #1

Review #3 Algebra II EOC
Name:_____________
Multiplying Matricies: The product (answer) will
be labeled as the row title of the first and column
title of the second.
A2x1 Means 2nd row and 1st column
Cow sheep
[A]=
Price
Jones 3 4
Jimenez 1 2
T = [A] * [B]
[B] =
Cow 425
Sheep 120 
T2x1 = 665 and represents Total
Price of Jimenez
0) Let [A] represent the number of customers in
each town that has a phone plan with 4
companies. Let [B] represent the price of the
individual plans and family plans. [T] = [A]*[B].
What does the element in T1 x 2 represent?
A) Total price of Atown individuals
B) Total price of Btown indivduals
C) Total price of Atown family
D) Total price of Btown family
C#1
C#2 C#3 C#4
# Atown 32
56
49
58
# Btown 12
2
51
60
Individual
Family
Company 1 $42
Company 2 $27

Company 3 $15

Company 4 $34
Solving Matrix Equations
1) Type in the left matrix into [A]
nd
2 x-1   1 Type2x2 Input4#’s 2nd MODE
2) Type in the very right equation into [B]
2nd x-1   2 Type 2x1 Input 2#’s 2nd MODE
3) Type [A] x-1 [B] into calculator
nd
2 x-1 1 x-1 2nd x-1 2 ENTER
4) Make it a fraction (if necessary)
MATH 1 ENTER
Ex 1: 1 2   x  7 .
3  5  y   8 

   
*Solve: Let [A] be 1
2  and [B] be 7  .
3  5
8 


 
[A]-1[B]= 4.636  51 / 11 x=51/11 y=13/11 (51/11,13/11)
1.818 


13 / 11


A-1
Finding Inverses
1) Type in [A]
2) Type [A]-1
2nd x-1 1 x-1
3) Make it a fraction (if necessary)
MATH 1 ENTER
4)Bring out denominator. 1 / 22
3 / 11 
1 1 6 
5 / 22  4 / 11    22 5  8




***If the problem asks “What would you multiply
to solve: 1 2   x   7 then answer is [A]-1.
3  5  y 

 
8 
 
Finding the Determinants (Det) or a b
c
d
Use the calculator by 1) Type matrix into [A]
2nd x-1   1 Type2x2 Input4#’s 2nd MODE
2) Find DET [A] under Matrix Math
nd
-1
2 x  1 2nd x-1 1 Enter
****If there is a variable then substitute each
answer choice for the missing variable.
$65
$35
$29

$48
1) Solve:  2
4  x  1
  3 5   y   0 

   
A) 5/22
B) 3/22 C) (2, -3) D) (5/22, 3/22)
2) Solve: 2 4  x   1
3 6  y 

 
A) (2,3)
0 
 
B) All Reals C) No solution D) (-3,4)
3) [A] = 1  3 . Find [A]-1
 4  6



1
1
 B) 1  6 3 C) 1  3
A) 1 
 4  6

6  4 1
6  2 1


4) 2 3  x   1 . What would you multiply both
3 5  y 

 
0 
 
sides of the equation to solve?
A)  5  3 B) 2 3 C)  3 5 D)  1
 3

2 
3 5


2

1
0
 
5) 7  9  x   2 . Which of the following shows
 4  5  y   3 

   
how to solve for x and y?
 x  5
A)  x     5 9 2 B)    
 y    4 7   3
 y  4
  
 
C)  x   7  9 2 D)  x   1 5
 y  3 4
 y   4  5  3 
 

  
 
1

3


6) [A] =
. Find |A|
 4  6


A) -6 B) 12 C) -18 D) 6
7)
2 3
x
5
A) -7 B) 9
 31 . Solve for x
C) 7
D) -6
 6  2
 5 3
 6  2
 5 3
Review #3 Algebra II EOC
Name:_____________
Solving for a Matrix or for x and y….
Type in each answer choice to see if it works
2 1
6 11
8) Solve for B: 3
  5 6   2 B  7 1 




1 2 4  6  0
4 
8  D)  0
B) 
C)






3 4 7 9  22 17  11 17 / 2
A) 
9) Solve for x and y
y  1 9 
 3 x  2  x


4

y  2 7  x  2  4

Writing and Solving System of Equations with
Matrices.
A) Rewrite the equations (if necessary) so that
both variables are on the left side under each
other and the non-variables are on the right side.
It will be referred to as “matrix-ready form.”
*Example of non-matrix ready form
2x - y = -6
2x = 9 + 3y (y needs to be on the left side)
*Example of Matrix-Ready form
2x - y = -6
2x – 3y = 9
B) Write a matrix equation with the four numbers
on the left making the 2x2 and the two on the
right making a 2x1.
**If there is no variable then the number is 0
**If there is a variable and no number then the
number is 1
Example from above: 2  1  x    6
2  3  y   9 

   
C) Solve by using matrices (see top of back side
for instructions) [A]-1[B]
***Top letter will be top answer
**A 3 variable/equation is solved the same way
except [A] is a 3x3 and [B] is a 3x1
Word Problems:
1)Label your variables (h=hamburger etc..)
2) Write equations
3) Solve using matrices
A)x=5,y=3 B)x=2,y=1 C)x=2,y=-5 D)x=3,y=4
10) Which matrix equation would be used to solve
the following system of equations:
2x – 3y = 5 & 4x + y = 6
A)  2 5  x   0 B) 2  3  x   5
  3 1  y 

 
7 
 
4

0   y 
6 
 
C) 2  3  x   6 D) 2  3  x   5
 4 1   y  6 
 4 1   y  5 

   

   
11) Which matrix equation would be used to solve
the following system of equations:(No mult. choic.
x + y = 10 & 2x – z = 9 & x – y = z
12) Which matrix equation would be used to solve
the following system of equations:
x=5+y & y=6
A) 1  1  x    5 B) 1  1  x   5
0 1   y   6 
0 1   y  6

   

   
1

1
x

5
1
1
x   5









C)
D)
1 0   y    6 
1 1  y    6 

   

   
13) Solve for y: 2x – 3y = -2
5x + y = 29
A) 5 B) 4 C) -4
D) 3
14) Solve fo x, y, and z:
8x – 2y – z = 10
-12x + 2y – 2z = 2
4x + 4y – 3z = 20
A)(2,2,2) B) (-1, 8, 13) C) (3/4,1/2,-5) D) (-3.75, 0,1)
15) Together, Alan, Philip and Grant have $31.
Philip has $3 less than Alan. Grant has one more
than Alan and Philip combined. Find how much
Grant has.
A) $6 B) $9 C) $12 D) $16
16) Shaun has a combination of 31 quarters and
dimes. He has $5.95 total. How many of each
does he have?
A)13 quarters & 18 dimes B)15 quarters & 16 dimes
C)17 quarters & 14 dimes D)19 quarters &12 dimes
Review #3 Algebra II EOC
Name:_____________
Regression Equations
1) “Diagnostic on”: 2nd 0 scroll“DiagonosticOn” Enter
2) Enter data:STAT EDIT Enter x’s into L1
y’s (dependent variable) into L2.
*Let t=0 be the beginning year.
3) Look at data: 2nd Y= ENTER Highlight ZOOM 9
4) Make a prediction equation:
STAT  and choose the regression (lin,
quad,exp) Analyze regression: If r and/or r2 is very close to
one, then it’s good regression. r is the coefficient of
correlation. Closer to 1 or –1 is ideal .
5)Putting equation in calculator Y= VARS 5 
 1 GRAPH
Or go to y= and type in equation
6) Go to tableset and Table to look at values:
2nd Window Tblestart=1 Tbl=.1 2nd Graph
**y-intercept is the starting value; slope is the
change of y/x.
17) What does a correlation coefficient of .7
mean?
A) strong positive B) weak positive C) strong
negative D) no correlation
18) Which quadratic equation models the
following table:
Day
0
1
2
3
4
5
Price($) 540
520 480
420
340
240
2
2
A) y=10x – 10x + 540 B) y=-10x +10x – 540
C) y = -10x2 – 10x + 540 D) y = 10x2 + 10x – 540
19) Which equation is the best to model the
following table (Let x=0 be 1950)
Year
1950
1955
1960
1970
1975
Price($) 5
5.52
6.10
7.43
8.203
A) y=.128x+3.91 B) y=.0012x2+.097x + 5.00197
C) y=5(1.02)x
D) y = .128x - 245.593
Wind speed
Windchill
5
7
10
3
15
0
20
-2
25
-4
30
-5
35
-7
40
-8
20) According the quadratic model, what does
the equation predict if the wind is 12mph?
A) 10 B) 20 C) 3o D) 5o
21)
Time (s)
1
4
6
10
Stairs climbed 2.3 3.2 3.8 5
According the linear model, what is the slope and
y-intercept and what do they represent?
No mult. Choice