Exam Review Study Guide

As you all know, the exams are coming up soon.This is a review of all the things we've learned in Math this semester, so you better start studying.

You must know how to define:
Translation: a slide along a straight line.
Rotation: a turn around a fixed point.
Reflection: flip over a mirror line.
















Remember: a mirror line can be anywhere, not only as an axis.

Make this shape: (0,0) (3,0) (3,8) (0,8)


Let's hope, you all remember what a coordinate grid is. If not, here's a review.

Cartesian Plain/Coordinate Grid: A vertical, up and down number line, that meets a horizontal number line.
x-horizontal number line
y- vertical number line.
Origin: where the x number line and y number line intersect.
Quadrants: The four regions on a coordinate grid.
Coordinates: the value of an ordered pair.

These are the quadrants on a coordinate grid(I hope you all know your roman numerals)


















You must also be able to identify the signs of each quadrant:

Quadrant 1: (+,+)
Quadrant 2: (-,+)
Quadrant 3: (-,-)
Quadrant 4: (+,-)

Now that you know this, try to find which quadrant each letter is in and it's coordinates.
















A- Quadrant 1 (3,1)
B- Quadrant 1 (1,3)
C- Quadrant 2 (-2,1)
D- Quadrant 3 (-1,-1)
E- Quadrant 4 (2,-2)

What is the horizontal and vertical movements of point C to E?

















4 units horizontal (right)
3 units vertical (down)

Note: The Horizontal movement is always identified first.

Where is the mirror line?

A line intersecting the y axis at positive 1.














If you still having trouble here's a link to a fun site that may be of use. Click here.

Effects of Outliers

Find the mean, median, mode, range, and outliers of the following data sets.

a) 12, 20, 18, 15, 10, 12

First you have to reorder the data set from least to greatest. 10, 12, 12, 15, 18, 20

mean= 14.50 (always round to 2 decimal places.)

median= 13.5

mode= 12

range= 10

outlier(s)= none

b) 48, 32, 67, 47, 95, 89, 888, 1

First you have to reorder the data set from least to greatest. 1, 32, 47, 48, 61, 67, 89, 95, 888

mean= 147.56 (always round to 2 decimal places.)

median= 61

mode= 152.78

range= 887

outlier(s)= 1 and 888


Effects of Outliers

Some outliers need to be removed from a data set. This is typically a judgement call.

Outliers have an effect on all measures of central tendency.


Here is a link that may help you understand outliers better.


HOMEWORK: pgs. 444-445 1-8

Range & Outliers

Range - The positive difference between the largest and smallest values in a set of data.

To find the range:

First, you have to reorder the numbers from least to greatest.
Second, you have to subtract the least number from the greatest number.



Eg.
1. Set of data: 6, 2, 9, 4, 3
a) 2, 3, 4, 6, 9
b) 9 - 2 = 7
Therefore, the range is 7.

1. Set of data: -8, -1, -3, -5
a) -8, -5, -3, -1
b) (-1) - (-8) = 7

Therefore, the range is 7.

Find the range:

1. Set of data: 7, 4, 3, 6, 2, 5, 8, 3
a) 2, 3, 3, 4, 5, 6, 7, 8
b) 8 - 2 = 6
Therefore, the range is 6.

2. Set of data: 11, 8, 8, 5, 7, 6, 7, 6, 6
a) 5, 6, 6, 6, 7, 7, 8, 8, 11
b) 11 - 5 = 6
Therefore, the range is 6.

3. Set of data: -4, 3, -1, 0, 2
a) -4, -1, 0, 2, 3
b) 3 - (-4) = 7
Therefore, the range is 7.




Outlier - Value that is much smaller or larger than the other data values. Also note that, a data set may contain one or more outliers, or none at all.

To find the outlier:
First, you have to reorder from least to greatest.
Second, identify the number(s) which are much greater or lower than the other values.

Find the outliers of the following:






















Here is a link on range.

Here is a video of range and outliers. Enjoy!

Range and Outliers

Range

• The positive difference between the largest and smallest value in a data.

Here are some examples:

1st- Reorder the data by least to greatest
2 ,3 ,4 ,6 ,9

2nd - Find the largest value and smallest value

2 and 9

3rd- Subtract the lowest value to the highest value

9-2=7
Then you'll get your range

Here are some more examples:

-8 , -1 , -3 , -5
reorder
-8 , -5 , -3 , -1
Find the high and low value then subtract
(-1)-(-8)=7

Outliers

• A value that is much smaller or larger than the other data values
  
• A data set may have one or more outliers or no outliers

Find the Range:

a) 7 , 4 , 3 , 6 , 2 , 5 , 8 , 3

2 , 3 , 3 , 4 , 5 , 6 , 7 , 8
8-2=6
6 is your range

b) 11 , 8 , 8 , 5 , 7 , 6 ,7 , 6 , 6

5 , 6 , 6 , 6 , 7 , 7 , 8 , 8 , 11
11-5=6
6 is your range

c)-4 , 3 , -1 , 0 , 2

-4 , -1 , 0 , 2 , 3
3-(-4)=7
7 is your range

Find the outliers:

a) 18 ,19 ,79 ,17 ,20 ,12
12 ,17 ,18 ,19 ,20 ,79 = 79

b) 14 ,14 ,16 ,15 ,1 ,16
1 ,14 ,14 ,15 ,16 ,16 = 1

c) 98 ,202 ,99 ,91 ,2 ,95 ,89 ,88 ,94
2 ,88 ,89 ,91 ,94 ,95 ,98 ,99 ,202= 2 and 202

Here is a website to help you.

Homework:
www.mytextbook.ca
Pages 437 - 439

Finding The Mean

MEAN: A measure of central tendency
-The sum(adding) of a set of values divide by the number of values in the set

E.G 9,5,8,4,9
Step 1: re-order from least to greatest
4,5,8,9,9
Step 2: add up all the numbers
4+5+8+9+9= 35
Step 3: divide the sum of the numbers by the amount of numbers
35 divided by 5= 7
that means that the Mean is 7- A.K.A the average

A) 4+5+6+7+7+7+8+8+9+9=70
70 divided by 10=7
Mean:7 Mode:7 Median:7

B) 250+250+300+300+400=1,500
1,500 divided by 5= 300
Mean:300 Mode:250&300 Median: 7

Here is a video that will help you understand how you find the mean:

Homework and extra practice

Your homework for the weekend is pages 426 - 427 numbers 1 - 17 plus the math link.

Try some of these problems for extra practice: Working With Data 1. List all the four-digit numbers that are even, have a 6 in the tens place, and whose digits add to 12. 2. Is 349 ´ 0.9 greater than, less than, or equal to 349? How do you know? ______________________________________________________________ ______________________________________________________________ 3. Suppose you know that 48 ÷ 16 = 3. Without finding the exact answer, tell whether the answer to 48 ÷ 15.99 is greater than, less than, or equal to 3. Why? ______________________________________________________________ ______________________________________________________________ 4. Use the multiplication below to answer the questions that follow. a) Can E be 2? Explain. ___________________________________________________________ ___________________________________________________________ b) What is the value of D? Why? ___________________________________________________________ ___________________________________________________________ c) What is the value of G? How do you know? ___________________________________________________________ ___________________________________________________________

algebraic equations

This diagram shows a cabin with 1 room has 2 doors, a cabin with 2 rooms has 5 doors, and a cabin with 3 rooms has 8 doors.


draw the next 2 cabins.

how many doors will a cabin have if there are 10 rooms?

write an algebraic equation.



answer

































algebraic expression- y=3x-1

y=3(10)-1
y=30-1
y=29


there will be 29 doors for a cabin with 10 rooms.













2)for the linear relationship y=2x-1 complete the following table of values.






create a graph representing these values.






describe a pattern in real life that the linear relation y=2x-1 could represent. make sure you explain what x and y represent.
















answer











here is a video on algebraic equations.
here is a link


HW

x-4=5, x-2=9, 10=x+6,x+6=8,x/6-5=1,2x+1=7,x/4+3=9,4x-2=12.
solve for x.

Practicing One Step Algebraic Equations and Solving Two Step Algebraic Equations

Today in class, we started off by practicing one step algebraic equations.

3+a=10 b-2=6 3c=9 D=2

3+a-3=10-3 b-2+2=6+2 3 3 5

a=7 b=6 c=3 Dx5=2x5

3+a=10 b-2=6 3c=9 5

3+7=10 8-2=6 3(3)=9 D=10

10=10 6=6 9=9 D=2

5

10=2

5

2=2

Solving two step algebraic equations

*Dude pays $19 for 2 t-shirts and a pair of sunglasses.

How much does dude pay for each t-shirt?

If sunglasses cost $7.00 how much are the t-shirts?

Write an equation

2t+7=19

2t+7-7=19-7 Reverse Order of Operations

2t=12

2 2

t=6

2t+7=19

2(6)+7=19

12+7=19

19=19

Chick saw a sign saying buy two pants and get socks for $2 a pair. If she pays $30 for 2 pants and 4 pairs of socks. What is the price of a pair of pants?

Model using blocks on a scale.

P=pants Socks cost $8

2p+8=30

-8 -8

2p=22

2 2

p=11

2p+8=30

2(11)+8=30

30=30

H.W.

1. 3w+3=6

2. 2n+4=10

Click Here to learn more about solving two step algebraic equations

Solving one step Algebra Equations

Their are 3 steps on solving one step algebra equations. In this blog I'll be showing the method of applying the opposite operation.

Steps on applying the opposite operation
A+5=7 -5=2 1.Isolate the Variable
-5 2. Apply the opposite operation
a=2 3. Check your answer
2+5=7

b-3=5 +3=8

+3
B=8
B-3=5
8-5=3
5=5


C/3=7
21/3=7
7=7
C=21

4D=16
4+12=16
16=16
D=16

(if their is nothing between to letter(s) or number(s) we suppose that it's multiplication)
Click here for a link to a math site that helps with this topic

Here's a video about the topic: