Transcript Document

Assignment, pencil, red pen, highlighter,
textbook, GP notebook, calculator
Simplify. Write improper fractions as mixed
numbers.
11  2 3 
4 2
2 5
  
2) 3 
3)
1)

15  5 10 
9 3
5 6
31 2
11 2  2 6 3 3 
6 2 5 5 +1
+1

   
 
  
9 3
15 2  5 6 10 3 
6 5 6 5
22  12 9  +1
31 2 3
12 25



 

+1
+1
30  30 30 
9 3 3
30 30
+1
31
6
22
21
37 +1
 

 
9 9
30  30  +1
30
1
25  2 7
7
+1
1
+1
9 +1
30 +1
9
30
total:
12
ab
Rule: x  x  x
adding powers
when
When multiplying powers with the SAME base,
multiplying
the base stays the same and add the
SAME base exponents.
a
b
Examples:
2 2
3
32
2
5
2
32
2
4
x x
4  9
x
5
x
9
2x 6x 
3
4
26 x
12x
7
34
subtracting
powers when
dividing the
SAME BASE
Rule:
xa
ab

x
xb
When dividing powers with the SAME base,
the base stays the same and subtract the
exponents.
Examples:
5
2
2
2
25  2
23
8
18x10
3
24x
18 103
x
24
3x 7
4
Power of a
Power
Rule:
x 
a b
 x
ab
When raising a power to power, the base stays
the same and multiply the exponents.
Examples:
5 4
3 
y 
54
29
3
3 20
2 9
y
18
y
Power of a
Product
Rule:
a
a
x

y
x  y  
a
When raising a product to a power, the exponent is
applied to EACH factor in the product.
Examples:
2x 
2 x
16x 4
4
 5y 
 5 y 
2 3
4
4
3
2 3
 125y6
We will review more rules tomorrow, but let’s
start working in our textbook…
Lona received a stamp collection from her grandmother. The
collection is in a leather book, and currently has 120 stamps.
Lona joins a stamp club which sends her 12 new stamps each
month. The stamp book holds a maximum of 500 stamps.
BB – 1
a) Complete the table below:
Months
(n)
Total Stamps
t(n)
0
1
2
3
4
5
120
132
144
156
168
180
b) How many stamps will she have
after one year?
She will have 264 stamps after one
year.
c) When will the book be filled?
The book will be filled after 32 months.
BB – 1
Lona received a stamp collection from her grandmother. The
collection is in a leather book, and currently has 120 stamps.
Lona joins a stamp club which sends her 12 new stamps each
month. The stamp book holds a maximum of 500 stamps.
d) Write an equation to represent the total number of stamps that Lona
has in her collection after n months. Let the total be represented by t(n).
She starts off with 120 stamps, and gains 12 stamps per month.
Therefore, t(n) = 120 + 12 n
Increase per month
Initial value
e) Solve your equation for n when t(n) = 500. Will Lona be able to
exactly fill her book with no stamps remaining? How do you know?
500 = 120 + 12n
–120 –120
380 = 12n
12
12
n  31.67 months
Since n is not a whole number, then Lona
will not be able to exactly fill her book with
no stamps remaining.
BB – 2
Samantha was looking at one of the function machines in the last
unit and decided that she could create a sequence generating
machine by connecting the output back into the input. She tested
her generator by dropping in an initial value of 8. Each output is
recorded before it is recycled.
a) The first result is 11, then 14, then 17, etc. What operation is the
sequence generator using?
The sequence generator is using “add 3.”
BB – 2
b) When Samantha uses the initial value of –3 and the sequence
generator “multiply by –2,” what are the first five terms of the
sequence? –3, 6, –12, 24, – 48
c) What sequence will she generate if she uses an initial value of 3
and the generator “square”?
3, 9, 81, 6561, …
BB – 3
Samantha has been busy creating new sequence generators
and has created several sequences. Her teacher has also
been busy creating sequences using his own devious
methods. In your book, there is a list of both Samantha’s
sequences and her teacher’s.
With your partner,
(i) Supply the next three terms for each sequence.
(ii) Describe in words how to find the next term.
(iii) Decide whether the sequence could have been produced by
repeatedly putting the output back into the machine as Samantha
did in the previous problem.
BB – 3
(i) Supply the next three terms for each sequence.
(ii) Describe in words how to find the next term.
(iii) Decide whether the sequence could have been produced by
repeatedly putting the output back into the machine as Samantha
did in the previous problem.
Use the following table to organize your work.
(i) Sequence
a) 0, 2, 4, 6, 8, 10
__, 12
__, 14
__
(ii) Describe the pattern
Add 2
(iii) Yes / No
Yes
Continue to fill in the table for parts (B) – (L).
(i) Sequence
a) 0, 2, 4, 6, 8, 10
__, 12
__, 14
__
b) 1, 2, 4, 8, 16
__, 32
__, 64
__
c) 7, 5, 3, 1, –1
__, –3
__, –5
__
d) 0, 1, 4, 9, 16
__, 25
__, 36
__
(ii) Describe the pattern
(iii) Yes / No
Add 2
Yes
Multiply by 2
Yes
Subtract 2
Yes
Add next odd or next square
No
8 9.5
11
e) 2, 3.5, 5, 6.5, __,
__, __
Add 1.5
8 13
21 Add the previous 2 terms
f) 1, 1, 2, 3, 5, __,
__, __
1 1 1
g) 27, 9, 3, 1, __,
Divide by 3
3 __,
9 __
27
5 5
5
h) 40, 20, 10, __, __,
Divide by 2
2 __4
i) 3,–1 –3, –3, –1,3, 9, 17
__,
Add next even number
27
__, 39
__
8 11
j) –4 –1, 2, 5, __,
__, 14
__
Add 3
k) 3, 6, 12, 24
__, 48
__, 96
__
Multiply by 2
Yes
No
125
l) 0, 1, 8, 27, 64, ___,
216
343
___, ___
No
Next cube
Yes
Yes
No
Yes
Yes