MATHEMATICS IN THE MODERN WORLD| F3= 2 F10=55
BATANGAS STATE UNIVERSITY| F4=3 F11=89
F5=5 F12=144
F6=8 F13=233
1. Pick a number. Multiply the number by
7. A student has 8 cups of iced tea in a
8, add 6 to the product, divide the sum
pitcher. The amount of iced tea she can
by 2, and subtract 3. Complete the
serve is a function of x, the amount of
procedure for several different numbers
iced tea she pours from the pitcher.
using inductive reasoning.
What is the x-coordinates of this
function?
8n+6/2-3
Answer: X={ 1,2,3,4,5,6,7,8}
8. Daniel’s family planned a vacation 25
Answer: 4n
months from July 2012. What year and
month is their family vacation?
2. Given the sequence -8, 16, -32,…. What
is the 9th term?
2 years and 1 month
Answer: 2048
July 2012- July 2013= 1 year
July 2013-July 2014= 2 years
3. What number comes next in this
July 2014-August 2014= 1 month
pattern? 17, 15, 25, 53, 105, …
Answer: 187
Answer: August 2014
9. Sets and Subsets
4. Operations of Functions
1879- Georg Cantor
If j(x) = √ x+ 6 and k(x) = 9-x, find j(k(-
Set- the collection of a well-defined
1)).
objects
Solution: j=√ x+ 6 Subsets- every element of A is also an
= √ 9−x+6 element of B
= √ 9−(−1 )+ 6 10. Closed
=√ 10+6 A set is closed under operation if the
= √ 16 operation assigns to every ordered pair
=4 of elements from the set an element of
the set.
Answer: 4 11. Each student in a class of 40 plays at
least one indoor game chess, carrom,
5. What is Fibonacci? and scrabble. 18 play chess, 20 play
- Named after the Italian scrabble and 27 play carrom. 7 play
mathematician Leonardo of Pisa chess and scrabble, 12 play scrabble
- Each term is created by adding its and carrom and 4 play chess, carrom
previous two elements and the and scrabble. Create venn diagram.
sequence starts with 0 and 1
6. What is Fibonacci 0 to Fibonacci 15?
F0= 0 F7=13 F14=377
F1=1 F8=21 F15=610
F2=1 F9=34
BATANGAS STATE UNIVERSITY| F4=3 F11=89
F5=5 F12=144
F6=8 F13=233
1. Pick a number. Multiply the number by
7. A student has 8 cups of iced tea in a
8, add 6 to the product, divide the sum
pitcher. The amount of iced tea she can
by 2, and subtract 3. Complete the
serve is a function of x, the amount of
procedure for several different numbers
iced tea she pours from the pitcher.
using inductive reasoning.
What is the x-coordinates of this
function?
8n+6/2-3
Answer: X={ 1,2,3,4,5,6,7,8}
8. Daniel’s family planned a vacation 25
Answer: 4n
months from July 2012. What year and
month is their family vacation?
2. Given the sequence -8, 16, -32,…. What
is the 9th term?
2 years and 1 month
Answer: 2048
July 2012- July 2013= 1 year
July 2013-July 2014= 2 years
3. What number comes next in this
July 2014-August 2014= 1 month
pattern? 17, 15, 25, 53, 105, …
Answer: 187
Answer: August 2014
9. Sets and Subsets
4. Operations of Functions
1879- Georg Cantor
If j(x) = √ x+ 6 and k(x) = 9-x, find j(k(-
Set- the collection of a well-defined
1)).
objects
Solution: j=√ x+ 6 Subsets- every element of A is also an
= √ 9−x+6 element of B
= √ 9−(−1 )+ 6 10. Closed
=√ 10+6 A set is closed under operation if the
= √ 16 operation assigns to every ordered pair
=4 of elements from the set an element of
the set.
Answer: 4 11. Each student in a class of 40 plays at
least one indoor game chess, carrom,
5. What is Fibonacci? and scrabble. 18 play chess, 20 play
- Named after the Italian scrabble and 27 play carrom. 7 play
mathematician Leonardo of Pisa chess and scrabble, 12 play scrabble
- Each term is created by adding its and carrom and 4 play chess, carrom
previous two elements and the and scrabble. Create venn diagram.
sequence starts with 0 and 1
6. What is Fibonacci 0 to Fibonacci 15?
F0= 0 F7=13 F14=377
F1=1 F8=21 F15=610
F2=1 F9=34
