Heart of mathematics exam
Exam guide
Ch 1:
1. Fill the 3 oz cup, pour it into the 5 oz cup, which has 2 oz left empty.
Fill the 3 oz cup again and pour it into the 5 oz cup until that cup is full. You now have 1 oz in the 3 oz cup. Dump out the 5 oz from the
5 oz cup. Pour the 1 oz into the 5 oz cup. Fill the 3 and dump it into the 5 oz cup, giving 4 oz.
2. player 2 marks exactly the opposite. For example, if player 1 begins the game by writing X in the first square, then player 2 should write
O for the first square, and vice versa. Works for all size boards
3. separate into groups of 3 on scale
4. Just do it. Make mistakes and fail, but never give up. Keep an open mind. Explore the consequences of new ideas. Seek the essential.
Understand the issue. Understand simple things deeply. Break a difficult problem into easier ones. Examine issues from several points of view. Look for patterns and similarities.
Ch 2.1:
5. 9, 13, 17
6. In a box there are 24 total crackers but only 18 possible shapes
7. 3, 12
8. assuming 365 day year there would have to be 366 for guarantee. 13 for birth months
9. with a population of 7 billion there should be 10 matching hairs
10. 3 thousand students
Ch 2.2:
11. 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610
12. tri petaled “trillium”, daisy seeds (21,34), Pineapple (8,13),
Pinecone (5,8), apple has five sections, bananas have 3
13. male honey bee has 1 parent, 2,3,5,8
14. phi=(1+√5)/2, 1.618
15. Fn=F(n+2)-1 , F(n+1)=
16. 2,8,610
17. 8,55,610
18. 3,16,18
19. F18-F16=F17 2584-987=1597
20. (F(n+1))^2+(F(n))^2=F(2n+1), (F(n+1))^2-(F(n-1))^2=F(2n)
21. Arrangement of leaves on a plant stem
Extra topics:
39. mathematician, 1170-1250 AD, Liber Abaci, used hindu-arabic #
40. methods of calculation without abacus
41. made easily accessible for many
42. 570-495 BC
Ch 1:
1. Fill the 3 oz cup, pour it into the 5 oz cup, which has 2 oz left empty.
Fill the 3 oz cup again and pour it into the 5 oz cup until that cup is full. You now have 1 oz in the 3 oz cup. Dump out the 5 oz from the
5 oz cup. Pour the 1 oz into the 5 oz cup. Fill the 3 and dump it into the 5 oz cup, giving 4 oz.
2. player 2 marks exactly the opposite. For example, if player 1 begins the game by writing X in the first square, then player 2 should write
O for the first square, and vice versa. Works for all size boards
3. separate into groups of 3 on scale
4. Just do it. Make mistakes and fail, but never give up. Keep an open mind. Explore the consequences of new ideas. Seek the essential.
Understand the issue. Understand simple things deeply. Break a difficult problem into easier ones. Examine issues from several points of view. Look for patterns and similarities.
Ch 2.1:
5. 9, 13, 17
6. In a box there are 24 total crackers but only 18 possible shapes
7. 3, 12
8. assuming 365 day year there would have to be 366 for guarantee. 13 for birth months
9. with a population of 7 billion there should be 10 matching hairs
10. 3 thousand students
Ch 2.2:
11. 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610
12. tri petaled “trillium”, daisy seeds (21,34), Pineapple (8,13),
Pinecone (5,8), apple has five sections, bananas have 3
13. male honey bee has 1 parent, 2,3,5,8
14. phi=(1+√5)/2, 1.618
15. Fn=F(n+2)-1 , F(n+1)=
16. 2,8,610
17. 8,55,610
18. 3,16,18
19. F18-F16=F17 2584-987=1597
20. (F(n+1))^2+(F(n))^2=F(2n+1), (F(n+1))^2-(F(n-1))^2=F(2n)
21. Arrangement of leaves on a plant stem
Extra topics:
39. mathematician, 1170-1250 AD, Liber Abaci, used hindu-arabic #
40. methods of calculation without abacus
41. made easily accessible for many
42. 570-495 BC