1
General Maths Unit 2
Contents
Rounding to Decimal Places and Significant Figures .......................................................................................... 2
Bivariate Data ........................................................................................................................................................... 5
7A Scatterplots ......................................................................................................................................................... 5
7B How to interpret a scatterplot ............................................................................................................................. 7
Pearson's correlation coefficient ............................................................................................................................ 10
Correlation and causation ...................................................................................................................................... 13
The Coefficient of Determination (Worksheet) ....................................................................................................... 14
7D Fitting a linear model to the data ....................................................................................................................... 15
7E Interpreting and predicting from a linear model ................................................................................................. 18
The Squared Transformation................................................................................................................................. 19
The log transformation ............................................................................................................................................ 22
The reciprocal transformation ............................................................................................................................. 23
Which Data Transformation? .................................................................................................................................. 24
Networks ................................................................................................................................................................ 29
8A What is a graph? ............................................................................................................................................ 29
8B Isomorphic connected graphs and adjacency matrices ................................................................................ 30
8C Planar Graphs and Euler’s Formula............................................................................................................... 31
8D Walks, trails, paths, circuits and cycles ........................................................................................................ 33
8E Eulerian Trails and Circuits & 8F Hamiltonian Paths and Cycles................................................................... 34
8G Weighted Graphs, Networks and Shortest Path Problems ........................................................................... 35
8H Minimum Spanning Trees................................................................................................................................ 35
The Hungarian Algorithm Example.......................................................................................................................... 42
Dummy Activities .................................................................................................................................................... 47
Flow problems ........................................................................................................................................................ 49
Section A: Review of Simple and Compound Interest ............................................................................................ 53
Simple Interest .................................................................................................................................................. 53
Compound Interest .......................................................................................................................................... 54
Section B: Recurrence Relations & Reducing Balance Loans ................................................................................ 56
Section C: Introduction to Finance Solver (CAS) .................................................................................................... 58
Section D: Amortisation Tables .............................................................................................................................. 63
Section E: Converting from Recurrence Relations to Finance Solver ..................................................................... 65
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Rounding to Decimal Places and Significant Figures
Rounding Transum
Decimal places The method for rounding a number is as follows:
1. For the number of decimal places stated, count that number of digits to the right of the decimal
and underline it.
2. The next number to its right is called the ‘rounder decider’.
3. If the ‘rounder decider’ is 5 or more, then round the previous digit up by 1. (round up)
4. If the ‘rounder decider’ is 4 or less then keep the previous digit the same. (round down)
Example 1
Take the number 7.83478.
• To round this number to 2 d.p. underline the second digit after the decimal point: 7.83478. As the
next number (4) is less than 5 the previous digit remains the same. All the following digits are
discarded, to give an answer of 7.83.
• To round the number to 3 d.p. underline the third digit after the decimal point: 7.83478. The next
digit to its right (the ‘7’) is greater than 5, you round the previous digit up by 1, to give an answer
of 7.835.
Example 2
Take the number 0.695.
• To round this to 2 d.p. underline the digit 9. The digit 5 is the ‘rounder decider’. That means
decides that 9 needs to be rounded up by 1 to the number 10.
• 0.695 is therefore rounded up to the final answer of 0.70. (2 decimal places!).
Round the following numbers are to 3 decimal places.
0.00237 0.04951 2345.07 99.99998
Significant figures
Here are the golden rules that you must learn and apply (by practising!) Determine how many
Significant figures are in each of the following.
• All non-zero digits are significant.
o 0.345 (3 s.f.) 123.34 ______ 42.5 _____
• Zeros sandwiched between non-zero digits are significant.
o 4205 (4 s.f.) 32.002 ____
• Zeros that come before all non-zero digits are not significant.
o 0.32 (2 s.f.) 0.00067 _____ 0.00204 _____
• Zeros after non-zero digits within a number without decimals are not significant.
o 523000 (3 s.f.) 10000_______
• Zeros after non-zero digits within a number with decimals are significant.
o 34,000 (2 s.f.) 340.00 ___________
Round the following numbers to 2 significant figures.
0.00237 0.04951 2345.07 99.99998
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NAME ____________________________ SCORE ______
FOLLOW DIRECTIONS
1. Read everything carefully before doing anything.
2. Put your name in the upper right-hand corner of this page.
3. Circle the word NAME in sentence two.
4. Draw five small squares in the upper left-hand corner.
5. Put an “X” in each square.
6. Put a circle around each square.
7. Sign your name under the title of this paper.
8. After the title write, “yes, yes, yes.”
9. Put a circle completely around sentence number seven.
10. Put an “X” in the lower left corner of this paper.
11. Draw a triangle around the “X” you just put down.
12. On the back of this paper, multiply 703 by 66.
13. Draw a rectangle around the word “corner” in sentence four.
14. Loudly call out your first name when you get this far along.
15. If you have followed directions carefully to this point, call out, “I have.”
16. On the bottom of this paper, add 8950 and 9305.
17. Put a circle around your answer and put a square around the circle.
18. Punch three small holes in the top of this paper with your pencil point.
19. If you are the first person to reach this point, LOUDLY, call out, I AM THE FIRST PERSON TO
REACH THIS POINT, AND I AM THE LEADER IN FOLLOWING DIRECTIONS.”
20. Underline all even numbers on the left side of this paper.
21. Loudly call out, “I AM NEARLY FINISHED. I HAVE FOLLOWED DIRECTIONS.”
22. Now that you have finished reading everything, do sentences 1 and 2! Keep busy so that
others will continue to read without disturbance from you. Do not make any sign to give a
clue to your having completed the assigned task.
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General Maths Unit 2
Contents
Rounding to Decimal Places and Significant Figures .......................................................................................... 2
Bivariate Data ........................................................................................................................................................... 5
7A Scatterplots ......................................................................................................................................................... 5
7B How to interpret a scatterplot ............................................................................................................................. 7
Pearson's correlation coefficient ............................................................................................................................ 10
Correlation and causation ...................................................................................................................................... 13
The Coefficient of Determination (Worksheet) ....................................................................................................... 14
7D Fitting a linear model to the data ....................................................................................................................... 15
7E Interpreting and predicting from a linear model ................................................................................................. 18
The Squared Transformation................................................................................................................................. 19
The log transformation ............................................................................................................................................ 22
The reciprocal transformation ............................................................................................................................. 23
Which Data Transformation? .................................................................................................................................. 24
Networks ................................................................................................................................................................ 29
8A What is a graph? ............................................................................................................................................ 29
8B Isomorphic connected graphs and adjacency matrices ................................................................................ 30
8C Planar Graphs and Euler’s Formula............................................................................................................... 31
8D Walks, trails, paths, circuits and cycles ........................................................................................................ 33
8E Eulerian Trails and Circuits & 8F Hamiltonian Paths and Cycles................................................................... 34
8G Weighted Graphs, Networks and Shortest Path Problems ........................................................................... 35
8H Minimum Spanning Trees................................................................................................................................ 35
The Hungarian Algorithm Example.......................................................................................................................... 42
Dummy Activities .................................................................................................................................................... 47
Flow problems ........................................................................................................................................................ 49
Section A: Review of Simple and Compound Interest ............................................................................................ 53
Simple Interest .................................................................................................................................................. 53
Compound Interest .......................................................................................................................................... 54
Section B: Recurrence Relations & Reducing Balance Loans ................................................................................ 56
Section C: Introduction to Finance Solver (CAS) .................................................................................................... 58
Section D: Amortisation Tables .............................................................................................................................. 63
Section E: Converting from Recurrence Relations to Finance Solver ..................................................................... 65
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Rounding to Decimal Places and Significant Figures
Rounding Transum
Decimal places The method for rounding a number is as follows:
1. For the number of decimal places stated, count that number of digits to the right of the decimal
and underline it.
2. The next number to its right is called the ‘rounder decider’.
3. If the ‘rounder decider’ is 5 or more, then round the previous digit up by 1. (round up)
4. If the ‘rounder decider’ is 4 or less then keep the previous digit the same. (round down)
Example 1
Take the number 7.83478.
• To round this number to 2 d.p. underline the second digit after the decimal point: 7.83478. As the
next number (4) is less than 5 the previous digit remains the same. All the following digits are
discarded, to give an answer of 7.83.
• To round the number to 3 d.p. underline the third digit after the decimal point: 7.83478. The next
digit to its right (the ‘7’) is greater than 5, you round the previous digit up by 1, to give an answer
of 7.835.
Example 2
Take the number 0.695.
• To round this to 2 d.p. underline the digit 9. The digit 5 is the ‘rounder decider’. That means
decides that 9 needs to be rounded up by 1 to the number 10.
• 0.695 is therefore rounded up to the final answer of 0.70. (2 decimal places!).
Round the following numbers are to 3 decimal places.
0.00237 0.04951 2345.07 99.99998
Significant figures
Here are the golden rules that you must learn and apply (by practising!) Determine how many
Significant figures are in each of the following.
• All non-zero digits are significant.
o 0.345 (3 s.f.) 123.34 ______ 42.5 _____
• Zeros sandwiched between non-zero digits are significant.
o 4205 (4 s.f.) 32.002 ____
• Zeros that come before all non-zero digits are not significant.
o 0.32 (2 s.f.) 0.00067 _____ 0.00204 _____
• Zeros after non-zero digits within a number without decimals are not significant.
o 523000 (3 s.f.) 10000_______
• Zeros after non-zero digits within a number with decimals are significant.
o 34,000 (2 s.f.) 340.00 ___________
Round the following numbers to 2 significant figures.
0.00237 0.04951 2345.07 99.99998
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NAME ____________________________ SCORE ______
FOLLOW DIRECTIONS
1. Read everything carefully before doing anything.
2. Put your name in the upper right-hand corner of this page.
3. Circle the word NAME in sentence two.
4. Draw five small squares in the upper left-hand corner.
5. Put an “X” in each square.
6. Put a circle around each square.
7. Sign your name under the title of this paper.
8. After the title write, “yes, yes, yes.”
9. Put a circle completely around sentence number seven.
10. Put an “X” in the lower left corner of this paper.
11. Draw a triangle around the “X” you just put down.
12. On the back of this paper, multiply 703 by 66.
13. Draw a rectangle around the word “corner” in sentence four.
14. Loudly call out your first name when you get this far along.
15. If you have followed directions carefully to this point, call out, “I have.”
16. On the bottom of this paper, add 8950 and 9305.
17. Put a circle around your answer and put a square around the circle.
18. Punch three small holes in the top of this paper with your pencil point.
19. If you are the first person to reach this point, LOUDLY, call out, I AM THE FIRST PERSON TO
REACH THIS POINT, AND I AM THE LEADER IN FOLLOWING DIRECTIONS.”
20. Underline all even numbers on the left side of this paper.
21. Loudly call out, “I AM NEARLY FINISHED. I HAVE FOLLOWED DIRECTIONS.”
22. Now that you have finished reading everything, do sentences 1 and 2! Keep busy so that
others will continue to read without disturbance from you. Do not make any sign to give a
clue to your having completed the assigned task.
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