Math 101:10 December 2017Exam Info
The exam isMonday, December 11, 9am-11:30am in gym, even rows 2-10.
You may bring a calculator and one letter-sized formula card (both sides, write as small as you want, write anything you want). You should also bring your student ID card.
The format of the exam will be written answer questions worth a total of 50 marks.
The material will cover everything we have done. There will be questions that you haven’t seen before (because an exam is supposed to test how well you have learned the material, not just how well you can regurgitate), there will be questions that involve more than one topic (to see that you can make connections), and there will be straightforward questions that are like ones you have seen before (so that you don’t totally freak out).
Tara’s office hours during the exam period (or by appointment):
Tuesday December 5: 1-3pm
Thursday December 7: 1-3pm
The best way to study is to go over old tests and assignments, try sample exam questions (though they are different from what yours will be- they are still good for practice), read through the notes and make sure you know what the key ideas are, do sample problems (see the sample exercises website for good questions and key ideas).
Here is a summary of the material that the exam will cover:
Chapter 1: The Art of Problem Solving (Sections 1.1-1.3)
- Inductive/deductive reasoning
- Different approaches to problem solving
- Triangular numbers/Gauss’ method
- Pascal’s Triangle
Chapter 2: Basic Concepts of Set Theory (Sections 2.1-2.4)
- Basic set theory notation, terminology and operations (union, intersection, difference, complement)
- Venn Diagrams to visualize sets
- Subsets and proper subsets
- Surveys and cardinality
- One-to-one correspondence and infinite sets
Chapter 3: Logic (Sections 3.1-3.4, 3.6)
- Basic concepts from logic: statements (simple and compound), quantifiers (universal and existential)
- Truth tables for different kinds of statements
- Different kinds of compound statements: conjunction (and), disjunction (or), negation (not)
- When statements are equivalent by looking at their truth tables, or by using De Morgan's Laws
- Conditional statements (if p then q), different ways to word a conditional, when a conditional is true and when it is false, what the conditional is equivalent to, what the negation of a conditional is
- Statements related to the conditional: converse, inverse and contrapositive
- How to analyze arguments with truth tables
Chapter 4: Numeration Systems (Sections 4.1-4.4, and addition/subtraction in other bases)
- Different kinds of number systems: simple grouping (ex. Egyptian), multiplicative grouping (ex. Chinese), and positional (ex. our Hindu-Arabic decimal system)
- Egyptian algorithm and lattice method for multiplication
- Positional systems with different bases, so converting between decimal and a different base, and doing addition and subtraction in other bases
Chapter 5: Number Theory (Sections 5.1, 5.2 and 5.5)
- What it means for a number to be divisible by another number
- Prime or composite
- Divisibility tests
- Fundamental Theorem of Arithmetic and prime factorizations
- Search for primes, Mersenne numbers, GIMPS
- Euclid’s proof that there are infinitely many primes
- Fibonacci sequence and the Golden Ratio
Chapter 6: The Real Numbers and Their Representations (Sections 6.1, 6.3, 6.4)
- Important sets of numbers: naturals, whole numbers, integers, rationals, irrationals and reals
- Rational numbers in terms of a fraction or a decimal
- Irrational numbers and their decimal representations
Connections
How do the golden ratio, Fibonacci numbers and Pascal’s triangle connect?