MATH 210, Study Guide for Midterm Test 2

11/16/2012

Test coverage

4. Prealgebra
   1. Letters, algebraic symbols, and expressions (4.1)
   2. Identities, properies, rules (4.2)
   3. Exponents (4.3)
5. Number theory
   1. On logic and proofs (5.1)
   2. Divisibility tests (5.2)
   3. Primes and the Fundamental Theorem of Arithmetic (5.3)
   4. Test of primeness. Factorials and their properties (5.4)
   5. Greatest common factor (divisor) and the least common multiple (5.5)
6. Fractions
   1. Fraction basics: fractional unit, interpretations and models (6.1)
   2. Mixed numbers and improper fractions, addition and subtraction (6.2)
   3. Multiplication of fractions (6.3)
   4. Division of fractions (6.4)
   5. Division word problems (6.5)
   6. Fractions in algebra (6.6)
7. Ratios, Percentages and proportions
   1. Ratios and proportions (7.1)

Key concepts

• Algebra as a way to express key properties of arithmetic calculations
• Algebraic expressions, composing and evaluating algebraic expressions
• Equations, inequalities, algebraic identities and rules
• Teacher's solutions using algebra
• Powers, exponents, rules of exponents
• Logical structure of proofs (proof is a sequence of logical steps)
• Divisibility tests (2, 3, 4, 5, 6, 8, 9, 10, 11)
• Prime and composite numbers. Prime factorization
• Factors (divisors) and multiples
• Greatest common divisor (factor) and Least common multiple
• Factorials (n!)
• Euclid's algorithm
• Fractions, fractional units, denominator, numerator, common denominator and its relation to least common multiple
• Partitive and measurement division with fractions
• Principles of word problem composition
• Simplifying complex (double) fractions
• Ratios, proportions, map scale system

Key types of questions (look for these types in the homework and quiz questions)

• Write an algebraic expression, evaluate an algebraic expression for given values of symbols
• Derive an algebraic identity (using pictures,or algebra)
• Mental math questions! Use algebraic identities, work with fractions, etc. This is guaranteed to be on the test!
• Give a teacher's solution to a word problem, using bar diagrams, or algebra -- you need to know how to do both!
• Test a number for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 11...
• Do the test for primeness, find prime factorization
• Find all factors of a number (prime factorization is helpful!)
• Find GCD and LCM using either prime factorization of Euclid's algorithm -- you need to know both ways
• Compose a word problem on division of fractions (measurement, or partitive interpretation)
• Illustrate arithmetic operations with fractions by bar diagrams/rectangular arrays/number line
• Simplify fractions, simplify algebraic expressions with exponents
• Solve proportions, use them in the context of word problems involving ratios
• Proof-based questions: even and odd numbers, divisibility lemma, homework questions in 5.1 and 5.4.

Here's a selection of sample questions, some of which were discussed in class: Review questions, with Solutions. This list is not all inclusive; make sure to check the homework assignment/quiz problems for other types of questions! Solutions to homework questions are also available, see the main page.