CS 225 Samina Ehsan

Upon entering this class, we expect all students to (red text = math expectations):

  • Know types of numbers and their properties: real numbers, integers (odd and even), natural numbers, rational numbers, irrational numbers, prime numbers, and perfect square numbers. https://en.wikipedia.org/wiki/List_of_types_of_numbers
  • Understand the associative, commutative, and distributive properties of numbers
  • Know how to expand terms: (x+4)(x-1) = x2 + 3x - 4
  • Know how to find a common factor: 6x2 - 2x = 2x(3x-1)
  • Know how to factor quadratic polynomials. For example, know how to factor the quadratic equation x2 + 7x + 6 into (x+1)(x+6). http://www.purplemath.com/modules/factquad.htm
  • Know algebraic formulas: square binomial, cube binomial, difference of squares etc.
  • Know what factorials (the exclamation mark operator, !) are and how to compute them:
  • x ! = x * (x-1) * (x-2) . . . *3 * 2 * 1
  • Know that (x+1) ! = (x+1) * x !
  • Know the laws of exponents: xa * xb = xa+b ; xa / xb = xa-b ; (xa)b = xab ; x-a = 1/xa
  • Know that 2x * 2 = 2x+1
  • Know the laws of fractional exponents: sqrt(x) = x1/2
  • Know about arithmetic and geometric progressions
  • Be able to solve inequalities, for example, “if x - 6 > 12, what values can x have”?
  • Fractions: know how to multiply fractions:
    A / B * C / D = AC / BD
  • Fractions: know how to add and subtract fractions by creating a common denominator:
    A / B + C / D = AD + CB / BD


mjb – July 5, 2017