MATH 105-142 Intermediate Algebra: Exam 2 Topics
This is a list (not necessarily exclusive) of topics that may appear on the
second exam. Note that there is some overlap with topics from the Midterm,
usually in areas where we have extended or built on the Midterm topic in
the second half of the course.
•Know how to use Pythagoras’ Theorem to find the distance between
two points.
•Know the definition of rate of change of a linear function, or of the
slope of a line. Be able to explain why the slope of a line is constant,
using similar triangles.
•Be able to find a formula for a linear function, given its rate of change
and one pair of input-output values. Equivalently, be able to find the
equation of a line, given the slope of the line and one point on the line.
Be able to solve linear problems with or without context.
•Be able to solve 2 linear equations simultaneously. Know that the
solution corresponds to the intersection point of two lines, be able to
locate the intersection point by graphing, and be able to connect the
algebraic solution to the geometric picture.
•Know the geometric definitions of parabolas, circles and ellipses, know
the standard forms of their algebraic equations, and be able to derive
the equations (especially the equations of a circle or a parabola) from
the geometric definition. (The derivation for a parabola is on Page 202
of the textbook; the geometric definition is in the box on Page 203.)
•Know how to put equations of conic sections (parabolas, circles or
ellipses) into standard form, by completing the square. Be able to
sketch the graph quickly once the equation is in standard form.
•Know the algebraic transformations that correspond to translating the
graph of an equation horizontally or vertically.
•Know the fundamental counting principles (on Page 637 of the Chap-
ter 12 Paul Foerster handout), especially the multiplication principle.
•Know how to use the multiplication principle to count the number of
ways of ordering a collection of nobjects, the number of permutations
of nobjects taken kat a time, and the number of combinations of n
