Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Intermediate Algebra Exam 2: Topics and Preparation, Exams of Algebra

The topics that may be covered on the second exam for intermediate algebra, including linear functions, conic sections, and counting principles. Students are expected to understand concepts such as pythagorean theorem, slope of a line, and the geometric definitions of parabolas, circles, and ellipses. They should also be able to perform calculations related to these topics, such as finding the distance between two points, solving linear equations, and expanding powers of binomials.

Typology: Exams

Pre 2010

Uploaded on 09/02/2009

koofers-user-5ef-1
koofers-user-5ef-1 🇺🇸

5

(2)

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
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
pf2

Partial preview of the text

Download Intermediate Algebra Exam 2: Topics and Preparation and more Exams Algebra in PDF only on Docsity!

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 n objects, the number of permutations of n objects taken k at a time, and the number of combinations of n

objects taken k at a time. (You should also know the difference be- tween permutations and combinations!) Be able to solve permutation or combination problems with or without context.

  • Be able to use the distributive law to multiply expressions with several terms. In particular, be able to derive formulas such as

(s + t)^2 = s^2 + 2st + t^2 or (s + t)^3 = s^3 + 3s^2 t + 3st^2 + t^3.

  • Know why the coefficients in the expansion of (x + y)n^ are the same as the combination numbers (^) nCk, and also that they are the num- bers in Pascal’s triangle. (You will not be asked to explain why they are the numbers in Pascal’s triangle.) Be able to use either of these facts to expand powers of binomials, or to find individual terms in the expansion.