Carol Fisher's Homepage


Throughout the year, you will go through every online Algebra I, Geometry, and Algebra II web exercise,
to assure that your foundational skills are solid and complete.

This review work will largely be done on your own, outside of class.
Feel free to ask review questions during class: however, due to time constraints, we cannot devote much in-class time to this material.
You may get as much help as needed, one-on-one, outside of class.

There will be regular in-class quizzes over this material.
The points accumulated from these review exercises are a substantial part of your grade, so please take them seriously.
Not only will this review help you to do well in this course, but it is also excellent preparation for standardized tests, like the SAT and ACT.
Many of these review exercises will be easy points—take advantage of them!

These review exercises are a WIN-WIN situation:
ones that are difficult for you are filling in gaps in your understanding;
ones that are easy for you are building up your course grade!



Tuesday, September 11 addition

TIMED QUIZZES: one full sheet (30 problems)
AP Calculus AB: 2 minutes, 30 seconds
Precalculus Honors: 3 minutes
Precalculus regular: 3 minutes, 30 seconds
Friday, September 14 expressions versus sentences
expressions versus sentences, concept questions
addition, concept questions
multiplication, concept questions
divisibility, concept questions
basic properties of zero and one
deciding if a number is a whole number, an integer, etc.
deciding if a number is a whole number, an integer, etc., concept questions
addition of signed numbers
addition of signed numbers, concept questions
subtraction of signed numbers
subtraction of signed numbers, concept questions
mixed addition and subtraction of signed numbers
Friday, September 21 fractions with a denominator of 2 to decimal form
the average of two signed numbers
the average of two signed numbers, concept questions
the average of three signed numbers
the average of three signed numbers, concept questions
identifying place values
multiplying by powers of ten
changing decimals to fractions
multiplying and dividing decimals by powers of ten
changing decimals to percents
changing percents to decimals
introduction to sets
interval and list notation
introduction to variables
reading set notation
Friday, September 28 going from a sequence of operations to an expression
going from an expression to a sequence of operations
solving simple sentences by inspection
using mathematical conventions
"undoing" a sequence of operations
solving for a particular variable
Getting bigger? Getting smaller?
scientific notation
significant figures and related concepts
rewriting fractions as a whole number plus a fraction
locating fractions on a number line
fractions involving zero
Friday, October 5 finding reciprocals
determining if a product is positive or negative
multiplying and dividing fractions
practice with the form  a(b/c)
more practice with the form  a(b/c)
renaming fractional expressions
practice with multiples
finding least common multiples
renaming fractions with a specified denominator
practice with factors
adding and subtracting fractions
adding and subtracting simple fractions with variables
divisibility equivalences
Friday, October 12 identifying inequalities as true or false
bigger, smaller, greater, lesser
practice with the phrases "at least" and "at most"
identifying inequalities with variables as true or false
solving equations of the form  xy = 0
recognizing zero and one
writing fractions in simplest form
deciding if a fraction is a finite or infinite repeating decimal
deciding if numbers are equal or approximately equal
rounding decimals to a specified number of places
Tables of Unit Conversion Information (just study this)
classifying units as length, time, volume, weight/mass
practice with unit abbreviations
practice with unit names
practice with unit conversion information
one-step conversions
Friday, October 19 multi-step conversions
rate problems
practice with exponents
practice with order of operations
basic exponent practice with fractions
practice with  xmxn = xm+n
practice with  (xm)n = xmn
practice with  xm/xn = xm-n
practice with  x-p = 1/xp
one-step exponent law practice
multi-step exponent law practice
Friday, November 2 practice with radicals
approximating radicals
writing radicals in rational exponent form
writing rational exponents as radicals
practice with rational exponents
practice with  x  and  -x
practice with products of signed variables
practice with the distributive law
equal or opposites?
recognizing the patterns xn and (-x)n
writing expressions in the form kxn
writing more complicated expressions in the form kxn
writing quite complicated expressions in the form kxn
identifying variable parts and coefficients of terms
combining like terms
simplifying expressions like  -a(3b - 2c - d
basic FOIL
more complicated FOIL
Friday, November 9 simplifying  (a + b)2  and  (a - b)2
simplifying expressions like  (a - b)(c + d - e
practice with the mathematical words and, or, and is equivalent to
recognizing products and sums; identifying factors and terms
identifying common factors
factoring simple expressions
listing all the factors of a whole number
finding the greatest common factor of 2 or 3 numbers
finding the greatest common factor of variable expressions
factoring out the greatest common factor
practice with the Addition Property of Equality
practice with the Multiplication Property of Equality
solving simple linear equations with integer coefficients
solving more complicated linear equations with integer coefficients
Thursday/Friday, November 15/16 solving linear equations involving fractions
solving linear equations, all mixed up
simple word problems resulting in linear equations
solving simple linear inequalities with integer coefficients
solving linear inequalities with integer coefficients
solving linear inequalities involving fractions
simplifying basic absolute value expressions
determining the sign (plus or minus) of absolute value expressions
solving simple absolute value sentences
solving sentences like 2x - 1 = ±5
solving absolute value equations
solving absolute value inequalities involving "less than"
Friday, November 30 solving absolute value inequalities involving "greater than"
solving absolute value sentences (all kinds)
identifying perfect squares
writing expressions in the form A2
factoring a difference of squares
solving simple equations involving perfect squares
solving more complicated equations involving perfect squares
translating simple mathematical phrases
word problems involving perfect squares
basic concepts involved in factoring trinomials
factoring   x2 + bx + c,   c > 0
factoring   x2 + bx + c,   c < 0
factoring trinomials, all mixed up
Friday, December 7 identifying quadratic equations
writing quadratic equations in standard form
solving simple quadratic equations by factoring
factoring  ax2 + bx + c
solving more complicated quadratic equations by factoring
multiplying and dividing fractions with variables
adding and subtracting fractions with variables
writing expressions involving percent increase and decrease
calculating percent increase and decrease
Friday, December 14 problems involving percent increase and decrease
more problems involving percent increase and decrease
locating points in quadrants and on axes
practice with points
the Pythagorean Theorem
the distance formula
the midpoint formula
Wednesday/Thursday, December 19/20 introduction to equations and inequalities in two variables
introduction to the slope of a line
practice with slope
Friday, January 4, 2008 graphing lines
finding equations of lines
point-slope form
horizontal and vertical lines
parallel and perpendicular lines
Friday, January 11 introduction to functions
introduction to function notation
more practice with function notation
domain and range of a function
Beginning Terminology, Points, Lines, and Planes
Friday, January 18 Segments, Rays, Angles
Introduction to Polygons
Introduction to Area and Perimeter
"If ... Then ..." Sentences
Contrapositive and Converse
Friday, January 25 Proof Techniques
More Terminology for Segments and Angles
Angles: Complementary, Supplementary, Vertical and Linear Pairs (algebraic questions)
Angles: Complementary, Supplementary, Vertical and Linear Pairs (concept questions)
Friday, February 8 Triangle Congruence
Relationships between Angles and Sides in Triangles
Exterior Angles in Triangles
Parallel Lines
Friday, February 15 Parallelograms and Negating Sentences
Area Formulas: Triangle, Parallelogram, Trapezoid
Similarity, Ratios, and Proportions
Perimeters and Areas of Similar Polygons
Two Special Triangles
Friday, February 22 introduction to recursion and sequences
arithmetic and geometric sequences
loans and investments
the compound interest formula
Friday, February 29 graphs of functions
basic models you must know
graphical interpretation of sentences like  f(x) = 0  and  f(x) > 0 
graphical interpretation of sentences like  f(x) = g(x)  and  f(x) > g(x
Friday, March 7 composition of functions
advanced set concepts
basic probability concepts
more probability concepts
probability tree diagrams
Friday, April 4 choosing things: does order matter?
factorial notation
combinations and permutations
summation notation
Friday, April 11 mean, median, and mode
measures of spread
introduction to systems of equations
solving systems using substitution
Friday, April 18 solving systems using elimination
simple word problems resulting in a system of equations
introduction to matrices
Friday, April 25 basic arithmetic with matrices
multiplying matrices
vertical and horizontal translations
vertical and horizontal scaling
Friday, May 2 reflecting about the x and y axes; the absolute value transformation
geometric transformations: all mixed up
equations of simple parabolas
Friday, May 9 quadratic functions and the completing the square technique
algebraic definition of absolute value
the quadratic formula
complex numbers
Friday, May 16 arithmetic with complex numbers
equations of circles
introduction to logarithms
properties of logarithms
Friday, May 23 change of base formula for logarithms
introduction to logarithmic functions
introduction to exponential functions
introduction to polynomials

Dr. Carol J.V. Fisher
Monterey, Massachusetts, USA