| Beginning
Algebra Contents |
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Sets |
Definition
of a set and notation |
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Set
membership |
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Set
builder notation |
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Cardinal
number |
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Ordinal
number |
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Equal
sets
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Subsets
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The
empty set or the null set
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Universal
set or universe
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Power
set
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Operations
on Sets and Venn Diagrams |
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Union,
intersection and difference
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Partition
of a set
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The
fundamental laws of the algebra of sets
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Sets
and Logic |
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The
"and", the conjunction or the logical product
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The
"or", the disjunction or the logical sum
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Logical
negation
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Relations |
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The Cartesian product
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The domain
and the range
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Function
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Relation
on a set
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Reflexive,
symmetric, transitive and equivalent relation |
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Boolean
Algebra |
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Definition
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Basic
theorems
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Boolean
operations on sets
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Logic
Gates and Circuits |
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The
"AND" gate, the "OR" gate and the "NOT"
gate
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Binary
Number System |
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Binary
to decimal conversion
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Decimal
to binary conversion
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Binary
addition
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The
half adder
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The
Binary
addition circuit - the full adder
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Binary
subtraction
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The
method of subtraction by adding the complement of the subtrahend
applied to decimals
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The
method of subtraction by adding the complement of the subtrahend
applied to binary numbers |
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The
Set of Real Numbers - The Real Number System |
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Sets
of
Numbers: |
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Natural numbers |
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Whole numbers |
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Integers |
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Rational numbers |
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Irrational numbers |
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Real numbers |
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The Real Number Line, and Relations |
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One-dimensional coordinate system |
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Unit
interval |
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Relations,
less than and greater than
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Interval definition and notation |
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Distance
and absolute value |
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Distance between two numbers |
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Properties of absolute value |
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Midpoint formula for the real
number line |
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Natural Numbers and Integers – The Basic Operations |
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Addition and subtraction |
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Multiplication and division |
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Order of operations |
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The divisibility rules |
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Prime and composite numbers |
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Prime
factorization |
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The greatest common divisor/factor
(GCD/GCF) |
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The least common multiple (LCM) |
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Fractions |
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Proper and improper fractions |
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Mixed numbers |
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Converting mixed numbers to
improper fractions |
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Converting
improper fractions to mixed numbers |
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Equivalent fractions |
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Comparing fractions |
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Converting and reducing fractions |
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Lowest terms |
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Decimal
fractions |
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Adding and subtracting like
fractions |
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Adding and subtracting fractions |
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Multiplying fractions |
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Dividing
fractions |
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Simplifying complex fractions |
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Decimal
Numbers |
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Decimal representation of rational
numbers or fractions
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Expanded form of
decimal number, decimal fractions
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Whole number part or integer part (integral part) and decimal
places
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Terminating decimals
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Recurring decimals (Infinite
decimals, period) |
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Purely recurring decimals
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Mixed recurring decimals
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Converting decimal number to a
fraction |
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Converting terminating decimal to a fraction |
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Converting the purely recurring decimal
to a fraction |
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Converting the mixed recurring decimal
to a fraction |
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Adding and subtracting decimals |
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Multiplying and dividing decimals
by power of ten
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Place
values and place holders
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Multiplying and dividing decimals
by decimal units
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Decimal numbers scientific notation
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Multiplication of decimal numbers
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Division of decimal numbers |
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Rational Numbers
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Definition |
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Comparing rational numbers
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Equivalent fractions |
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Reducing or simplifying fractions |
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Adding and subtracting rational
numbers or fractions
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Multiplication of
rational numbers
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Reciprocal fractions, multiplicative inverse |
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Division of
rational numbers |
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Simplifying complex or compound
fractions |
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Properties of Real Numbers
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Exponentiation
- Powers or Indices
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Integral exponentiation - integer exponents
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Square or the second power
(potency)
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The square of a product and quotient
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The
rules for the manipulation of powers - Fundamental laws of exponents
(Index laws) |
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Adding
and subtracting same powers |
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Multiplying like bases
with exponents |
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Dividing like bases
with exponents |
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Zero as an exponent |
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Power rule for exponents |
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A product raised to an exponent |
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A quotient raised to an exponent |
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Negative exponents |
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Simplifying an exponential expression |
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Scientific notation |
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Quadratic
equation
x2
=
a,
a
> 0 |
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Square root |
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Properties
of square roots |
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Adding,
subtracting, multiplying and dividing square roots |
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Rationalizing a denominator |
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The
graph of the quadratic function
f
(x)
= x2 |
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Translation of the source quadratic function in the direction of
the y-axis, |
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Quadratic
function of the form f
(x)
= x2 + y0 |
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The principal square root function
- the inverse of the square of x (quadratic) function |
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Definition
of the inverse function |
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The
graph of the principal square root function |
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Translation
of the principal square root function in the direction of
the x-axis |
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Algebraic Expressions
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Terms,
variables, constants - coefficients |
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Monomial, binomial, trinomial, . . . , polynomial
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Simplifying algebraic
expressions |
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Evaluating algebraic expressions |
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Expanding
algebraic expression by removing parentheses (i.e. brackets) |
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Factoring algebraic
expressions, methods |
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Factoring and
expanding algebraic
expressions, rules
for transforming algebraic
expressions |
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Ratios and Proportions
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Ratio
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Proportion
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Ratios
and proportion properties
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Direct proportion
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Cross product, means and extremes
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Proportionality
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Graphical representation of
proportionality
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Proportion practice problems, use
of the rule of three
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Inverse proportion
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Graphical representation of inverse
proportionality
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Coefficient of inverse
proportionality
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Inverse proportion practice
problems |
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Percentage,
Percent
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Percent, decimal number and
fraction conversions |
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Percent - base, rate and portion (part or
amount)
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Basic percent formulas |
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Percent problems
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Percent
increase or decrease
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Linear Equations
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Linear
equation |
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Solving linear equations |
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Applications
of the linear equations, word problems |
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Numbers word problem |
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Geometry and physics word problems
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Linear Inequalities
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Inequality signs
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Properties
of inequalities
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Solving
linear inequalities |
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Polynomial |
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Terms, the degree of a polynomial |
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Addition and subtraction of
polynomials
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Multiplication of polynomials
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Division of polynomials
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Factoring,
factoring by
grouping, GCF (Greatest Common Factor) |
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Factoring
trinomials
and polynomials |
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Rational Expressions
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Simplification of rational expressions, reducing to lowest
terms
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Multiplication and division of rational
expressions
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Addition and subtraction of rational
expressions
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Solving complex rational expressions
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The Rectangular (Two-dimensional,
Cartesian) Coordinate System |
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Rectangular coordinate axes, x-axis
and y-axis,
origin, quadrants
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Ordered
pair (x, y), coordinates of a point (abscissa x, ordinate y) |
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Midpoint of a line segment
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Graphing
Linear Equation, Linear Function (First Degree Polynomial)
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Linear
function f(x) = mx + c |
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The graph of the linear function |
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Slope
or gradient, y-intercept and x-intercept |
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Slope-intercept form of a line
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Properties
of the linear function
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Lines
parallel to the axes, horizontal and vertical lines
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The
point-slope form of a line
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Parallel
and perpendicular lines
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General
form of the equation of a line
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The
two point form of the equation of a line
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| Interest
Calculations |
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Simple interest
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Amount
of interest, principal (start amount), interest rate and amount after n
years |
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Plane
Geometry - Sets of
Points in a Plane |
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Line, a half-line and line segment
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The line segment bisector
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Angle, measurement of angles
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Complementary, supplementary,
alternate and vertically opposite angles
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Angle bisector
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Construction of angles; 60°, 30°, 90°
and 45° (degrees)
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| Plane
Geometry – Plane Figures |
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Triangles |
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Types of triangles
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Main
properties of triangles
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Congruence of triangles
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Theorems about congruence
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Similarity
of triangles, division of a line segment in a given ratio |
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Similarity criteria of triangles
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Area of a triangle
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Right-angled
Triangle
- The Pythagorean Theorem |
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The
Pythagorean theorem |
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Trigonometric functions of an acute angle defined in a right triangle
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Solving the right triangle |
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Equilateral
and Isosceles Triangle
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Equilateral
triangle
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Isosceles
triangle
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Oblique
or Scalene Triangle |
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Properties and rules
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Perpendicular bisectors,
triangles circumcenter
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Angle bisectors, the center of the triangle’s incircle
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The
median, the centroid of a triangle |
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The altitude of a triangle, orthocenter
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Triangle formulas |
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Similarity and congruence of
triangles use
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Congruence |
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Quadrilaterals |
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Square
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Rhombus
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Rectangle |
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Parallelogram |
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Kite
or deltoid
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Trapezium
or trapezoid
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Isosceles
trapezoid
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Cyclic quadrilateral |
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Tangential quadrilateral
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Polygons
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Regular
polygons |
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Circle
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Central angle, inscribed angle
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Construction of a tangent
from a point
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Circumference, length of an arc
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Circle and circular sector
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Circular segment
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Annulus and annulus segment |
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Three-Dimensional (3D) Space |
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Points,
Lines and Planes in Three-Dimensional (3D) Space |
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Position
of two lines in a three-dimensional space
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Coplanar lines and skew lines
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Line and plane in a three-dimensional space
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Two planes in a
three-dimensional space
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The line of intersection of two planes
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Orthogonality of line and plane
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Orthogonality of two planes
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Orthogonal projection of a point onto a plane
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The distance from a point to a plane
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Angle between a line
and a plane, and angle between two planes |
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Solid
Geometry - Three-dimensional geometric figures |
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Prisms |
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Cube |
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Rectangular
prism – cuboid |
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Right
triangular prism |
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Regular
right triangular prism |
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Regular
right hexagonal prism |
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Pyramids |
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Regular
square pyramid |
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Regular
triangular pyramid |
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Regular
hexagonal pyramid |
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Right
pyramidal frustum |
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Solids
of Revolution |
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Cone |
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Conical
frustum |
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Cylinder |
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Sphere |
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Spherical cap |
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Spherical segment |
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Spherical sector |
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Regular
Polyhedrons |
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Tetrahedron |
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Octahedron |
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Dodecahedron |
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Icosahedron |
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| Coordinate Geometry or
Analytic Geometry |
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Plane Analytic Geometry |
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Coordinate
plane, points, line segments and lines
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The distance formula
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The midpoint formula
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Dividing
a line segment in a given ratio |
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Area
of a triangle |
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The
coordinates of the centroid of a triangle |
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| Copyright
© 2004 - 2012, Nabla Ltd. All rights reserved. |