I. ARITHMETIC
A. Whole numbers
1. Operations—addition, subtraction, multiplication, division
2. Prime and composite numbers
3. Factors and divisors
B. Fractions
1. Types—proper, improper, mixed numbers
2. Operations
C. Decimals
1. Operations
2. Conversions
a) Decimals to fractions
b) Fractions to decimals
3. Rounding and approximation
4. Powers of 10
a) Multiplication
b) Division
c) Scientific notation
D. Percent
1. Conversions
a) Percent to decimal
b) Decimal to percent
2. Percent problems
E . Ratio and proportion
F . Square roots
G. Averages
H . Metric measurement
II. ALGEBRA
A . Signed numbers
1. Absolute value
2. Inequality and order of signed numbers
3. Addition, subtraction, multiplication, division
4. Order of operations
5. Grouping symbols
6. Evaluating algebraic expressions and formulas
B. Properties of operations
1. Commutative properties
2. Associative properties
3. Distributive properties
4. Special properties of zero
5. Special properties of one
6. Additive and multiplicative inverses
C . Operations with polynomials
1. Exponents and coefficients
2. Addition and subtraction
3. Multiplication
4. Division
D . Equations in one variable
1. Methods of solution
2. Literal equations
E . Inequalities in one variable
F . Systems of equations and inequalities in two variables
G. Verbal Problems
1. Number
2. Consecutive integer
3. Motion
4. Coin
5. Mixture
6. Age
7. Work
8. Variation—direct and inverse
H. Special products and factoring
1. Common monomial factors
2. Trinomials of the form ax2 + bx + c
3. Difference of two squares
4. Complete factoring
I. Algebraic fractions
1. Simplifying fractions
2. Multiplication
3. Division
4. Addition and subtraction
a) Same denominators
b) Different denominators
5. Complex fractions
6. Equations involving fractions
J . Radicals and irrational numbers
1. Simplifying radicals
2. Addition and subtraction of radicals
3. Multiplication and division of radicals
4. Rationalizing denominators
5. Radical equations
6. Fractional exponents
K. Solution of quadratic equations
1. Factoring
2. Completing the square
3. Formula
L. Graphing
1. Ordered pairs in the plane
2. Methods of graphing linear equations
a) Pairs in the solution set
b) Intercepts
c) Slope and slope-intercept method
3. Parallel and perpendicular lines
4. Graphing inequalities
5. Graphical solution of systems of equations
M . Solution of simple cubic equations
1. Factor theorem
2. Remainder theorem
3. Synthetic division
4. Irrational and complex roots
5. Solving simple cubic equations
III. GEOMETRY
A . Angles
1. Types—acute, right, obtuse
2. Complements and supplements
3. Vertical angles
B . Lines
1. Parallel lines and their angles
2. Perpendicular lines
C. Triangles
1. Sum of the angles
2. Congruent triangles
3. Similar triangles
4. Special triangles
a) Isosceles
b) Equilateral
c) Right (Pythagorean Theorem)
5. Vectors
D . Polygons
1. Quadrilaterals
a) Parallelogram
b) Rectangle
c) Square
d) Rhombus
e) Trapezoid
f) Regular Polygons
E. Circles
1. Special lines and their related angles
a) Radius and diameter
b) Chord
c) Tangent
d) Secant
2. Angle and arc measurement
3. Polygons inscribed in circles
F . Perimeter and area
1. Triangles
2. Polygons
3. Circles
a) Circumference and arc length
b) Area of sectors and segments
G . Volume
1. Pyramid
2. Prism
3. Cylinder
4. Cone
5. Sphere
6. Cube
7. Rectangular solid
H . Coordinate geometry
1. Coordinate representation of points
2. Distance between two points
3. Midpoint of a line segment
4. Slope of a line
5. Parallel and perpendicular lines
I. Basic trigonometry
1. Definitions of sine, cosine, tangent
2. Trigonometry in special triangles
a) 30°–60°–90° triangle
b) Isoceles right triangle
3. Trigonometric problems
a) Angle of elevation
b) Angle of depression
IV. FUNCTIONS AND THEIR GRAPHS
A . Relations and functions
1. Ordered pairs
2. Function notation
3. Domain and range
4. One-to-one functions
5. Inverse functions
6. Combining functions
a) Addition, subtraction, multiplication, division
b) Composition
B. Graphs
1. Linear
a) Slope
b) Intercepts
2. Special functions
a) Absolute value function
b) Step functions
3. Polynominal and rational functions
a) Quadratic—parabola
i. Axis of symmetry
ii. Vertex
b) Cubics
c) Hyperbola of the form xy = k
4. Related non-function graphs
a) Circle
b) Ellipse
c) Hyperbola of the form ax2 – by2 = c
5. Graphs of inverse functions
V. REAL NUMBER SYSTEM
A . Subsets of the real numbers
1. Natural numbers
a) Primes
b) Composites—prime factorization
2. Integers
a) Multiples and divisors
i. Factors
ii. Divisibility
iii. Least common multiple
iv. Greatest common divisor
v. Perfect squares
b) Odd and even integers
3. Ration
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