Key Idea 1 - Mathematical Reasoning
1.1 direct Euclidean proof
1.2 direct analytic proof
1.3 indirect Euclidean proof
Key Idea 2
- Numbers and Numeration
2.1 nature of the roots/sum and product of the roots
2.2 rationalize denominators
2.3 simplifying algebraic fractions (polynomial denominators)
2.4 simplify complex fractions
2.5 imaginary unit
2.6 standard form of complex number
Key Idea 3
- Operations
3.1 + , - , ´ , ¸ with fractions with polynomial denominators
3.2 apply composition of transformations
3.3 identify graphs symmetric to an axes or origin
3.4 identify isometries, both direct and opposite
3.5 graphically represent the inverse of a function
3.6 apply transformations on figures and functions in the coordinate plane
3.7 use slope and midpoint to demonstrate transformations
3.8 use transformations to investigate relationships of two circles
3.9 use translation and reflection to investigate parabolas
3.10 absolute value of complex numbers
3.11 evaluate expressions with fractional exponents
3.12 operations with complex numbers
3.13 simplify square roots with negative numbers
3.14 multiply complex number and its conjugate
3.15 cyclic nature of the powers of i
3.16 solve quadratic equations
3.17 laws of rational exponents
3.18 determine value of compound (composite) functions
Key Idea 4
- Modeling/Multiple Representations
4.1 express quadratic, circular, exponential, and logarithmic functions in problems
4.2 use symbolic form to represent an explicit rule for a sequence
4.3 define and graph an inverse variation (hyperbola)
4.4 use positive, negative and zero exponents
4.5 scientific notation
4.6 rewrite log ba = c as a = bc
4.7 solve log equations and exponential equations
4.8 rewrite expressions involving exponents and logarithms
4.9 recognize conic sections: circles, parabolas, hyperbola and ellipse
4.10 solve systems of equations: linear, quadratic, and trigonometric and
exponential
4.11 use Law of Sines and Law of Cosines in a variety of problems involving the resolution of forces
4.12 represent graphically the sum and difference of two complex numbers
4.13 model quadratic inequalities both algebraically and graphically
4.14 model composition of transformations
4.15 sketch the effects of changing the value of a in the function y=ax and emphasize domain, range, the
point (0,1) and the function is one-to-one; if y = ax graph rises, but if
0 < a < 1 graph falls
4.16 note that the graphs y = ax and y = a-x , a
> 0 and 
, are reflections of each other in the y-axis
4.17 note log function is inverse of the exponential function and emphasize domains, ranges, (1,0)
4.18 note the graphs y = ax and x = ay , a >
0 and , are reflections in the line y = x
4.19 solve real world problems using linear, quadratic, trigonometric, and exponential functions
4.20 write equation of circles given center and radius and determine radius and center given equation.
4.21 recognize parabola by equation and be able to graph, find axis of symmetry, y intercepts,
turning point, maximum or minimum
4.22 unit circle including use of radian measure, sine, cosine, tangent and reciprocal trig functions
4.23 use reference angle, amplitude and period
4.24 graph quadratics noting where the graph crosses the x-axis or that it does not
Key Idea 5
- Measurement
5.1 unit circle, including sine, cosine, tangent and their reciprocals, coordinates (cos A,
sin A)
5.2 radian measure definition
5.3 degree-radian conversion
5.4 reference and coterminal angles
5.5 derivation for sine, cosine, tangent and their reciprocals
5.6 sum and difference of two angles
5.7 double and half angles for sine and cosine
5.8 vectors
5.9 angles formed by arcs, chords, tangents and secants/measure of segments
related to a circle
5.10 special angles 30o, 45o, and 60o
5.11 amplitude and period
5.12 inverse functions
5.13 reflections in the line y = x
5.14 Law of Sines
5.15 Law of Cosines
5.16 ambiguous case
5.17 area of triangle using trigonometry
5.18 normal curve (interpretations based on Mathematics B Regents examination
sheet)
5.19 normal curve/distribution
5.20 standard deviation
5.21 Pythagorean theorem, perimeter, circumference, area, and volume
5.22 bias / random sample
5.23 choose appropriate statistical measures
5.24 scatter plots
5.25 lines of best fit
5.26 right triangle proportions
Key Idea 6
- Uncertainty
6.1 determine effects of changing the parameters of graphs of linear, quadratic, exponential, trigonometric and circular functions
6.2 probability of exactly, or at least, at most r successes in n trials of a Bernoulli experiment
6.3 binomial theorem
6.4 linear, logarithmic, exponential and power regressions
6.5 linear correlation coefficient
6.6 measures of central tendency
6.7 sigma notation 
6.8 measures of dispersion
6.9 range
6.10 mean absolute deviation
6.11 variance and standard deviation using the calculator for population and
sample data
6.12 normal approximation for the binomial distribution
6.13 domain and range
6.14 interpolate and extrapolate from graphs of linear, quadratic,
trigonometric, circular, exponential and logarithmic functions
Key Idea 7
- Patterns/Functions
7.1 definition of a relation and function
7.2 determining if a relation is a function
7.3 definition of inverse function
7.4 notation for absolute value, composite functions
7.5 expressing exponential functions as logs
7.6 functions: inverses, exponential, logarithmic
7.7 represent and analyze exponential, logarithmic, quadratic, and trigonometric functions
7.8 relate algebraic expressions to the graphs of functions
7.9 use transformations to investigate the relationships between functions
7.10 find the solution of quadratic equations both algebraically and graphically
7.11 use the quotient identities, reciprocal identities and Pythagorean identities
7.12 discriminant used to determine roots as rational, irrational, or imaginary
7.13 evaluate composite functions
7.14 solve:
a. quadratic
equations
b. fractional
equations
c. radical
equations
d. logarithmic
equations
e. exponential
equations
f. absolute value
equations
g. linear
inequalities
h. absolute value
inequalities
i. quadratic
inequalities
j. first-degree
trig equations
k quadratic trig
equations
7.15 transformations that provide congruence: reflections, translations and
rotations
7.16 direct isometrics
7.17 opposite (indirect) isometrics
7.18 dilations
7.19 inverse functions which are reflections in the line y = x
7.20 standard deviation for grouped data
7.21 use of double-and half-angle formulas