What formulae does one need to know for Subtest I?
First, I don't recommend that anybody "memorize" the formulae below! Of course, one ought to have mastered them, but preferably through diligent application and practice than through mechanical recitation. Furthermore, these relationships are like to be most adhesive if their "origins" are understood!
Pedagogically too, it is better to expose students to the provenance of a formula: the derivations can be fun, and are almost always gloriously illuminating as they incorporate concepts and skills learnt before!
Anyway, following are the key formulae that ought to be assimilated thoroughly for Subtest I & II! Since it is difficult to format and reproduce the actual relationships and equations - some of them have complicated "operators"! - only their titles or descriptions are provided. The actual formulas can be unearthed by
a) Consulting a regular Algebra II / Precalculus textbook: most college texts have a formula "sheet" on the inside cover
b) "Googling" the description: you're sure to pull up 87587568754344327 pages with the required information (including dating sites for mathematicians!)
1. Factorization
a. (a + b)^2
b. (a - b)^2
c. (a + b)(a - b)
d. (a + b)^3
e. (a - b)^3
f. a^3 - b^3
g. a^3 + b^3
2. Lines
a. Distance, Mid-Point and Slope of a Line Formulae
b. Equation of a line in Slope Intercept Form and Point-Slope Form
c. Condition for Parallel and Perpendicular Lines
3. Quadratic Functions & Equations
a. Quadratic Formula
b. Equation of a Parabola in Standard Form, Vertex Form, Intercept Form
c. Axis of Symmetry, Vertex & X-Intercepts of a Parabola in Standard Form, Vertex Form, Intercept Form
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4. Exponential and Logarithmic Functions
a. General Form of the Exponential Growth and Decay Functions
b. Product, Quotient and Power Laws of Exponents
c. General Form of the Logarithmic Function
d. Properties of Logarithmic Function
e. Product, Quotient and Power Laws of Logarithms
f. Continuous Compounding Formula
5. Conic Sections
a. Standard Equation of Circles
b. Standard Equation of Parabolas [Up/Down and Right/Left]
c. Standard Equation of Ellipses [Up/Down and Right/Left]; formula for Foci of Ellipse
d. Standard Equation of Hyperbolas [Up/Down and Right/Left]; formula for Foci and Hyperbola; Slope and Equation of Asymptote of Hyperbola
6. Matrices and Determinants
a. Inverse of a 2X2 Matrix
b. Cramer's Rule for Solving Systems of Equations using Determinants
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7. Vectors
a. Magnitude & Direction of a Vector
b. Unit Vector
c. Dot & Cross Product of 2 Vectors
d. Condition for Parallel & Orthogonal Vectors
e. Trigonometric Ratios and values for 30-45-60-90 degrees
f. Convert degrees to radians and vice versa
8. Sequence and Series
a. n-th term of an Arithmetic Sequence
b. Sum of n terms of an Arithmetic Sequence
c. n-th term of a Geometric Sequence
d. Sum of n terms of a Geometric Sequence
e. Sum of Infinite terms of a Geometric Series
9. Binomial Theorem
a. Binomial Expansion
b. (r + 1)-th term of (x+ y)^n
10. Area, Perimeter & Volume Formulae
a. Area and Perimeter of Square, Triangle, Rectangle, Parallelogram, Trapezoid, Circle
b. Ratio of sides in a 30-60-90 and 45-45-90 triangle
c. Area of an Equilateral Triangle
d. Surface Area and Volume of Prisms, Cylinders, Cones, Pyramids and Spheres
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