Barron's SAT Subject Test Math Level 2, 10th Edition (2012)

Summary of Formulas

CHAPTER 1: FUNCTIONS

1.2 Polynomial Functions

Linear Functions

General form of the equation: Ax + By + C = 0

Slope-intercept form: y = mx + b, where m represents the slope and b the y-intercept

Point-slope form: y – y₁ = m(x – x₁), where m represents the slope and (x₁,y₁) are the coordinates of some point on the line

Slope: , where (x₁,y₁) and (x₂,y₂) are the coordinates of two points

Parallel lines have equal slopes.

Perpendicular lines have slopes that are negative reciprocals.

  If m₁ and m₂ are the slopes of two perpendicular lines, m₁ · m₂ = –1.

Distance between two points with coordinates (x₁,y₁) and ( x₂ , y₂ ) =

Coordinates of the midpoint between two points =

Distance between a point with coordinates (x₁,y₁) and a line Ax + By + C = 0 =

If is the angle between two lines, tan , where m₁ and m₂ are the slopes of the two lines.

Quadratic Functions

General quadratic equation: ax² + bx + c = 0

General quadratic formula:

General quadratic function: y = ax² + bx + c

Coordinates of vertex:

Axis of symmetry equation:

Sum of zeros (roots) =

Product of zeros (roots) =

Nature of zeros (roots):

  If b² – 4ac < 0, two complex numbers

  If b² – 4ac = 0, two equal real numbers

  If b² – 4ac > 0, two unequal real numbers

1.3 Trigonometric Functions and Their Inverses

Length of arc in circle of radius r and central angle is given by .

Area of sector of circle of radius r and central angle is given by .

Trigonometric Reduction Formulas

In any ABC:

Law of sines:

Law of cosines:

Area =

1.4 Exponential and Logarithmic Functions

Exponents

Logarithms

Log_bN = x if and only if b^x = N

1.6 Miscellaneous Functions

Absolute Value

If x 0, then |x| = x.

If x < 0, then |x| = –x.

Greatest Integer Function

[x] = i, where i is an integer and i x < i + 1

CHAPTER 2: GEOMETRY AND MEASUREMENT

2.1 Coordinate Geometry

Standard Equation of a Circle

(x – h)² + (y – k)² = r² with
center at (h,k) and radius = r

Standard Equation of an Ellipse

= 1, major axis horizontal

= 1, major axis vertical,

where a² = b² + c².

Standard Equation of a Hyperbola

=1, transverse axis horizontal

=1, transverse axis vertical

where c² = a² + b².

Polar Coordinates

2.2 Three-Dimensional Geometry

Distance between two points with coordinates

Distance between a point with coordinates (x₁,y₁,z₁) and a plane with equation

  Ax + By + Cz + D = 0 =

Triangle

bh ; b = base, h = height

ab sin C; a, b = any two sides, C = angle included between sides a and b

Heron’s formula:

  ; a, b, c are the three

  sides of the triangle,

Rhombus

Area = bh = d₁d₂; b = base, h = height, d₁ and d₂ = diagonals

Cylinder

Volume = πr²h

Lateral surface area = 2πrh

Total surface area = 2πrh + 2πr²

In all formulas, r = radius of base, h = height

Cone

Volume

Lateral surface area

Total surface area

In all formulas, r = radius of base, h = height

Sphere

Volume

Surface area = 4πr²

In all formulas, r = radius

CHAPTER 3: NUMBERS AND OPERATIONS

3.1 Counting

Permutations

, where n! = n(n − 1)(n − 2) · · · 3 · 2 · 1

Combinations

3.2 Complex Numbers

i ⁰ = 1, i ¹ = i, i ^–2 = –1, i ³ = –i, i ⁴ = 1, . . .
(a + bi)(a – bi) = a² + b²

3.3 Matrices

Determinants of a 2 × 2 Matrix

3.4 Sequences and Series

Arithmetic Sequence (or Progression)

nth term = t_n = t₁ + (n – 1)d

Sum of n terms

Geometric Sequence (or Progression)

nth term = t_n = t₁r^n–1

Sum of n terms = S_n

If

3.5 Vectors

Two vectors are perpendicular if and only if .

CHAPTER 4: DATA ANALYSIS, STATISTICS, AND PROBABILITY

4.2 Probability

Independent events: P(A B) = P(A) · P(B)

Mutually exclusive events: P(A B) = 0 and P(A B) = P(A) + P(B)