Summary of Formulas - Barron's SAT Subject Test Math Level 2

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: ww38, 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 ) = ww39

Coordinates of the midpoint between two points = ww40

Distance between a point with coordinates (x1,y1) and a line Ax + By + C = 0 = ww41

If 299 is the angle between two lines, tan ww42, where m1 and m2 are the slopes of the two lines.

Quadratic Functions

General quadratic equation: ax2 + bx + c = 0

General quadratic formula: ww43

General quadratic function: y = ax2 + bx + c

Coordinates of vertex: ww44

Axis of symmetry equation: ww45

Sum of zeros (roots) = ww46

Product of zeros (roots) = ww47

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

ww48

Length of arc in circle of radius r and central angle 299 is given by image.

Area of sector of circle of radius r and central angle 299 is given by ww49.

Trigonometric Reduction Formulas

ww50

In any ww51ABC:

Law of sines: ww52

Law of cosines: ww53

Area = ww54

1.4 Exponential and Logarithmic Functions

Exponents

ww55

Logarithms

ww56

LogbN = x if and only if bx = N

1.6 Miscellaneous Functions

Absolute Value

If x q14 0, then |x| = x.

If x < 0, then |x| = –x.

Greatest Integer Function

[x] = i, where i is an integer and i q13 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

ww57 = 1, major axis horizontal

ww58 = 1, major axis vertical,

where a2 = b2 + c2.

Standard Equation of a Hyperbola

raj14 =1, transverse axis horizontal

ww59 =1, transverse axis vertical

where c2 = a2 + b2.

Polar Coordinates

ww60

2.2 Three-Dimensional Geometry

Distance between two points with coordinates

ww61

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

  Ax + By + Cz + D = 0 = ww62

Triangle

ww63bh ; b = base, h = height

ww63ab sin C; a, b = any two sides, C = angle included between sides a and b

Heron’s formula:

  ww64; a, b, c are the three

  sides of the triangle, ww65

Rhombus

Area = bh = wwhalf 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 ww66

Lateral surface area ww67

Total surface area ww68

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

Sphere

Volume ww69

Surface area = 4πr2

In all formulas, r = radius

CHAPTER 3: NUMBERS AND OPERATIONS

3.1 Counting

Permutations

ww70, where n! = n(n − 1)(n − 2) · · · 3 · 2 · 1

Combinations

ww71

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

ww72

3.4 Sequences and Series

Arithmetic Sequence (or Progression)

nth term = tn = t1 + (n – 1)d

Sum of n terms ww73

Geometric Sequence (or Progression)

nth term = tn = t1rn–1

Sum of n terms = Sn ww74

If ww75

3.5 Vectors

ww76

Two vectors are perpendicular if and only if ww77.

CHAPTER 4: DATA ANALYSIS, STATISTICS, AND PROBABILITY

4.2 Probability

ww78

Independent events: P(A ww79 B) = P(A) · P(B)

Mutually exclusive events: P(A ww79 B) = 0 and P(A ww80 B) = P(A) + P(B)