SAT math IIc summary note
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1. Num Number bers ① Prime Factorization:
Break up a number into prime factors. (2, 3, 5, 7, ... )
× × × × × × × × × × × × × × ② Greatest Greatest Common Factor Factor (GCF): multiply multiply common common prime factors. factors. GCF(100, 54) → × ×
× G C F
× ××
③ Least Common Multiple Multiple (LCM): (LCM):
or
check multiples multiples of the the largest largest number. number.
LCM(100, 54) × ×
2. Func Functi tion on ① : is input value (domain) and (range) is output value. ② one input input and and one out output! output! ③ vertica verticall line line test! test! ④ Inverse Inverse function function → Horizontal line test.
3. Ineq Inequa uali liti ties es (1). What is the range of the result value if the input has a certain period of values. (2). → (between) (3). → or (bigger than big one and smaller than small one) (4). → (5). → or
Joonho Choi PhD rev. 2016
SAT math IIc summary note
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4. linear functions (1). midpoint between and ①
(2). distance between and ①
(3).
① slope between and is ② is y-intercept.
(4). Parallel and perpendicular lines between and ① parallel relationship: ② perpendicular relationship: ×
5. Domain and range in functions (1). domain in function: x values : ≧ ①
②
≠
③ check! vertical asymptotes.
(2). range in function: y values ① check! horizontal asymptotes. ② quadratic functions → check! vertex
6. inverse functions ① change and . ② the inverse functions are reflected by graph.
Joonho Choi PhD rev. 2016
SAT math IIc summary note
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7. odd/even functions (1). odd function ① reflected by origin (0,0). ② ③ : odd number power. ④ si n
(2). even function ① reflected by y-axis. ② ③ ④ cos
8. reflection graphs ① x-axis reflection: → ② y-axis reflection: → ③ origin reflection: → ④ reflection: → ⑤ reflection: →
9. quadratic functions: (1). Vertex
①
② Vertex x-coordinate =
③ Vertex y-coordinate can be max or min of the function.
(2). Quadratic formula ± ① quadratic formula
② solutions = roots = zeros = x-intercepts
(3). number of solutions ① 2 real solutions → ② 1 real solution
→
③ no real solution →
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SAT math IIc summary note
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(4). factoring ① ② ③ ④
10. Exponential functions (1). basic rules ① ⋅
②
③ ④ ⑤
⑥ ⋅
(2). Exponential function ① : decreasing function ② : increasing function
(3). solving
⇒
Joonho Choi PhD rev. 2016
SAT math IIc summary note
5/12
11. logarithmic functions (1). basic rules ① log log log
② log
log log
③ log ⋅ log ④ log ⑤ log ⑥ log ⑦
log
log log
⑧ log ⇒
12. rational functions and limits (1). limit ① factoring ② remove potential zero terms!
13. trigonometry (1). basic trigonometry
c
b
q
a
① si n
② cos
③ tan
④ csc ⑤ sec ⑥ cot
opposite hypotenuse
adjacent hypotenuse opposite a dj acent
si n
cos
tan
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SAT math IIc summary note
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(2). All Student Take Calculus
sin
All
tan
cos
(3). basic rule ① si n cos ② si n si n cos ③ * cos cos si n cos si n
tan tan
④ * tan
(4). radian and degree ① radian(r) to degree = × ② degree(d) to radian = ×
(5). special triangles
30 2
45
60
5
2
3
1
4
45
1
1
3
① ② ③ ④ *
Joonho Choi PhD rev. 2016
SAT math IIc summary note
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(6). amplitude, period and period=
①
:
amplitude= and period=
②
cos :
amplitude=
③
:
period=
④ : amplitude= and period=
⑤ cos : amplitude= and period=
⑥ : period=
(7). sine and cosine laws ① Law of Sines:
si n
si n
si n
② Law of Cosines: cos
A
c
B
b
a
C
Joonho Choi PhD rev. 2016
SAT math IIc summary note
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(8). Section area and arc length
Arc length
q
r
Area
① section area = × ② arc length = ×
×
×
14. Graph shifting (translations) (1). x-direction shifting: → (2). y-direction shifting: → (3). Translations →
: units right and units up.
15. Polar coordinate system (1). polar coordinate system ① is the distance from origin to the point. ② is the angle from x-axis (counterclockwise)
(2). relationship between two systems. ① ② si n
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SAT math IIc summary note
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16. Complex number (1). basic rules
①
② ,
(2). complex plane ① real-axis and imaginary-axis ② x-axis is used by real-axis ③ y-axis is used by imaginary-axis ④ is located on coordinate system ⑤ is the distance from origin to the ( coordinate
17. Conic (1). Circle ① A circle is the located of all points equidistant from a central point. ② ③ Center ( ) and radius
(2). Ellipse ① For two given points, the foci, an ellipse is the locus of points such that the sum of the distance to each focus is constant.
②
③ Center: ( ) and
(3). *Hyperbola ① For two given points, the foci, a hyperbola is the locus of points such that the difference between the distances to each focus is constant.
②
③ Center: ( ) and
④ Asymptotes: ±
Joonho Choi PhD rev. 2016
SAT math IIc summary note
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18. Matrix (1). multiplication ① matrix A × × matrix B × = matrix C × ② the middle number should be same
(2). determinant ① →
(3). inverse matrix ①
(4). how to use a calculator ① → ②
19. Sequences (1). Arithmetic sequence ① ②
(2). Geometric sequence ① ⋅ ②
③
∞
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SAT math IIc summary note
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20. Probability (1). total probability = 1 (2). probability =
desired outcomes total outcomes
(3). “and” = multiplication (×) (4). “or” = adding ( )
21. Combination and permutation (1). Combination: (selecting numbers from total ) ①
(use Calculator)
(2). Permutation: (selecting numbers from total with order) ①
(use Calculator)
(3). The number of permutations of things, of which are indistinguishable, of which are indistinguishable, etc., is
22. Data analysis (1). average (mean) ① average
sum of terms n umber o f terms
② average speed
total distance total time
(2). median: middle number in the sorted list. (3). mode: most frequently appeared number. (4). standard deviation
① A low standard deviation: the data points tend to be close to the mean of the set. ② A high standard deviation: the data points are spread out over a wide range of values.
(5). range = max – min (6). example: ① A set {1, 2, 3, 3, 4, 5, 6, 7, 9} average =
, median = 4, mode = 3, range = 9-1 = 8
② A set {2, 3, 3, 3, 4, 5, 6, 9} average =
, median =
, mode = 3, range = 9-2 = 7
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SAT math IIc summary note
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23. Solid geometry (1). Rectangular solid ① The distance between opposite corners of a rectangular solid
length width height
diagonal
height
width length (2). Right Cylinder ① Volume ② Surface Area
h r
Joonho Choi PhD rev. 2016
