Dr chung 63tips 16tests

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Dr. John Chung”s Fifth Edition

SAT Math

16 Complete Tests

SAT isa registered trademark of the College Entrance Examination Board, which is not involved in the productionc
jor r

COPYRIGHT BY DR. JOHN CHUNG

Dr. John Chung”s

SAT MAT

Fifth Edition

Good Luck!

Copyright by Dr. John Chung
Made in the USA

Copyright by Dr. John Chung-2018
Made in the USA

————' CONTENTS

63 TIPS

TIP 01 Linear Function Page 008
Page 012

TIP 02 | Rate of Change
Page 014
TIP 03 Parallel and Perpendicular Lines
Page 015
TIP 04 | Midpoint and Distance between Two Points Page 016
Page 018
TIP 05 | System of Linear Equations Page 019
Page 020
TIP 06 =| Area enclosed by Lines Page 022
Page 023
TIP 07 | Line Reflection
Page 025
TIP 08 =| Quadratic Function Page 026
Page 027
TIP 09 = | System of Linear and Quadratic Equations
Page 028
TIP 10 | System of Linear Inequalities Page 029
Page 030
TIP 11 System of Linear and Quadratic Inequalities Page 031
Page 032
TIP 12 Area enclosed by Curves
Page 033
TIP 13 Domain and Range
Page 034
TIP 14 | Composition of Function
Page 035
TIP 15 | Function Undefined
Page 036
TIP 16 | Identical Equation Page 037

TIP 17 | Even and Odd Functions Page 038

TIP 18 | Factoring Page 039
Page 040
TIP 19 Direct Variation (Direct Proportion)
Page 041
TIP 20 | Inverse Variation

TIP 21 Sum and Product of the Roots of a Quadratic Equation

TIP 22 | Remainder Theorem

TIP 23 | Factor Theorem

TIP 24 Circle in the xy-plane

TIP 25 | Average Speed

TIP 26 | Percentage

TIP 27 Ratios and Proportion

——————n CONTENTS Cc

TIP 28 | Ratios in Similar Figures Page 42
Page 44
TIP 29 | Percent ofa Solution (Mixture) Page 45
TIP 30 | Exponents Page 46
TIP 31 | Exponential Growth and Decay Factor Page 47
TIP 32 | Defined Operations Page 48

Tip 59 | Two-way frequency table
Tip 60 | Two-way relative frequency table

Tip 61 | Statistical Study and Sample Technics
Tip 62 | Confidence Interval and Margin of Error

Tip 63 | Solid

CONTENTS _——— ]

Tips Answ s and Explanations: Page 87 Page 111
Page 145
Practice Tests Page 173
Page 201
Practice Test 01 Page 231

Practice Test 02 Page 261
Practice Test 03 Page 291

Practice Test 04 Page 415
Practice Test 05 Page 445
Page 473
Practice Test 06 Page 503
Practice Test 07 Page 533
Practice Test 08 Page 561
Practice Test 09
Practice Test 10
Practice Test 11
Practice Test 12
Practice Test 13

Practice Test 14
Practice Test 15
Practice Test 16

Dr. John Chung’s
SAT Math

63 TIPS

cD Linear Function

The functions are called “linear” because they are precisely the functions whose graph in the xy-pl ane is a straight
line.

Such a function can be written as

1) Slope-intercept form
f(x) =mx-+b, where m is the slope and ở is the y-intercept,

2) Point-slope form

yon m(x— x,), where (x;,),) is the known point on the line.

3) General form
ax+by+c=0

4) Standard form
ay+bp=e
Note: The slope between any two points on the line is constant. Note:
Ay £8)—45) Ty, = Fm) 4 = s(n]

Notation of a point:

1) x and y coordinates: P(x
2) P(x, f(x)
3) f) y

Example means a point(—3
f(3)

SAT Practice

1, Fora linear function f, f(0)=2 and f(3)=5. If 2. The table above shows some values for the function
f. If f isa linear function, what is the value of
k= (5), what is the value of k? a+b?
A) 24
A)S B) 36
B) 6 ©) 48
€)7
DB) s D) 60

3. Allinear function is given by ax+dy+c=0 and @>0,b<0, and c>0. Whicofhthe following graphs best

represents the graph of the function?

A) „+ B)

x oO

©) tý D)
+

4. If f isa linear function and f(3)=2 and

ƒ(S)=6, what is the y-intereepL ofthe graph of /?

A) 4
B) 2
€) -2

D) -4

6. The graph ofa function f is shown in the
above. If b = 2a, what is the value of a?

A B) >5 15
) l u 4 C) —
13

5. If/ isalinearfunctionand ƒ@)=-2 and

ƒ(4)=~—4, what is the x-intercept of the graph of / ?

A)3
B) 2.5
@ 2
D) 0

Dr. John Chung's SAT Math 63 Tips

x [f((xx) , 3»

-1| 6 P(8,)
0| 4
1 2 5 x
2 0
-
7... The table above shows some values of the linear
function ƒ' for selected values of x. Which of the 10. In the +y-plane above, a circle is tangent to lìne
following represents the function /?
A) /@)=4-x , the x-axis, and the y-axis, If the radiofutshe

B) f(x) =4-2x circle is 5, what is the value of 1?

€) /@)=4+2x A)7

D) /(x)=4+x B)8

€9
D) 10

'cusa 11. If / isa linear function and (3) =6 and

5 (C) are related by the = 12, what is the slope of the graph of
8. Fahrenheit (F) and Celsius
A)2
equation above. If Fahrenheit temperature increased
B)3
by 27 degrees, what is the degree increase in Celsius? G4
D) 5
A) 15
B) 20

C) 32
D) 81

9. Inthe formula P= K +60, iPfis increased by 35, 12. Inthe xy-plane above, line£ passes through point ?
and has a slope of — +. What isthe x-intercept of
what is the increase in K?
line /?
A) 35
B) 60 A) (4,0) B)(50) O(60) D)(7,0)
© 80
D) 140

10

x | 7a)

27 oe 5

§ 23

a b

13. The table above shows values of the linear function f-
for selected values of x. What is the value of b?

A) ll
B) 2
OQ 2
D) 42

x I(x)

2 a

5 6

8 b

14. The table above gives values of the linear function f

for selected values of x. What is the value of a+b?

A) 8
B) 10
€ 12
D) 18

15. Inthe xy-plane above, point P(42, m) lies on line £
What is the value of m?
A) 24
B) 30

C) 36
D) 42

Dr. John Chung's SAT Math 63 Tips

Rate of change

1) Fora line, the constant rate ofchange is the slope of the line and the slope is constant no matter what two

points you calculated it on the line.

2) Fora curve, the average rate of change is the slope of the secant line that passes through the two points on

the curve.

Line y Secant: A line which passes through

(x5.92) at two points ofa curve.

Average rate of change

1, What is the average rate of change of SAT Practice

r(x)=4 4 as x changes from 0 to 4? 2. If an object is dropped from a cliff, then the distance,
in meters, it has fallen after ¢ seconds is given by the
A) 2 B)3 €)4 D)§
function d (1)= 4.97, Whats its averag speed
(average rate of change) over the interval between
t=1 and 1=3?

A) 4.9 meters per second

B) 9.8 meters per second

C) 19.6 meters per second

D) 39.2 meters per second

12

Questions 3 and 4 refer to the following information. 1 h(t)
$0
Height of red rose (inches) 0 2
40 10 | 35
2 | 74
30 40 50 60 0 80.
30 19.8
DAYS
40 | 298
50 | 334
60 | 375
7 | 392

80. 39.4

A flower plant is measured every day f. The height, /(¢) inches, of the plant can be modeled by a function which is
shown in the graph and table above.

3. Find the average rate of change in height from 10 to 4. Which of the following intervals has the greatest
70 day
average rate ofchange?

A) From 10 to 20 days
B) From 20 to 30 days
C) From 30 to 40 days
D) From 40 to 50 days

Dr. John Chung's SAT Math 63 Tips 13

Parallel and Perpendicular Lines

1, Two lines are parallel if and only if their slopes {mm} are equal with different y-intercepts{h,,b>}.

2. Two are perpendicular if and only if the product of their slopes is 1. (Negative reciprocal each other)

yf t

Lines are parallel: m, =m, and & #b, Lines are perpendicular: m,=-—— mạ or mm, =-1

SÁT Practice

1. Which of the following is an equation for the line 3. Which of the following is a linear equation for the

passing through the point (—4, 1) that is parallel to line that is parallel to 3x+4y=12 through the
point (~2, ~3)?

2. Which of the following is an equation for the line

passing through the point (—4, 1) that is perpendicular

to 4a y=3?

A)3

14

Midpoint and Distance between Two Points

‘The midpoint of a line segment: Each coordinate of the midpoint of a line segment is equal to the average of the

corresponding coordinates of the endpoints of the line segment. Given the two end points (41.9) and(a3, y2), the
coordinates of the midpoint M(x,y) ofthe line segment are
x +2, +
M{(x.y)= 7 5

The distance between two points: The distance @ between two points (3, vị} and (x;, v›) iven by the formula

d y›) is divided into two parts, and P is on AB

Note: When line segment 48 with endpoint:

such that A. :PB= 2b then point P is
ax, thx, ay, +b)

(sy) =[ S22

1) Formidpoint, a=1, b=l,and a+b=2 > P(x, y)

SAT Practice

1, Inthe xy-plane, the midpoint of AB is (10, 4), If | 4. Intriangle ABC in the ay-plane, the coordinates of

the coordinates of point 4 are (5,1), what are the point A are (—4, 4) and the coordinates of point

coordinates of point B? B are (4,4). Ifthe area of AABC is 24, which of

A) (53) B) (64) C) (15,7) D)(20, 10) the following could be the coordinates of point C?

L A) (3.8) B) (2,10)

2. Ifpoint M (5, ~3) is the midpoint of the line €) (2-3) D) (-6,-4)

segment connecting point A(2a, b) and point
B(b, a), what is the value of a?

A8 B12 O16 D2 5. If the distance between (a,3) and (b,8) is 13, whatsite
—pl9
3. Line segment AB has endpoints 4(—6,5) and isthe value of ab)?

B(14,10). Ifpoint P ison AB such that A4 B& OR D)I16

AP: BP = :3, what are the coordinates of point P?

A)(4.75) B)(2,7) ©(6,4.8) D)(3,6)

Dr. JOhn Chung's SAT Math 63 Tips 1S

System of Linear Equations

A system of lin ear equations means two or more linear equations. If two linear equations inte that point of
led the solution to the sy tem of equations.

1) The stem has exactly one solution. tem has only one and only one solution.
When two lines ave different slopes, the

2) The system has no solution.

When two lines are parallel and have different y-intercept, the system has no solution,

3) The

When two lines are parallel and the lines have the same y-intercept.

From the standard form for the system of equations,

axthy=c, and œx+by=e;

ou - oáie h One solution
2ncứ há No solution
3) If a
Infinitely many solutions
a bb G

From the slope-intercept form for the system of equations

=mx+h and y=myx+b,

1) If m, # my One solution

2) If m=m, and h +b, No solution

3) If m=m, and bị Infinitely many solutions

SAT Practice

y=§ ax+by=6
4x+ly=17
2. In the sysofteqeuatmions above, a and b are
1. For which of the following values of k, will] constants, If the system has infinitely many solutions,
the system of equations above have no what is the value of a+b?
solution? A6 B4 Ø0 D)-4

A)10 BS CC) D) -10

16

3x+by=3
ax-4y=6

In the sysofteqeuatmions above, a and b are

constants, For which of the following values of {a, b}

will the system have no solution?

A) {-1, 2} B) {1,1}
© {24} D) {3-4}

ax+3y=6
(a~1)x+(a-l)y=2

In the system of equations above, a is a constant, If
the system has no solution, what is the value of a?

A) -3 B) 1 @3 D)§

The cost of long distance telephone call is determined

by a basic fixed charge for the first 5 minutes anda

fixed charge for each additional minute. If a 15-

minute call costs $3.50 and a 20-minute call costs
$4.75, what is the total cost, in dollars, ofa 40-minute
call?

A) 8.25 B) 9.50 C) 9.75 D) 10.25

The tickets fora movie cost $8.00 for adults and $5.00
for children. If the total of 200 tickets were sold and
the total amount of $1360 was collected, how many
adult tickets were sold?

Dr. John Chung's SAT Math 63 Tips 17

lì) 5A Arceacnclosed by Lines

In order to find the area enclosed by lines, mostly we need to find
1) x-intercept, y-intercept,

2) Points of intersection of the lines.

SAT Practice

1. The graph of y= mx +4 is shown in the xy-plane | 3. The grapohf sthe functions f and g are shown in
above. If the area of triangle POR is 6, what is the the xy-plane above, What is the area of ARS
value of m?
A) 25
A)) 2 B)-êi24 ©)O-T=3 YDy) -+-71 B) 50

C)75 h
D) 100

m „ ¡

(2.6)

2. Inthe xy-plane above, line mm and lìne£ are

perpendiculaanrd intersect at point R(2,6). What

is the area of triangle POR?

A) 18
B) 24
C) 32
D) 36

18

Line Reflection

When we look in the mirror, we can see the reflection. Mathematically, the image of figures by reflecting over a given
line are created as follows.
P(x, y) >P(x,—y) Reflecting across the P(x, ») > P(-¥, =x)
Reflecting across the x-axis: P(x, y) > P'(-x, y) P(x, ») > P(-x,-y)
Reflecting rossthe origin:
Reflecting across (he y-a P(x, vy) >P(y, x)

Reflecting across the 3

SAT Practice

1. Inthe xy-plane, line is the reflection of line m — | 3, If the graph of 2x 6 is reflected across the
across the x- xis, If the equation of line m is x-axis, which of the following represents the
— 6, what is the slope of line £? equation of the reflected graph?

A) 2x+3y=-6 B) 2x+3y
YS B-> 1 OF ©) 2x-3y=-6 D)
D)s

2. Inthe xy-plane, line / is the reflection of line m

across the y-axis. If these two lines intersect at point

(a,b), which of the following must be true?

A)a=-2 B)a=0 C)ya= D) a<0

Dr. John Chung's SAT Math 63 Tips 19

Quadratic Function

bra, a quadratic function is a polynomial function in which the highest degree term is of the second

Form Axis of Symmetry Vertex

1) Standard form: f(x)=ar> +he+e (a#0)

2) Vertex form: f(x) =a(x—h) +k (a#0)

a = Vertical dilation factor

3) Factored from: f(x) =a(x—3, -)(x-25), X +X2

where 3; and x, are the roots of the quadratic x= ——

function. _

1) a>0 and y
y
+

Axis of - symmetry =-—b or x= x+y +.“
2a 2

oO Vertex (li, k)

2) a<0 and y Axis of symmetry
vertex(h, k)

Ø

20

Dr chung 63tips 16tests

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