Made in the USA
Preview - tusachduhoc.com
CONTENTS 50 TIPS
Page
50 Tips
1
Tips Answer
75
Test 1
20 PRACTICE TESTS 93
Test 2
121
Test 3
149
Test 4
177
Test 5
203
Test 6
229
Test 7
257
Test 8
283
Test 9
309
Test 10
335
Test 11
361
Test 12
387
Test 13
413
Test14
441
Test 15
467
Test 16
495
Test 17
523
18
551
Test 19
577
Test 20
605
Test
Preview - tusachduhoc.com
Dr.
John Chung's SAT Math
50 TIPS
Dr. John Chung's SAT Math
-1 -
Preview - tusachduhoc.com
50 TIPS
-
2
-
Tip1
Absolute Value
Tip26
Coordinates of a Circle
Tip2
Ratio of Similar Figures
Tip27
Paths in Grid
Tip3
Combined Range
Tip28
Transformation
Tip4
Classifying a Group
Tip29
The Least & Greatest Number
Tip5
Direct Variation
Tip30
Maximum & Minimum
Tip6
Inverse Variation
Tip31
Percentage
Tip?
Special Triangles
Tip32
Proportion & Ratios
Tip8
Exponents
Tip33
Probability
Tip9
Geometric Probability
Tip34
Number of Guarantee
Tip10
Domain & Range
Tip35
Midpoint & Distance
Tip11
Linear Function
Tip36
Odd & Even Numbers
Tip12
Triangle Inequality
Tip37
Inequality
Tip13
Permutation & Counting
Tip38
Solids
Tip 14
Handshake
Tip39
Sequences & Series
Tip15
Percent of Solution
Tip40
Defined Operation
Tip 16
Slope of a Line
Tip41
Functions as Models
Tip17
Number of Factors
Tip42
Data Interpretation
Tip18
Composition of Functions
Tip43
Expected Value
Tip19
Consecutive Numbers
Tip44
Counting Digits
Tip20
Must be or Could be True
Tip45
Counting Multiples
Tip21
Sum of Consecutive Numbers
Tip46
Average Speed
Tip22
No Solution
Tip47
Factorings
Tip23
Identical Equations
Tip48
Divisibility & Prime
Tip24
Pythagorean Theorem
Tip49
Rate of Work
Tip25
Similar in Right Triangle
Tip50
Parallel Lines
B
SAT Practice
Preview - tusachduhoc.com
Note: Figure not 1.
In the
figure above,circle P and Q are inscribed in a circle. Ifthe radius ofcircle P is 4, and the radius ofcircle Q is 2, what is the ratio ofthe shadedregion to the area ofthe largest circle?
2.
t.ABC above, AB II PQ II RS and the ratio of the lengths, AQ: QS: SC = 2: 2: 3. Ifthe area of quadrilateral PRSQ is 4 8,what is the area of t.ABC ? In
(A) 84
(B)
2 (A)
92
105 (D) 1 44 (E) 147 (C)
9
4
(B)
drawn to scale.
9
5
(C)
9
(D) 2._
12
(E) }_
12
Note: Figure not drawn to scale. 3.
In the
figure above, PQ is parallel to RS. Ifthe ratio ofthe area of t::,PQM to the area of t::,SRM is 4:9 and the perimeter of t.PQM is 15, what is the perimeter of t.SRM ?
(A) 22.!. (B) (C)
(D) (E)
-
6
-
2 3 3�4
35.!. 2 37.!. 2 39.!. 3
2.
A group of workers can harvest all the grapes from
SAT Practice
10 square meters of a vineyard in .!.. 3
Preview - tusachduhoc.com
minutes. At this rate, how many minutes will the group need to harvest all the grapes from 300 square meters of this vineyard?
3.
1.
(Sol) The area of the vineyard is directly proportional to time. area - 10 - 300 x = 10 minutes. time ---:;--
Ans:
In the figure above, 6.ABC is similar
to t:,,DEF . What is the length of DF ?
(A) 6 (B) 82
}j' -
13 90 (C) 13
10 minutes
(D) 8 (E) 100
13 To make an orange dye, 5 parts of red dye are mixed with 3 parts of yellow dye. To make a green dye, 4 parts of blue dye are mixed with 2 parts of yellow dye. If equal amount of green and orange are mixed,what fraction of the new mixture is yellow dye?
(Sol) Orange Green
5 red + 3 yellow
8 parts 4 blue + 2 yellow 6 parts =
=
To make equal amount, LCM= 24 parts Orange Green
15 red + 9 yellow 16 red + 8 yellow Total
Therefore, there are new mixture. Ans:
-1 0.
17 48
24 parts 24 parts 48 parts
=
=
17 parts of yellow in the
2.
In the table above,
y
is directly proportional to
x, where a* 0. Which of the following is the value of a?
(A)
3
(B) 4
(C) 5
(D) 6 (E) 7
SAT Practice
B
A
c 3.
D
Inthe
figure above,the radius ofcircle 0 is 8 and LAOB 60째 What is the area of 6.AOB?
Preview - tusachduhoc.com
=
1.
Inthe
figure above, ABDE is a square and 6.BCD is an equilateral triangle. If the area of 6.BCD is 16./3, what is the area ofthe square?
.
(A) 8./3 (B) 10.J3
(C) 12,J2
(A) 32
(D) 15,fj,
(B) 32./3
(E) 16./3
(C) 64
(D) 64-J2 (E) 72
B
C
A
D
B
A
figure above, AB = BC = CD = 10 and AE = ED . What is the perimeterofthe figure?
Inthe
(A) 40
Inthe
(B) 100.J2.
(C) 30+10./3
(D) 200,fj, (E) 200./3
16
-
2o.J3 3
NC
figure above, M is the midpoint of AB, AM = MC,and the length of MC is 20. What is the area of 6.ABC?
(B) 50
(E) 30+
-
4.
(A) 200
(D) 30+20./3
.JV
Note: Figure not drawnto scale.
Note: Figure not drawnto scale.
2.
.c
(C) 100.J3
Preview - tusachduhoc.com
TIP 8
52 =25
{
2.
Exponents
43 + 43 + 4 3 + 43 = 2",what is the value of n?
If
( A) 2
(B) 4 (C) 6
5 =b ase
(D) 8
2=exponent
(E) 10
25=power The Operations of exponents
am an= am+n (2) (am r = amn (3) (ab r = a"b" ( 1)
( 4)
(�J = ::
(6)
(ab)" =a"b"
(7) ( 8)
a-n = J_ a" m a-;;= Y
SAT Practice
1.
3.
I
1 I
If m and n are positive and 5m5n-3 20m3n, what is the value of m in tenns of n? =
1 ( A) _ 4n
(B) _i_1 n
4 If { ( -2 )3 ·82 } = (24 r 'what is the positive
(C) _i_3
value of n?
(D) 2n2
( A) 6
(E) 4n2
(B) 7
n
(C) 8
(D) 9
(E) 10
Dr. John Chung's SAT Math
-
17
-
Preview - tusachduhoc.com
Dr. John Chung's SAT Math
TEST 5
Dr. John Chung's SAT Math Test 5
. 203 .
I
AN SWER SHEET
Preview - tusachduhoc.com
231 546 78 109
©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®©
1 2 3 4 5 6 7 8 9 10
9 . ,...
...:.
©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©®© ©©©©©
..!.. ..!.. .
0 1
10
.
_
1
1
0
.
.
0
1
>o2 2 2 2
4 4 4 4 � s s 5
._-
1 1 1 � ..,,, 8
- �� .
.
.
1
1
1
0
0
.
0 1
�3 32 32 32 � 4 4 4
,.c:
�
5 5 5 "";'
� 11 6 6 6
""'
7 7 7 ..,?.. 8
=
8
8
8
...,.
...2, 9 9 9
-
204
-
©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©©
I I .
.
1
1
0
0
11 _
.
.
0 � 1
1
2122 2324 262725 292830 21 22 23 24 25 26 27 28 29 30
�
1_,;;
0
0 "" 1
.
1
.
6 6 6 6 7 7 7 7
6 6 6 6 7 7 7 �
15 . 1
8
3 3 3 3
>: 8
.
1
1
0
0
.
0 1
2 2 2 2'
3 3 3 3
4 4 4 4
8
8
16
- �� I
l l !
0
.
0
.
0
2 2' 2 2
3 3 3 3
4 -4 _...4 .. 4
6 11 6 6 6 7 7 7 7
5 5 5 5 6 6 6 6 7 7 7 7
9 9 9 9
9 9 9 9
5 11 5 5 5 8
8
8
8
8
8
8
8
- ""' -
.
_
1
1
0
8
8 ""
8
.
0
� 1
.
I l
l
0
0
0
!
2 2 2 2 3 3 3 3
4 4 4 4 �
�
5 5 5 5
6 6 6 6 ... 7 ;. 7 .!...
=
8
=
8
8
8
9 9 9 9
.
0
.
0
.
0
J>.<1;:o '!< 1;x1 1 1 1
3 3 3 3
'4 4 4 4 1''-�s" >so<;l;•s(l>so<;I I- .- .6 6 6 6
1'7 1 1 1
8 �
.
��
'2 2 2 2
8
-
�� .
©©©©© ©©©®© ©©©®© ©©©®© ©©©®© ©©©®© ©©©®© ©©©®© ©©©®© ©©©®©
,_
.
,_
8
-
8
-
8
'.'.<1.x1;iar.1 11�;:o 9 I(� 9 9 9
9 � 9 K�
.
©@©®© ©@©®© ©@©®© ©@©® © ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®©
13
6 6 6 6 7 � 7 7
17
.
0 � 1
31 32 33 34 35 36 37 38 39 40
3 3 3 3
8
.
.
34
4 4 4 4 s '; s -s ...
>.ii9 ll 9 9 ...9
9 9 9
.
1
��
3132 33 3536 3738 403 9
2 2 2 2
4 4 4 4 s 5 s s
8
�� -
.
_
0 1
3 3 3 3
8
©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©© ©©©©©
.
'i' 2 i 2' >o
�89
©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®© ©@©®©
12
2 2 2 2
>:
8 ""
9 II 9 9 9
14
11 12 13 14 15 16 17 18 19 20
4 4 4 4 s s s s
6 6 6 6 8
©@©®© ©@©®© © @©®© ©@©®© ©@©®© ©@©® © © ©©®© ©@©® © ©@©® © ©@©®©
..,,,
3 3 3 3
8 ,,.
1112 1314 1516 1718 2019
TE ST #:
18
-�� .
.
.
'i'
1
1
0
0
.
0 1
� 2 2 2 3 3 3 3
v r.4".'(J,X 4 l>.<;I>.<I 4 4
>;= 5 5 5 ::;:= 6 6 6 i;::ic 7 7 .;..�.x 1 1-.z. 1:><:1><1 8
8
8
8
D � �.Xl>.<;I><I
-2, 9 9 9
I
3.
3 D D 3DD 3 D D 3
Two acatbasebal eam areareto15beplselayersected astheatpieplam,tcaheryershowandmany cher.diffIerlftethere nt outcomes are possible? (A) 515 30210 225 in
in
5.
Igreatf -3estspossis -1ble andvalue0 ofs s 2? , what is the ((BA)) --26 02 6 m
n
mn
(C)
(B)
(D)
(C)
(E)
(D)
Preview - tusachduhoc.com
(E)
4.
A/j / 12 4 AB Note: Figure not drawn to scale. point andid. Whatare onis thethe vertlengththeicesfiofgurofthee above, rect an gul ar sol (not shown)? (A) 1413 1516 17 I I I I I I
/)..
Note: Figure not drawn to scale. the Iffigure above,65째 andis perpendicul78째ar t,owhat is the value of ? (A) 2512 3547 53
In
DO .
(B)
(C)
(D)
(E)
AO
LAOC = LBOC
LBOD =
6.
In
_ _ _ _
A
B
AB
(B) (C)
(D) (E)
>
I GO ON TO THE NEXT PAGE . 208 .
IO.f Oxlmgal2lons10of water is added, then =-. Therefore 100 m+x 2 2 xlOO � 10m+l0x=m • O l m lO(m+x)=O. x= m2 -lOm 10 y
b=
--
4.
---
19. (B)
Preview - tusachduhoc.com
Ifd = 160.20, then a = 160 , c = 20 , and Therefore, a+c+d=340. =100% Day 1 and2 � 20-10 10 Day 3 and4 � 4025-25 - 60o/c Day4 and 5 � 6040-40 - 50o/c 30-60 50% decreased Day 5 and6 � --= 60 20-30 Day 6 and � --= 30 33.3% decreased Sianices lefourss thofansix numbers must be less than Since (5 t) = 6 and (3 .1.) = 2 , (5t)(3.1.) =12. Therefore, 13-1-= 12. { 1, 2, 3 } � I 2 -2(1 ) + 1 = -2 (False) { 0, 1 , 2 } � 02 -2(0)+1=1, 1 2 -2(1) +1=0, 2 2 -2(2)+1=1 ( T rue) { -1, 0,1 } �(-1) 2 -2(-1 ) +1=3 (False) 0, 2 �02 -2(0)+l=l(False) (A)
--
--
0
0
7
natievselofy.point PISinnandthceePRHifigures=(22above, ,and0) andQHt(3,he=0coordi )1,respect the area of t:.PQR 2xl is 2 =l. -lOt x-Theintmi(et-10) rceptdpoisn=0.tarefS t5.= 0 and t = 10. �x A TheTherefore, maximtumht�5 heightmumoccursheigatht tis 5. e maxi h(5) =-10(5)2 +100(5) = 250.
20.
5.
7.
6.
(B)
7.
I
s
(B) (B)
2.
3.
(C)
-
43 6
-
(B)
(D)
}
y
SECTION 5
(Proport D) ion: Since 2 minutes is equal to 120 120w seconds, -=w -. 120x Therefore, x = -k=-1, 11-2(-1)1 =-1+4 �3=3.
1.
8.
7,
(E)
{
=
TEST 1 3
(A)
s
O P(8-J3, 0) In the figure above, t:.OPQ is a special tradirianglus,et.hIfe areaOP=ofs,J3,the ciPQrcle=is8.JrSir2n=ce64Jr8 is. the -���......
�--___. x
Preview - tusachduhoc.com
9.
3 a= 3b c = 5b, 5ac = 5(3b)5b = 3. 45 =a =3a. a+3a2 a=l5. --=2a=30 3a = 2.5 ,% and
Since
10.
2.
In the figure above, each triangle has an area of Therefore, the unshaded region has an area of 8.
and larger number
Let smaller number
TimeA�B .!2 and TimeB�A .!2 .
Therefore,
�
or
y
10
17.
8
+
4
and y 8 .
x
48 mph.
82 .
From can be any real number. Or If can be any real number. If = Therefore, the smallest value of
(x + y)(x - y)
x
hours. Therefore,
and Sum.students 8 + Therefore, Summ+n students Thus,
13. 80
x+ x-y=
48mph.
Summstuctents
Therefore,
Thus,
5D � . There1ore, -
16. 4
K(constant)
Inverse proportion:
2D DI
Average speed=
and OB = 4, height
Therefore, the slope of OA
12.
the average speed =
Time A.-.B - + -
B(4, 0)
= 25 AH= 5. 125 (m)(n2 ) = 2 )=m(o.22 ). )(5 2 (0. m= 0.0.2 x2522 125. = 36. y=361 12 9 66 2 = X 20 x )( = 10 =
Since the area is
D
=
Or, use a convenient number. Let distance from is a multiple of because A to B and 40. Now
A
H
D
. The entire time
45.
11.
= 40 . -+ 40 120 60 -= 5 /120 = 60 = 120, 120 . = 12060 12040 = 5 2405 = = 80m 0m 90n= 90n . = m+n = m=4n. mn = 4nn =4. 100 (p -lO)(q -10)=0, pq = 1010,, qp p2 q2 = 102 0 0 102 42 = 60
15. 48
18.
+
or
+
•
B
14. 8
b
Dr.
a
a b
John Chung's SAT Math Test 1 3
, a+b=l8,m+n=24, a+ m n =
In the figure above,
DE II AC
and LDFA = LFA C (alternate angles are congruent). AADF and AVEF are isosceles triangles. Therefore, the 42. b+ + perimeter of ABDE is -
43 7
-
7
7
7
SECTION 7 Time- 20 minutes 16 Questions
7
Tum to Section 7 (Page 2) of your answer sheet to answer the questions in this section .
Preview - tusachduhoc.com
r
Directions: For this section, solve eachproblem and decide which is 1he best of1he choices given. Fill in 1he corresponding circle on 1he answer sheet You may use any available space for scratchworlc.
1 . The use of a calculator is pennitted 2. All nwnbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide infonnation useful in solving 1he problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. All figure lie in a plane unless other indicated 4. Unless otherwise specified, the domain ofany function f is assumed to be set of all real numbers x for which f ( x) is a real number.
"'
�
�
'-
s
G1
0
'i <8 i::
A = trr2 C = 2;rr
...... <U
g
� �
A = Cw
l w � LJwh b 1 A = -bh 2
c V = Cwh
t=j h � V = ;rr2h
c2 = a2 + b2
The numbers of degrees of arc in a circle is 360°. The sum of the measures in degrees of the angles is 1 80°.
�
1.
c
If a six-pack of soda costs k cents, how many individual cans can be purchased for d dollars?
(A) :!_ k
(B) 6dk (C) (D) (E)
lOOd k
2.
45
Special Right Triangles
If the average (arithmetic mean) of 1 0, is 20, what is the average of a and b ?
a, and b
(A) 25
(B) 28 30
(C)
(D) 40 (E) 50
600d
k kd 600
I -
�x s r:t xf3 s
622
-
>
GO ON TO THE NEXT PAGE
Preview - tusachduhoc.com
3.
7
7
7
Abby, Bernard, and Cabin made a total of95 candy bars. Bernard made 5 times as many as Cabin, and Cabin made three times as many as Abby. How many candy bars did Abby make? (A) (B) (C) (D) (E)
5 10 15 45 75
7
y
Note: Figure not drawn to scale. 5.
In the figure above, what is the equation of
line ÂŁ ?
4.
2 (A) y = - - x - 2 3 3 (B) y = --x - 2 2 3 (C) y = -- x - 3 2 2(D) y = x - 2 3 3(E) y = x - 3 2
If O. lk percent of n is 5, what is 3k percent of n ? (A) (B) (C) (D) (E)
15 50 75 120 1 50
6.
If x < 0, which of the following could have solution? I. II. III .
j xj = -x j xj = x
j xj = N
(A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III
>
I GO ON TO THE NEXT PAGE Dr.
John Chung's SAT Math Test 20
-
62 3
-
Preview - tusachduhoc.com
II. lxl == x , for x < 0 , no solution.
III. lxl == N , for any x < 0 will be the solution.
---7.
(C)
The pairs of ( x, y ) are as follows. (1, 1 9) (2, 1 8) (3, 1 7) .... (1 0, 10) . The difference between two numbers must be even integers. Or, Let x - y == k ---- (1) , x + y 20 --- (2) From (1)+(2) 2 x = k + 20 , that is, k + 20 x == -- . 2 Because x is an integer, k should be even integers. ==
8.
(B) The probability that the arrow lands on 5 is -3 8
Year
1
2
3
4
5
Profit
10
12
16
24
28 30 3 1 3 1 .2
Increased by
(B)
8
4
4
2
8
7
1
0.2
In the table, increase faster, but later on slow. (E) is the best representing the table. 14.
(D) From cross-multiplication, 2(a - 2b) == 3(b - 2a) 7b Sa = 7b , a = - . Therefore, 4
(7:)
2 2a -- -7 = == b b 4 15.
(B) 3 k + 3 k + 3k 3 3 k 3 i+k , and (27) 5 == ( 33 )5 = 31 5 Therefore, 1 + k = 1 5 , that is, k = 14 . ==
The expected times= 24 x � = 9 times. 8 9.
2
6
16.
·
==
(B)
5
In the figure above, n(X U Y) == n(X) + n(Y) - n(X n Y) 45 == 25 + 30 - k ' k = 10 10.
(D) Only number of movie Y == 30 - 1 0 == 20
11.
(C)
12.
(B) 2 (n + (n + 1)) = 5n - k , n == k + 2 . Therefore, The larger one is, n + 1 == k + 3
13.
(E)
AB 2 = AD x AC , AB 2 == 3 x 1 5 == 45 . AB == J45
Dr. John Chung's SAT Math Test 20
In the graph, the value of p and t can be obtained from the equation. 3 = -p 2 + 12 . p 2 = 9 , then p == ± 3 . you can find the value of t. The greatest slope will be between (-3, 3) and (-4, -4) . 3 - (-4) = 7 . Therefore, the greatest slope -3 - (-4) =
-
633
-