PSAT MATHEMATICS PRACTICE BOOK 3 TEST BANK WITH SOLUTIONS

SAT
PRACTICE BOOK
WITH SOLUTIONS

, PREFACE



"The struggle is real." That is how I describe my many years of
teaching Mathematics! From finding reference materials that contain
almost everything I need to preparing students for international
assessments like SAT, PSAT, CIE and IB have been quite a huge
challenge because textbooks and other resources vary accordingly.

This practice book contains more exercises with solutions based on
blended SAT Math curriculum. I have compiled as many
questions as possible with corresponding solution for each type.
SAT and PSAT exam preparation exercises are the central
components and main focus of this workbook. I want users of this
book to have an all-in-one go-to material where they can find everything
they need to enhance their Math skills and eventually earn mastery of
the topics.

Preparing students for SAT was my inspiration on why I came up with
designing this practice book. My objective is to be able to help
students achieve 600 points and above. This book is special as it
contains questions with handwritten solutions.

This practice book is a product of my many years of teaching
experience, and it took me a year to finally complete it. I am sure this
will be a big help for students. Though this has a simple structure, I
still suggest that students first review the topics from different
resources, then take hold of this book and solve all practice questions
to attain the target score.




Arif Yetik, MA

, Table of Contents


CHAPTERS

Exponents and Square Roots
Test 1 ………………………………………………………. 1
Test 2 ………………………………………………………. 5
Test 3 ………………………………………………………. 9
Test 4 ………………………………………………………. 13

Polynomials
Test 1 ………………………………………………………. 17
Test 2 ………………………………………………………. 21
Test 3 ………………………………………………………. 25
Test 4 ………………………………………………………. 29

Quadratic Equations
Test 1 ………………………………………………………. 33
Test 2 ………………………………………………………. 37
Test 3 ………………………………………………………. 41
Test 4 ………………………………………………………. 45
Test 5 ………………………………………………………. 49

Functions and Quadratic Functions
Test 1 ………………………………………………………. 53
Test 2 ………………………………………………………. 57
Test 3 ………………………………………………………. 60
Test 4 ………………………………………………………. 63
Test 5 ………………………………………………………. 66
Test 6 ………………………………………………………. 70
Answer Key ………………………………………………………. 74
Solutions ………………………………………………………. 76

,1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
1


1 3
2
Which of the following is equal to b 5 ?
If a = 4 2 and 2a = 4b , what is the value
of b ? 2
A) b5
A) 8
5
B) 16 B) b2
C) 32
C) 2
b5
D) 64
D) 5
b2




2 4
2
x
If a 2 = a 54 , a > 1 and x - y = 6 , what is the m+3 -n =0
ay In the equation above, if n = 6 , what is the
value of x + y ? value of m?
A) 3 A) 3
B) 9 B) 9
C) 24 C) 27
D) 27 D) 33




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,1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
1


5 7
3 1
-3
Which of the following is equal to 25 4 ? Which of the following is equal to a × b ?
2

-4
a ×b
A) 3
25
A) a
B) 5 5 2 b
C) 4
5 B) a
D) 5 b
C) 1
-7
a b
D) a ×b 2


b




6 8
If x + 16 = 25 , what is the value of x ? -
1
If a 3
= m, where a > 0, , what is the value of m ?
A) 1
A) 1
B) 9 3
a
C) 6
B) 3
a
D) 9
C) 3
a2
D) 2
a -3




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, 1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
1


9 11

25a 2
1
If a>0, which of the following is equivalent to Which of the following is equivalent to ( 4t ) 3 ?
the given expression?
A) 3
4t
A) 50a4
B) 10a B) 23 t
C) 5a2 C) 1
D) 5a 12t 3
( 4t )
3
D)




10 12

y2 = y
Which of the following values of y is NOT If a3 = b , where b > 0, what is the value of
solution to the equation above? a in terms of b?
A) 2 1
A) b7
B) 1
5
C) 0 B) b 12

D) -2 1
C) b12
3
D) b4




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, 1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
1


13 15

Which of the following is equal to 1 ? If y is positive integer and x = 2 y +3 + 2 y , what
2 +1
is 2 y + 2 in terms of x?
A) 2 1
-
2 2 x
A)
B) 2 -1 9
2 1 B) 4x
C) +
2 2 9
D) C) 13x
2 +1
D) 36x




14 16
If x3 = 30, and y2 = 10 , what is the value
What is the value of 5 8 + 6 32 ?
of ( x × y )6 ?
A) 10 2
A) 3 ´104
B) 11 40
B) 9 ´104
C) C) 34 2
3 ´105
D) 9 ´105
D) 36 2




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,1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
2


1 3

What is the value of 4 50 - 3 32 ? What is the value of 9 24 ?
4 27
A) 8 2
B) A) 3 2
12 40
C) 3 2
20 2 B)
2
D) 32 2
C) 2 2
2 2
D)
3




2 4

If 16b = 2a +5 , what is the value of b ?
-x - y = 5
A) 32 × 2 a
In the equation above, if y = 2 , what is the
B) 2a+ 2 value of x?
A) -49
C) 2 × 2a+ 2
B) -27
D) 2a +1
C) 27
D) 49




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,1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
2


5 7
4x
Which of the following is equal to 25 ? Which of the following is equivalent to
1253 x
1
(a + a + a + a) × (a + a) ?
A) 4-1
5
A) 16 × a
B) 1
B) 32 × a
5x
C) 5
C) 16 × a2
D) 5x
D) 32 × a 2




6 8
If 8 = 4 , what is the value of x ?
12 x
Which of the following is equivalent to
A) 9 32 + 4 18 ?
B) 12 8
C) 18 A) 2
D) 36 B) 2 2
C) 8
D) 8 2




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, 1 PASSPORT TO ADVANCE MATH Exponents & Square Roots
Test
2


9 11

If a 2 = 9, b2 = 16, and ( a + 3) × ( b - 4 ) ¹ 0 what If 1 = 3 3 what is the value x?
x
3
is the value of a + b ?
A) 3
A) -2 -
2
B) -1
B) 2
C) 1 -
3
D) 2
2
C)
3
D) 3
2




10
12
If 1
= 2 what is the value x?
x-2 If ( 3,000 ) × ( 4,000 ) = 1.2 ´10m what is the value m?

2+4 A) 6
A)
2 B) 7
2 -4 C) 8
B)
2 D) 9

C) 2 -2
2

D) 2+2
2




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