Download Mathayom 1

Answer Key
Mathayom 1
Test: Chapter 4: Factors, Fractions, and Exponents
Directions: You will have 40 minutes to complete this test. Remember to SHOW ALL WORK and LABEL ALL
UNITS!! You may write on the back of the test if you run out of room.
In problems 1-4 tell whether each number is prime, composite, or neither. If the number is composite then find
the prime factorization of the number.
1. 441
2. 175
32 72
52 7
3. 132
4. 19
22 3 11
19
5. Are two prime numbers always relatively prime? Explain
Yes – prime numbers have no factors, and therefore they can’t have any commom factors with each other.
Find the Greatest Common Factor (GCF) of each group of numbers or monomials
6. 48, 196
7. 72, 90, 24
48 = 24 3
196 = 22 72
72: 23 32
90: 2 32 5
24: 23 3
GCF = 22 = 4
GCF: 2 * 3 = 6
30bc 3 , 25b 3c 2 d
8.
9.
15mn , 14m 3 , 55n 2
2 3 5 b c3
52 b3 c2 d
GCF: 5 * b* c2
15: 3 5 m n
14: 2 7 m3
55: 5 11 n2
Relatively Prime: GCF: 1
Find the Least Common Multiple (LCM) of each group of numbers or monomials.
4
LCM: 2*3*5*11 = 330
12.
2
3
11. 12 y , 16 y , 72 y
12: 22 3 y4
16: 24 y2
72: 23 y3
LCM: 24 3 y4 = 144y4
10. 30, 110
30: 2 3 5
110: 2 5 11
9 x 2 y , 36 x 4 y 2 , 30y 7
9: 32 x2y
36: 22 32 x4y2
30: 2 3 5 y7

LCM: 22 32 5 x4y7 = 180 x4y7
13. What value of x will make the following fractions equivalent?
8 24 x

 , x  24
18 54 54

8
x
 .
18 54
Answer Key
Complete the statement with <, >, or =. (Don’t forget to show work!!)
14.
9
9
16
_____
19
2
15.
9
9
16
9
9
19
>
2
16
_____
9
8
3
16
_____
1
8
= 9
2
16
8
37
4
3
1
< 9
16
4
Tell if the fractions are equivalent. Show your work to justify your answer.
16.
21 84
,
28 96
21 3

28 4
84 28 7


96 32 8
They are not equivalent
17. Boxes that are 14 centimeters tall are being stacked next to boxes that are 18 centimeters tall. What is the shortest
height at which the two stacks will be the same height?
14: 2 7
18: 2 32
LCM: 2 * 32 7 = 126 cm
18. You must cut four pieces of wood that measure 36 cm, 45 cm, and 81 cm, and 108 cm into smaller sized pieces.
What is the longest each piece can be so that each piece is the same length?
36 : 22 3
45: 32 5
81: 34
108: 22 33
GCF : 32 Make each piece 9 cm long
Simplify the expression using only positive exponents
19. 5355= 58
21. (5-3)(c5)(5c-2) = (5-2) c3=
23.
20. 5a3 (5a)2= 53a5= 125a5
c3
25
22. (3a2)4 = 34a8 = 81a8
p 3q 9
= p3-2 q9-3 = pq6
2 3
p q
25.
33 m 9
36 m 5
27.
(5a3b2)3 (5a-2)3 = (53a9b6) (53a-6)= 56a3b6
=
m4
33
24.
26.
12a 4b 3
24a 7b  2
p 3q 9 3-(-2) -9-3 p 5
=p
q = 12
p 2 q 3
q
=
b5
2a11
Answer Key
28. Is the following statement true?
Yes -
( x a ) b  ( x b ) a Why or Why not? Explain.
( x a )b  x ab
( x b ) a  x ab 
29. What exponent will make the following statement true?
( x 3 )5  x15
x 5 x10  x15
Therefore:
( x 3 )5  x 5 x ?
?=10
30. Write 0.00000423 in scientific notation.
4.23 106
31. Write
3.61107 in standard form.
36,100,000
32. Find the product in scientific notation.

(7.6 108 )  (4.8 106 )
(7.6)  (4.8)108106  36.48 1014  3.648 1013

33. Find the quotient in scientific notation.
(3.6 108 )
(4.8 106 )
(4 pts)
x
Extra Credit: (5 pts)
Simplify the expression using only positive exponents
9 x 2
3
3
y4
 ( x 1 )( 2 y 2 x) 2  3  ( x 1 )( 24 y 4 x 2 )  3  3
12 x
4x
4x 4x
Write and Solve and equation to find the value of x that makes the statement true.
5x-353x= 513
x-3 + 3x = 13
4x – 3 = 13
4x = 16
x=4
Simplify the expression
6 y5
4 y  2  3 y( y 2 )  _______
2y
6 y5
4 y 3  2  3 y( y 2 )  4 y 3  3 y 3  3 y 3  4 y 3
2y
3