guía 8thgrade 2015 sem1 solemne
DESCRIPTION
Exercises for 8 graders MathTRANSCRIPT
-
1Review_8thGrade_2015_Sem1_Solemne
Objetivos:Powers
Percentages & proportions.Productos Notables
Word problems leading to linear equations.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1 Jos has three times as many pencils as
Manuel. Together they have 184. How
many does each one have?
A Jos: 51 , Manuel: 143
B Jos: 138 , Manuel: 46
C Jos: 143 , Manuel: 51
D Jos: 46 , Manuel: 138
2 How many people in generation # 20?
A
2
20
B
2
21
C
2
19
D
20 22
3 Write as a single power:
27
3
35
3
7
1
:3
2
A
81
5
B
81
3
C
3
9
D
3
4
4 Whats the correct statement?
A 3( )2
> (2)3
B 3( )2
= (2)3
C 3( )2
< (2)3
D 0( )2
> (2)0
5 A classroom is furnished with two
different types of chairs (3 and 4 legs). If
there are 12 seats and the total number
of legs is 47, how many of each type are
there?
A 11 (4L) and 47 (3L)
B 11 (4L) and 1 (3L)
C 1 (4L) and 11 (3L)
D 12 (4L) and 1 (3L)
6 Write as a reduced fraction:
11
8
2
A
64
121
B
121
64
C -
121
64
D -
64
121
-
Name: ________________________ ID: A
2
7 (8a 4)
2
=?
A
64a
2
64a + 16
B
64a
2
16
C
64a
2
+ 4a + 16
D
64a
2
+ 16
8 Translate the following expression into the language of Algebra . Use the variable yin
your answer.
A multiple of 10 / Un mltiplo de 10
A y+ 9 B 10y C $y:6 D 2y+1
9 Diga el grado del polinomio
c
a
8
3c
2
a
4
6c
7
6
A 9
B 1
C ca
D 16
10 Work out
(5)
2
A 10
B 25
C 10
D 25
11 Write as a single power:
64
3
:80
8
3
8
2
4
A
8
11
B
8
0
C
8
6
D 8
3
12 Write the answer as an integer number:
3
3
A 27
B 9
C 9
D 27
13 The total cost of a 8-days Mediterranean
cruise for 8 people is 15.500,00 . What
is the cost for a 14-days cruise for 8
people?
A 27.129,00
B 27.125,00
C 27.127,00
D 27.128,82
14 (k9)(k+8) =?
A
k
2
k 72
B
k
2
72k 1
C k
2
k
D
72k
2
15 Write as a single power:
8
3
2
8
2
2
9
:2
6
7
A
16
3
B
2
35
C
2
34
D 16
8
-
Name: ________________________ ID: A
3
16 Find the missing data
A
3
4
B
3
9
C
3
3
D
3
0
17 (b9)(b6) =?
A
b
2
15b
B
54b
2
C
b
2
+ 54b 15
D b
2
15b + 54
18 Reduce:
z
2
:z
3
A
z
1
B
z
0
C
z
5
D
z
5
19 Expressed as a single power
8
3
2
3
is equal
to:
A
4
3
B 4
6
C 4
0
D
6
4
20 Yesterday,Camila saw a dress at the mall
at $14000 , but she did not have the
money with her, so she decided to return
today to buy it. Luckily, today the dress
was on special at 10% discount.How
much did she save?
A $1410
B $12600
C $1400
D $1392
21 Write as a single power:
81
3
:94
9
2
: 9
0
10
A
9
12
B
9
9
C
9
3
D
9
4
22 How many cubes in shape # 7?
A
7 210
B
10 27
C
10 26
D
10 25
23 Write as an integer:
2( )4
A 16
B 8
C 8
D 16
24 If c=3, w=0,38 and z=
1
8
, evaluate the
expression 7 c+1
z
w
A 11,62
B 42,5
C 7,0
D 41,5
25 How many cubes in shape # 9?
A
3 29
B
3 28
C
9 23
D
3 27
-
Name: ________________________ ID: A
4
26 Write as a fraction
17
7
2
A
289
49
B -
49
289
C
49
289
D -
289
49
27 If y=2, w=-0,02 and z=
1
9
, evaluate the
expression 6 y +1
z
+w
A 22,0
B 16,98
C 15,0
D 23,0
28 Reduce:
z
2
z6
A
z
4
B
z
0
C
z
8
D
z
4
29 The sum of three consecutive numbers is
183. Find the one in the middle.
A 61
B 60
C 62
D 64
30 Work out:
225
A 22
B 15
C 9
D 14
31 Find the perimeter of the square:
A 105
B 100
C 104
D 113
32 What % is 2 of 2
1
7
?
A 9,3%
B 186,6%
C 93,3%
D 428,5%
33 Reduce:
z
4
z
6
z
9
A
z
9
B
z
11
C
z
10
D
z
10
34 Work out:
4
-1
2
-2
+ 3-2
A
1
9
B
1
8
C 9
D
17
149
35 Fill the blank
30 = 31A 991
B 1.000
C 990
D 982
-
Name: ________________________ ID: A
5
36 In a farm there is a corral with cows and
chickens. If we can count 21 heads and
58 legs, how many animals of each
specie are there?
A 21 cows and 13 chickens
B 8 cows and 13 chickens
C 8 cows and 58 chickens
D 13 cows and 8 chickens
37 Reduce:
5c
7
10c
A
83c
8
B
50c
6
C
40c
8
D
36c
6
38 Fill the blank:
A
1
32768
B 40
C 5
D 8
39 Work out the missing percentage in the experiment:
A 53 % B 50 % C 36 % D 48 %
-
Name: ________________________ ID: A
6
40 At the beginning of day 1 there are 49
bacteria on a Petri dish growth. One day
later there are 196, another day passes
by and there are 784, and every day
henceforth they kept fourfolding its
population. According to that, the
expression for the number of bacteria
born on day 17 should be:
A
784 449
B
17 449
C
49 416
D
147 415
41 Write as a single power:
125
2
:52
5
7
5
0
9
A
5
15
B
5
13
C
25
2
D
25
2
42 How many sides in shape # 18?
A
4
17
C
3
17
B
3 417
D
9 416
43 How many cubes in shape # 12?
A
3 211
B
12 23
C
3 212
D
3 210
44 In a school 20% of all the students
practice sports and 35% play a musical
instrument. If the total number of
students that practice sports is 140, how
many students
play a musical instrument?
A 245
B 235
C 237
D 244
-
Name: ________________________ ID: A
7
45 Write as a reduced fraction:
4
7
0
A -7
B
1
1
C -
1
1
D 7
46 Reduce
-(3d10z)+(6z+4d)
A 4z+7d
B 10z5d
C 3d+7z
D 4d+7z
47 My age, plus
1
5
my age, plus
1
2
my age ,
plus 11 years is equal to my age in 18
years time. How old am I?
A 2 years old
B 10 years old
C 9 years old
D 14 years old
48 The following flow diagram represents a products sale on a special Christmas discount. Fill
the blank.
A $4454 B $4465 C $4455 D $4463
49 Expressed as a single power
50
8
25
8
is equal
to:
A 2
16
B
16
2
C 2
0
D
2
8
50 Work out:
5
-1 + 4 -1
2
-2
A 1
4
5
B 1
14
25
C
5
9
D 1
9
10
51 What % is 51 of 306?
A 23.7%
B 23.3%
C 13.3%
D 16.7%
52 A man was born on 48 B.C. , had an only
son when he was 23 and died on 12 A.D.
If the son only lived half as many years as
the father, when did the son die?
A 12 A.D.
B 5 A.D.
C 12 B.C.
D 7 B.C.
-
Name: ________________________ ID: A
8
53 If we increase a number by a percentage
and then we reduce that result by the
same percentage, the value we obtain is:
A Not enough data to answer.
B Equal to the original.
C Greater than the original.
D Less than the original.
54 Which one is a perfect square?
A 36
B 197
C 290
D 101
55 Write as a reduced fraction:
5
2
6
A
15625
64
B -
15625
64
C -
64
15625
D
64
15625
56 Fill the blank:
A 16
B
1
64
C 8
D 2
57 Solve the equation:
7 8y=5 12y
A 1
B 3
C 3
D 0
58 Expressed as a single power
44
5
2
5
is equal
to:
A
10
22
B 22
10
C 22
0
D
22
5
59 My age, plus 50% my age, plus 66
2
3
%
my age , plus 10 years is equal to my age
in 24 years time. How old am I?
A 2 years old
B 12 years old
C 19 years old
D 9 years old
60 The % of white triangles in the figure is:
A 60%
B 33
1
3
%
C 41
2
3
%
D 37
1
2
%
61 The % of black triangles in the figure is:
A 50%
B 41
2
3
%
C 66
2
3
%
D 54
1
6
%
-
Name: ________________________ ID: A
9
62 At the beginning of day 1 there are 24
bacteria on a Petri dish growth. One day
later there are 48, another day passes by
and there are 96, and every day
henceforth they kept doubling its
population. According to that, the
expression for the number of bacteria
born on day 19 should be:
A
96 224
B
19 224
C
24 218
D
24 217
63 How many cubes in shape # 20?
A
3 220
B
3 218
C
3 219
D
20 23
64 At the beginning of day 1 there are 18
bacteria on a Petri dish growth. One day
later there are 90, another day passes
and there are 450, and every day
henceforth they kept fivefolding its
population. According to that, the
expression for the population of bacteria
on day 20 should be:
A
18 520
B
20 518
C
72 518
D
18 519
65 Fill the blank:
A 6
B 3
C
1
216
D 18
66 The following flow diagram represents a products sale on a special Christmas discount. Fill
the blank.
A $7300 B $7295 C $7290 D $7293
-
Name: ________________________ ID: A
10
67 What percentage of the rectangle is
shaded?
A 50%
B 58
1
3
%
C 41
2
3
%
D 54
1
6
%
68 Diga el grado del polinomio
11c
a
8
11ca
7
+ 10c
12
3
A 15
B ca
C 11
D 12
69 Write as a reduced fraction:
- 0,07
2
A -
8100
49
B
90
7
C
49
8100
D -
90
7
70 If the total time taken for the process was 45 minutes, what % is already done so far?
A 20 % B 78 % C 43 % D 80 %
71 The number 66 is increased by 45% and the outcome is reduced by 45%. What is the final
result?
A 36.3 C 95.7
B 52.64 D 66
72 Translate the following expression into the language of Algebra . Use the variable cin
your answer.
A number increased by 8 units / Un nmero aumentado en 8 unidades
A c+ 8 B 10c C 2c+1 D c+8
-
Name: ________________________ ID: A
11
73 Write as a single power:
25
3
:5
6
5
5
10
:5
1
3
A
5
148
B
5
6
C
5
3
D
5
147
74 Two numbers are in a ratio 4:3 and their
sum is 9
1
3
. Find the numbers.
A 3 and 4
B 4 and 5
1
3
C
1
3
and 9
D 140 and 9
75 I gave
3
5
of my pencils to Karla,
2
3
of the
rest to Manuel and Ive got 8 left. With
how many pencils did I start?
A 66 pencils
B 57 pencils
C 60 pencils
D 70 pencils
76 In a figth between flies and spiders we
have a total of 23 heads and 164 legs.
How many insects there were on each
side? (Remember that a fly has 6 legs
and a spider 8).
A 23 spiders and 10 flies
B 13 spiders and 10 flies
C 13 spiders and 164 flies
D 10 spiders and 13 flies
77 21 laser polishers can finish 868
microscope lenses in 8 hours. How many
lenses will 9 machines polish in 18
hours?
A 842 lenses
B 837 lenses
C 845 lenses
D 837 lenses
78 If the price of a dress on special at 20%
discount is $11500 , what is the regular
price?
A $14372
B $9200
C $14376
D $14375
79 (7y +9)
2
=?
A
49y
2
9y + 81
B
49y
2
81
C
49y
2
+ 81
D 49y
2
+ 126y + 81
80 5 typists can type 830 pages in 20 hours.
How many pages will 10 typists type in 8
hours?
A 664 pages
B 664 pages
C 669 pages
D 677 pages
81 Reduce
-(d6d)+(8b10b)
A 18d+5b
B 18b+5d
C 6b+4d
D d+5b
-
Name: ________________________ ID: A
12
82 Write as a reduced fraction:
0,08
2
A
45
4
B
16
2025
C -
45
4
D
2025
16
83 If -8b -6 = 26, then the value of 9b + 9
is
A 19
B 18
C 27
D 20
84 If the age of a person in 14 years time
is going to be 38, how much is twice his
or her current age minus 6 ?
A 24
B 8
C 60
D 42
85 The following flow diagram represents a products sale on a special Christmas discount. Fill
the blank.
A $16468 B $16459 C $16460 D $16467
86 (4y 4)
2
=?
A
16y
2
16
B
16y
2
+ 4y + 16
C
16y
2
+ 16
D
16y
2
32y + 16
87 Reduce:
2a
2
4a8
A
8a
10
B
82a
6
C
72a
6
D
79a
0
88 If the time taken so far represent 60% of the total , how long it took the whole process?
A 59 minutes B 5 minutes C 3 minutes D 40 minutes
-
Name: ________________________ ID: A
13
89 What is 25 % of 500?
A 100,0
B 175,0
C 125,0
D 126,0
90 Write as a reduced fraction:
5
9
4
A
625
6561
B -
625
6561
C -10
311
625
D 10
311
625
91 Diga el grado del polinomio
3b
3
a
4
+ 5b
6
a
3
+ 8b
7
+ 8
A 9
B 3
C 24
D ba
92 Writeed as a single power
16
2
:4
2
is equal
to:
A
4
2
B 4
4
C
4
4
D 4
0
93 The side of a square can be given by the
expression 7w+6c . Whats the
expression for its perimeter?
A 28w+6c
B 28w+24c
C -w+7c
D 3w+6c
Numeric Response
94 How many squares do we have in figure number 50?
Short Answer
95 5 factory workers need 18 minutes to
make 20 cars. How many minutes should
it take for 3 workers to make 14 cars?
96 The total cost of a 7-days Mediterranean
cruise for 2 people is 25.956,00 . If a
family of 12 members is willing to
expend 578.448,00 ,how many days
can they afford?
-
Name: ________________________ ID: A
14
97 6 laser polishers can finish 750
microscope lenses in 4 hours. How many
lenses will 15 machines polish in 20
hours?
98 The following flow diagram represents a products sale on a special Christmas discount. Fill
the blank.
99 If 10a -4 = 46, then the value of 6a - 5
is
100 (a+1)(a4) =?
101 A team of miners working 12 hours per
day can finish a tunnel in 28 days. Had
they worked 1 hour(s) less per day, how
much longer would it have taken to
finish the tunnel?
102 Fill up the blanks:
Percentage Ratio Fraction Decimal
-
Name: ________________________ ID: A
15
103 To combat rising costs , Willy Wonka has
to make a decision. He could either
increase the price of of a chocolate bar
by
1
10
or decrease its weight by
1
10
.
If you were him, what would be your
decision and why?
104 Find the perimeter of the square:
105 If the age of a person in 6 years time
is going to be 20, how much is
three times his or her current age plus 18
?
106 If twice the age of a person plus 6 is equal to 36, how old is he or she going to be in 6
years time?
107 In a school 20% of all the students
practice sports and 30% play a musical
instrument. If the total number of
students that practice sports is 120, how
many students
play a musical instrument?
108 Solve the equation:
6
5
+3
5
b=
3
7
b
3
5
3
35
b
109 The sum of three consecutive numbers is
114. Find the one in the middle.
110 Reduce:
3b
9
6b8
111 To combat rising costs , Willy Wonka has
to make a decision. He could either
increase the price of of a chocolate bar
by 11 % or decrease its weight by 11%.
If you were him, what would be your
decision and why?
112 Reduce:
x
9
x
2
x
6
113 Reduce:
x
8
x
6
114 Reduce:
y
7
y
8
115 Solve the equation:
4 10a=2 9a
-
Name: ________________________ ID: A
16
116 If d=8, y=-0,79 and b=
1
3
, evaluate the
expression 4 d +1
b
y
117
118 Si la balanza est equilibrada y cada pote
de miel pesa lo mismo, cul es el peso
de un pote de miel?
119 The side of a square can be given by the
expression 13d+8g . Whats the
expression for its perimeter?
120 Reduce
-(5f+6w)+(7f3w)
121 The side of a square can be given by the
expression 11x+2b . Whats the
expression for its perimeter?
122 Translate the following expression into the language of Algebra . Use the variable nin
your answer.
The perimeter of a square with side n / El permetro de un rectngulo con lado n
-
ID: A
1
Review_8thGrade_2015_Sem1_Solemne
Answer Section
MULTIPLE CHOICE
1 ANS: B PTS: 1
2 ANS: C PTS: 1
3 ANS: C PTS: 1
4 ANS: C PTS: 1
5 ANS: B PTS: 1
6 ANS: A PTS: 1
7 ANS: A PTS: 1
8 ANS: B PTS: 1
9 ANS: A PTS: 1
10 ANS: B PTS: 1
11 ANS: A PTS: 1
12 ANS: A PTS: 1
13 ANS: B
Direct Direct
Days People
x (+) 14 (+) 8 (+)
15.500,00 (+) 8 (-) 8 (-)
x =15500.00 14 8
8 8=27.125,00
PTS: 1
14 ANS: A PTS: 1
15 ANS: B PTS: 1
16 ANS: A PTS: 1
17 ANS: D PTS: 1
18 ANS: C PTS: 1
19 ANS: A PTS: 1
20 ANS: C PTS: 1
21 ANS: A PTS: 1
22 ANS: C PTS: 1
23 ANS: A PTS: 1
24 ANS: A PTS: 1
25 ANS: B PTS: 1
26 ANS: A PTS: 1
27 ANS: B PTS: 1
-
ID: A
2
28 ANS: C PTS: 1
29 ANS: A PTS: 1
30 ANS: B PTS: 1
31 ANS: C PTS: 1
32 ANS: C PTS: 1
33 ANS: B PTS: 1
34 ANS: A PTS: 1
35 ANS: A PTS: 1
36 ANS: B PTS: 1
37 ANS: B PTS: 1
38 ANS: A PTS: 1
39 ANS: C PTS: 1
40 ANS: D
Population on Day 17:
49 416
Population on Day 16:
49 415
Born on Day 17:
49 416
-
49 415
=
49 415
4 1( ) =
147 415
PTS: 1
41 ANS: A PTS: 1
42 ANS: B PTS: 1
43 ANS: A PTS: 1
44 ANS: A PTS: 1
45 ANS: B PTS: 1
46 ANS: A PTS: 1
47 ANS: B PTS: 1
48 ANS: C PTS: 1
49 ANS: D PTS: 1
50 ANS: A PTS: 1
51 ANS: D PTS: 1
52 ANS: B PTS: 1
53 ANS: D PTS: 1
54 ANS: A PTS: 1
55 ANS: A PTS: 1
56 ANS: B PTS: 1
57 ANS: C PTS: 1
58 ANS: D PTS: 1
59 ANS: B PTS: 1
60 ANS: A PTS: 1
-
ID: A
3
61 ANS: C PTS: 1
62 ANS: D
Population on Day 19:
24 218
Population on Day 18:
24 217
Born on Day 19:
24 218
-
24 217
=
24 217
2 1( ) =
24 217
PTS: 1
63 ANS: C PTS: 1
64 ANS: D PTS: 1
65 ANS: C PTS: 1
66 ANS: A PTS: 1
67 ANS: C PTS: 1
68 ANS: D PTS: 1
69 ANS: A
- 0,07
2
= - 7
90
2
= -
8100
49
PTS: 1
70 ANS: D
x% -------------36 min
100% ------------- 45 min
x=
10036
45
=80%
PTS: 1
71 ANS: B PTS: 1
72 ANS: A PTS: 1
73 ANS: D PTS: 1
74 ANS: B PTS: 1
75 ANS: C PTS: 1
76 ANS: B PTS: 1
77 ANS: B
Direct Direct
Lenses Machines Hours
x (+) 9 (+) 18 (+)
868 (+) 21 (-) 8 (-)
x =868 9 18
21 8=837
PTS: 1
78 ANS: D PTS: 1
79 ANS: D PTS: 1
-
ID: A
4
80 ANS: B
Direct Direct
Pages Typists Hours
x (+) 10 (+) 8 (+)
830 (+) 5 (-) 20 (-)
x =830 10 8
5 20=664
PTS: 1
81 ANS: B PTS: 1
82 ANS: B
0,08
2
=
4
45
2
=
16
2025
PTS: 1
83 ANS: C PTS: 1
84 ANS: D
38 (in 14 years time)
38 - 14 = 24 (now)
224 - 6 = 48 - 6 = 42
PTS: 1
85 ANS: A PTS: 1
86 ANS: D PTS: 1
87 ANS: A PTS: 1
88 ANS: B PTS: 1
89 ANS: C PTS: 1
90 ANS: A PTS: 1
91 ANS: A PTS: 1
92 ANS: A PTS: 1
93 ANS: B PTS: 1
NUMERIC RESPONSE
94 ANS: 2500
PTS: 1
-
ID: A
5
SHORT ANSWER
95 ANS:
21 minutes
Inverse Direct
Minutes Workers Cars
x (+) 3 (-) 14 (+)
18 (+) 5 (+) 20 (-)
x =18 5 14
3 20=21
PTS: 1
96 ANS:
26 days
Inverse Direct
Days People
x (+) 12 (-) 578.448,00 (+)
7 (+) 2 (+) 25.956,00 (-)
x =
7 2 578.448,00
12 25.956,00=26
PTS: 1
97 ANS:
9375 lenses
Direct Direct
Lenses Machines Hours
x (+) 15 (+) 20 (+)
750 (+) 6 (-) 4 (-)
x =750 15 20
6 4=9375
PTS: 1
98 ANS:
13%
PTS: 1
99 ANS:
25
PTS: 1
100 ANS:
a
2
3a 4
PTS: 1
-
ID: A
6
101 ANS:
2
6
11
days
PTS: 1
102 ANS:
Percentage Ratio Fraction Decimal
PTS: 1
103 ANS:
Scenario #1: Price increased.
Lets suppose a 100 g bar costs 1.00 . If we increase the price by
1
10
the new price would be
1.10. So you are selling chocolate now at 0.011 per gram.
Scenario #2: Weight decreased.
Same bar, same price. If we decrease the weight by
1
10
the new weight would be 90 g, so
youd be selling chocolate now at 0.011111111111 per gram.
Conclusion: Therefore, from a manufacturers point of view, decreasing the weight is the best
bussines proposition.
PTS: 1
104 ANS:
56
PTS: 1
105 ANS:
60
20 (in 6 years time)
20 - 6 = 14 (now)
314 + 18 = 42 + 18 = 60
PTS: 1
-
ID: A
7
106 ANS:
21
2x + 6 = 36
2x = 36 - 6
2x = 30
x =
30
2
= 15 (Now)
x+6 = 15+6 = 21 (In 6 years time)
PTS: 1
107 ANS:
180
PTS: 1
108 ANS:
7
PTS: 1
109 ANS:
38
PTS: 1
110 ANS:
18b
17
PTS: 1
111 ANS:
Scenario #1: Price increased.
Lets suppose a 100 g bar costs 1.00 . If we increase the price by 11% the new price would
be 1.11. So you are selling chocolate now at 0.0111 per gram.
Scenario #2: Weight decreased.
Same bar, same price. If we decrease the weight by 11% the new weight would be 89 g, so
youd be selling chocolate now at 0.011235955056 per gram.
Conclusion: Therefore, from a manufacturers point of view, decreasing the weight is the best
bussines proposition.
PTS: 1
112 ANS:
x
PTS: 1
113 ANS:
x
14
PTS: 1
-
ID: A
8
114 ANS:
y
1
PTS: 1
115 ANS:
2
PTS: 1
116 ANS:
-0,21
PTS: 1
117 ANS:
14
PTS: 1
118 ANS:
94g
PTS: 1
119 ANS:
52d+32g
PTS: 1
120 ANS:
12f9w
PTS: 1
121 ANS:
44x+8b
PTS: 1
122 ANS:
4n
PTS: 1