Dimensions Math
Placement Test 5A
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Dimensions Math
Placement Tests
This test covers material taught in Dimensions Math 5A.
1
Use the number 357,014,296 to answer the following questions.
(a) Write the number in words.
( b) The value of the digit in the one millions place is
(c) The digit
is in the hundred millions place.
(d ) The digit 5 is in the
2
.
place.
Find the values.
(a) 35,510 × 100 =
( b) 1,000 × 500,000 =
(c) 2,600 × 20 =
(d ) 2,000 × 350 =
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1
3
Find the values.
(a) 317,000 ÷ 1,000 =
( b) 80,000 ÷ 10 =
(c) 21,000,000 ÷ 700 =
(d ) 320,000,000 ÷ 4,000 =
4
Fill in the blanks.
(a) 20,000,000 + 2,000,000 + 800,000 + 9,000 + 500 =
( b) 500,000,000 + 70,000,000 + 40,000 + 50 + 1 =
(c) 605,700,016 = 600,000,000 +
+ 16
(d ) 310,019,005 = 9,000 + 10,000,000 +
5
Write >, <, or = in each
.
(a) 30,000 + 100,000,000 + 20,000,000
( b) 514,189,043
+ 5 + 10,000
80,000 + 900,000 + 9,000,000
514,819,430
(c) One hundred and five millions
(d ) 39,642,000 + 10,000,000
10 hundred thousands
49,800,000 – 100,000
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2
6
Find the values.
(a) 100 – 5 × 9 ÷ 3 =
( b) 40 + 40 ÷ 8 − 10 =
(c) 35 ÷ 5 + 2 × 7 =
(d ) 24 ÷ 4 × 3 =
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3
7
Find the values.
(a) 80 ÷ (5 + 5) − 8 =
( b) 3 × (18 ÷ 3) + ( 4 ÷ 2) =
(c) (60 ÷ 10) + (7 – 3) ÷ 2 =
(d ) 3 × (8 − 35 ÷ 7) ÷ 3 + 2 × 2 =
(e) 8 × (13 + 9) = 8 ×
+
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×9
4
8
The admission price to a concert is $12 for an adult and $5 for a child. Aida bought
3 adult tickets and 3 child tickets. Write an expression with parenthesis to find the
total amount she spent on tickets, and then find the value.
9
Find the values.
(a) 65 × 39 =
( b) 98 × 788 =
(c) 5,071 × 36 =
(d ) 13 × 115 × 4 =
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5
10 Divide.
(a) 94 ÷ 17
( b) 105 ÷ 38
(c) 675 ÷ 20
(d ) 7,240 ÷ 51
11 Brandon has $200 less than Jordan. Grace has $500 more than Jordan. Together
they have $2,700. How much does Brandon have?
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6
12 Add. Express each answer in simplest form.
3
(a) 25 + 10
=
( b) 57 + 52 =
(c) 83 + 75 =
(d ) 12 + 25 + 34 =
13 Subtract. Express each answer in simplest form.
(a) 56 − 13 =
( b) 12 − 15 =
(c) 75 − 97 =
(d ) 89 − 16 − 13 =
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7
14 Add. Express each answer in simplest form.
(a) 514 + 58 =
( b) 37 + 213 =
2
(c) 215 + 815
=
1
(d ) 116 + 310
=
15 Subtract. Express each answer in simplest form.
(a) 678 − 234 =
6
( b) 10 − 113
=
(c) 425 − 317 =
(d ) 519 − 456 =
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8
16 Find the values. Express each answer in simplest form.
(a) 14 × 84 =
( b) 18 × 13 =
9
(c) 89 × 10
=
(d ) 74 × 34 =
5
12
(e) 12
× 10
=
6
( f ) 11
× 11
6 =
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9
17 Find the values. Express each answer in simplest form.
(a) 6 × 138 =
( b) 323 × 47 =
(c) 114 × 235 =
9
(d ) 119 × 10
=
18 Find the reciprocal of each number.
(a) 19
( b) 30
14
(c) 13
(d ) 625
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10
19 Find the values. Express each answer in simplest form.
1
(a) 12
÷4=
( b) 53 ÷ 3 =
(c) 37 ÷ 2 =
(d ) 9 ÷ 43 =
20 Find the values. Express each answer in simplest form.
3
3
1
(a) 20 – (10
− 20
) − 510
=
( b) 5 − 16 × 14 ÷ 2 =
(c) 13 × (10 – 913) ÷ 19 =
1
(d ) (12 × 7) ÷ (25 + 10
)=
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11
# A baker made 120 cookies. She sold 25 of them in the morning and 34 of the remainder
21
in the afternoon. How many cookies did she have left?
22 A ribbon 35 m long was cut into several pieces of equal length. Each piece of ribbon
1
is 10
m. How many pieces of ribbon are there?
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12
23 34 of the rice in a sack weighs 6 lb. How much does 23 of the rice in the sack weigh?
Express the answer in simplest form.
24 Fill in the blanks.
9
(a) 710
cm =
cm
mm
( b) 812 min =
min
s
(c) 512 kg =
g
(d ) 223 ft =
in
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13
25 Find the area of the figure. Express the answer in simplest form.
3
4m
5
6m
26 Find the area of the figure. Express the answer in simplest form.
10 cm
445 cm
7 cm
115 cm
12 cm
6 cm
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14
27 Find the area of Triangle XYZ.
3 in
X
12 in
Y
10 in
Z
28 Find the area of Triangle ABC.
A
3 1 cm
3
8 cm
C
15 cm
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B
15
29 Find the area of Figure PQRST.
9 cm
P
5 cm
10 cm
S
T
6 cm
Q
24 cm
R
30 Find the volume of the cuboid.
8 in
10 in
5 in
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16
31 Find the length of the missing edge.
?
7m
4m
Volume = 84 m3
Height =
m
32 Find the volume of the solid.
8 cm
6 cm
3 cm
4 cm
3 cm
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17
33 A rectangular tank with a length of 30 cm and a width of 20 cm was filled with water
to a height of 6 cm. After a rock was placed in the tank, the height of the water rose
to 9 cm. What is the volume of the rock?
6 cm
20 cm
9 cm
30 cm
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18
Answer Key
1
2
(a) Three hundred fifty-seven
million, fourteen thousand,
two hundred ninety-six
( b) 7,000,000
(c) 3
(d ) ten millions
(a)
( b)
(c)
(d )
3,551,000
500,000,000
52,000
700,000
3
(a) 317
(c) 30,000
4
(a)
( b)
(c)
(d )
5
6
( b) 8,000
(d ) 80,000
22,809,500
570,040,051
5,700,000
300,000,000
7
(a) 0
(c) 8
(e) 13; 8
8
3 × (12 + 5) = 3 × 17 = 51
or
(3 × 12) + (3 × 5) = 36 + 15 = 51
$51
9
(a) 2,535
(c) 182,556
10 (a) 5 R 9
(c) 33 R 15
( b) 20
(d ) 7
( b) 77,224
(d ) 5,980
( b) 2 R 29
(d ) 141 R 49
11 Solution may vary, bar model is
optional.
$200
Brandon
(a) >
(c) >
( b) <
(d ) <
(a) 85
(c) 21
( b) 35
(d ) 18
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$500
Jordan
$2,700
Grace
3 units
2,700 − 200 − 200
− 500 = 1,800
1,800
1 unit
3 = 600
$600
19
Answer Key
4
3
7
12 (a) 10
+ 10
= 10
7
10
35 45
3
( b) 10
14 + 14 = 14 = 3 14
3
3 14
21 61
1
(c) 40
15 + 15 = 15 = 4 15
1
415
10
8
15 33
13
(d ) 20
+ 20
+ 20
= 20 = 120
13
120
13 (a) 56 – 26 = 36 = 12
1
2
5
2
3
( b) 10
– 10
= 10
3
10
49 45
4
(c) 35
− 35 = 35
4
35
3
6
7
(d ) 16
18 – 18 – 18 = 18
7
18
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14 (a) 528 + 58 = 578
578
9
7
16
( b) 21
+ 221
= 221
16
221
3
2
5
(c) 215
+ 815
= 1015
= 1013
1013
5
3
8
4
(d ) 130
+ 330
= 430
= 4 15
4
4 15
15 (a) 678 − 268 = 418
418
6
7
( b) 9 − 13
= 8 13
7
8 13
14
5
9
(c) 435
− 335
= 135
9
135
2
15
15
5
(d ) 5 18
− 4 18
= 420
18 − 4 18 = 18
5
18
20
Answer Key
16 (a) 21
8
(c) 10
= 25
2
5
(e) 12
1
( b) 24
1
1
1
(a) 12
÷ 4 = 12
× 14 = 48
5
(d ) 21
16 = 116
( b) 53 ÷ 3 = 53 × 13 = 59
5
116
3
(c) 37 ÷ 2 = 37 × 12 = 14
(f ) 1
11 33
1
17 (a) 6 × 11
8 = 3 × 4 = 4 = 84
814
4 44
2
( b) 323 × 47 = 11
3 × 7 = 21 = 221
2
221
13
1
(c) 114 × 235 = 54 × 13
5 = 4 = 34
314
9
9
(d ) 119 × 10
= 10
9 × 10 = 1
1
18
19
3
(d ) 9 ÷ 43 = 9 × 34 = 27
4 = 64
3
3
1
20 (a) 20 − (10
− 20
) − 510
6
3
2
= 20 − (20
− 20
) − 520
3
2
= 20 − 20
− 520
17
2
= 1920
− 520
15
= 1420
= 1434
( b) 5 − 16 × 14 ÷ 2 = 5 − 4 ÷ 2 = 3
(c) 13 × 23 ÷ 19 = 13 × 23 × 9 = 2
1
5
(d ) (12 × 7) ÷ (25 + 10
) = 72 ÷ 10
=
7 1 7
2÷2=2×2=7
(a) 9
1
( b) 30
(c) 13
14
(d ) 625 = 32
5
5
32
21 Cookies left to sell in the afternoon
3
5 of 120
1
Cookies left
4 of cookies left to
sell in the afternoon
1 3
4 × 5 × 120 = 18
18
1
22 35 ÷ 10
=6
6
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21
Answer Key
23 6 ÷ 34 = 6 × 43 = 8
2
16
1
3 × 8 = 3 = 53
513 lb
24 (a)
( b)
(c)
(d )
7; 9
8; 30
5,500
32
25 56 × 34 = 58
5
8 m2
26 10 × 445 = 48
3
3 × 115 = 3 × 65 = 18
5 = 35
12 − 445 − 115 = 6
6 × 6 = 36
48 + 335 + 36 = 8735
8735 cm2
27 12 × 10 × 12 = 60
60 in2
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28 8 − 313 = 423
1
2
1 14
2 × 43 × 15 = 2 × 3 × 15
= 7 × 5 = 35
35 cm2
29 10 × 6 = 60
9 × 11 = 99
1
55
1
2 × 5 × 11 = 2 = 272
60 + 99 + 2712 = 18612
18612 cm2
30 8 × 10 × 5 = 400
400 in2
31 784
×4=3
3m
32 8 × 2 × 3 = 48
4 × 3 × 3 = 36
48 + 36 = 84
84 cm3
33 30 × 20 × 3 = 1,800
1,800 cm3
22