Proficiency Exam Sample Questions and Answers

Proficiency Exam Sample Questions and Answers
1)
2)
3)
4)
5)
PLACE VALUE
What is the place value of the digit 6 in the following numbers?
a) 872,061
b) 90,627,045
Round 79,236 to the nearest ten-thousand.
Round 439,071to the nearest hundred.
Write each of the following in words.
a) 19,253
b) 4,103,918
Write the number 105,027 in expanded form, using exponents.
Write 7 • 105 + 4 • 103 + 2 • 102 + 8 • 10 + 4 in standard form.
Write each number using numerals.
a) eighty thousand, six
b) nine hundred seventeen thousand, one hundred sixty-three
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6)
7)
WHOLE NUMBERS
1)
2)
3)
4)
5)
6)
Add: 9732 + 276
Subtract: 5921 - 684
Find the sum of 768, 82, 5937 and 17
Find the difference of 83,012 and 763
Find the average of 80, 92, 83, 56 and 84
What number must be added to 896 to obtain 1000?
7)
8)
9)
Multiply: 56 • 423
Find the product of 4007 and 360.
Find the quotient and the remainder when 30823 is divided by 60.
7)
Simplify: 3 + 7 • 5 – 9
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INTEGERS
Evaluate each of the following:
1)
-23 + 7
2)
-8 + (-19)
3)
5 - (-34)
4)
5)
6)
-72 ÷ 6
(-8)(-12)
(-6)(-7)(0)(-2)
7)
32 + 25 ÷ 5 • 2 - 26
7 - 4(3 - 8 • 6)
Evaluate the expression 5x2 when x = -4.
Write the following integers in order from smallest to largest:
7, -15, 0, -14, 9, -2
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8)
9)
10)
1
Proficiency Exam Sample Questions and Answers
1)
FRACTIONS
Name the fraction represented by this set model:
• • • • o o
•
o
o
o
2)
•
o
o
o
•
o
o
o
•
o
o
o
o
o
o
o
o
o
o
o
The shaded dots have a value of
6
. Draw a circle around “1”.
8
• • • • • • o
• • • • • • o
• • • o o o o
3)
• • • o o o o
o o o o o o o
Name the fraction represented by the point labeled “A” on the number line.
←|--|--|--|--|--|--|--|--|--|--|--|--|--|--|→
0
A
1
2
4)
5)
6)
7)
8)
9)
10)
Write in lowest terms:
56
84
8
with a denominator of 75.
15
3 2
Add: +
4 5
Write
3 2
−
4 5
3 2
Multiply: •
4 5
3
1
Divide: 1 ÷ 2
4
10
Subtract: 1
Name a fraction between
3
2
and .
4
5
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DECIMALS
1)
Write
8
as a decimal.
20
2)
Add: 7.45 + 8.3
3)
Multiply: 8.09 • 0.37
4)
5)
6)
Divide: 2.7 ÷ 6.03 (Round quotient to the nearest hundredth.)
Perform the following operations: 5.12 - 8.6 + 7.54
Name the place value of the underlined digit: 897.03241
2
Proficiency Exam Sample Questions and Answers
7)
8)
9)
10)
Round 54.908732 to the nearest ten-thousandth.
What must be added to 0.57 to get 15?
Write six hundred three and eighty-eight ten-thousandths as a decimal.
Write in order from smallest to largest:
5.0236, 5.02, 5.236, 5.063, 5.3
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PERCENTS
1)
Write 0.783 as a percent.
2)
Write
3)
4)
5)
6)
Change 7.5% to a decimal.
Change 24% to a fraction in lowest terms.
What is 110% of 400?
Shade 40% of the grid:
3
as a percent.
5
7)
8)
46.5 is 15% of what number?
32 is what percent of 140?
(Round answer to the nearest tenth of a percent.)
9)
0.4% of what number is 16?
10)
A basketball player attempts 120 free throws. She makes 90% of them. How many free throws
does she make?
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ANSWERS ON THE FOLLOWING PAGES
3
Proficiency Exam Sample Questions and Answers
PLACE VALUE ANSWERS
1)
2)
3)
4)
5)
What is the place value of the digit 6 in the following numbers?
a) 872,061
b) 90,627,045
ANSWERS:
a) tens
b) hundred-thousands
Round 79,236 to the nearest ten-thousand.
ANSWER: 80,000
Round 439,071to the nearest hundred.
ANSWER: 439,100
Write each of the following in words.
a) 19,253
b) 4,103,918
ANSWERS:
a) nineteen thousand, two hundred fifty-three
b). four million, one hundred three thousand, nine hundred eighteen
Write the number 105,027 in expanded form, using exponents.
ANSWER: 1 • 10 + 5 • 10 + 2 • 10 + 7 • 10
5
3
1
0
Write 7 • 105 + 4 • 103 + 2 • 102 + 8 • 10 + 4 in standard form.
ANSWER: 704,284
7)
Write each number using numerals.
a) eighty thousand, six
b) nine hundred seventeen thousand, one hundred sixty-three
ANSWERS: a) 80,006 b) 917,163
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6)
WHOLE NUMBERS ANSWERS
1)
2)
3)
4)
5)
Add: 9732 + 276
ANSWER: 10,008
Subtract: 5921 – 684
ANSWER: 5237
Find the sum of 768, 82, 5937 and 17
ANSWER: 5937+768 + 82 +17 = 6804
Find the difference of 83,012 and 763
ANSWER: 83,012 – 763 = 82,249
Find the average of 80, 92, 83, 56 and 84
ANSWER:
80 + 92 + 83 + 56 + 84
= 79
5
6)
What number must be added to 896 to obtain 1000?
ANSWER: 1000 – 896 = 104
7)
8)
Multiply: 56 • 423
ANSWER: 23,688
Find the product of 4007 and 360
9)
ANSWER: 4007 • 360 = 1,442,520
Find the quotient and the remainder when 30823 is divided by 60.
ANSWER: 30823 ÷ 60 = 513 R 43
4
Proficiency Exam Sample Questions and Answers
10)
Simplify: 3 + 7 • 5 – 9
3+7•5–9
3 + 35 – 9
38 – 9
29
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ANSWER:
INTEGERS ANSWERS
Evaluate each of the following:
1)
-23 + 7
ANSWER: Different signs, subtract and keep the sign of the larger absolute value -16
2)
-8 + (-19
ANSWER: Same signs, add and keep the common sign: -27
3)
5 - (-34)
ANSWER: 5 – (-34) = 5 + 34 = 39
4)
5)
6)
7)
-72 ÷ 6
ANSWER: Different signs, answer is negative:
(-8)(-12)
ANSWER: Same signs, answer is positive: 96
(-6)(-7)(0)(-2)
ANSWER: 0 (any number times 0 = 0)
-12
32 + 25 ÷ 5 • 2 - 26
ANSWER:
32 + 25 ÷ 5 • 2 − 26
9 + 5 • 2 − 26
9 + 10 − 26
19 − 26
−7
8)
7 - 4(3 - 8 • 6)
9)
Evaluate the expression 5x2 when x = -4
7 − 4(3 − 8 • 6 )
7 − 4(3 − 48)
ANSWER: 7 − 4(− 45)
7 + 180
187
ANSWER:. 5 x = 5(− 4 ) = 5(16 ) = 80
2
2
10)
Write the following integers in order from smallest to largest: 7, -15, 0, -14, 9, -2
ANSWER: -15, -14, -2, 0, 7, 9
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5
Proficiency Exam Sample Questions and Answers
1)
FRACTIONS ANSWERS
Name the fraction represented by this set model:
• • • • o o
•
o
o
o
•
o
o
o
•
o
o
o
•
o
o
o
ANSWER:
2)
o
o
o
o
o
o
o
o
8shaded
4
=
30total
15
The shaded dots have a value of
6
. Draw a circle around “1”.
8
• • • • • • o
• • • • • • o
• • • o o o o
• • • o o o o
o o o o o o o
ANSWER:
6 18
=
8
x
6 x 144
, so 24 dots should be circled
=
6
6
x = 24
3)
Name the fraction represented by the point labeled “A” on the number line.
←|--|--|--|--|--|--|--|--|--|--|--|--|--|--|→
0
A
1
2
ANSWER:
4)
5)
3
7
56
84
56 ÷ 7 8 ÷ 4 2
ANSWER:
=
=
84 ÷ 7 12 ÷ 4 3
8
Write
with a denominator of 75.
15
8 • 5 40
=
ANSWER:
15 • 5 75
Write in lowest terms:
6
Proficiency Exam Sample Questions and Answers
6)
3 2
+
4 5
3 15
=
ANSWER:
4 20
2
8
+ =
5 20
Add:
__________
23
3
=1
20
20
7)
Subtract: 1
ANSWER:
3 2
−
4 5
3
15
1 =1
4
20
2
8
− =−
5
20
____________
1
8)
9)
7
20
3 2
•
4 5
3 2 3• 2
6
3
=
=
ANSWER: • =
4 5 4 • 5 20 10
3
1
Divide: 1 ÷ 2
4
10
Multiply:
ANSWER:
1
5
7 21 7/ 10/ 1 • 5 5
=
÷
= •
=
4 10 4/ 21/ 2 • 3 6
2
10)
Name a fraction between
3
3
2
and .
4
5
15
8
and
.
20
20
9 10 1 11 12 3 13 14
7
,
= , ,
= , ,
= .
Some possibilities:
20 20 2 20 20 5 20 20 10
ANSWER: Choose a fraction between
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7
Proficiency Exam Sample Questions and Answers
DECIMALS ANSWERS
8
as a decimal.
20
8
ANSWER:
= 8 ÷ 20 = 0.4
20
1)
Write
2)
Add: 7.45 + 8.3
ANSWER: Line up decimal points, then bring down decimal point in the answer: 15.75
3)
Multiply: 8.09 • 0.37
ANSWER: Multiply as usual, count the number of decimal places in the factors, then place
that many decimal places in the answer: 2.9933
4)
Divide: 2.7 ÷ 6.03 (Round quotient to the nearest hundredth.)
ANSWER: Move decimal point in the divisor (6.03) to the right until you have a whole
number (603). Move the decimal point in the dividend (2.7) the same
number of places (270). Bring the decimal point up into the
quotient (answer) and then divide.
.447
603 270.000
Since the directions said to round to the nearest hundredth, you need to carry the division
out to the thousandths place and then round back to the hundredths place: 0.45.
5)
Perform the following operations: 5.12 - 8.6 + 7.54
ANSWER:
5.12 – 8.6 +7.54
-3.48 + 7.54
4.06
6)
Name the place value of the underlined digit: 897.03241
ANSWER: thousandths
7)
Round 54.908732 to the nearest ten-thousandth.
ANSWER: Since 7 is in the ten-thousandths place, we look to the right. Since the 3 is less
than five the 7 will remain a 7: 54.9087 (If the number to the right of 7 was 5 or greater, we
would have changed the 7 to an 8.)
8)
What must be added to 0.57 to get 15?
ANSWER: 15.00 – 0.57 = 14.43
9)
Write six hundred three and eighty-eight ten-thousandths as a decimal.
ANSWER: The last digit of the number should appear in the decimal place given (tenthousandths): 603.0088
10)
Write in order from smallest to largest: 5.0236, 5.02, 5.236, 5.063, 5.3
ANSWER: Line up the decimal points, fill in with zeroes so that all numbers have the same
number of decimal places and then compare their values: 5.02, 5.0236, 5.063, 5.236, 5.3
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PERCENTS ANSWERS
1)
Write 0.783 as a percent.
ANSWER: Move the decimal point 2 places to the right: 78.3%
8
Proficiency Exam Sample Questions and Answers
3
as a percent.
5
2)
Write
3)
ANSWER: Divide 5 into 3, which equals 0.6, then move the decimal point 2 places to the
right: 60%
Change 7.5% to a decimal.
ANSWER: Move the decimal point 2 places to the left: 0.075
Change 24% to a fraction in lowest terms.
4)
ANSWER: 24% =
24
6
=
100 25
For #5 – 10, the proportion method will be used,
5)
%
is
part
=
=
.
100 of total
What is 110% of 400?
ANSWER:
110
x
=
100 400
100 x 44000
=
100
100
x = 440
6)
Shade 40% of the grid:
ANSWER:
40
x
=
100 70
100 x 2800
, so 28 squares should be shaded
=
100
100
x = 28
7)
46.5 is 15% of what number?
ANSWER:
15
46.5
=
100
x
15 x 4650
=
15
15
x = 310
9
Proficiency Exam Sample Questions and Answers
8)
32 is what percent of 140? (Round answer to the nearest tenth of a percent.)
ANSWER:
x
32
=
100 140
140 x 3200
=
140
140
x = 22.9%
9)
0.4% of what number is 16?
ANSWER:
0.4 16
=
100
x
0.4 x 1600
=
0.4
0.4
x = 4000
10)
A basketball player attempts 120 free throws. She makes 90% of them. How many free throws
does she make?
ANSWER:
90
x
=
100 120
100 x 10800
, so she makes 108 free throws
=
100
100
x = 108
10