HSPT Math Exam Review with Complete
Solutions
States that two or more numbers can be added or multiplied in any order and still arrive
at the same sum or product. i.e. 8 + 20 = 20 + 8 7 • 12 = 12 • 7 - ANS-Commutative
Property
If you multiply a sum by a number, you will get the same result if you multiply each
addend by that number and then add the products. i.e. 4(7 + 6) = 4(7) + 4(6) - ANS-
Distributive Property
A raised number that tells the power of the base.
i.e. 43 = 4 • 4 • 4 = 64
62 = 6 • 6 = 36 - ANS-Exponent
Has 2 parts. The sum of any number and Zero is that number. The product of any
number and One is that number. i.e. 8 + 0 = 8
45(1) = 45 - ANS-Identity Property
A mathematical sentence that shows the relationship between quantities that are not
equivalent.
i.e. 5‹8
5b + 2 ≥ 12 - ANS-Inequality
The set of positive whole numbers, negative whole numbers and zero.
i.e. ...-4, -3, -2, -1, 0, 1, 2, 3, 4 - ANS-Integers
A number that cannot be expressed as a ratio of two integers or as a repeating or
terminating decimal.
i.e. 4.45683127406792103694396...
∏ = 3.14159265358979323846... - ANS-Irrational Number
In a numerical data set, the sum of all the data divided by the number of data items.
i.e. Find the mean of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31
1. 12+45+32+15+40+25+29+49+22+27+31+33+31 = 391 2. 391 ÷ 13 = 30.076923
3. Round to the hundredths place = 30.08 - ANS-Mean
The middle item in a data set ordered from least to greatest.
i.e. Find the median of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33,
31
1. Arrange data from least to greatest
, 12, 15, 22, 25, 27, 29, 31, 31, 32, 33, 40, 45, 49
2. Find the center # 31 - ANS-Median
The item or items that appear the most often in a data set.
i.e. Find the mode of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31
The # that appears the most is 31. - ANS-Mode
A number from 0 to 1 that tells how likely an event is to happen.
i.e. What is the probability that I will get "heads" when I flip a coin?
1 out of 2, 50%, 0.5, 1:2, 1⁄2 - ANS-Probability
An equation that states that two ratios are equivalent.
i.e. 5 = 25
12 60 - ANS-Proportion
The difference between the greatest data value and the least data value in a data set.
i.e. Find the range of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31
The largest data item is 49. The smallest data item is 12. Subtract the two: 49 - 12 = 37.
Therefore the range is 37 for this data set. - ANS-Range
Any number that can be expressed as a ratio of two integers.
i.e. 6 can be expressed as 6, and 0.5 as 1.
12 - ANS-Rational Number
A number that is written as the product of a decimal greater than or equal to 1 and less
than ten and a power of 10.
i.e. Write 6,224,000,000,000 in scientific notation. 6.224 • 1012 - ANS-Scientific
Notation
The product of any number and zero equals zero.
i.e. 3•0=0 - ANS-Zero Product Property
Numbers that can be divided evenly; useful in estimating quotients
Ex. 27.2÷4.14 ≈ 28÷4=7...28and4arecompatible#s. - ANS-Compatible numbers
A number that can be multiplied by another number to make 1 (numerator and
denominator
are switched)
Ex. is the reciprocal of because
× = 1 - ANS-Reciprocal
A ratio that compares a number to 100
Ex. 25% is a percent that represents ( ). - ANS-Percent
Solutions
States that two or more numbers can be added or multiplied in any order and still arrive
at the same sum or product. i.e. 8 + 20 = 20 + 8 7 • 12 = 12 • 7 - ANS-Commutative
Property
If you multiply a sum by a number, you will get the same result if you multiply each
addend by that number and then add the products. i.e. 4(7 + 6) = 4(7) + 4(6) - ANS-
Distributive Property
A raised number that tells the power of the base.
i.e. 43 = 4 • 4 • 4 = 64
62 = 6 • 6 = 36 - ANS-Exponent
Has 2 parts. The sum of any number and Zero is that number. The product of any
number and One is that number. i.e. 8 + 0 = 8
45(1) = 45 - ANS-Identity Property
A mathematical sentence that shows the relationship between quantities that are not
equivalent.
i.e. 5‹8
5b + 2 ≥ 12 - ANS-Inequality
The set of positive whole numbers, negative whole numbers and zero.
i.e. ...-4, -3, -2, -1, 0, 1, 2, 3, 4 - ANS-Integers
A number that cannot be expressed as a ratio of two integers or as a repeating or
terminating decimal.
i.e. 4.45683127406792103694396...
∏ = 3.14159265358979323846... - ANS-Irrational Number
In a numerical data set, the sum of all the data divided by the number of data items.
i.e. Find the mean of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31
1. 12+45+32+15+40+25+29+49+22+27+31+33+31 = 391 2. 391 ÷ 13 = 30.076923
3. Round to the hundredths place = 30.08 - ANS-Mean
The middle item in a data set ordered from least to greatest.
i.e. Find the median of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33,
31
1. Arrange data from least to greatest
, 12, 15, 22, 25, 27, 29, 31, 31, 32, 33, 40, 45, 49
2. Find the center # 31 - ANS-Median
The item or items that appear the most often in a data set.
i.e. Find the mode of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31
The # that appears the most is 31. - ANS-Mode
A number from 0 to 1 that tells how likely an event is to happen.
i.e. What is the probability that I will get "heads" when I flip a coin?
1 out of 2, 50%, 0.5, 1:2, 1⁄2 - ANS-Probability
An equation that states that two ratios are equivalent.
i.e. 5 = 25
12 60 - ANS-Proportion
The difference between the greatest data value and the least data value in a data set.
i.e. Find the range of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31
The largest data item is 49. The smallest data item is 12. Subtract the two: 49 - 12 = 37.
Therefore the range is 37 for this data set. - ANS-Range
Any number that can be expressed as a ratio of two integers.
i.e. 6 can be expressed as 6, and 0.5 as 1.
12 - ANS-Rational Number
A number that is written as the product of a decimal greater than or equal to 1 and less
than ten and a power of 10.
i.e. Write 6,224,000,000,000 in scientific notation. 6.224 • 1012 - ANS-Scientific
Notation
The product of any number and zero equals zero.
i.e. 3•0=0 - ANS-Zero Product Property
Numbers that can be divided evenly; useful in estimating quotients
Ex. 27.2÷4.14 ≈ 28÷4=7...28and4arecompatible#s. - ANS-Compatible numbers
A number that can be multiplied by another number to make 1 (numerator and
denominator
are switched)
Ex. is the reciprocal of because
× = 1 - ANS-Reciprocal
A ratio that compares a number to 100
Ex. 25% is a percent that represents ( ). - ANS-Percent
