HSPT Math Review with complete
solution
Commutative Property - 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
Distributive 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)
Exponent - A raised number that tells the power of the base.
i.e. 43 = 4 • 4 • 4 = 64
62 = 6 • 6 = 36
Identity Property - 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
Inequality - A mathematical sentence that shows the relationship between quantities
that are not equivalent.
i.e. 5‹8
5b + 2 ≥ 12
Integers - The set of positive whole numbers, negative whole numbers and zero.
i.e. ...-4, -3, -2, -1, 0, 1, 2, 3, 4
Irrational Number - 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...
Mean - 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
Median - 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
Mode - 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.
Probability - 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
Proportion - An equation that states that two ratios are equivalent.
i.e. 5 = 25
12 60
Range - 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.
Rational Number - 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
Scientific Notation - 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
Zero Product Property - The product of any number and zero equals zero.
i.e. 3•0=0
Compatible numbers - Numbers that can be divided evenly; useful in estimating
quotients
Ex. 27.2÷4.14 ≈ 28÷4=7...28and4arecompatible#s.
Reciprocal - A number that can be multiplied by another number to make 1 (numerator
and denominator
are switched)
Ex. is the reciprocal of because
×=1
Percent - A ratio that compares a number to 100
Ex. 25% is a percent that represents ( ).
solution
Commutative Property - 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
Distributive 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)
Exponent - A raised number that tells the power of the base.
i.e. 43 = 4 • 4 • 4 = 64
62 = 6 • 6 = 36
Identity Property - 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
Inequality - A mathematical sentence that shows the relationship between quantities
that are not equivalent.
i.e. 5‹8
5b + 2 ≥ 12
Integers - The set of positive whole numbers, negative whole numbers and zero.
i.e. ...-4, -3, -2, -1, 0, 1, 2, 3, 4
Irrational Number - 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...
Mean - 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
Median - 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
Mode - 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.
Probability - 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
Proportion - An equation that states that two ratios are equivalent.
i.e. 5 = 25
12 60
Range - 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.
Rational Number - 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
Scientific Notation - 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
Zero Product Property - The product of any number and zero equals zero.
i.e. 3•0=0
Compatible numbers - Numbers that can be divided evenly; useful in estimating
quotients
Ex. 27.2÷4.14 ≈ 28÷4=7...28and4arecompatible#s.
Reciprocal - A number that can be multiplied by another number to make 1 (numerator
and denominator
are switched)
Ex. is the reciprocal of because
×=1
Percent - A ratio that compares a number to 100
Ex. 25% is a percent that represents ( ).
