PRAXIS 5164 LATEST 2026 TEST PAPER QUESTIONS AND
ANSWERS RATED A+
✔✔independent events - ✔✔Two or more events in which the outcome of one event
does not affect the outcome of the other event(s).
✔✔dependent events - ✔✔Two or more events in which the outcome of one event
affects the outcome of the other event(s).
✔✔mutually exclusive outcomes - ✔✔cannot occur simultaneously
✔✔random variable - ✔✔a variable whose value is a numerical outcome of a random
phenomenon
✔✔objective probability - ✔✔based on mathematical formulas and documented
evidence
✔✔subjective probability - ✔✔based on personal or professional feelings and
judgements
✔✔ real number - ✔✔all rational and irrational numbers
✔✔irrational number - ✔✔cannot be written as fractions/decimals because the number
of decimal places is infinite and there is no recurring pattern of digits within the number
✔✔rational number - ✔✔all integers, decimals and fractions. any terminating or
repeating decimal
✔✔integer - ✔✔any positive or negative whole number including zero, no fractions,
decimals, or mixed numbers
✔✔whole number - ✔✔positive integers and zero
✔✔natural number - ✔✔counting numbers or all positive numbers beginning with 1
✔✔a^1 = - ✔✔a
✔✔1^n = - ✔✔1
✔✔a^n x a^m = - ✔✔a^n+m
✔✔a^n / a^m = - ✔✔a^n-m
✔✔(a^n)^m = - ✔✔a^nm
, ✔✔a^-n = - ✔✔1/a^n
✔✔(ab)^n = - ✔✔a^n x b^n
✔✔(a/b)^n = - ✔✔a^n / b^n
✔✔commutative property - ✔✔the property that says that two or more numbers can be
added or multiplied in any order without changing the result.
a+b=b+a
axb=bxa
✔✔associative property - ✔✔changing the grouping of numbers will NOT change the
value.
a+(b+c)=(a+b)+c
a(bc)=(ab)c
✔✔distributive property - ✔✔a property indicating a special way in which multiplication
is applied to the addition of two or more numbers in which each term inside a set of
parentheses can be multiplied by a factor outside the parentheses
a(b+c)= ab+ac
✔✔identity property - ✔✔a) the sum of a number and 0 is the number;
b) the product of a number and 1 is the number
a+0=a
ax1=a
✔✔inverse property - ✔✔the sum of a number and its opposite is 0
a+(-a)=0
a(1/a) = 1
✔✔n squareroot of a = b - ✔✔b^n = a
✔✔add/subtract fractions - ✔✔get a common denominator and then add/subtract the
numerators
✔✔multiply fractions - ✔✔multiply straight across
✔✔divide fractions - ✔✔copy change flip
✔✔decimal to fraction - ✔✔put decimal in numerator over 1. multiply the numerator and
denominator by tens until there are no more decimals and simplify
✔✔decimal to percent - ✔✔move decimal two places right
ANSWERS RATED A+
✔✔independent events - ✔✔Two or more events in which the outcome of one event
does not affect the outcome of the other event(s).
✔✔dependent events - ✔✔Two or more events in which the outcome of one event
affects the outcome of the other event(s).
✔✔mutually exclusive outcomes - ✔✔cannot occur simultaneously
✔✔random variable - ✔✔a variable whose value is a numerical outcome of a random
phenomenon
✔✔objective probability - ✔✔based on mathematical formulas and documented
evidence
✔✔subjective probability - ✔✔based on personal or professional feelings and
judgements
✔✔ real number - ✔✔all rational and irrational numbers
✔✔irrational number - ✔✔cannot be written as fractions/decimals because the number
of decimal places is infinite and there is no recurring pattern of digits within the number
✔✔rational number - ✔✔all integers, decimals and fractions. any terminating or
repeating decimal
✔✔integer - ✔✔any positive or negative whole number including zero, no fractions,
decimals, or mixed numbers
✔✔whole number - ✔✔positive integers and zero
✔✔natural number - ✔✔counting numbers or all positive numbers beginning with 1
✔✔a^1 = - ✔✔a
✔✔1^n = - ✔✔1
✔✔a^n x a^m = - ✔✔a^n+m
✔✔a^n / a^m = - ✔✔a^n-m
✔✔(a^n)^m = - ✔✔a^nm
, ✔✔a^-n = - ✔✔1/a^n
✔✔(ab)^n = - ✔✔a^n x b^n
✔✔(a/b)^n = - ✔✔a^n / b^n
✔✔commutative property - ✔✔the property that says that two or more numbers can be
added or multiplied in any order without changing the result.
a+b=b+a
axb=bxa
✔✔associative property - ✔✔changing the grouping of numbers will NOT change the
value.
a+(b+c)=(a+b)+c
a(bc)=(ab)c
✔✔distributive property - ✔✔a property indicating a special way in which multiplication
is applied to the addition of two or more numbers in which each term inside a set of
parentheses can be multiplied by a factor outside the parentheses
a(b+c)= ab+ac
✔✔identity property - ✔✔a) the sum of a number and 0 is the number;
b) the product of a number and 1 is the number
a+0=a
ax1=a
✔✔inverse property - ✔✔the sum of a number and its opposite is 0
a+(-a)=0
a(1/a) = 1
✔✔n squareroot of a = b - ✔✔b^n = a
✔✔add/subtract fractions - ✔✔get a common denominator and then add/subtract the
numerators
✔✔multiply fractions - ✔✔multiply straight across
✔✔divide fractions - ✔✔copy change flip
✔✔decimal to fraction - ✔✔put decimal in numerator over 1. multiply the numerator and
denominator by tens until there are no more decimals and simplify
✔✔decimal to percent - ✔✔move decimal two places right
