AFOQT | Questions with 100% Verified Answers | Latest Update
2026/2027
Question: Synonum
Answer: Same meaning or definition means the same or almost the same.
Question: Antonym (n)
Answer: a word that means the opposite of another word
Question: Classification
Answer: #1 is a specific type of or belongs to #2
Question: homonyms
Answer: Words that sound the same but have different meanings also called homophones
Question: Fractions into lowest terms
Answer: To reduce a fraction to lowest terms (also called its simplest form), divide both the numerator and
denominator by the GCD. For example, 2/3 is in lowest form, but 4/6 is not in lowest form (the GCD of 4 and 6
is 2) and 4/6 can be expressed as 2/3.
Question: Volume of a cube
Answer: To find the volume of any cube you need to know the length, width and height. The formula to find the
volume multiplies the length by the width by the height. The good news for a cube is that the measure of each
of these dimensions is exactly the same.
Question: factorial or !
Answer: The factorial function (symbol: !) means to multiply a series of descending natural numbers.
Examples: 4! = 4 × 3 × 2 × 1 = 24 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 1! = 1
Question: Dividing Fractions
Answer: 1/3 ÷ 2/5 = becomes: 1/3 * __ = Now we flip the second fraction (2/5) over to find its reciprocal, 5/2:
1/3 * 5/2 = Now multiply the numerators (top numbers) of the two fractions, 1*5 = 5. 1/3 * 5/2 = 5/ Now
multiply the denominators (bottom numbers) of the two fractions, 3*2 = 6. We now have: 1/3 * 5/2 = 5/6 This
particular fraction cannot be simplified further, so we have our answer.
Question: Types of analogies
Answer: synonym, antonym, action, function, size, degree, amount, part to whole, member to group, units of
measurement, mathematical
Question: Types of numbers
Answer: natural: greater than 0 and has no decimal or fraction Whole: natural numbers and 0 Integer:
positive/negative numbers and 0 Rational: can be represented as fraction or decimal , must terminate or
resolve into repeating pattern Irrational: cannot be represented as a fraction, decimal never ends or resolves
into pattern (ex. pi) Real: number that can be represented by a point on a number line. Includes all
rational/irrational Imaginary: includes the imaginary unit i = square root of -1. complex: in the form of a + bi
where a and b are real numbers
,Question: Closed number system
Answer: a system is closed under an operation if performing that operation on two elements of the system
results in another element of that system
Question: Properties of number systems
Answer: adding, subtracting, and multiplying are closed. dividing is not. rational numbers are closed under all
operations except division real numbers are closed under all operations complex numbers are closed under all
four operations irrational numbers are not closed under any of the operations
Question: Commutative property
Answer: holds for a operation if the order doesnt matter
Question: Associative property
Answer: the elements of an operation can be regrouped without changing the result
Question: Distributive property
Answer: multiplication over addition allows a product of sums to be written as a sum of products: a(b+c)= ab +
ac
Question: Identity element
Answer: operation performed with an element and the identity element the result is the element (a x 1 = a)
Question: Inverse element
Answer: operation performed with the inverse element results in the identity element a + (-a) = 0
Question: American units
Answer: length: inch/foot/yard/mile mass: ounce/pound/ton volume: cup/pint/quart/gallon force: pound-force
pressure: pound-force per square inch work and energy: cal/british thermal unit temperature: fahrenheit
charge: faraday
Question: SI units
Answer: length: meter mass: gram volume: liter force: newton pressure: pascal work and energy: joule
temperature: kelvin charge: coulomb
Question: metric prefixes
Answer: tera: 10^12 T giga: 10^9 G mega: 10^6 M kilo: 10^3 k hecto: 10^2 h deca: 10^1 da deci: 10^-1 d
centi: 10^-2 c milli: 10^-3 m micro: 10^-6 u nano: 10^-9 n pico: 10^-12 p
Question: conversions (inch, meter, yard, mi, gal, oz, lb, cal, F)
Answer: 1 inch = 2.54cm 1 meter = 3.28 ft 1 yd = .914m 1 mi = 1.61km 1 gal = 3.785 L 1 oz = 28.35 g 1 lb =
.454 kg 1 cal = 4.19 J 1 degree F: 5/9 (F-32C)
Question: proper fraction
Answer: fraction that equals less than 1
Question: improper fraction
Answer: fraction that equals more than 1
,Question: IQR
Answer: interquartile range = Q3-Q1
Question: Measures of variation/dispersion
Answer: range, IQR, variance, standard deviation
Question: formula for standard deviations (sample/population)
Answer: pg. 33
Question: formula for variance
Answer: pg. 33
Question: Complement (probablility)
Answer: The probability that an event won't occur
Question: Independent probability
Answer: the probability of one occurring does not affect the probability of the other
Question: Dependent probability
Answer: the probability of one occurring does have an effect on the probability of the other
Question: conditional probability
Answer: the probability that one event occurs given that another has occurred.
Question: Mutually exclusive probability
Answer: two events cant happen at the same time
Question: Mutually inclusive probability
Answer: events share common outcomes/ can happen at same time
Question: Formula for finding nth term
Answer: pg. 38
Question: Formula for finding partial sum
Answer: pg.38
Question: Formula for finding X/Y intercepts and slope
Answer: X: C/A Y: C/B Slope: -A/B in Ax + By = C form
Question: Formula for slope given two points
Answer: (Y2-Y1)/(X2-X1)
Question: distance formula
Answer: pg.54
, Question: midpoint formula
Answer: pg.54
Question: zeros/roots of a quadratic are the...
Answer: x intercepts
Question: standard form of a quadratic
Answer: Ax^2 + Bx + C axis of symmetry: x = -b/2a vertex: pg. 59
Question: vertex form of a quadratic
Answer: y = a(x-h)^2 + k axis of symmetry: x=h vertex: (h, k)
Question: The effect of A (first term) on a parabola
Answer: if negative: opens downward if positive: opens upward if a fraction less than 1: wider if above 1:
narrower
Question: How to convert standard form to vertex form
Answer: complete the square 1, move c to the left side of the equation
2. divide the entire equation through by a (to make the coefficient of x^2 be 1).
3. Take half of the coefficient of x, square it, and then add it to both sides of the equation.
4. convert the right side of the equation to a perfect binomial squared, (x + m)^2.
5. Isolate y to put the equation in proper vertex form.
Question: quadratic formula
Answer: pg. 61
Question: if (B^2 - 4AC) is 0, + or - then...
Answer: 0: only 1 real root/ vertex on x axis +: 2 real roots, 2 x intercepts -: 2 complex roots, 0 x intercepts
Question: colinear
Answer: 2 points on the same line
Question: Line segment
Answer: line with 2 endpoints and a finite length
Question: ray
Answer: line with one endpoint and extends indefinitely in one direction
Question: line
Answer: extends indefinitely in both directions
Question: complementary angles
Answer: add up to 90
Question: supplementary angles
Answer: add up to 180
2026/2027
Question: Synonum
Answer: Same meaning or definition means the same or almost the same.
Question: Antonym (n)
Answer: a word that means the opposite of another word
Question: Classification
Answer: #1 is a specific type of or belongs to #2
Question: homonyms
Answer: Words that sound the same but have different meanings also called homophones
Question: Fractions into lowest terms
Answer: To reduce a fraction to lowest terms (also called its simplest form), divide both the numerator and
denominator by the GCD. For example, 2/3 is in lowest form, but 4/6 is not in lowest form (the GCD of 4 and 6
is 2) and 4/6 can be expressed as 2/3.
Question: Volume of a cube
Answer: To find the volume of any cube you need to know the length, width and height. The formula to find the
volume multiplies the length by the width by the height. The good news for a cube is that the measure of each
of these dimensions is exactly the same.
Question: factorial or !
Answer: The factorial function (symbol: !) means to multiply a series of descending natural numbers.
Examples: 4! = 4 × 3 × 2 × 1 = 24 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 1! = 1
Question: Dividing Fractions
Answer: 1/3 ÷ 2/5 = becomes: 1/3 * __ = Now we flip the second fraction (2/5) over to find its reciprocal, 5/2:
1/3 * 5/2 = Now multiply the numerators (top numbers) of the two fractions, 1*5 = 5. 1/3 * 5/2 = 5/ Now
multiply the denominators (bottom numbers) of the two fractions, 3*2 = 6. We now have: 1/3 * 5/2 = 5/6 This
particular fraction cannot be simplified further, so we have our answer.
Question: Types of analogies
Answer: synonym, antonym, action, function, size, degree, amount, part to whole, member to group, units of
measurement, mathematical
Question: Types of numbers
Answer: natural: greater than 0 and has no decimal or fraction Whole: natural numbers and 0 Integer:
positive/negative numbers and 0 Rational: can be represented as fraction or decimal , must terminate or
resolve into repeating pattern Irrational: cannot be represented as a fraction, decimal never ends or resolves
into pattern (ex. pi) Real: number that can be represented by a point on a number line. Includes all
rational/irrational Imaginary: includes the imaginary unit i = square root of -1. complex: in the form of a + bi
where a and b are real numbers
,Question: Closed number system
Answer: a system is closed under an operation if performing that operation on two elements of the system
results in another element of that system
Question: Properties of number systems
Answer: adding, subtracting, and multiplying are closed. dividing is not. rational numbers are closed under all
operations except division real numbers are closed under all operations complex numbers are closed under all
four operations irrational numbers are not closed under any of the operations
Question: Commutative property
Answer: holds for a operation if the order doesnt matter
Question: Associative property
Answer: the elements of an operation can be regrouped without changing the result
Question: Distributive property
Answer: multiplication over addition allows a product of sums to be written as a sum of products: a(b+c)= ab +
ac
Question: Identity element
Answer: operation performed with an element and the identity element the result is the element (a x 1 = a)
Question: Inverse element
Answer: operation performed with the inverse element results in the identity element a + (-a) = 0
Question: American units
Answer: length: inch/foot/yard/mile mass: ounce/pound/ton volume: cup/pint/quart/gallon force: pound-force
pressure: pound-force per square inch work and energy: cal/british thermal unit temperature: fahrenheit
charge: faraday
Question: SI units
Answer: length: meter mass: gram volume: liter force: newton pressure: pascal work and energy: joule
temperature: kelvin charge: coulomb
Question: metric prefixes
Answer: tera: 10^12 T giga: 10^9 G mega: 10^6 M kilo: 10^3 k hecto: 10^2 h deca: 10^1 da deci: 10^-1 d
centi: 10^-2 c milli: 10^-3 m micro: 10^-6 u nano: 10^-9 n pico: 10^-12 p
Question: conversions (inch, meter, yard, mi, gal, oz, lb, cal, F)
Answer: 1 inch = 2.54cm 1 meter = 3.28 ft 1 yd = .914m 1 mi = 1.61km 1 gal = 3.785 L 1 oz = 28.35 g 1 lb =
.454 kg 1 cal = 4.19 J 1 degree F: 5/9 (F-32C)
Question: proper fraction
Answer: fraction that equals less than 1
Question: improper fraction
Answer: fraction that equals more than 1
,Question: IQR
Answer: interquartile range = Q3-Q1
Question: Measures of variation/dispersion
Answer: range, IQR, variance, standard deviation
Question: formula for standard deviations (sample/population)
Answer: pg. 33
Question: formula for variance
Answer: pg. 33
Question: Complement (probablility)
Answer: The probability that an event won't occur
Question: Independent probability
Answer: the probability of one occurring does not affect the probability of the other
Question: Dependent probability
Answer: the probability of one occurring does have an effect on the probability of the other
Question: conditional probability
Answer: the probability that one event occurs given that another has occurred.
Question: Mutually exclusive probability
Answer: two events cant happen at the same time
Question: Mutually inclusive probability
Answer: events share common outcomes/ can happen at same time
Question: Formula for finding nth term
Answer: pg. 38
Question: Formula for finding partial sum
Answer: pg.38
Question: Formula for finding X/Y intercepts and slope
Answer: X: C/A Y: C/B Slope: -A/B in Ax + By = C form
Question: Formula for slope given two points
Answer: (Y2-Y1)/(X2-X1)
Question: distance formula
Answer: pg.54
, Question: midpoint formula
Answer: pg.54
Question: zeros/roots of a quadratic are the...
Answer: x intercepts
Question: standard form of a quadratic
Answer: Ax^2 + Bx + C axis of symmetry: x = -b/2a vertex: pg. 59
Question: vertex form of a quadratic
Answer: y = a(x-h)^2 + k axis of symmetry: x=h vertex: (h, k)
Question: The effect of A (first term) on a parabola
Answer: if negative: opens downward if positive: opens upward if a fraction less than 1: wider if above 1:
narrower
Question: How to convert standard form to vertex form
Answer: complete the square 1, move c to the left side of the equation
2. divide the entire equation through by a (to make the coefficient of x^2 be 1).
3. Take half of the coefficient of x, square it, and then add it to both sides of the equation.
4. convert the right side of the equation to a perfect binomial squared, (x + m)^2.
5. Isolate y to put the equation in proper vertex form.
Question: quadratic formula
Answer: pg. 61
Question: if (B^2 - 4AC) is 0, + or - then...
Answer: 0: only 1 real root/ vertex on x axis +: 2 real roots, 2 x intercepts -: 2 complex roots, 0 x intercepts
Question: colinear
Answer: 2 points on the same line
Question: Line segment
Answer: line with 2 endpoints and a finite length
Question: ray
Answer: line with one endpoint and extends indefinitely in one direction
Question: line
Answer: extends indefinitely in both directions
Question: complementary angles
Answer: add up to 90
Question: supplementary angles
Answer: add up to 180
