ACT MATh 2025/2026 | OFFICIAL EXAM MATERIAL
WITh STUDY GUIDE AND PRACTICE TEST | VERIFIED
QUESTIONS AND ANSWERS FROM ThE REAL EXAM |
UPDATED EDITION | PROVEN SUCCESS RATE
Percent Formula - ANSWER Part=Percent x Whole
Multiply Power Exponents - ANSWER add exponents and keep the same base
EX: X₃ · X₂ = X₅
Dividing Power Exponents - ANSWER subtract exponents and keep same base
EX: X₄ ÷ X₂ = X₂
Raising Power to Powers - ANSWER multiply the exponents
EX: X² · X³ = X⁶
Negative Exponent - ANSWER X⁻ⁿ = 1/Xⁿ
Rational Exponent - ANSWER ⁿ√x
Absolute Value - ANSWER |-3| = 3
FOIL - ANSWER First, Outside, Inside and Last.
EX: (x-3) + (x+5) =
,x² + 5x -3x -15=
x² + 2x-15
Chord - ANSWER A segment whose endpoints are on a circle
Arc - ANSWER Any part of the circumference. The curved portion between the
points of a circle.
Sector - ANSWER The part of a circle that looks like a piece of pie. A sector is
bounded by 2 radii and an arc of the circle.
Circumfrence - ANSWER Distance around a circle.
The formula for the area of a circle is - ANSWER πr²
The formula for the circumference is - ANSWER 2πr or πd
Four-sided figures /Quadrilateral - ANSWER - All angles add up to 360 degrees.
-
Rectangle . - ANSWER A parallelogram with four right angles
- Area is bh (base)(height)
- Perimeter is all sides added up
,Square - ANSWER A quadrilateral with 4 sides that are equal and has all 90
degree angles
- Area is bh (base)(height)
- Perimeter is all sides added up
Parallelogram - ANSWER A quadrilateral with two pairs of parallel sides.
- Opposite angles are equal
- Opposite sides are parallel and equal
-
Trapezoid - ANSWER A four-sided figure in which two sides are parallel.
- Area is 1/2(base 1)(base 2)(height)
- You can divide it by two triangles, or two triangles and a rectangle/square
Rhombus - ANSWER A parallelogram with 4 congruent sides.
- Area is 1/2(base 1)(base 2)(height)
- You can divide it by two triangles, or two triangles and a rectangle/square
Angle Facts - ANSWER - The longest side is opposite the largest angle
- The shortest side is opposite the smallest angle
- The third side of any triangle is always less than the sum and greater the
difference of the other two sides.
, Median - ANSWER middle number - put all numbers in order and pick the middle
number
Mode - ANSWER the number that occurs the MOST
Angles in a Triangle - ANSWER the three interior angles add to 180 degrees
Y Intercept - ANSWER y = mx +b (y intercept is b; when x = 0 what is y; where a
line crosses the y axis)
Slope - ANSWER change in y / change in x; rise / run
Permutations & Combinations - ANSWER Use the dash method (ex. _____ *
_____ * _____ )
Distributing - ANSWER
Properties of an Isosceles Trapezoid - ANSWER -opposite sides are equal; -top
two angles are congruent; -bottom two angles are congruent; -diagonals are
congruent
Triangle Side Lengths - ANSWER A side length of a triangle is: (1) greater than
the other two sides subtracted; (2) less than the sum of the other two sides
Perpendicular lines - ANSWER 1 point in common, form a right angle, slope are
negative reciprocals (i.e. 2/3 and -3/2)
WITh STUDY GUIDE AND PRACTICE TEST | VERIFIED
QUESTIONS AND ANSWERS FROM ThE REAL EXAM |
UPDATED EDITION | PROVEN SUCCESS RATE
Percent Formula - ANSWER Part=Percent x Whole
Multiply Power Exponents - ANSWER add exponents and keep the same base
EX: X₃ · X₂ = X₅
Dividing Power Exponents - ANSWER subtract exponents and keep same base
EX: X₄ ÷ X₂ = X₂
Raising Power to Powers - ANSWER multiply the exponents
EX: X² · X³ = X⁶
Negative Exponent - ANSWER X⁻ⁿ = 1/Xⁿ
Rational Exponent - ANSWER ⁿ√x
Absolute Value - ANSWER |-3| = 3
FOIL - ANSWER First, Outside, Inside and Last.
EX: (x-3) + (x+5) =
,x² + 5x -3x -15=
x² + 2x-15
Chord - ANSWER A segment whose endpoints are on a circle
Arc - ANSWER Any part of the circumference. The curved portion between the
points of a circle.
Sector - ANSWER The part of a circle that looks like a piece of pie. A sector is
bounded by 2 radii and an arc of the circle.
Circumfrence - ANSWER Distance around a circle.
The formula for the area of a circle is - ANSWER πr²
The formula for the circumference is - ANSWER 2πr or πd
Four-sided figures /Quadrilateral - ANSWER - All angles add up to 360 degrees.
-
Rectangle . - ANSWER A parallelogram with four right angles
- Area is bh (base)(height)
- Perimeter is all sides added up
,Square - ANSWER A quadrilateral with 4 sides that are equal and has all 90
degree angles
- Area is bh (base)(height)
- Perimeter is all sides added up
Parallelogram - ANSWER A quadrilateral with two pairs of parallel sides.
- Opposite angles are equal
- Opposite sides are parallel and equal
-
Trapezoid - ANSWER A four-sided figure in which two sides are parallel.
- Area is 1/2(base 1)(base 2)(height)
- You can divide it by two triangles, or two triangles and a rectangle/square
Rhombus - ANSWER A parallelogram with 4 congruent sides.
- Area is 1/2(base 1)(base 2)(height)
- You can divide it by two triangles, or two triangles and a rectangle/square
Angle Facts - ANSWER - The longest side is opposite the largest angle
- The shortest side is opposite the smallest angle
- The third side of any triangle is always less than the sum and greater the
difference of the other two sides.
, Median - ANSWER middle number - put all numbers in order and pick the middle
number
Mode - ANSWER the number that occurs the MOST
Angles in a Triangle - ANSWER the three interior angles add to 180 degrees
Y Intercept - ANSWER y = mx +b (y intercept is b; when x = 0 what is y; where a
line crosses the y axis)
Slope - ANSWER change in y / change in x; rise / run
Permutations & Combinations - ANSWER Use the dash method (ex. _____ *
_____ * _____ )
Distributing - ANSWER
Properties of an Isosceles Trapezoid - ANSWER -opposite sides are equal; -top
two angles are congruent; -bottom two angles are congruent; -diagonals are
congruent
Triangle Side Lengths - ANSWER A side length of a triangle is: (1) greater than
the other two sides subtracted; (2) less than the sum of the other two sides
Perpendicular lines - ANSWER 1 point in common, form a right angle, slope are
negative reciprocals (i.e. 2/3 and -3/2)
