2026-2027 Acadec MATH - All Sections

What is simple interest?

Amount of interest charged doesn't change

What is simple interest formula?

P(1+rt)

P = initial money

r = interest rate

t = time

What is compound interest?

Interest earned during time period is added to principal amount (interest upon interest)

What is the compound interest formula?

P(1 + r/n)^nt

P = initial amount of money

r = interest rate

n = compounded? times per year

t = years

What is the multiplication principle?

When selecting k objects form different groups, the potal possibilities is n1 * n2 * n3

What is a permutation?

Selection of objects where no object is allowed to be selected more than once + the order of selection matters

What is a combination?

Selection of objects where no object is allowed to be selected more than once + order doesn't matter

What is the permutation formula?

n!/(n-k)!

n = objects

k = how many objects you are selecting

What is the combination formula?

n!/(n-k)!k!

n = objects

k = how many objects you are selecting

What is the formula for arranging things but there are repeating things?

n!/a!b!c!

n = objects

a = repeating # of thing 1...etc

What is the pythagorean theorem?

a^2 + b^2 = c^2

What is a pythagorean triple?

A set of three positive integers a, b, and c that satisfy the equation a² + b² = c².

What are three common pythagorean triples?

3-4-5

5-12-13

8-15-17

What is the diagonal of a 3D box?

sqrt(l^2 + w^2 + h^2)

What is a 45-45-90 triangle's sides?

x, x, x(sqrt2)

What is the hypothenuse if the length of a side of a 45-45-90 triangle is a?

asqrt2

sqrt(2a^2)

What is a 30-60-90's sides?

x, xsqrt3, 2x

If the length is a for a 30-60-90 triangle's shortest side, what is the hypotenuse and the other side?

hypotenuse: 2a

length: sqrt(3a^2), asqrt3

What is the midpoint of a line?

(x1+x2)/2, (y1+y2)/2

How do you do midpoints of 4 dimensional things?

Just take the middle of the w, y, x, z

What does collinear mean?

points that lie on the same line

How do you calculate slope?

(y2-y1)/(x2-x1)

If the x coordinates of 2 points on the graph of y=x^2 add up to 3, what does that mean?

The slope between those two points is 3

What is the distance formula?

sqrt((x2-x1)^2 + (y2-y1)^2)

What is the distance formula for 3D?

sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

What is the circle formula?

(x-a)^2 + (y-b)^2 = r^2

(a,b) = center, r = radius

What is the sphere formula?

(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2

(a,b,c) = center, r = radius

How do you find the distance between a point and a line?

Find the perpendicular slope of the line, convert the OG line to standard form (Ax + By + C = 0)

Apply point-to-line distance formula

What is the point-to-line distance formula?

d = |Ax1 + By1 + C| / sqrt(A^2+B^2)

How do you find the slope of the line perpendicular?

Negative reciprocal (-1/m)

What direction is perpendicular to the direction

Infinite # of ways

Wehn are two movements perpendicular to each other in 3D?

Given the equation Ax + by + Cz = D, what does this mean perpendicular wise?

Any movement between two points in this plane is perpendicular to the movement

How do you find the distance between a point and a line in the 3D space?

Convert the line formula to Ax + By + Cz + D = 0

Apply 3D distance formula

What is the 3D distance formula?

d = |Ax1 + by1 + Cz1 + D| / sqrt(A^2 + B^2 + C^2)

What is a quadrilateral?

A polygon having four sides.

What are the types of quadrilaterals?

Square (you know)

Rectangle (you know)

Parallelogram (Opposite sides are parallel and equal in length, opposites angles are equal).

Rhombus (All four sides are equal length. Opposite sides are parallel)

Trapezoid (Has one pair of opposite sides that are parallel)

Kite: (Two pairs of side lengths that are equal and next to each other, but not opposite)

What does convex mean?

Interior angles are less than 180

What is a concave polygon?

1+ interior angles measuring more than 180 degrees

What is the sum of the angles in a polygon?

(n-2) * 180 degrees

What is the # of diagonals in a convex polygon?

n(n-3) / 2

What is a regular polygon?

Polygon with equilateral and equiangular sides

What is the general formula for a regular polygon's area?

A = ns^2 / 4 * tan((n-2)*180 / 2n)

n = number of sides

s = side length

OR: Just find the height by using tangent and multiply the triangles together

What is a prism?

Solid with common polygon at top and bottom, rectangles for other faces

What is the surface area and volume of a prism?

Just kind of envision it and solve lol

What is the surface area of a cylinder?

2r^2pi + 2rhpi

What is the volume of a cylinder?

pi * r^2h

What is a pyramid?

Polygon base + pyramid sides meet a vertex

What is the volume of a pyramid?

1/3 * Bh

What is the surface area of a cone?

pir^2 + pirl

(l = slant height)

What is the surface area of a sphere?

4pir^2

What is teh volume of a sphere?

4/3 * pir^3

What is similarity?

Two things are similar if their angles are all equal in measure + constant ratio between side lengths

What is the surface area and volume ratio between similar figures?

If the ratio is r:

Ratio of the perimeters = r

Ratio of surface areas = r^2

Ratio between volumes = r^3

What is an inscribed angle?

Angle with vertex on edge of the circle, the angle measure is 1/2 of the arc angle it intercepts

What is a chord?

Line between two points on a circle, does not have to pass through center of the circle

What is the angle between two intersecting chords?

Average of the arc angles formed by the chords

What is a secant?

Extension of a chord through a circle

When two secants intersect outside a circle, what is the angle between them?

Half the distance between the angles of the intercepted arcs

What is a tangent line?

Line touching circle at only point

From a point outside the circle, what is the distance to the two possible points of tangency?

Equal

When two chords intersect inside a circle, what are their lengths?

Product of the lengths of the segments of one chord = product of the lengths of the segments of the other chord

When two secants interesect outside a circle, what happens?

Those secant form two line segments created by circle + point of intersection

Product of length of line segment from point of intersection to circle * sum of the lengths of both line segments = equal for both secant lines

What is the graph of a line?

y=mx+b

You know limits, right?

Yep!