Acadec 2026-2027 MATH - All Sections

What is simple interest formula?

P(1 + rt)

P = Initial amount of money

r = interest rate

t = time

What is compound interest formula?

P * (1 + r/n)^nt

P = initial amount of money invested

r = interest rate

n = compound number of times per year

t = number of years

What is the multiplication principle?

When selecting two objects, the total number of possible ways to select both of them at the same time is the

product of the number of ways to select each object.

What is a permutation?

n! / (n-k)!

What is a combination?

n! / (n-k)!k!

What is the probability of an event E occuring?

P(E) = (number of ways E can occur) / (total number of outcomes)

What is the binomial distribution formula?

An event with n outcomes has p outcomes considered success, q outcomes that considered failure. If this event is repeated r times, the probability of getting s successes and f failures is:

What is the pythagorean theorem?

a^2 + b^2 = c^2

What are some 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 are the sides of a 45-45-90 triangle?

x, x, x√2

What are the sides of a 30-60-90 triangle?

x, x√3, 2x

What is the midpoint formula?

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

What does collinear mean?

points that lie on the same line

How do you calculate slope?

y2-y1/x2-x1

What is the vector equation of a line?

If the x coordintes of 2 points on the graph of y = x^2 at up to 3, what does this mean?

The slope between these 2 points is 3

What is the distance formula?

What is the distance formula for 3D?

What is the equation of a circle in the xy coordinate plane?

What is the equation of a sphere in the xyz coordinate plane?

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

d = |ax0 + by0 + c| / sqrt(a^2 + b^2)

ax + by + c = 0 for the line

x0, y0 for the point

What does parallel mean?

Lines have the same slope

What does perpendicular mean?

Right angles, given a line with slope m, the perpendicular is -1/m

When are two movements in the xyz coordinate plane perpendicular to ech other?

Movement 1:

Movement 2:

When ax + by + cz = 0

(DOT PRODUCT)

Given a plane, any movement between two points are perpendicular to what?

Given the equation Ax + By + Cz = D

Always perpendicular to movement

What is the movement between two points calculated to be?

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

d = |Ax1 + By1 + Cz1 + D| / sqrt(A^2 + B^2 + C^2)

Ax + By + Cz + D = 0 -> Plane

x1, y1, z1 -> point

What are the properties of parallelograms?

Opposite sides of the quadrilateral are parallel for both

What are the properties of rhombuses?

Opposite sides of the quadrilateral are parallel for both

All four sides equal in length to each other

What are the properties of kites?

Two pairs of adjacent congruent sides

Perpendicular diagonals where just one of the diagonals bisects the other

What are the properties of rectangles and squares?

You should know this lol

What is a concave polygon?

A polygon that has at least one interior angle greater than 180 degrees.

What is a convex polygon?

a polygon in which each interior angle has a measure less than 180

What is the sum of the angles in a polygon formula?

(n-2) * 180 degrees

What is the number of diagonls in a convex polygon with n sides?

n(n-3) / 2

What is a regular polygon?

a polygon that is both equilateral and equiangular

What is the area of a regular polygon given n sides?

1/2 * a * P

a = apothem (perpendicular distance from the center of the polygon to midpoint of any side)

P = perimeter

What is surface area?

The total area that the surface of an object has.

What is volume?

The amount of space an object takes up

What is a prism?

Solid with common polygon as top and bottom and rectangles for other faces

What is a cylinder?

Prism that has circle as a base

What is the surface area of a cylinder with height h and radius r

2pir^2 + 2pirh

What is the volume of a cylinder?

pir^2h

What is a pyramid?

Polygon base and all sides of a pyramid meet at a vertex at top of a pyramid

What is the volume of a pyramid?

1/3 * B * h

How do you find the surface area of a pyramid?

Add (areas of all triangles) and the (area of the base). Make sure you calculate slant height.

What is the surface area of a cone?

pir^2 + pirl

r = radius

l = slant height

What is the surface area of a sphere?

4pir^2

What is the volume of a sphere?

4/3 * pir^3

What is similarity?

All angles are in equal measure, there is a constant ratio between side lengths

What can we conclude ratio wise if two figures are similar?

Ratio between side lengths: r

Ratio of perimeters: r

Ratio between areas: r^2

Ratio between volume: r^3

What is the area of a circle?

pir^2

What is the central angle?

Angle at center of the circle

What is the arc angle?

Angle of the arc

What is the relationship between central angle and arc angle?

Equal to each other

What is the inscribed angle?

an angle with the vertex on the circle

An inscribed angle whose ray passes through the cneter of the center of the circle has what measure?

1/2 of the arc angle it intercepts

What is a chord?

Line between two points on a circle, not necessarily passing through the center of the circle

What happens when two chords intersect in a circle?

Angle between them is equal to the average of the arc angles formed by the chords

What is a secant?

Extension of a chord through a circle

What is the measure of the angle at the intersection of the secants?

Half of the difference between the big arc angle and small arc angle

What is a tangent line?

Line that touches circle at only 1 point

What is the relationship angle-wise betewen point of tangency and tangent line?

Radius to the point of tangency and tangent line are perpendicular to each other

From a point outside the circle, what is the relationship between the two possible points of tangency?

They are equal

When two chords intersect inside a circle, what is the length of them?

Product of length of segment of one chord = product of the lnegths of the segments of the other chord

Example: AE * EB = CE * CD

What happens when 2 secants intersect outside a circle?

Each scant forms 2 line segmnts created by line segment created by circle and point of intersection

PA * PB = PC * PD

How do you calculate rate of change?

m = change in y/change in x

basically slope bruh

What is a limit?

A value a graph approaches

Do you know derivatives?

Yes I do :)

What is the equation of tangent lines?

y-y1 = m(x-x1)