Pre-Algebra and Algebra

Acceleration (see Rates)

Accounting,

word problem, M1D9-Ch, M1D9-Y

Arithmetic progression/sequence, M4D5-C1

Arithmetic series, M4D5-C2

Arithmetic tricks, M4D4-C-1

Axes, coordinate M4D14-C1

Binomial, M4D11-Y2

Change of variable, M4D11-Y5

Computer memory storage, M4D1-Y4,

Continued fraction (see Fractions, nested)

Coordinates, M4D15-C1

Decimals,

converting to fractions, M1D1-Ch-1, M1D1-Ch-1, M4D8-C1, M4D8-Y1

non-repeating non-terminating, conversion to fraction, M4D8-C-3

repeating, M1D1-C2, M1D8-Y1, M1D8-Y2, M4D8-C2

0.111..., M1D9-Y2

Denominator (see Fractions)

Difference of squares, M2D7-C4, M4D1-C1, M4D6-C3, M4D6-Y1

Dimensions of a box, M1D6-C1

Distance from point to a line, M4D14-Y1

Distance (see Rates)

Distributive Law, M5D5-C2

Dividing by Zero, M5D13-Y3

Equations, M1D6-C2

in geometry problems, M2D10-Y2

integer equations, M5D13-C1, M5D13-Y

of a line (see Line)

quadratic, M4D11-C1, M4D11-Y1, M4D12-C1, M4D12-Y1

factoring method, M4D11-C1, M4D11-Y1

formula, M4D12-C1, derivation of, M4D12-Y1

Loh Method of Solving, M4D12-C4

rate equations, M1D13-C2, M1D13-Y3

rational, M1D2-C2, M1D4-C2, M1D15-C3, M4D4-Y1, M4D9-Y1

systems of equations, M4D9-C2, M4D10-C1

Estimation, M1D10-C1, M4D1-C1

Expanding, M4D1-Y2, M4D2-Y3, M4D6-C-1, M4D11-C2, M4D11-Y2, M4D16-C1

Exponents,

dividing, M4D7-C3

fractional, M4D7-C2

order of operations, M4D7-C1

powers of 2, 1024⁴, M4D1-Y1

powers of 2, sum of, M4D5-Y-1

powers of 5, M1W2D5-Ch-3

power tower, M4D7-Y1, M5D14-Ch-1

rules for, M4D7-C1

Fermi estimate, M1W3D10-Y-1

Factoring, M4D2-C2, M4D5-Y4

Factoring a quadratic, M4D11-C2

Fibonacci Sequence, M4D4-C1

Floor function, M5W2D6-Ch-1

Fractions,

common denominator, M1D1-Y2, M1D4-Y1, M1D13-Y4, M5D5-Y2

comparing, M1D3-C1, M1D4-Y1

continued fraction (see nested)

conversion to decimals, M1D1-Y1, M4D4-Y1, M4D4-Y3

difference of, M0D14-C1

distributions, M1D12-C2

equal to terminating decimals, M5D16-C1

improper, M1D3-Y

in word problems, M1D2-Y1

nested, M1D2-C1

multiplying, M1D1-C3

rationalizing the denominator, M2D2-C4, M2D13-C3, M4D6-C3

reciprocals, M1D15-C3

simplifying, M1D1-C3, M1D5-C1

subtracting, M1D5-Y

Function, M4D4-Y1

Geometric sequence, M4D5-Y2, M4D7-Y1

Geometric series, M4D5-Y2, M4D8-Y1

Geometric mean, M4D7-Y2, derivation of, M4D7-Y3

Graphs, M4D13-C1

continuous, speed and time, M1D16-Y1

bar graph, M1D16-C3

Inequalities,

and geometry, M2D15-Y1

Infinite descent, M5D16-Y3

Intercept of a line, M4D13-Y1

Intersection point using geometry, M4D14-C1

Inverse function, M4D4-Y1

Irrational numbers, M1D2-C4

Limit, M4D16-C3

Line, 

equation of, M4D14-C2

graph of, M4D13-C1, M4D14-C1

midpoint of, M4D13-C6

perpendicular, M4D14-Y2, bisector, M4D13-Y1

Loh method (see Quadratics)

Magic square, M0W2D5

Means (average), M0D5-C1, M3D13-C2, M4D5-C2

sports averages, M1D3-C4, M1D4-C1

geometric, M1D6-C4, M4D7-Y2, derivation, M4D7-Y3

harmonic, M1D15-C1, M1D15-Y1

Mental math, M4D2-Y1

Midpoint of a line, M4D13-C6

Multiplying

by 11, M1D3-C2

Parabola, M4D16-C2

Percents, M0D11-C1, M0D11-Y1

converting to decimal, M1D7-C2, M4D1-C1

converting to fraction, M1D8-C1

percent decrease, M1D7-C3

percent increase, M1D7-C1

successive changes in, M1D7-Y, M1D8-C, M4D1-C2

Pi, π, approximation for, M1D3-Y, M1D10-C-3, F254

Polynomials, M4D10-C1

Powers or Power Tower (see Exponents or Number Theory)

Proof of √2 irrational, M5D16-Y4

Proof techniques, M5D16-Y

Proportion (see Ratio/Proportion)

Quadratic equations (see Equations)

Rates, M1D5-Y

acceleration, M1D16-Y2

around a lap, M1D15-Y1

average speed, M1D15-C2

changing rates, M1D16-C1

distance and time, M0D9-C2, M1D15-C1

distance as area under speed curve, F269

distributions, M1D12-C1

relative, M0D9-C1

diagrams for, M0D9-C2

of rotation, M1D11-C1

ratios of, M0D9-Y2, M1D11-Y3

unit rates, M1D13-C1, M1D15-Y2

speed of rotation, M1D11-C2

Rational expressions, M4D3-C1, M4D3-Y2, M4D4-Y1, M4D11-Y3

Rationalizing the denominator (see Fractions)

Reciprocals, M4D3-Y2

Ratio / Proportion, M1D5-C1, M1D6-Y1, M1D12-Y

of gear speeds, M1D11-C2

Roots,

square root of 2, approximation, M1D2-C4

complex/imaginary, M4D12-Y1

cube roots, M4D7-C1

of a quadratic, M4D11-C3

sixth roots, M4D7-C1

Round down function, M5D6-C1

Scientific Notation, M1D9-Y2, M1D10-C1

Sequences (see Arithmetic Progression)

Simplifying,

shortcuts, M1D10-Y3

radicals, M2D1-C2, M4D7-Y3, M2D13-C3, M2D13-Y2

Slope-intercept form of a line, M4D13-Y-5

Slope, 

of a curved line, M4D16-C3

of a line, M4D13-Y3, M4D15-Y1, , F519, 

perpendicular, M4D13-Y4

Solutions (see Roots)

Square Root (see Root)

Squaring Numbers Ending in 5, M4D1-C4

Sum of consecutive numbers, M0D5-C1, M0D5-Y1, M1D16-C2

Systems of equations

with two variables, M4D9-C1

with three variables, M0D2-C2, M0D2-Y1, M4D10-C1

in proof of Heron's, M2D16-B2

with too many variables, M5D13-C1

adding/subtracting, M4D10-C4

Telescoping Sum, M0D14-C1

Triangular Numbers, M3D13-C2

Units, M1D13-Y

canceling, M1D10-Y2

Word problem, M4D2-C1,  M4D6-Y1, M4D9-C1, M4D12-C1, M4D12-Y1, M4D13-C1, M5D13-C1

Variables, M1D4-C2

Combinatorics

Arrangements, increasing and decreasing M3D13-Y1

Beads,

in a line, M3D11-C1, M3D11-Y

on a necklace, M3D5-Y

Binomial coefficients, M3D6-C1, M5D6-Y

formula for, M3D6-C2

Bounding Boxes, M3D4-C2

Breadth-First Search, M3D15-C3

Casework, M3D5-C2, M3D8-C1, M3D10-C1, M3D10-Y2, M3D11-C1, M3D12-C3

counting angles, M2D8-C3

squares on a grid, M3D4-C1

counting triangles using Triangle Inequality, M2D15-C1, M2D15-Y1

Chess tournament pairings, M3D14-C1

Choose notation, M0D8-C2, M0D8-Y2, M3D5-C2

Choosing 

5 choose n, M3D5-C4

9 choose 3, M3D4-Y5

11 choose 2, M3D8-C3

a subset of n things, M0D8-C1, M3D2-C2

toppings for a hamburger, M3D2-C2

Complementary counting, M0D3-C3, M0D3-Y1, M3D4-Y5, M3D8-Y, M3D9-C3, M3D9-Y2, M3D12-C5, M3D12-Y3, M6D1C1

Counting

arrangements in a line, M0D4-Y1

circular arrangements, M0D4-C1

complementary, see Complementary counting

numbers with repeated digits, M0D3-C1

rectangles on a grid, M0D8-Y1

triangles on a grid, M3D4-Y

with lists, M0D3-C1

Depth-Breadth Search, M3D15-Y2

Double factorial, !!, M3D14-C4

Euler's Polyhedral Formula, M3D16-C2

Factorials, M3D1-C2, M3D5-C1, M5D6-C1

Fibonacci Numbers, M4D4-C

and relationship to paths in a grid, M0D15-C2

and relationship to tiling, M3D10-C2, M3D10-C3

GCD of, M5D8-Y

Graph of States, M3D15-C2

Graphs, M3D12-C1

Graph theory, M3D12-C4

Greatest Common Denominator, M5D7-C1

Grid,

representation of ways, M2D15-C2, M2D15-Y1

counting squares on, M3D4-C1

Hockey Stick Identity, M3D6-Y, M3D13-C2, M3D13-C3, F383

Left-Hand Hockey Stick, F477

Inclusion-Exclusion Principle, M3D3-C3, M5D12-Y1, M6D1C1, M6D3C1

Least Common Multiple, M5D7-C1

Line arrangements, M3D1-C

List, ordered, M3D1-C1

Map colorings, M3D12-C1, M3D12-Y1

Matchings, M3D14-C

Multiplication Principle, M0D3-C3, M0D12-C4, M3D13-Y2, M6D1C1

Order, M3D14-C2

Overcounting, M0D8-C3, M3D2-Y, M3D3-C4, M3D14-C1

Pascal's Triangle, M0D15-Y2, M3D6-C2

patterns in, M3D7-C2

sum of row of, M3D7-C3

Paths,

in a hexagonal grid, M0D15-C1

in a square grid, M0D15-Y3, M3D9-C1, M3D9-Y1

Permutations, M0D8-C2, M3D1-C2, M3D5-C, M3D5-Y, M3D14-C1

with repeated objects, M3D5-C1, M3D9-C2

Pigeonhole Principle, M3D12-C3

Pirates splitting gold, M3D8-Y1

Platonic Solid, M3D16-C2

Pouring Buckets, M3D15-C, M3D15-Y

Powers 

of 5, M5D6-C3

of 11, M3D7-Y1

Product of GCD and LCM, M5D7-C1

Quotient of LCM and GCD, M5D7-Y

Recursion, M0D15-C2, M3D10-C3, M3D10-Y3, M3D11-C2, M3D11-Y2, M3D14-Y2

Recursive formula, M3D10-Y3, M3D14-Y2

Seating arrangement, M3D14-Y1

Set notation, M3D3-C1

Sets, 

intersection of, M3D3-C1, M3D3-C2

union of, M3D3-C1, M3D3-C2

Stars and bars, M3D8-C2, M3D8-Y, M3D13-C3

Symmetry, M0D4-C2, M3D1-Y2, M3D9-Y2, M6D2C1

rotational, M3D5-Y2

Tiling, M3D11-C4, M3D11-Y3, M3D14-Y2

tiling a strip, M3D10-C1, M3D10-Y1

Tree Diagram, M0D3-C2, M0D8-C3, M3D1-C3, M3D1-Y1, M6D2C1


Venn Diagram, M3D2-C, M3D2-Y, M3D3-C, M3D3-Y, M5D9-C5, M5W3D12-Y-1, M6D3C1

Geometry

Altitude,

dropping an, M2D4-Y2

Angle chasing, M2D5-Y2, M2D13-C2

Angle Bisector,

line, M2D12-C1

Theorem, applications of, M2D13-Y2

Theorem, proof of, M2D13-C4, 

Angles,

alternate interior angles, M0D13-C1, M2D2-Y1, M2D5-C2

between chord and radius, M2D7-C1

central angles of a circle, M2D6-C2,

complementary angles, M2D5-Y2

corresponding, M2D2-Y1

exterior angle of a non-regular polygon, M0D13-C4

exterior angle of a regular polygon,  M2D1-C1, M0D10-Y2

Sum of, M0D13-C5, M2D1-C1 ,

octagon, M2D2-C1

in a line, M0D13-C2

inscribed in a circle, M2D6-C3, M2D8-C1, , 

Interior angle of a regular polygon,  M2D1-C1, M0D13-Y

sum of angles in a pentagon, M0D13-C3

sum of angles of a triangle, proof, M0D13-C1

supplementary angles, M2D8-C3

Arc measure, M2D6-C4, M2D8-C1, M2D10-Y1

Arcs,

inscribed, M2D10-C1

Area,

difference of areas, M2D3-Y2

in parts, M2D2-C2, M2D3-C4

of a circle, F212

of a crescent (lune), M2D3-Y1

of a half-almond, M2D3-C2

of a parallelogram, M2D4-C1

of a trapezoid, M2D4-Y3

of a triangle, M0D1-C1, M0D1-Y1, M2D4-C2, M2D13-C1,

Heron's Formula, M2D16-C2, 

of a wedge, M2D3-C3

Chords

intersecting in a circle, M2D6-Y2

angles of, M2D7-C2

intersecting a diameter, M2D7-C4

common chords between circles, M2D7-Y1, M2D16-Y

common chord endpoints lie on a circle, M2D7-Y2

of concentric circles, M2D9-C1

Circles

area, M2D3-C3, F212

circumference, M0D10-C1, M0D10-Y1, M1D11-Y1

concentric, M2D9-C1

diameter, M0D10-C1, M2D11-Y1

inscribed in a quadrilateral, M2D12-C2

inscribed in a triangle, M2D13-Y1

pi, M0D10-C1, approximations for, M0D10-C4

overlapping, area of, M2D3-C1

radius,  

tangent circles, M2D9-Y1

Congruent

example of, triangles, M2D9-C3, M2D13-C1

Coordinates, graphing, M4D13-C1

Cyclic quadrilateral, M2D8-C1, M2D1-Y1

opposite angles of, M2D8-C2

proving it is, M2D8-C4

Distance,

between point and line, M4D14-Y1

Edges of a 3-D shape, M3D16-C1

Euler's Polyhedral Formula, M3D16-C3, M3D16-Y2

Extending Lines in a Figure, M2D1-Y1, M2D4-C3

Exterior Angles (see Angles)

Exterior Angle Theorem, M2D6-C2

Faces of a 3-D shape, M3D16-C1

Heron's Formula for area of a triangle, M2D16-C2, M2D16-Bonus

proof of, M2W4D16-B

Icosahedron, M3D16-C2

Inscribed

circle in a quadrilateral, M2D12-C2

sum of opposite sides, M2D12-C2, M2D12-C3

circle in a triangle, M2D13-Y1

Kites, M2D5-Y1, M2D10-Y1, M2D12-C1, M4D15-C1,

Lines, 

sliding lines over, M2D11-C1, M2D11-Y-2

Parallel lines,

cut by a transversal, M2D2-Y1

Paralellogram,

diagonals of, creating four equal-area triangles, F284

Paths,

shortest path on a cube, M2D14-Y1

Platonic Solid, M3D16-C2

Polyhedron, M3D16-C2

Power of a Point, M2D7-C3, M2D7-Y1

for a point outside the circle, M2D8-Y2

Pythagorean Theorem, M0D1-Y2

derivation of, M0D1-C2, M0D1-C4

applications of, M2D1-Y2, M2D1-Y2, M2D2-C3, M2D7-C1, M2D11-Y2, M2D11-C2, M2D14-C3

in proof of Heron's, M2D16-B2

Pythagorean triples, M2D16-C1

Quadrilateral

tangential, M2D12-C1

proof of sum of opposite sides, M2D12-C3

area of, M2D12-Y1

Radii, M2D6-C1

Reflections

of a path in a rectangle, M2D14-C1

Scaling,

of areas, M0D6-C1, M0D6-Y2, M2D3-Y3

of volume, M0D6-C3

with triangles, M2D1-C3, F203,

Secant lines

from an exterior point to a circle, M2D6-Y1, M2W2D8-Y-1

Secant-tangent lines from exterior point to a circle, M2D8-Y2, M2D10-C2 

Semi-perimeter, M2D16-C2, M2D16-B1

Similar shapes

similar triangles, M2D1-C3, M2D5-C2, M2D7-C2, M2D8-Y1, M2D11-Y1, M2D13-C1, M2D14-C3, M4D13-C1

similar triangles from dropping altitude, F138, F274

used to find intersection of lines, M4D14-C1

Stellated Dodecahedron, M3D16-Y1

Tangent to a curve, M4D16-Y1

Tangent to a circle

equal length tangents to a circle, M2D12-C1

inner tangent to circles, M2D11-Y1, M2D11-Y2

perpendicular to radius, M2D11-Y1

proof of, M2D9-C2

tangent to two tangent circles, M2D11-C1

Tangent-tangent inscribed angles, M2D10-Y1

Trapezoid,

diagonal length, M2D5-C1

isosceles trapezoid, M2D4-Y1

right trapezoid, M2D5-C1

Triangle Inequality, M2D14-C2, M2D15-C2, M2D15-Y1, 

proof of, M2D15-C1

Triangles

3-4-5 triangle, M2D1-C1

3-5-7 triangle, M2D1-Y1

30°-60°-90° triangle, M2D1-C4

45°-45°-90° triangle, M2D2-C3, M2D2-Y2

5-12-13 triangle, M0D1-Y1, M2D11-C2

8-15-17 triangle, M2D5-C4, M2D7-C1

9-40-41 triangle, M0D1-Y1

13-14-15- triangle, M2D16-C1

equilateral,  M2D1-C1

area of, M2D1-C2

formed from circle intersections, M2D3-C1

from centers of tangent circles, M2D9-Y2

golden, M2D13-C1

isosceles, M2D6-C1

Unfolding, technique for finding shortest paths, M2D14-Y1

Vertices of a 3-D shape, M3D16-C1

Volume

of a box, M0D2-C1

of a sphere, M0D6-C1

Number Theory

Bases, 

base 2,

Chinese Remainder Theorem, M5D10-C1, M5D10-Y1

Congruence, M5D11-C1, M5D12-C1

Congruent numbers, M5D1-C1

Divisibility, M3D3-Y1

by 3, M5D2-Y1

by 4, M5D3-C4

by 7, M5D15-Y3

by 8, M5D3-Y1

by 9, M5D2-C1

by 12, M5D3-C1

Euclidean Algorithm, M5D8-C1

Euler's Totient Function, M5D9-C6, M5D9-Y1, M5D12-Y1

Factors, M0D2-C1, M0D12-C1, M5D4-C1

average of, M5D5-C1

number of, M0D12-C3, M0D12-Y1

prime, M0D7-C1

reciprocals of factors, M5D5-Y1

sum of, M5D5-C2

of 11, M5D4-C2

Integer equations, M4W2D6-Ch, M4W2D6-Y

Last digit 

of a square, M5W1D1-Ch-1

of a power tower, M5W4D14-Ch-1

Least Common Multiple, M0W2D7-Ch-2

Mod notation, M5W1D1-Ch-4

numbers mod 10, M5W1D1-Ch-5

mod 11, M5W1D1-Y-1

Modular multiplication, M5W1D1-Ch-6

Modulus, M5W1D1-Ch-4, M5W3D10-Y

Multiplicative inverse, M5W4D15-Ch-4, M5W4D15-Y

Palindromes, M5W1D4-Ch-1

Powers 

           of 2,  

of 5, M5W2D6-Ch-3

of 11, M3W2D7-Y-1

Prime factorization, M0W1D2-Ch-2, M0W2D7-Ch-3, M0W3D12-Ch-4, M5W2D5-Ch-1

of 1001, M0W1D2-Ch-2, M1W2D7-Ch-4, M1W3D11-Y-3

of 111, M1W4D13-Y-4, M4W2D8-Ch-1

Prime numbers, M0W3D12-Ch-2, M5W2D5-Ch-1

Proof of √2 irrational, M5W4D16-Y-4

Relatively prime, M5W3D9-Ch-4, M5W3D12-Ch-3

pairwise relatively prime, M5W3D12-Ch-3

Remainders, M0W4D16-Y

cycles of, M5W3D9-Ch-3, M5W3D10-Ch-4, M5W3D11-Ch-3

mod 2, M5W1D3-Ch-3

of any power, M5W4D14-Y

of powers of 7, M5W4D14-Ch-2

mod 99, M5W1D4-Y-1

of Square Numbers, M0W4D16-Ch-1

negative, M5W1D1-Ch-7, M5W1D1-Y-2, M5W1D3-Y-3, M5W1D4-Ch-4

table of, M5W3D9-Ch, M5W3D10-Ch, M5W3D11-Ch-2, M5W3D12-Ch-3, M5W4D14-Y-2, M5W4D15-Ch-1

Simon's Favorite Factoring Trick, M5W4D13-Ch-2, M5W4D13-Y

Square numbers, M0W3D12-Ch-3

Probability