Pre-Algebra and Algebra

Acceleration (see Rates)

Accounting,

word problem, M1W3D9-Ch, M1W3D9-Y

Arithmetic progression, M4W2D5-Ch

Arithmetic series, M4W2D5-Ch

Axes, coordinate M4W4D14-Ch

Binomial, M4W1D1-Y

Change of variable, M4W3D11-Y

Computer memory storage, M4W1D1-Y

Coordinates, M4W4D15-Ch

Decimals,

converting to fractions, M1W1D1-Ch-1M1W1D1-Ch-1M4W2D8-ChM4W2D8-Y

repeating, M1W1D1-Ch-2, M1W2D8-Y-1, M1W2D8-Y-2, M4W2D8-Ch, M4W2D8-Y

0.111..., M1W3D9-Y-2

Denominator (see Fractions)

Difference of squares, M2W2D7-Ch-4, M4W1D1-Ch, M4W2D6-Ch, M4W2D6-Y

Dimensions of a box, M1W2D6-Ch-1

Distance (see Rates)

Distributive Law, M5W2D5-Ch-2

Dividing by Zero, M5W4D13-Y-3

Equations, M1W2D6-Ch-2

in geometry problems, M2W3D10-Y-2

integer equations, M5W4D13-Ch-1, M5W4D13-Y

quadratic, M4W3D11-Ch, M4W3D11-Y, M4W3D12-Ch, M4W3D12-Y

Loh Method of Solving, M4W3D12-Ch

rate equations, M1W4D13-Ch-2, M1W4D13-Y-3

rational, M1W1D2-Ch-2, M1W1D4-Ch-2, M1W4D15-Ch-3, M4W1D4-Y, M4W3D9-Y

Estimation, M1W3D10-Ch-1, M4W1D1-Ch

Expanding, M4W1D1-Y, M4W1D2-Y, M4W3D11-Ch, M4W3D11-Y, M4W4D16-Ch

Exponents,

fractional, M4W2D7-Ch

powers of 5, M1W2D5-Ch-3

rules for, M4W2D7-Ch

1024 to the fourth power, M4W1D1-Y

Fermi estimate, M1W3D10-Y-1

Fibonacci Sequence, M4W1D4-Ch

Floor function, M5W2D6-Ch-1

Fractions,

common denominator, M1W1D1-Y-2, M1W1D4-Y-1, M1W4D13-Y-4M5W2D5-Y-2

comparing, M1W1D3-Ch-1, M1W1D4-Y-1

conversion to decimals, M1W1D1-Y-1M4W1D4-Y

difference of, M0W4D14-Ch-1

distributions, M1W3D12-Ch-2

equal to terminating decimals, M5W4D16-Ch

improper, M1W1D3-Y

in word problems, M1W1D2-Y-1

nested, M1W1D2-Ch-1

multiplying, M1W1D1-Ch-3

rationalizing the denominator, M2W1D2-Ch-4, M2W4D13-Ch-3M4W2D6-Ch

reciprocals, M1W4D15-Ch-3

simplifying, M1W1D1-Ch-3, M1W2D5-Ch-1

subtracting, M1W2D5-Y

Geometric sequence, M4W2D5-Y, M4W2D7-Y

Geometric series, M4W2D5-YM4W2D8-YM5W2D5-Y-2

Graphs, M4W4D13-Ch

continuous, speed and time, M1W4D16-Y-1

bar graph, M1W4D16-Ch-3

Inequalities,

and geometry, M2W4D15-Y-1

Infinite descent, M5W4D16-Y-3

Intercept of a line, M4W4D13-Y

Intersection point using geometry, M4W4D14-Ch

Irrational numbers, M1W1D2-Ch-4

Limit, M4W4D16-Ch

Line, 

equation of, M4W4D14-Ch

graph of, M4W4D13-Ch, M4W4D14-Ch

midpoint of, M4W4D13-Ch

Loh method of solving quadratics, M4W3D12-Ch

Magic square, M0W2D5

Means (average), M0W2D5-Ch-1, M3W4D13-Ch-2, M4W2D5-Ch

sports averages, M1W1D3-Ch-4, M1W1D4-Ch-1

geometric, M1W2D6-Ch-4M4W2D7-Y

harmonic, M1W4D15-Ch, M1W4D15-Y

Mental math, M4W1D2-Y

Multiplying

by 11, M1W1D3-Ch-2

last two digits of product, M4W1D2-Y

Parabola, M4W4D16-Ch

Percents, M0W3D11-Ch-1, M0W3D11-Y-1

converting to decimal, M1W2D7-Ch-2M4W1D1-Ch

converting to fraction, M1W2D8-Ch-1

percent decrease, M1W2D7-Ch-3

percent increase, M1W2D7-Ch-1

successive changes in, M1W2D7-Y, M1W2D8-Ch, M4W1D1-Ch

Pi, π, approximation for, M1W1D3-Y, M1W3D10-C-3F254

Power tower, M5W4D14-Ch-1

Powers, see Number Theory

Proof of √2 irrational, M5W4D16-Y-4

Proof techniques, M5W4D16-Y

Quadratic equations (see equations)

Rates, M1W2D5-Y

acceleration, M1W4D16-Y-2

around a lap, M1W4D15-Y-1

average speed, M1W4D15-Ch-2

changing rates, M1W4D16-Ch-1

distance and time, M0W3D9-Ch-2, M1W4D15-Ch-1

distance as area under speed curve, F269

distributions, M1W3D12-Ch-1

relative, M0W3D9-Ch-1

diagrams for, M0W3D9-Ch-2

of rotation, M1W3D11-Ch-1

ratios of, M0W3D9-Y-2M1W3D11-Y-3

unit rates, M1W4D13-Ch-1, M1W4D15-Y-2

speed of rotation, M1W3D11-Ch-2

Rational expressions, M4W1D3-Ch, M4W1D3-Y, M4W3D12-Ch

Reciprocals, M4W1D3-Y

Ratio / Proportion, M1W2D5-Ch-1, M1W2D6-Y-1, M1W3D12-Y

of gear speeds, M1W3D11-Ch-2

Roots,

square root of 2, approximation, M1W1D2-Ch-4

cube roots, M4W2D7-Ch

of a quadratic, M4W3D11-Ch

sixth roots, M4W2D7-Ch

Round down function, M5W2D6-Ch-1

Scientific Notation, M1W3D9-Y-2, M1W3D10-Ch-1

Simplifying,

shortcuts, M1W3D10-Y-3

radicals, M2W1D1-Ch-2, M2W4D13-Ch-3, M2W4D13-Y-2

Slope of a line, M4W4D13-Y, M4W4D15-Y

slope of a curved line, M4W4D16-Ch

Square Root (see Root)

Squaring Numbers Ending in 5, M4W1D1-Ch

Sum of consecutive numbers, M0W2D5-Ch-1, M0W2D5-Y-1, M1W4D16-Ch-2

Systems of equations

with two variables, M4W3D9-Ch, M4W3D9-Y

with three variables, M0W1D2-Ch-2, M0W1D2-Y-1M4W3D10-Ch

in proof of Heron's, M2W4D16-B-2

with too many variables, M5W4D13-Ch-1

operations with, M4W3D10-Y

Telescoping Sum, M0W4D14-Ch-1

Triangular Numbers, M3W4D13-Ch-2

Units, M1W4D13-Y

canceling, M1W3D10-Y-2

Vieta's Formulas, M4W3D11-Ch, M4W3D12-Ch

Word problem, M4W1D2-Ch,  M4W2D6-YM4W3D9-Ch, M4W3D12-Ch, M4W3D12-Y, M4W4D13-Ch, M5W4D13-Ch-1

Variables, M1W1D4-Ch-2, M1W2D8-Ch-2, M1W3D12-Y-2, M4W1D2-ChM4W1D4-ChM4W2D5-YM4W2D6-ChM4W2D7-YM4W2D8-Ch

Combinatorics

Arrangements, increasing and decreasing M3W4D14-Y-1

Beads,

in a line, M3W3D11-Ch-1, M3W3D11-Y

on a necklace, M3W2D5-Y

Binomial coefficients, M3W2D6-Ch-1, M5W2D6-Y

formula for, M3W2D6-Ch-2

Bounding Boxes, M3W1D4-Ch-2

Breadth-First Search, M3W4D15-Ch-3

Casework, M3W2D5-Ch-2, M3W2D8-Ch-1, M3W3D10-Ch-1, M3W3D10-Y-2, M3W3D11-Ch-1, M3W3D12-Ch-3

counting angles, M2W2D8-Ch-3

squares on a grid, M3W1D4-Ch-1

counting triangles using Triangle Inequality, M2W4D15-Ch-1, M2W4D15-Y-1

Chess tournament pairings, M3W4D14-Ch-1

Choose notation, M0W2D8-Ch-2, M0W2D8-Y-2M3W2D5-Ch-2

Choosing 

5 choose n, M3W2D5-Ch-4

9 choose 3, M3W1D4-Y-5

11 choose 2, M3W2D8-Ch-3

a subset of n things, M0W2D8-Ch-1M3W1D2-Ch-2

toppings for a hamburger, M3W1D2-Ch-2

Complementary counting, M0W1D3-Ch-3, M0W1D3-Y-1M3W1D4-Y-5M3W2D8-YM3W3D9-Ch-3M3W3D9-Y-2M3W3D12-Ch-5M3W3D12-Y-3

Counting

arrangements in a line, M0W1D4-Y-1

circular arrangements, M0W1D4-Ch-1

complementary, 

numbers with repeated digits, M0W1D3-Ch-1

rectangles on a grid, M0W2D8-Y-1

triangles on a grid, M3W1D4-Y

with lists, M0W1D3-Ch-1

Depth-Breadth Search, M3W4D15-Y-2

Double factorial, !!, M3W4D14-Ch-4

Factorials, M3W1D1-Ch-2, M3W2D5-Ch-1, M5W2D6-Ch-1

Fibonacci Numbers, M4W1D4-Ch

and relationship to paths in a grid, M0W4D15-Ch-2

and relationship to tiling, M3W3D10-Ch-2, M3W3D10-Ch-3

GCD of, M5W2D8-Y

Graph of States, M3W4D15-Ch-2

Graphs, M3W3D12-Ch-1

Graph theory, M3W3D12-Ch-4

Greatest Common Denominator, M5W2D7-Ch-1

Grid,

representation of ways, M2W4D15-Ch-2, M2W4D15-Y-1

counting squares on, M3W1D4-Ch-1

Hockey Stick Identity, M3W2D6-Y, M3W4D13-Ch-2, M3W4D13-Ch-3, F383

Inclusion-Exclusion Principle, M3W1D3-Ch-3, M5W3D12-Y-1

Least Common Multiple, M5W2D7-Ch-1

Line arrangements, M3W1D1

List, ordered, M3W1D1-Ch-1

Map colorings, M3W3D12-Ch-1, M3W3D12-Y-1

Matchings, M3W4D14-Ch

Multiplication Principle, M0W1D3-Ch-3, M0W3D12-Ch-4M3W4D13-Y-2

Order, M3W4D14-Ch-2

Overcounting, M0W2D8-Ch-3M3W1D2-YM3W1D3-Ch-4M3W4D14-Ch-1

Pascal's Triangle, M0W4D15-Y-2M3W2D6-Ch-2

patterns in, M3W2D7-Ch-2

sum of row of, M3W2D7-Ch-3

Paths,

in a hexagonal grid, M0W4D15-Ch-1

in a square grid, M0W4D15-Y-3M3W3D9-Ch-1M3W3D9-Y-1

Permutations, M0W2D8-Ch-2M3W1D1-Ch-2M3W2D5-ChM3W2D5-YM3W4D14-Ch-1

with repeated objects, M3W2D5-Ch-1, M3W3D9-Ch-2

Pigeonhole Principle, M3W3D12-Ch-3

Pirates splitting gold, M3W2D8-Y-1

Platonic Solid, M3W4D16-Ch-2

Pouring Buckets, M3W4D15-Ch, M3W4D15-Y

Powers 

of 5, M5W2D6-Ch-3

of 11, M3W2D7-Y-1

Product of GCD and LCM, M5W2D7-Ch-1

Quotient of LCM and GCD, M5W2D7-Y

Recursion, M0W4D15-Ch-2M3W3D10-Ch-3M3W3D10-Y-3M3W3D11-Ch-2M3W3D11-Y-2M3W4D14-Y-2

Recursive formula, M3W3D10-Y-3, M3W4D14-Y-2

Seating arrangement, M3W4D114-Y-1

Set notation, M3W1D3-Ch-1

Sets, 

intersection of, M3W1D3-Ch-1, M3W1D3-Ch-2

union of, M3W1D3-Ch-1, M3W1D3-Ch-2

Stars and bars, M3W2D8-Ch-2, M3W2D8-Y, M3W4D13-Ch-3

Symmetry, M0W1D4-Ch-2, M3W1D1-Y-1, M3W3D9-Y-2

rotational, M3W2D5-Y-2

Tiling, M3W3D11-Ch-4, M3W3D11-Y-3, M3W4D14-Y-2

tiling a strip, M3W3D10-Ch-1, M3W3D10-Y-1

Tree Diagram, M0W1D3-Ch-2, M0W2D8-Ch-3M3W1D1-Ch-3M3W1D1-Y-1


Venn Diagram, M3W1D2-Ch, M3W1D2-Y, M3W1D3-Ch, M3W1D3-Y, M5W3D9-Ch-5, M5W3D12-Y-1

Geometry

Altitude,

dropping an, M2W1D4-Y-2

Angle chasing, M2W2D5-Y-2, M2W4D13-Ch-2

Angle Bisector,

line, M2W3D12-Ch-1

Theorem, applications of, M2W4D13-Y-2

Theorem, proof of, M2W4D13-Ch-4

Angles,

alternate interior angles, M0W4D13-Ch-1, M2W1D2-Y-1M2W2D5-Ch-2

between chord and radius, M2W2D7-Ch-1

central angles of a circle, M2W2D6-Ch-2,

complementary angles, M2W2D5-Y-2

corresponding, M2W1D2-Y-1

exterior angle of a non-regular polygon, M0W4D13-Ch-4

exterior angle of a regular polygon,  M2W1D1-Ch-1, M0W3D10-Y-2

Sum of, M0W4D13-Ch-5, M2W1D1-Ch-1 

octagon, M2W1D2-Ch-1

in a line, M0W4D13-Ch-2

inscribed in a circle, M2W2D6-Ch-3, M2W2D8-Ch-1,

Interior angle of a regular polygon,  M2W1D1-Ch-1, M0W4D13-Y

sum of angles in a pentagon, M0W4D13-Ch-3

sum of angles of a triangle, proof, M0W4D13-Ch-1

supplementary angles, M2W2D8-Ch-3

Arc measure, M2W2D6-Ch-4, M2W2D8-Ch-1, M2W3D10-Y-1

Arcs,

inscribed, M2W3D10-Ch-1

Area,

difference of areas, M2W1D3-Y-2

in parts, M2W1D2-Ch-2, M2W1D3-Ch-4

of a circle, F212

of a crescent (lune), M2W1D3-Y-1

of a half-almond, M2W1D3-Ch-2

of a parallelogram, M2W1D4-Ch-1

of a trapezoid, M2W1D4-Y-3

of a triangle, M0W1D1-Ch-1, M0W1D1-Y-1M2W1D4-Ch-2M2W4D13-Ch-1,

Heron's Formula, M2W4D16-Ch-2

of a wedge, M2W1D3-Ch-3

Chords

intersecting in a circle, M2W2D6-Y-2

angles of, M2W2D7-Ch-2

intersecting a diameter, M2W2D7-Ch-4

common chords between circles, M2W2D7-Y-1, M2W4D16-Y

common chord endpoints lie on a circle, M2W2D7-Y-2

of concentric circles, M2W3D9-Ch-1

Circles

area, M2W1D3-Ch-3F212

circumference, M0W3D10-Ch-1, M0W3D10-Y-1M1W3D11-Y-1

concentric, M2W3D9-Ch-1

diameter, M0W3D10-Ch-1, M2W3D11-Y-1

inscribed in a quadrilateral, M2W3D12-Ch-2

inscribed in a triangle, M2W4D13-Y-1

pi, M0W3D10-Ch-1, approximations for, M0W3D10-Ch-4

overlapping, area of, M2W1D3-Ch-1

radius,  

tangent circles, M2W3D9-Y-1

Congruent

example of, triangles, M2W3D9-Ch-3, M2W4D13-Ch-1

Coordinates, graphing, M4W4D13-Ch

Cyclic quadrilateral, M2W2D8-Ch-1, M2W3D10-Y-1

opposite angles of, M2W2D8-Ch-2

proving it is, M2W2D8-Ch-4

Distance,

between point and line, M4W4D14-Y

Edges of a 3-D shape, M3W4D16-Ch

Euler's Polyhedral Formula, M3W4D16-Ch-3, M3W4D16-Y-2

Extending Lines in a Figure, M2W1D1-Y-1, M2W1D4-Ch-3

Exterior Angles (see Angles)

Exterior Angle Theorem, M2W2D6-Ch-2

Faces of a 3-D shape, M3W4D16-Ch-1

Heron's Formula for area of a triangle, M2W4D16-Ch-2, M2W4D16-Y

proof of, M2W4D16-B

Icosahedron, M3W4D16-Ch-2

Inscribed

circle in a quadrilateral, M2W3D12-Ch-2

sum of opposite sides, M2W3D12-Ch-2, M2W3D12-Ch-3

circle in a triangle, M2W4D13-Y-1

Kites, M2W2D5-Y-1, M2W3D10-Y-1, M2W3D12-Ch-1, M4W4D15-Ch,

Lines, 

sliding lines over, M2W3D11-Ch-1, M2W3D11-Y-2

Parallel lines,

cut by a transversal, M2W1D2-Y-1

Paralellogram,

diagonals of, creating four equal-area triangles, F284

Paths,

shortest path on a cube, M2W4D14-Y-1

Platonic Solid, M3W4D16-Ch-2

Polyhedron, M3W4D16-Ch-2

Power of a Point, M2W2D7-Ch-3, M2W2D7-Y

for a point outside the circle, M2W2D8-Y-2

Pythagorean Theorem, M0W1D1-Y-2

derivation of, M0W1D1-Ch-2, M0W1D1-Ch-4

applications of, M2W1D1-Y-2, M2W1D1-Y-2, M2W1D2-Ch-3, M2W2D7-Ch-1, M2W3D11-Y-2, M2W3D11-Ch-2, M2W4D14-Ch-3

in proof of Heron's, M2W4D16-B-2

Pythagorean triples, M2W4D16-Ch-1

Quadrilateral

tangential, M2W3D12-Ch-1

proof of sum of opposite sides, M2W3D12-Ch-3

area of, M2W3D12-Y

Radii, M2W2D6-Ch-1

Reflections

of a path in a rectangle, M2W4D14-Ch-1

Scaling,

of areas, M0W2D6-Ch-1, M0W2D6-Y-2M2W1D3-Y-3

of volume, M0W2D6-Ch-3

with triangles, M2W1D1-Ch-3F203,

Secant lines

from an exterior point to a circle, M2W2D6-Y-1, M2W2D8-Y-1

Secant-tangent lines from exterior point to a circle, M2W2D8-Y-2M2W3D10-Ch-2, 

Semi-perimeter, M2W4D16-Ch-2, M2W4D16-B-1

Similar shapes

similar triangles, M2W1D1-Ch-3, M2W2D5-Ch-2, M2W2D7-Ch-2, M2W2D8-Y-1, M2W3D11-Y-1, M2W4D13-Ch-1, M2W4D14-Ch-3, M4W4D13-Ch

similar triangles from dropping altitude, F138, F274

used to find intersection of lines, M4W4D14-Ch

Stellated Dodecahedron, M3W4D16-Y-1

Tangent to a curve, M4W4D16-Y

Tangent to a circle

equal length tangents to a circle, M2W3D12-Ch-1

inner tangent to circles, M2W3D11-Y-1, M2W3D11-Y-2

perpendicular to radius, M2W3D11-Y-1

proof of, M2W3D9-Ch-2

tangent to two tangent circles, M2W3D11-Ch-1

Tangent-tangent inscribed angles, M2W3D10-Y-1

Trapezoid,

diagonal length, M2W2D5-Ch-1

isosceles trapezoid, M2W1D4-Y-1

right trapezoid, M2W2D5-Ch-1

Triangle Inequality, M2W4D14-Ch-2, M2W4D15-Ch-2, M2W4D15-Y-1

proof of, M2W4D15-Ch-1

Triangles

3-4-5 triangle, M2W1D1-Ch-1

3-5-7 triangle, M2W1D1-Y-1

30°-60°-90° triangle, M2W1D1-Ch-4

45°-45°-90° triangle, M2W1D2-Ch-3, M2W1D2-Y-2

5-12-13 triangle, M0W1D1-Y-1, M2W3D11-Ch-2

8-15-17 triangle, M2W2D5-Ch-4, M2W2D7-Ch-1

9-40-41 triangle, M0W1D1-Y-1

13-14-15- triangle, M2W4D16-Ch-1

equilateral,  M2W1D1-Ch-1

area of, M2W1D1-Ch-2

formed from circle intersections, M2W1D3-Ch-1

from centers of tangent circles, M2W3D9-Y-2

golden, M2W4D13-Ch-1

isosceles, M2W2D6-Ch-1

Unfolding, technique for finding shortest paths, M2W4D14-Y-1

Vertices of a 3-D shape, M3W4D16-Ch

Volume

of a box, M0W1D2-Ch-1

of a sphere, M0W2D6-Ch-1

Number Theory

Bases, 

base 2,

Chinese Remainder Theorem, M5W3D10-Ch, M5W3D10-Y

Congruence, M5W3D11-Ch, M5W3D12-Ch

Congruent numbers, M5W1D1-Ch-1

Divisibility, M3W1D3-Y

by 3, M5W1D2-Y-1

by 4, M5W1D3-Ch-4

by 7, M5W4D15-Y-3

by 8, M5W1D3-Y-1

by 9, M5W1D2-Ch-1

by 12, M5W1D3-Ch-1

Euclidean Algorithm, M5W2D8-Ch

Euler's Totient Function, M5W3D9-Ch-6, M5W3D9-Y, M5W3D12-Y

Factors, M0W1D2-Ch-1, M0W3D12-Ch-1M5W1D4-Ch-1

average of, M5W2D5-Ch-1

number of, M0W3D12-Ch-3, M0W3D12-Y-1

prime, M0W2D7-Ch-1

reciprocals of factors, M5W2D5-Y-1

sum of, M5W2D5-Ch-2

of 11, M5W1D4-Ch-2

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-4M5W2D5-Ch-1

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

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

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

Proof of √2 irrational, M5W4D16-Y-4

Relatively prime, M5W3D9-Ch-4M5W3D12-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