School in a Book: Basic Algebra, Geometry and Statistics

Math isn’t that bad. It’s a pain, but doable. Hopefully this list will give you a clear map for mastering these subjects in a self-guided way. Please make use of some of the excellent resources out there, such as the free online lecture series by the Khan Academy, to learn and practice.

Note that I include here more than is strictly necessary for most elementary school and high schoolers to learn. Do learn basic statistics, but skip everything else after algebra I and geometry I if it doesn’t interest you or if it doesn’t fit with your college and career plans. (You’ll be fine, I promise.)

Pre-Algebra and Algebra 1:

Using factors and multiples
Using variables
Using algebraic symbols (parentheses, brackets, dots, slashes, etc.)
Solving basic algebraic equations
Solving inequalities
Calculating ratios, rates, percentages and proportions
Calculating exponents, radicals, and scientific notation
Solving algebraic expressions
Solving functions
Solving linear word problems
Understanding sequences
Systems of equations
Using absolute value
Using rational exponents
Using exponential growth
Using systems of equations
Working with expressions with exponents
Working with polynomials
Working with factorization
Working with quadratics
Working with rational and irrational numbers
Radicals
Integer exponents
Definitely, evaluate and compare functions
Congruence and similarity
Polynomials
Vectors and vector quantities
Matrices
Finding square roots
Definitely, evaluate and compare functions
Congruence and similarity
Polynomials
Vectors and vector quantities
Matrices
Construct and compare linear, quadratic and exponential models
Prove geometric theorems
Use coordinates to prove simple geometric theorems algebraically
Make geometric constructions based on a given set of numbers
Understand congruence in terms of rigid motions
Find arc lengths and areas of sectors of circles

Basic Geometry:

Calculating area
Calculating diameter
Calculating square footage
Calculating perimeter
Calculating volume
Graphing lines and slope
Understanding the differences between angles, polygons, lines, circles, triangles, right triangles and shapes
Calculating linear equations
Understanding transformations
Understanding congruence
Understanding similarity
Working with coordinate plane
Working with the Pythagorean theorem
Doing solid geometry
Doing analytic geometry
Construct and compare linear, quadratic and exponential models
Prove geometric theorems
Use coordinates to prove simple geometric theorems algebraically
Make geometric constructions based on a given set of numbers
Understand congruence in terms of rigid motions
Find arc lengths and areas of sectors of circles

Basic Statistics:

Understanding data sets and samples
Knowing common experiment designs and the differences between them
Understanding data distribution
Reading and interpreting data
Graphing and modeling simple data
Understanding scatterplots
Calculating probability
Independence
Conditional probability
Understanding randomization
Understanding and calculating mean, median and average
Understanding and calculating standard deviation
Understanding correlation and regression
Understanding statistical significance
Understanding positive correlation and negative correlation
Understanding bivariate numerical data
Statistical variability
Statistical distributions
Random sampling
Informal inferences and conclusions
Chance
Probability models
Bivariate data
Survey creation
Researcher bias
Running t-Tests, chi-square tests and ANOVA tests using statistical computation software

Algebra 2:

Continuing to learn the concepts taught in Algebra 1, including a more in-depth study of graphing and solving equations, inequalities, and functions.

Trigonometry:

Applying algebra and geometry skills to circular and periodic functions. This includes an understanding of sine, cosine and tangent.

Pre-Calculus:

Learning about series and sequences, probability, statistics, limits, and derivatives.

Calculus:

Continuing to learn about the concepts taught in pre-calculus, with an emphasis on integration and differentiation.

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