Basic Algebra, Geometry and Statistics (The ‘School in a Book’ Series)

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

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

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

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

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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