THE LIBRARY
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Build your mathematical toolkit.
15 lessons
Absolute Value Basics
Interpret absolute value as distance and solve equations by accounting for both directions.
Absolute Value Inequalities
Convert absolute-value inequalities into inside or outside intervals and use midpoint-radius form.
Coordinate Geometry
Use slope, line equations, midpoint, distance, and parallel or perpendicular relationships efficiently.
Permutations and Combinations
Choose between arrangement and selection counting by deciding whether order changes the outcome.
Relative Speed
Solve catch-up, meeting, and pass-then-separate motion problems by tracking how the gap changes.
Average Speed and Motion Variants
Handle average speed, equal-distance trips, currents, mixed units, and staggered starts without common setup errors.
Work and Machine Rates
Convert completion times into work rates and combine changing workers correctly.
Mixture Equations
Solve mixture problems by conserving total amount and the amount of pure ingredient.
Alligation
Use concentration differences to get a fast mixing ratio when one low and one high concentration create a target.
Probability
Use complements, multiplication, and inclusion-exclusion to model common probability questions.
Sets and Overlap
Compute unions, neither, exactly one, and the possible range of overlap between two sets.
Primes and Divisors
Recognize primes quickly and identify numbers with exactly three positive divisors.
Common Sums and Consecutive Integers
Use compact formulas for consecutive sums and exploit the average of consecutive integers.
Arithmetic Sequences
Find terms, count terms, and sum evenly spaced lists using the common difference.
Geometric and Alternating Sequences
Recognize constant-ratio sequences, compute geometric sums, and handle simple alternating patterns.
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