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All Games

301

Math

20

Arithmetic5

SpeedMath

Exact

Race through arithmetic. Addition, subtraction, multiplication, and more.

Percentage Pro

Closeness

Calculate percentages, discounts, and markups in your head.

Fraction Blitz

Closeness

Master fractions: convert, add, subtract, multiply, and divide.

Order of Operations

Exact

Master PEMDAS with expressions that punish left-to-right guessing.

Mental Multiply

Exact

Multi-digit mental multiplication under time pressure.

Estimation4

Square Root Estimation

Closeness

Estimate square roots to the nearest hundredth.

Logarithm Estimation

Closeness

Estimate logarithm values in different bases.

Power Estimation

Closeness

Estimate powers and exponentials from memory.

Ratio Estimation

Closeness

Estimate ratios and proportions from given quantities.

Number Theory5

Square & Root

Exact

Powers, squares, cubes, and square roots. Mental math fundamentals.

Prime Hunter

Exact

Find primes, count primes, and master number theory.

Sequence Solver

Exact

Find the pattern and predict the next number in the sequence.

Scientific Notation

Exact

Convert between scientific notation and standard form.

GCD & LCM

Exact

Calculate greatest common divisors and least common multiples.

Statistics6

Mean Machine

Closeness

Calculate the average (mean) of a dataset. Mental arithmetic meets statistics.

Median Finder

Closeness

Find the middle value in a dataset. Sort, locate, calculate.

Standard Deviation

Closeness

Calculate the population standard deviation of a dataset.

Probability Pop

Closeness

Calculate probabilities for dice, coins, cards, and more.

Combinatorics

Exact

Factorials, permutations, and combinations.

Z-Score

Closeness

Calculate and interpret z-scores in normal distributions.

Focus

6

Estimation5

The Total Is

Closeness

Watch prices flash by. Estimate the total.

The Average Is

Closeness

Watch values flash by. Estimate the average.

The Spread Was

Closeness

Watch values flash by. Estimate max − min.

The Net Was

Closeness

Watch gains and losses flash by. Estimate the net change.

The Mystery Stat

Closeness

Values flash. You won't know which statistic you're asked for until the end.

Counting1

How Many Big Ones?

Exact

Watch values flash by. Count items over the threshold.

Finance

15

Investing9

Compound Interest

Closeness

Future value, present value, and the Rule of 72. Know what your money is actually doing.

P/E Ratio

Closeness

Price-to-earnings ratio calculations. Value investing fundamentals.

Dividend Yield

Closeness

Calculate dividend yields and income from stocks. Income investing fundamentals.

CAGR

Closeness

Compound Annual Growth Rate. Normalize investment returns across different time periods.

Dollar Cost Average

Closeness

Calculate average cost basis from multiple purchases at different prices.

Options Intrinsic Value

Exact

Calculate intrinsic value of call and put options.

Options Breakeven

Exact

Calculate breakeven prices for option trades.

Bond Yield

Closeness

Calculate current yield and approximate yield to maturity for bonds.

Portfolio Return

Closeness

Calculate weighted portfolio returns and risk metrics.

Loans & Mortgages6

Monthly Payment

Closeness

Calculate mortgage and loan monthly payments using the standard amortization formula.

Total Interest Paid

Closeness

Calculate the lifetime interest cost on a loan.

Payoff Accelerator

Closeness

Calculate time and interest saved by making extra payments on loans.

Refinance Math

Closeness

Calculate break-even month and savings when refinancing a loan.

Amortization Split

Closeness

Break down loan payments into interest and principal components.

APR vs Rate

Closeness

Calculate effective annual rate from nominal rate and compounding frequency.

Everyday

15

Bills & Tips5

Tip Calculator

Closeness

Calculate tips, split bills, and figure out your share. No phone allowed.

Split the Bill

Closeness

Calculate your fair share when dining with others. Tax, tip, and shared items.

Auto Loan Payment

Closeness

Calculate monthly car loan payments with interest.

Utility Bill

Closeness

Calculate electric, gas, and water bills from usage rates and tiered pricing.

Subscription Cost

Closeness

Compare monthly vs annual plans, bundle costs, and family plan savings.

Taxes & Income5

Tax Bracket

Closeness

Calculate federal income tax using 2024 US tax brackets.

Paycheck Math

Closeness

Calculate take-home pay from gross salary after taxes and deductions.

Auto Sales Tax

Closeness

Calculate sales tax on vehicle purchases.

Hourly to Annual

Closeness

Convert hourly wages to annual salary with overtime, benefits, and deductions.

Sales Tax Compare

Closeness

Compare total costs across different tax rates and categories.

Shopping & Deals5

Discount Stack

Closeness

Multiple discounts, coupons, and BOGO deals. How much do you actually pay?

Lease vs Buy

Closeness

Compare total costs of leasing versus buying a vehicle.

Unit Price

Closeness

Compare unit prices across package sizes to find the best deal.

Coupon Stack

Closeness

Stack percentage and dollar-off coupons. Order matters!

Cashback Rewards

Closeness

Calculate credit card cashback on categorized spending.

Vehicles

15

Fuel Economy5

Cost Per Mile

Closeness

Calculate how much each mile costs in fuel. Know your true driving expenses.

Road Trip Cost

Closeness

Calculate fuel costs for road trips. Plan your budget before you drive.

MPG from Trip Data

Closeness

Calculate your real fuel efficiency from actual trip data.

Fuel Tank Range

Closeness

Calculate how far you can drive on a tank of gas.

Fill-Up Cost

Closeness

Calculate the cost to fill your tank at the gas pump.

Electric Vehicles5

EV vs Gas Savings

Closeness

Compare annual fuel costs between electric and gas vehicles.

EV Range

Closeness

Calculate electric vehicle driving range from battery and efficiency.

EV Charging Cost

Closeness

Calculate the cost to charge an electric vehicle at home or on the road.

Charging Time

Closeness

Calculate how long it takes to charge an electric vehicle.

EV Battery Degradation

Closeness

Calculate battery capacity loss over time and charge cycles.

Ownership Costs5

Depreciation

Closeness

Calculate how much a vehicle loses in value over time.

Total Cost of Ownership

Closeness

Calculate the true 5-year cost of owning a vehicle.

Cost Per Year

Closeness

Calculate the annualized cost of owning a vehicle.

Insurance Cost

Closeness

Calculate annual vehicle insurance premiums with various factors.

Lease Payment

Closeness

Calculate monthly vehicle lease payments with various terms.

Measurement

35

Length5

Length

Closeness

Convert between cm, m, km, inches, feet, yards, and miles.

Length Chain Conversion

Closeness

Convert lengths through multiple units in sequence.

Length Word Problems

Closeness

Solve real-world length conversion word problems.

Length Comparison

Closeness

Compare two lengths in different units and find the difference.

Length Estimation

Closeness

Estimate length measurements using real-world references.

Mass5

Mass

Closeness

Convert between grams, kilograms, ounces, and pounds.

Mass Chain Conversion

Closeness

Convert masses through multiple units in sequence.

Mass Word Problems

Closeness

Solve real-world mass conversion word problems.

Mass Comparison

Closeness

Compare two masses in different units and find the difference.

Mass Estimation

Closeness

Estimate mass measurements using real-world references.

Volume5

Volume

Closeness

Convert between mL, liters, fluid ounces, cups, pints, quarts, and gallons.

Volume Chain Conversion

Closeness

Convert volumes through multiple units in sequence.

Volume Word Problems

Closeness

Solve real-world volume conversion word problems.

Volume Comparison

Closeness

Compare two volumes expressed in different units.

Volume Estimation

Closeness

Estimate volumes using real-world references.

Speed5

Speed

Closeness

Convert between m/s, km/h, mph, and ft/s.

Speed Chain Conversion

Closeness

Convert speeds through multiple units in sequence.

Speed Word Problems

Closeness

Solve real-world speed conversion word problems.

Speed Comparison

Closeness

Compare two speeds expressed in different units.

Speed Estimation

Closeness

Estimate speeds using real-world references.

Time5

Time

Closeness

Convert between seconds, minutes, hours, days, and weeks.

Time Chain Conversion

Closeness

Convert time through multiple units in sequence.

Time Word Problems

Closeness

Solve real-world time conversion word problems.

Time Comparison

Closeness

Compare two time durations expressed in different units.

Time Estimation

Closeness

Estimate time durations using real-world references.

Temperature5

Temperature

Closeness

Convert between Celsius and Fahrenheit.

Temperature Chain Conversion

Closeness

Convert temperature through multiple scales in sequence.

Temperature Word Problems

Closeness

Solve real-world temperature conversion word problems.

Temperature Comparison

Closeness

Compare two temperatures expressed in different scales.

Temperature Estimation

Closeness

Estimate temperatures using real-world references.

All Units5

All Units

Closeness

Convert between all unit types: length, mass, volume, speed, time, and temperature.

Mixed Chain Conversion

Closeness

Multi-step conversions across all unit types.

Mixed Word Problems

Closeness

Word problems from all unit categories.

Mixed Compare

Closeness

Compare quantities from any unit category.

Mixed Estimation

Closeness

Estimation challenges from any unit category.

Sports

50

Baseball5

Baseball Batting

Closeness

Calculate batting average, OBP, slugging, OPS, and more from realistic stat lines.

Baseball Pitching

Closeness

Calculate ERA, WHIP, K/9, and more from realistic pitching lines.

Baseball Fielding

Closeness

Calculate fielding percentage, range factor, and more from realistic fielding stats.

Baseball Baserunning

Closeness

Calculate stolen base rates, runs created, and baserunning metrics.

Baseball Sabermetrics

Closeness

Calculate WHIP, ERA, K/9, BB/9, and advanced pitching metrics from season stats.

Basketball5

Basketball Stats

Closeness

Calculate FG%, TS%, eFG%, fantasy points, and more from realistic box scores.

Basketball Shooting

Closeness

Calculate 2P%, 3P%, FT%, points per shot, eFG%, and TS% from shooting splits.

Basketball Advanced

Closeness

Calculate usage rate, game score, and per-36 stats from advanced box scores.

Basketball Rebounding

Closeness

Calculate ORB%, DRB%, rebound rate, and per-game rebounding stats.

Basketball Playmaking

Closeness

Calculate assist/turnover ratio, assist rate, and playmaking metrics.

American Football5

Football Passing

Closeness

Calculate completion percentage, passer rating, and more from realistic QB stat lines.

Football Rushing

Closeness

Calculate yards per carry, fantasy points, and more from realistic RB stat lines.

Football Receiving

Closeness

Calculate catch rate, yards per reception, PPR fantasy points, and more from realistic WR/TE stat lines.

Football Defense

Closeness

Calculate tackle rate, sack rate, INT rate, and QB pressure percentage from defensive stat lines.

Football Special Teams

Closeness

Calculate field goal percentage, punt average, return average, and touchback rate from special teams stats.

Cricket5

Cricket Batting

Closeness

Calculate batting average, strike rate, and more from realistic cricket batting stats.

Cricket Bowling

Closeness

Calculate economy rate, bowling average, and more from realistic bowling figures.

Cricket Fielding

Closeness

Calculate catch success rate, run-out efficiency, and stumping rate from fielding stats.

Cricket Economy

Closeness

Calculate economy rate, dot ball percentage, and maiden over rate from bowling economy stats.

Cricket All-Rounder

Closeness

Calculate all-rounder index, batting-bowling ratio, and combined batting+bowling value.

Tennis5

Tennis Match Stats

Closeness

Calculate first serve percentage, break points, and more from realistic match statistics.

Tennis Serving

Closeness

Calculate ace percentage, double fault rate, serve win percentages, and hold rates.

Tennis Returning

Closeness

Calculate return games won, break point conversion, and return point statistics.

Tennis Rally

Closeness

Calculate winners/UE ratio, net approach success, and aggression metrics.

Tennis Match Efficiency

Closeness

Calculate sets won, tiebreak win rate, deciding set records, and match efficiency stats.

Soccer5

Soccer Stats

Closeness

Calculate goals per game, shot accuracy, xG difference, and more from realistic season stats.

Soccer Goalkeeping

Closeness

Calculate save percentage, goals against average, clean sheet rate, and more.

Soccer Defensive

Closeness

Calculate tackle success, interceptions per 90, aerial duels, and defensive action rates.

Soccer Possession

Closeness

Calculate pass completion, progressive passes per 90, key passes, and carrying stats.

Soccer Attacking

Closeness

Calculate shot conversion, xG overperformance, chances created per 90, and goal involvement.

Golf5

Golf Stats

Closeness

Calculate scoring average, GIR percentage, scrambling, and more from realistic tournament stats.

Golf Scoring

Closeness

Calculate scoring average, par averages, birdie percentage, and bogey avoidance from tournament data.

Golf Driving

Closeness

Calculate driving accuracy, average distance, fairway hit rate, and distance differential.

Golf Putting

Closeness

Calculate putts per GIR, 1-putt percentage, 3-putt percentage, and total putts per round.

Golf Approach

Closeness

Calculate GIR percentage, proximity to hole, sand save percentage, and up-and-down rate.

Hockey5

Hockey Stats

Closeness

Calculate goals per game, shooting percentage, save percentage, GAA, Corsi, and PDO from realistic stat lines.

Hockey Scoring

Closeness

Calculate points per game, even-strength production, power play percentage, and shooting percentage.

Hockey Goaltending

Closeness

Calculate GAA, save percentage, shutout rate, and quality start percentage from goalie stats.

Hockey Possession

Closeness

Calculate Corsi%, Fenwick%, zone start%, and PDO from advanced hockey stats.

Hockey Special Teams

Closeness

Calculate power play%, penalty kill%, shorthanded goals/60, and 5v5 goal differential.

Motorsports5

Motorsports Stats

Closeness

Calculate win rate, average finish, pole-to-win conversion, and more from realistic motorsport stat lines.

Motorsports Qualifying

Closeness

Calculate qualifying deltas, lockout rates, and position averages from realistic qualifying data.

Motorsports Race Pace

Closeness

Calculate average lap times, pit stop deltas, tire degradation rates, and more from realistic race data.

Motorsports Championship

Closeness

Calculate points projections, constructor totals, and championship gaps from realistic standing data.

Motorsports Pit Strategy

Closeness

Calculate optimal pit windows, undercut/overcut deltas, and strategy comparisons from realistic race data.

Combat Sports5

Combat Sports Stats

Closeness

Calculate win rate, KO rate, striking accuracy, takedown accuracy, and more from realistic MMA stat lines.

Combat Striking

Closeness

Calculate striking accuracy, absorbed strikes per minute, and strike differential from realistic MMA data.

Combat Grappling

Closeness

Calculate takedown accuracy, submission rate, and control time percentage from realistic MMA grappling data.

Combat Judging

Closeness

Calculate 10-point must scoring, split decisions, and judge totals from realistic MMA judging data.

Combat Record

Closeness

Calculate win percentage, finish rate, average fight time, and KO rate from realistic fighter records.

Chemistry

10

Periodic Table5

Atomic Number

Exact

Given an element name or symbol, type its atomic number

Atomic Mass

Closeness

Given an element, type its atomic mass

Electron Config Count

Exact

Count electrons in a specific shell or subshell

Valence Electrons

Exact

How many valence electrons does this element have?

Oxidation State

Exact

What is the most common oxidation state of this element?

Chemical Calculations5

Molar Mass

Closeness

Calculate the molar mass of a compound

pH Calculator

Closeness

Calculate pH from hydrogen ion concentration

Molarity

Closeness

Calculate solution concentration from mass, molar mass, and volume

Stoichiometry

Closeness

Calculate molar ratios from balanced equations

Gas Laws

Closeness

Boyle's, Charles's, Combined, and Ideal gas law

Physics

15

Mechanics5

Kinematics

Closeness

Solve motion equations: velocity, displacement, and acceleration

Force Calculator

Closeness

Calculate forces using Newton's laws

Energy

Closeness

Calculate kinetic energy, potential energy, and work

Gravity

Closeness

Calculate gravitational forces and field strength

Momentum

Closeness

Momentum, impulse, and collision calculations

Waves & Circuits5

Wave Speed

Closeness

Calculate wave speed, frequency, and wavelength

Circuit Solver

Closeness

Solve electrical circuits using Ohm's law and resistance networks

Sound Intensity

Closeness

Calculate sound intensity levels in decibels

Optical Lens

Closeness

Thin lens equation and magnification calculations

Resonance Frequency

Closeness

LC circuits, pipe harmonics, and standing waves

Physical Constants5

Constants Quiz

Closeness

Recall fundamental physics constants

Speed of Light Problems

Closeness

Applications of the speed of light (c = 3×10⁸ m/s)

Gas Constant Problems

Closeness

Ideal gas law PV = nRT applications

Gravity Constant Problems

Closeness

Gravitational force and orbital mechanics using G

Planck Constant Problems

Closeness

E=hf, photoelectric effect, and de Broglie wavelength

For Kids

Sign in to play — always free.

K-12 Math

120

Grade 18

Counting On

Exact

Count forward (or backward) from a given number.

Add It Up!

Exact

Addition within 20. Build Grade 1 fact fluency.

Take Away!

Exact

Subtraction within 20. Results always non-negative.

What's Missing?

Exact

Find the unknown number in an equation.

Tens & Ones

Exact

Place value — tens, ones, and multiples of ten.

Bigger or Smaller?

Exact

Compare two-digit numbers by typing the bigger (or middle) one.

How Long?

Exact

Length word problems using whole-inch units.

What Time?

Exact

Tell time to the hour and half-hour.

Grade 28

Century Sums

Exact

Two-digit addition. Build Grade 2 fluency with and without regrouping.

Take From 100

Exact

Two-digit subtraction. Practice with and without regrouping.

Skip Counter

Exact

Find the next number in a skip-counting sequence.

Hundreds Place

Exact

Place value — hundreds, tens, and ones within 1000.

Coin Counter

Exact

Count coins and make change. Grade 2 money sense (2.MD.8).

Clock Reader

Exact

Tell time to the minute. Practice 5-minute intervals and elapsed time.

Even or Odd?

Exact

Practice parity by typing the next even number, or finding the leftover when sharing.

Array Builder

Exact

Rows and columns — a bridge to multiplication.

Grade 38

Times Table Blitz

Exact

Multiplication facts 0-10. Build Grade 3 times-table fluency.

Division Dash

Exact

Division facts within 100. Build Grade 3 fact fluency.

Story Solver

Exact

Single-step Grade 3 word problems (3.OA.3).

Fraction Numerator Recall

Exact

Supplementary practice — recall the numerator of a fraction. Visual fraction representations come later.

Area Counter

Exact

Calculate the area of rectangles and L-shapes.

Perimeter Patrol

Exact

Find the perimeter of squares, rectangles, and polygons.

Time Traveler

Exact

Figure out how much time has passed.

Round It!

Exact

Round whole numbers to the nearest 10, 100, or 1000.

Grade 410

Multi-Digit Multiply

Exact

Multi-digit multiplication. Build toward the standard algorithm.

Long Division

Exact

Division with 1- and 2-digit divisors. Quotients and remainders.

Factors & Multiples

Exact

Identify factors, compute multiples, count divisors, and test primality.

Equivalent Fractions

Exact

Find equivalent fractions by scaling numerator and denominator.

Fraction Add & Subtract

Exact

Add and subtract fractions and mixed numbers with like denominators.

Fraction × Whole

Exact

Multiply a fraction by a whole number. Type the resulting numerator.

Decimal Place Value

Exact

Convert fractions to decimals and compare decimal values.

Angle Measure

Exact

Read angles from a protractor and compute supplementary, complementary, and triangle sums.

Area & Perimeter

Exact

Calculate area, perimeter, and find missing sides of rectangles.

Pattern Rules

Exact

Find the next number in arithmetic, geometric, and alternating patterns.

Grade 58

Decimal Operations

Exact

Add, subtract, and multiply decimals. Build Grade 5 place-value fluency (5.NBT.7).

Fraction Multiply

Exact

Multiply fractions and simplify. Type the numerator (5.NF.4).

Fraction Divide

Exact

Divide fractions by whole numbers and whole numbers by unit fractions (5.NF.7).

Volume Cubes

Exact

Calculate volumes of cubes and rectangular prisms (5.MD.3).

Powers of Ten

Exact

Multiply and divide by powers of 10 (5.NBT.2).

Coordinate Grid

Exact

Read coordinates, measure distances, and find perimeters on a grid (5.G.1 / 5.G.2).

Order of Operations

Exact

Evaluate expressions using PEMDAS with +, −, ×, ÷ (5.OA.1). No exponents.

Fraction Blitz

Exact

Mixed fraction operations: add, subtract, multiply, divide (5.NF).

Grade 612

Ratio Reasoning

Exact

Unit rates, equivalent ratios, and rate comparisons (6.RP.2).

Number Line Integers

Exact

Compare, order, and place integers on a number line (6.NS.6-7).

Absolute Value

Exact

Evaluate absolute values and use them to compare and find distances (6.NS.7).

Fraction Division

Exact

Divide fractions using the reciprocal method (6.NS.1).

Expression Evaluation

Exact

Substitute values into algebraic expressions and evaluate (6.EE.2).

One-Step Equations

Exact

Solve one-step equations with addition, subtraction, multiplication, and division (6.EE.7).

GCF & LCM

Exact

Find the greatest common factor and least common multiple (6.NS.4).

Surface Area

Exact

Calculate surface area of cubes, rectangular prisms, triangular prisms, and open boxes from unfolded nets (6.G.4).

Percentage Pro

Exact

Find the part, percent, or whole in percentage problems (6.RP.3c).

Mean, Median, Mode

Exact

Find the mean, median, mode, and range of datasets (6.SP.5).

Unit Conversions

Exact

Convert between metric units of length, mass, and time (6.RP.3d).

Order of Operations (Grade 6)

Exact

PEMDAS with exponents: evaluate expressions with powers (6.EE.1).

Grade 710

Proportion Solver

Exact

Solve proportions using cross-multiplication and unit rates.

Percent Change

Exact

Calculate percent increase, decrease, and successive changes.

Rational Ops

Exact

Operations with negative fractions: add, subtract, multiply, divide.

Equation Solver

Exact

Solve two-step linear equations for x.

Angle Pairs

Exact

Identify and calculate vertical, supplementary, and parallel-line angle relationships.

Circle Measures

Closeness

Calculate circumference and area of circles using π.

Probability Pop

Exact

Calculate probabilities and express them as whole-number percentages.

Tip & Tax

Exact

Calculate tips, taxes, and total prices.

Scale Master

Exact

Apply scale factors to find actual sizes, drawing sizes, and areas.

Inequality Crunch

Exact

Solve one- and two-step inequalities and find the bounding integer.

Grade 810

Square & Root

Exact

Evaluate square roots and cube roots of perfect squares and cubes.

Sci Notation

Exact

Read, write, and operate with numbers in scientific notation.

Slope Finder

Exact

Find the slope between two points on a coordinate plane.

Line Master

Exact

Solve linear equations with one variable.

Pythagorean Pro

Closeness

Apply the Pythagorean theorem to find missing sides and distances.

Exponent Rules

Exact

Apply product, quotient, power, and negative exponent rules.

Function Machine

Exact

Evaluate linear functions and function compositions.

Volume: Cylinders

Closeness

Calculate the volume of cylinders, cones, and spheres using π.

Square Root Est.

Closeness

Estimate square roots of non-perfect-square integers.

Trend Predictor

Exact

Identify the linear trend in a scatter plot and predict missing values.

Grade 910

System Solver

Exact

Solve systems of two linear equations to find x and y.

Quadratic Roots

Exact

Find the roots of quadratic equations using factoring, the quadratic formula, and discriminant analysis.

Polynomial Power

Exact

Add, subtract, and multiply polynomials — identify a specific coefficient or term.

Factor It!

Exact

Factor quadratic expressions by identifying binomial factors and missing values.

Growth & Decay

Exact

Apply exponential growth and decay models — doubling, percent growth, half-life, and rate identification.

Sequence Solver

Exact

Find the next term or nth term in arithmetic and geometric sequences.

Radical Simplify

Exact

Simplify radical expressions by finding perfect square factors and rationalizing denominators.

Domain & Range

Exact

Evaluate functions, find domain restrictions for square roots and rational functions, and work with piecewise functions.

Compound Interest

Exact

Calculate compound interest with annual, semi-annual, and quarterly compounding, and solve for time.

Region Finder

Exact

Graph linear inequalities and identify points inside the solution region.

Grade 1010

Triangle Match

Exact

Angle-sum, isosceles/equilateral properties, exterior-angle theorem, and congruent-triangle corresponding sides.

Similar Triangles

Exact

Apply scale factors, shadow proportions, and mirror problems to find missing sides in similar triangles.

Trig Ratios

Closeness

Apply sine, cosine, and tangent to right triangles and angle-of-elevation word problems.

Circle Theorems

Closeness

Apply circle geometry to compute circumferences, arc lengths, sector areas, and inscribed angles.

Coordinate Proof

Exact

Use the distance formula, midpoint formula, and coordinate geometry to prove geometric properties on the coordinate plane.

Transformations

Exact

Apply reflections, translations, and rotations to triangles and determine image coordinates.

Area Composite

Closeness

Decompose L-shapes, T-shapes, and rect+semicircle figures to compute total area.

Volume Advanced

Closeness

Compute volumes of prisms, pyramids, cylinders, hemispheres, and composite solids.

Polygon Angles

Exact

Find missing angles in quadrilaterals, compute interior angle sums, and determine side counts from exterior angles.

Combinatorics

Exact

Count arrangements and selections using factorials, permutations, and combinations.

Grade 1115

Logarithm Estimation

Exact

Evaluate logarithms by recognizing base-power patterns and applying the change-of-base formula.

Polynomial Division

Exact

Master polynomial division and apply the remainder theorem and factor theorem to find quotients and remainders.

Rational Equations

Exact

Solve equations with variables in denominators — proportions, unit-fraction sums, extraneous solutions, and work-rate problems.

Trig Functions

Exact

Evaluate sin/cos/tan and inverse trig at standard angles, including quadrant-aware identities.

Arithmetic Series

Exact

Sum arithmetic sequences using Gauss's formula and related identities to find totals, terms, and unknown parameters.

Geometric Series

Exact

Sum geometric sequences — finite sums, infinite convergent series, and bouncing-ball totals.

Complex Numbers

Exact

Add, subtract, multiply, and divide complex numbers and evaluate powers of i.

Matrix Operations

Exact

Compute 2×2 matrix determinants, add and multiply matrices element-wise, and find inverse elements.

Standard Deviation

Closeness

Compute the population standard deviation of a small dataset, rounded to the nearest tenth.

Z-Score

Exact

Compute z-scores and convert between percentile and z-score using the standard normal distribution.

Exponential & Logarithm Equations

Exact

Solve equations involving exponents and logarithms by recognizing base-power structure and applying log rules.

Piecewise Functions

Exact

Evaluate piecewise-defined functions at a given input and compose them with linear functions.

Trig Equations

Exact

Count and find solutions of basic trigonometric equations in the interval [0°, 360°).

Polar Conversion

Exact

Convert between rectangular (x, y) and polar (r, θ) coordinates.

Conic Sections

Exact

Identify parameters of circles, parabolas, and ellipses from their standard-form equations.

Grade 1211

Limits Intro

Exact

Evaluate limits by direct substitution, factor-and-cancel, at infinity, and one-sided.

Derivative Rules

Exact

Apply power, sum, product, and chain rules to evaluate derivatives at a point.

Integral Basic

Exact

Evaluate antiderivatives and definite integrals over integer bounds.

2D Vectors

Exact

Compute magnitudes, sums, dot products, and angles between 2D vectors.

Probability Advanced

Exact

Compute joint, conditional, and Bayes probabilities; expected value.

Normal Distribution

Exact

Apply the 68-95-99.7 empirical rule to compute normal-distribution probabilities and percentile scores.

Regression Line

Exact

Find slopes, make predictions from a regression line, and compute the Pearson correlation coefficient.

Parametric Eval

Exact

Evaluate parametric equations, eliminate parameters, and compute derivatives dx/dt.

Related Rates

Exact

Apply implicit differentiation to connected quantities: expanding circle, ladder, shadow, cone.

Optimization

Exact

Find maxima and minima via calculus: fence area, box volume, cylinder surface, inscribed rectangle.

FTC Evaluate

Exact

Apply the Fundamental Theorem of Calculus to evaluate definite integrals (polynomial, trig, exponential).