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Algebra
- Find a coefficient in a binomial expansionBinomial theorem
- Find a half-life from two measurementsHalf-life formula
- Find a logarithm in a base your calculator doesn't haveChange of base formula
- Find a missing exponentLaws of exponents
- Find a number from its logarithm (antilog)Definition of a logarithm
- Find a product of powers with the same baseLaws of exponents
- Find an unknown exponent by taking logsLogarithm power rule
- Find a² − b² quickly by factorisingDifference of two squares
- Find how long exponential growth takes to reach a targetExponential growth and decay
- Find how many real roots a quadratic hasDiscriminant
- Find how much is left after radioactive decayHalf-life formula
- Find the age of a sample from its half-life (dating)Half-life formula
- Find the base when you know the number and its logDefinition of a logarithm
- Find the expansion of (ax + b)ⁿBinomial theorem
- Find the growth rate from two measurementsExponential growth and decay
- Find the log of a fraction (quotient)Logarithm quotient rule
- Find the log of a powerLogarithm power rule
- Find the log of a product as a sum of logsLogarithm product rule
- Find the logarithm of a number in any baseDefinition of a logarithm
- Find the maximum or minimum value of a quadraticVertex of a parabola
- Find the missing constant c when you know one rootQuadratic formula
- Find the original value before a percentage change (reverse percentage)Percentage change
- Find the percentage increase or decreasePercentage change
- Find the roots (solutions) of a quadratic equationQuadratic formula
- Find the size of a population after exponential growthExponential growth and decay
- Find the value of b that gives equal (repeated) rootsDiscriminant
- Find the vertex (turning point) of a parabolaVertex of a parabola
Geometry
- Find a missing short side of a right trianglePythagorean theorem
- Find a missing side of a triangle from its area and two sidesHeron's formula
- Find the angle of a sector from its areaArea of a sector
- Find the area of a circle from its radiusArea of a circle
- Find the area of a parallelogram or rhombusArea of a parallelogram
- Find the area of a rectangle or squareArea of a rectangle
- Find the area of a regular hexagon, pentagon or octagonArea of a regular polygon
- Find the area of a sector (slice) of a circleArea of a sector
- Find the area of a trapezoid (trapezium)Area of a trapezoid (trapezium)
- Find the area of a triangle from its base and heightArea of a triangle
- Find the area of a triangle from its three sidesHeron's formula
- Find the area of an ellipse (oval)Area of an ellipse
- Find the central angle from an arc lengthArc length
- Find the circumference (perimeter) of a circleCircumference of a circle
- Find the diagonal of a rectangle or screenPythagorean theorem
- Find the height of a box from its surface areaSurface area of a box (cuboid)
- Find the height of a box from its volumeVolume of a box (cuboid)
- Find the height of a cone from its volumeVolume of a cone
- Find the height of a cylinder from its surface areaSurface area of a cylinder
- Find the height of a cylinder from its volumeVolume of a cylinder
- Find the height of a parallelogram from its areaArea of a parallelogram
- Find the height of a pyramid from its volumeVolume of a pyramid
- Find the height of a trapezoid from its areaArea of a trapezoid (trapezium)
- Find the height of a triangle from its areaArea of a triangle
- Find the hypotenuse of a right trianglePythagorean theorem
- Find the length of an arc of a circleArc length
- Find the number of sides from the angle sumInterior angles of a polygon
- Find the radius from the circumferenceCircumference of a circle
- Find the radius of a circle from its areaArea of a circle
- Find the radius of a cylinder from its volumeVolume of a cylinder
- Find the radius of a sphere from its surface areaSurface area of a sphere
- Find the radius of a sphere from its volumeVolume of a sphere
- Find the side of a regular polygon from its areaArea of a regular polygon
- Find the slant height of a cone from its surface areaSurface area of a cone
- Find the sum of the interior angles of a polygonInterior angles of a polygon
- Find the surface area of a box or cuboidSurface area of a box (cuboid)
- Find the surface area of a coneSurface area of a cone
- Find the surface area of a cylinder or canSurface area of a cylinder
- Find the surface area of a sphereSurface area of a sphere
- Find the volume of a box, room or tankVolume of a box (cuboid)
- Find the volume of a coneVolume of a cone
- Find the volume of a cylinder, can or tankVolume of a cylinder
- Find the volume of a pyramidVolume of a pyramid
- Find the volume of a sphere or ballVolume of a sphere
- Find the width of a rectangle from its area and lengthArea of a rectangle
Coordinate geometry
- Find a line parallel to another at a given distance from a pointDistance from a point to a line
- Find a missing coordinate from the slopeSlope formula
- Find a missing endpoint from the midpoint and the other endMidpoint formula
- Find a point at a given distance from another pointDistance formula
- Find a point on a line from its equationSlope-intercept form
- Find the centre of a circleEquation of a circle
- Find the distance between two pointsDistance formula
- Find the equation of a line through a point with a given slopePoint-slope form
- Find the gradient of a normal lineSlopes of perpendicular lines
- Find the midpoint of a line segmentMidpoint formula
- Find the points on a circle at a given xEquation of a circle
- Find the radius of a circle from its centre and a pointEquation of a circle
- Find the shortest distance from a point to a lineDistance from a point to a line
- Find the slope (gradient) of a line through two pointsSlope formula
- Find the slope from a point on a linePoint-slope form
- Find the slope of a perpendicular lineSlopes of perpendicular lines
- Find the y-intercept of a line through a pointSlope-intercept form
- Find where a line reaches a given heightSlope-intercept form
Trigonometry
- Find a side of a right triangle from an angle and another sideSOH CAH TOA (right-triangle trigonometry)
- Find a side of a triangle from two angles and a sideLaw of sines
- Find an angle from the sine of its doubleDouble-angle formulas
- Find an angle in degrees from radiansDegrees and radians
- Find an angle in radians from degreesDegrees and radians
- Find an angle of a right triangle from two sidesSOH CAH TOA (right-triangle trigonometry)
- Find an angle of a triangle from its three sides (SSS)Law of cosines
- Find an angle of a triangle from two sides and a non-included angle (SSA)Law of sines
- Find cos 2θ from θDouble-angle formulas
- Find cos θ from sin θPythagorean identity
- Find cos(A + B) from A and BAngle sum and difference formulas
- Find sin 2θ from θDouble-angle formulas
- Find sin θ from cos θPythagorean identity
- Find the amplitude of a sine wave through a pointSine wave (amplitude, period and phase)
- Find the angle that gives a triangle a certain areaArea of a triangle from two sides and an angle
- Find the area of a triangle from two sides and the angle between themArea of a triangle from two sides and an angle
- Find the exact value of sin 75° or sin 15°Angle sum and difference formulas
- Find the hypotenuse from an angle and a sideSOH CAH TOA (right-triangle trigonometry)
- Find the third side of a triangle from two sides and the angle between them (SAS)Law of cosines
- Find the value of a sine wave at a pointSine wave (amplitude, period and phase)
- Find when a sine wave reaches a given heightSine wave (amplitude, period and phase)
Sequences and series
- Find how many squares add up to a totalSum of the first n squares
- Find how many terms give a certain totalArithmetic series (sum)
- Find how many terms of a geometric sequence reach a totalGeometric series (sum)
- Find the common difference from two termsArithmetic sequence (n-th term)
- Find the common ratio from two termsGeometric sequence (n-th term)
- Find the n-th term of a geometric sequenceGeometric sequence (n-th term)
- Find the n-th term of an arithmetic sequenceArithmetic sequence (n-th term)
- Find the ratio from the first term and the sum to infinityInfinite geometric series (sum to infinity)
- Find the ratio that gives a certain totalGeometric series (sum)
- Find the sum 1 + 2 + … + nSum of the first n whole numbers
- Find the sum of a geometric sequenceGeometric series (sum)
- Find the sum of an arithmetic sequenceArithmetic series (sum)
- Find the sum of the first n square numbersSum of the first n squares
- Find the sum to infinity of a geometric seriesInfinite geometric series (sum to infinity)
- Find whether a number is triangularSum of the first n whole numbers
- Find which term a number is in a geometric sequenceGeometric sequence (n-th term)
- Find which term a number is in an arithmetic sequenceArithmetic sequence (n-th term)
Probability and statistics
- Find how many items there were from the number of arrangementsPermutations
- Find how many items were chosen from the number of combinationsCombinations
- Find the expected value of a game or random variableExpected value
- Find the margin of error of a pollMargin of error (proportion)
- Find the mean (average) of a list of numbersMean (average)
- Find the number of combinations (order doesn't matter)Combinations
- Find the number of ordered arrangements (order matters)Permutations
- Find the prior probability that fits a given resultBayes' theorem
- Find the probability of a cause given the evidence (e.g. a positive test)Bayes' theorem
- Find the probability of A given B (conditional probability)Conditional probability
- Find the probability of A or BAddition rule (or)
- Find the probability of a value below, above or between values in a normal distributionNormal distribution probability
- Find the probability of at most (or at least) k successesBinomial distribution
- Find the probability of both A and B from the or-probabilityAddition rule (or)
- Find the probability of exactly k successes in n trialsBinomial distribution
- Find the probability that two independent events both happenMultiplication rule for independent events (and)
- Find the sample size needed for a surveyMargin of error (proportion)
- Find the standard deviation of a populationStandard deviation
- Find the standard deviation of a sampleStandard deviation
- Find the value with a given percentage below it (percentile, inverse normal)Normal distribution probability
- Find the value with a given z-scoreZ-score (standard score)
- Find the variance of a set of dataStandard deviation
- Find the z-score (standard score) of a valueZ-score (standard score)
Finance maths
- Find how long an investment takes to double or reach a targetCompound interest
- Find how long it takes to earn a given amount of simple interestSimple interest
- Find how long money takes to double (quick estimate)Rule of 72
- Find how many deposits it takes to reach a goalFuture value of an annuity
- Find how many payments it takes to pay off a loanLoan repayment formula
- Find how much to invest now to reach a future amountPresent value
- Find how much to invest now to reach a targetCompound interest
- Find how much to save each month to reach a goalFuture value of an annuity
- Find how much you can borrow for a given paymentLoan repayment formula
- Find the effective annual rate (AER, APY) from a nominal rateEffective annual rate
- Find the future value of money invested todayPresent value
- Find the income a lump sum can pay outPresent value of an annuity
- Find the interest rate implied by a loan paymentLoan repayment formula
- Find the interest rate implied by an annuityPresent value of an annuity
- Find the interest rate needed to reach a savings goalCompound interest
- Find the monthly payment on a loan or mortgageLoan repayment formula
- Find the nominal rate that gives an effective rateEffective annual rate
- Find the rate needed to double money in a given timeRule of 72
- Find the rate that turns one amount into anotherPresent value
- Find the simple interest on a loan or investmentSimple interest
- Find the simple interest rateSimple interest
- Find the time to grow with continuous compoundingContinuous compounding
- Find the value with continuously compounded interestContinuous compounding
- Find what a series of payments is worth todayPresent value of an annuity
- Find what regular savings grow toFuture value of an annuity
- Find what savings grow to with compound interestCompound interest
Calculus basics
- Find a definite integral of a polynomialDefinite integral (area under a curve)
- Find a derivative from first principles (difference quotient)Difference quotient
- Find the area under a curve between two x-valuesDefinite integral (area under a curve)
- Find the average value of a function over an intervalAverage value of a function
- Find the coefficient that gives an integral a set valuePower rule for integrals
- Find the derivative of a fraction (quotient) of functionsQuotient rule
- Find the derivative of a function inside a function (composite)Chain rule
- Find the derivative of a power of xPower rule for derivatives
- Find the derivative of a product of two functionsProduct rule
- Find the derivative of e^x or ln xDerivatives of eˣ and ln x
- Find the derivative of sin or cosDerivatives of sin and cos
- Find the equation of the tangent line to a curve at a pointEquation of a tangent line
- Find the integral of a power of xPower rule for integrals
- Find the integral of an exponential functionIntegral of eᵏˣ
- Find the slope (gradient) of a curve at a pointPower rule for derivatives
- Find the slope of a secant lineDifference quotient
Motion (kinematics)
- Find average speed from distance and timeSpeed, distance and time
- Find how far a projectile travelsProjectile range
- Find how far an object travels while acceleratingDisplacement: s = ut + ½at²
- Find how long a journey takesSpeed, distance and time
- Find the acceleration from a change in speedFinal velocity: v = u + at
- Find the acceleration from distance and timeDisplacement: s = ut + ½at²
- Find the acceleration from speeds and distanceVelocity and displacement: v² = u² + 2as
- Find the distance covered while speeding up or slowing downDisplacement from average velocity
- Find the distance travelled at a given speedSpeed, distance and time
- Find the final velocity after constant accelerationFinal velocity: v = u + at
- Find the launch angle needed to hit a target distanceProjectile range
- Find the launch speed needed to reach a distanceProjectile range
- Find the speed after falling or accelerating over a distanceVelocity and displacement: v² = u² + 2as
- Find the stopping distance from a speed and decelerationVelocity and displacement: v² = u² + 2as
- Find the time taken to change speed over a distanceDisplacement from average velocity
- Find the time to cover a distance with constant accelerationDisplacement: s = ut + ½at²
- Find the time to reach a speedFinal velocity: v = u + at