Mathematics, in plain words
Plain-language definitions of school Mathematics terms, A to Z, each with an example, where marks go, and the board's own source.
95 terms
Terms starting with A
- Algebraic expressionAn algebraic expression is a mix of numbers and letters joined by signs like + and ×, such as 3x + 5, with no equals sign.
- AM-GM inequalityThe AM-GM inequality says that for two numbers that are zero or positive, the average (a + b)/2 is at least √(ab).
- Angle of depressionThe angle of depression is the angle between the horizontal and the line of sight when you look down at something below your eye level.
- Angle of elevationThe angle of elevation is the angle between the horizontal and the line of sight when you look up at something above your eye level.
- AreaArea is the amount of flat surface a shape covers, measured in square units such as cm² or m².
- Arithmetic progressionAn arithmetic progression, or AP, is a list of numbers in which the step from each number to the next never changes, as in 3, 7, 11, 15.
- Assumed mean methodThe assumed mean method finds the mean of grouped data by picking one class mark as a starting guess and adjusting it.
Terms starting with B
- Basic Proportionality TheoremThe Basic Proportionality Theorem says that when a line runs parallel to one side of a triangle, it splits the other two sides in equal ratios.
- Binomial coefficientA binomial coefficient, written ⁿCᵣ, is the number of ways to choose r things from n different things when order does not matter.
Terms starting with C
- Ceva's theoremCeva's theorem gives a test for when three lines, each from a corner of a triangle to the opposite side, all pass through one point.
- Chinese remainder theoremThe Chinese remainder theorem says that if no two of the divisors share a factor other than 1, a number's remainders on them fix the number up to their product.
- Class markThe class mark is the middle value of a class interval, found by adding its lower and upper limits and halving the total.
- Co-prime numbersTwo numbers are co-prime when the only factor they share is 1, even if neither number is prime itself.
- Common differenceThe common difference of an arithmetic progression is the fixed amount added to each term to get the next one.
- Complementary eventsTwo events are complementary when exactly one of them must happen, like E and not E, so their probabilities add up to 1.
- Composite numberA composite number is a whole number above 1 with more than two factors, such as 12, which is 3 × 4.
- Congruence modulo nTwo integers are congruent modulo n when they leave the same remainder on division by n, written a ≡ b (mod n).
- Consistent and inconsistent pairsA pair of linear equations is consistent if it has at least one solution, and inconsistent if it has no solution at all.
- Cosine ruleThe cosine rule gives the third side of any triangle from the other two sides and the angle between them.
- Criteria for similarity of trianglesThe criteria for similarity are the tests that prove two triangles similar: AAA or AA, SSS and SAS.
- Cumulative frequencyThe cumulative frequency of a class is its own frequency added to the frequencies of all the classes before it.
- Curved surface areaThe curved surface area of a solid is the area of its curved face only, leaving out any flat base or top.
Terms starting with D
Terms starting with E
- Elementary eventAn elementary event is an event made of just one outcome of an experiment, such as getting a 4 on one throw of a die.
- Elimination methodThe elimination method solves a pair of linear equations by adding or subtracting them so that one variable cancels out.
- Euler's totient functionEuler's totient function φ(n) counts the whole numbers from 1 to n that share no factor with n other than 1.
- ExponentAn exponent is the small raised number that says how many copies of the base are multiplied together, so 2⁵ means 2 × 2 × 2 × 2 × 2.
Terms starting with F
- FactorA factor of a number is a whole number that divides it exactly, leaving no remainder, so 3 is a factor of 12.
- Fermat's little theoremFermat's little theorem says that if p is prime and p does not divide a, then aᵖ⁻¹ leaves remainder 1 on division by p.
- Functional equationA functional equation is a puzzle where the unknown is a rule, not a number, and you find the rule from facts it obeys.
- Fundamental Theorem of ArithmeticThe Fundamental Theorem of Arithmetic says every composite number can be written as a product of primes in exactly one way, apart from the order.
Terms starting with G
Terms starting with H
Terms starting with I
- Impossible eventAn impossible event is one that cannot happen in an experiment, so its probability is 0.
- Inclusion-exclusion principleThe inclusion-exclusion principle counts the things in two groups by adding both groups, then taking away the ones counted twice.
- IntegerAn integer is a whole number or its negative, so the integers are ..., -3, -2, -1, 0, 1, 2, 3 and so on in both directions.
- Irrational numberAn irrational number, such as √2 or π, cannot be made by dividing one integer by another.
Terms starting with L
- Length of a tangentThe length of a tangent is the distance from an outside point to the point where the tangent from it touches the circle.
- Length of an arcThe length of an arc is the distance along the curved edge of a circle between two points, a fraction of the whole circumference.
- Line of sightThe line of sight is the straight line from an observer's eye to the point on the object being looked at.
- Linear congruenceA linear congruence is a statement of the form ax ≡ b (mod n), where you look for integers x that make it true.
- Linear Diophantine equationA linear Diophantine equation is an equation like 3x + 5y = 22 in which x and y must be integers.
- Linear equation in one variableA linear equation in one variable has one letter, with no squares or higher powers, such as 3x + 4 = 19.
Terms starting with M
- MeanThe mean of a set of numbers is their total divided by how many numbers there are, often called the average.
- MedianThe median is the middle value of a set of numbers sorted from smallest to largest, or halfway between the two middle values if the count is even.
- Median classThe median class is the class interval that holds the middle value of grouped data, found using cumulative frequencies.
- Menelaus' theoremMenelaus' theorem gives a test for when three points, one on each side line of a triangle, lie on one straight line.
- Mid-point formulaThe mid-point formula gives the middle point of the line joining (x₁, y₁) and (x₂, y₂) as ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Modal classThe modal class is the class interval with the highest frequency in grouped data, and the mode lies inside it.
- ModeThe mode of a set of numbers is the value that appears most often.
- MultipleA multiple of a number is what you get when you multiply it by 1, 2, 3 and so on, so 4, 8 and 12 are multiples of 4.
- Multiplication principleThe multiplication principle says that if one choice has m options and a second has n options, the two together have m × n options.
Terms starting with N
Terms starting with P
- Pair of linear equations in two variablesA pair of linear equations in two variables is two equations, each of the form ax + by + c = 0, in the same two unknowns x and y.
- PercentageA percentage is a fraction with 100 as its denominator, so 25% means 25 out of every 100, the same as 25/100 or 1/4.
- PerimeterThe perimeter of a flat shape is the total length of its boundary, the distance you would walk going once all the way round it.
- Pigeonhole principleThe pigeonhole principle says that if you put more objects than boxes into the boxes, at least one box must hold two or more objects.
- Place valuePlace value is the worth a digit gets from its position in a number, so the 5 in 520 stands for 500, not 5.
- Point of contactThe point of contact is the single point where a tangent touches a circle.
- Prime factorisationPrime factorisation means writing a number as a product of prime numbers only, such as 60 = 2 × 2 × 3 × 5.
- Prime numberA prime number is a number greater than 1 that has exactly two factors, 1 and itself, such as 2, 3, 5, 7 and 11.
- ProportionA proportion says that two ratios are equal, such as 2 : 3 = 4 : 6, where both terms of one are the other's times the same number.
Terms starting with Q
- Quadratic equationA quadratic equation is an equation that can be written as ax² + bx + c = 0, where a is not 0.
- Quadratic formulaThe quadratic formula gives the roots of ax² + bx + c = 0 as x = (-b ± √(b² - 4ac))/2a, if b² - 4ac is not negative.
- Quadratic polynomialA quadratic polynomial is a polynomial of degree 2, written as ax² + bx + c, where a, b and c are real numbers and a is not 0.
Terms starting with R
- RatioA ratio compares two quantities of the same kind by division, written a : b, such as 3 : 2 for 3 cups of rice to 2 of dal.
- Rational numberA rational number is any number that can be written as p/q, where p and q are integers and q is not zero.
- Real numberA real number is any number that has a place on the number line, whether it is rational, like 3/4, or irrational, like √2.
- Recurrence relationA recurrence relation is a rule that gives each term of a list using the terms that come before it.
Terms starting with S
- SecantA secant is a line that cuts a circle at two different points.
- Section formulaThe section formula gives the point that divides the line joining (x₁, y₁) and (x₂, y₂) internally in the ratio m₁ : m₂.
- Sector of a circleA sector is the part of a circle enclosed by two radii and the arc between them, shaped like a slice of pizza.
- Segment of a circleA segment is the part of a circle cut off between a chord and the arc it joins.
- Similar trianglesTwo triangles are similar when they have the same shape: each angle matches its partner, and every side is the same multiple of its partner.
- Sine ruleThe sine rule says that in any triangle, each side divided by the sine of the opposite angle gives the same number.
- Solution by factorisationSolving a quadratic equation by factorisation means writing it as two linear factors multiplied to give 0, then setting each factor equal to 0.
- Square rootA square root of a number is a value that, multiplied by itself, gives that number, so a square root of 49 is 7.
- Substitution methodThe substitution method solves a pair of linear equations by writing one variable in terms of the other, then putting that into the second equation.
- Sum of first n terms of an APThe sum of the first n terms of an AP is Sₙ = n/2 [2a + (n - 1)d].
- Surface area of a combination of solidsThe surface area of a combination of solids is the area of only the outer faces you can see after two or more solids are joined.
Terms starting with T
- Tangent to a circleA tangent is a straight line that meets a circle at one point only and does not cross into it.
- Theoretical probabilityThe theoretical probability of an event is the number of outcomes that favour it divided by the number of all possible outcomes, when every outcome is equally likely.
- Trigonometric identityA trigonometric identity is an equation in trigonometric ratios that holds for every angle where both sides are defined, such as sin² A + cos² A = 1.
- Trigonometric ratiosA trigonometric ratio compares two sides of a right triangle, seen from one of its sharp angles, such as sin A, cos A or tan A.
- Trigonometric ratios of specific anglesThese are the exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°, used in board questions where calculators are not allowed.
Terms starting with V
- VariableA variable is a letter, such as x or n, that stands for a number which can change or is not yet known.
- VolumeVolume is the amount of space a solid object takes up, measured in cubic units such as cm³ or m³.
- Volume of a combination of solidsThe volume of a combination of solids is the space it fills, found by adding the volumes of its parts or taking away a part that was removed.