A method of ranking the pages of a network of hyperlinks by the long-run proportion of time a random surfer, following links at random (with occasional random jumps), spends on each page.
The apparent change in the direction of an object when it is viewed from two different positions; for a star, the parallax angle is half the shift seen from opposite sides of Earth's orbit.
Parallel forms reliabilityHL only · also parallel forms, alternate forms reliability, alternate forms, parallel-forms reliability
A method of checking reliability in which two different but equivalent versions of a test, designed to measure the same thing at the same level of difficulty, are given to the same group of people, and the two sets of scores are compared using a correlation coefficient; strong positive correlation indicates a reliable test.
Parametric equations of a lineHL only · also parametric form, parametric equations, parametric form of a line
The separate equations x=x0+λl, y=y0+λm
Parent populationHL only · also parent distribution, population distribution
The population, or the probability distribution, from which the observations in a sample are drawn; its mean μ and variance σ2 describe a single observation.
Partial sumalso S_n, sum of the first n terms, partial sums
The sum Sn=u1+u2+⋯+un
Particular solutionHL only · also particular solutions, specific solution
The single solution of a differential equation that satisfies a given initial condition, found by substituting the condition into the general solution to fix the arbitrary constant.
Pascal's trianglealso Yang Hui's triangle, Yang Hui triangle, arithmetic triangle
A triangular array of numbers in which each row begins and ends with 1 and every other number is the sum of the two numbers above it; row n lists the binomial coefficients (0n),(1n),…,(nn)
PathHL only · also paths
A walk in which no vertex is repeated, and therefore no edge is repeated.
The change in a quantity expressed as a percentage of its original value, original valuenew value−original value×100%, positive for an increase and negative for a decrease.
Perpendicular bisectoralso perpendicular bisectors, perpendicular bisector of [AB], mediator
The line that passes through the midpoint of a line segment and is perpendicular to it; it is the set of all points that are the same distance from the two endpoints of the segment.
Perpendicular componentHL only · also component of a perpendicular to b, perpendicular part, normal component
The length of the part of a vector a acting at right angles to a vector b, in the plane containing both, given by ∣b∣∣a×b∣=∣a∣sinθ
Perpendicular distance from a point to a lineHL only · also shortest distance from a point to a line, distance from a point to a line, perpendicular distance
The shortest distance from a point P to a line, measured along the line through P that meets it at right angles; for a line through A with direction b, it equals ∣b∣∣AP×b∣
Perpendicular linesalso perpendicular line
Lines that meet at a right angle; two lines with gradients m1 and m2, neither vertical, are perpendicular exactly when m1×m2=−1
Perpendicular vectorsHL only · also orthogonal vectors, orthogonal, perpendicular
Two non-zero vectors at right angles to each other; v and w are perpendicular if and only if v⋅w=0.
Personal engagementalso criterion C, personal engagement criterion
Criterion C of the exploration, worth 3 marks, which assesses how far the student makes the mathematics their own through independent or creative thinking, an individual presentation of ideas, different perspectives, and predictions that are made and tested; it does not measure effort.
Personal questionHL only · also sensitive question, personal questions, sensitive questions
A question that asks for private or sensitive information, so that respondents may refuse to answer or may answer untruthfully.
A logarithmic measure of the acidity of a solution, given by pH=−log10[H+], where [H+]
Phase planeHL only · also x–y plane of a system, state plane
The plane with the two dependent variables of a coupled system, such as x and y, on its axes, in which each solution is drawn as a curve and time is not shown on either axis.
Phase portraitHL only · also phase portraits, phase diagram, phase diagrams
A sketch in the phase plane of a representative set of trajectories of a coupled system, with arrows showing the direction of motion, which displays its equilibrium points and long-term behaviour.
Phase shiftHL only · also horizontal translation of a sinusoid, horizontal shift, phase shifts
The horizontal translation c of a sinusoidal model f(x)=asin(b(x−c))+d; the graph of asin(bx)+d
PhasorHL only · also phasors, phasor diagram
The complex number Aeiϕ that represents the sinusoid Acos(ωt+ϕ) of a known angular frequency ω, with modulus equal to the amplitude and argument equal to the phase angle ϕ
Piecewise functionHL only · also piecewise model, piecewise-defined function, piecewise functions, function defined in pieces
A function defined by two or more formulae, each applying on its own interval of the domain, where the intervals do not overlap.
Point-gradient formalso point-slope form, point gradient form, y − y1 = m(x − x1)
The equation of a straight line written as y−y1=m(x−x1), where m
Poisson distributionHL only · also Po(m), X ~ Po(m), Poisson model, Poisson random variable, Poisson distributions
The probability distribution of the number of occurrences X of an event in a fixed interval of time or space, when the events occur independently and at a uniform average rate; it has one parameter m, the mean number of occurrences in the interval, and is written X∼Po(m).
Poisson testHL only · also test for a Poisson mean, Poisson hypothesis test, Poisson tests
A hypothesis test for the mean of a Poisson distribution, in which the observed count in a stated interval is modelled by Po(m0) when the null hypothesis m=m0 is true.
Polar formHL only · also modulus–argument form, modulus-argument form, mod-arg form, r(cos θ + i sin θ)
The form z=r(cosθ+isinθ) of a non-zero complex number, where r=∣z∣>0
Polynomialalso polynomials, polynomial expression, polynomial function
An expression in one variable made of one or more terms, each a constant multiplied by a non-negative integer power of the variable, such as anxn+an−1xn−1+⋯+a1x+a0
Polynomial equationalso polynomial equations
An equation that can be rearranged into the form p(x)=0, where p(x) is a polynomial; its degree is the degree of p(x).
Population correlation coefficientHL only · also ρ, rho, population product-moment correlation coefficient, population PMCC
The product-moment correlation coefficient between two variables in the whole population, written ρ; the sample correlation coefficient r is its estimate.
Position vectorHL only · also position vectors, vector OA
The vector OA from the origin O to a point A, usually written a
Positive correlationalso positively correlated
A relationship in which larger values of one variable tend to go with larger values of the other, so the points of a scatter diagram rise from left to right.
A curve has a positive gradient at a point if its derivative there is greater than zero, f′(x)>0, so that the tangent slopes upwards from left to right and the function is increasing.
Power lawHL only · also power relationship, power function, power model, power laws
A relationship of the form y=axn, where a and n are constants, so that multiplying x by any factor m
Power law of logarithmsHL only · also log of a power, power rule for logarithms, power law for logarithms
For a,x>0 with a=1 and any real number m, loga(xm)=mlogax
Power of a testHL only · also power, statistical power, power of the test
The probability of rejecting the null hypothesis when it is false, for a specified value of the parameter under the alternative hypothesis; it equals 1−P(Type II error).
Presentationalso criterion A, presentation criterion
Criterion A of the exploration, worth 4 marks, which assesses how well the report is organised, how coherently its argument develops and how concise it is.
Prim's algorithmHL only · also Prim, Prim's, Prim's matrix method, Jarník's algorithm
A method for finding a minimum spanning tree that starts at a chosen vertex and repeatedly adds the edge of least weight joining a vertex already in the tree to a vertex not yet in the tree, until every vertex is included.
Principal valueHL only · also calculator value of sin⁻¹, principal solution, principal values
The single value returned by an inverse trigonometric function: for sin−1 and tan−1 an angle from −2π
Prismalso right prism, prisms
A solid with two identical, parallel polygonal ends joined by rectangular faces, so that every cross-section parallel to the ends is the same shape and size.
A number from 0 to 1 that measures how likely an event is to occur, where 0 means the event is impossible and 1 means it is certain; the probability of an event A is written P(A).
A function P(x) giving the income left after costs when x items are made and sold, equal to revenue minus cost, P(x)=R(x)−C(x)
Projectile motionHL only · also projectile, projectiles, projectile motion model
The motion of an object moving freely under gravity alone, in which the horizontal component of velocity is constant and the vertical component decreases at the constant rate g, so that the path is a parabola.