Maths AA terms: P

45 of the Maths AA glossary’s terms, each with the part of the syllabus where you first meet it.

IB Maths AA glossary: P | Augment Education

P

Parabola: The U-shaped curve that is the graph of a quadratic function. It opens upwards when $a > 0$ , downwards when $a < 0$ , and is symmetric about a vertical line through its vertex.
Introduced in 2.6 Quadratic functions
Parallel linesalso parallel: Lines in the same plane that never meet. Two non-vertical lines are parallel when they have equal gradients, $m_1 = m_2$ , and different $y$ -intercepts.
Introduced in 2.1 Equations of straight lines
Parallel vectorsHL only: Non-zero vectors that are scalar multiples of each other: $\boldsymbol{w} = k\boldsymbol{v}$ with $k \neq 0$ . They point in the same direction if $k > 0$
ParameterHL only: A variable such as $\lambda$ or $t$ whose value picks out one point of a line or curve. Each real value of the parameter gives exactly one point.
Introduced in 3.14 Vector equations of lines
Parent functionalso base function: The simplest function of a family, such as $y = x^2$ or $y = \frac{1}{x}$
Partial fractionsHL only: Simpler fractions whose sum equals a given algebraic fraction, for example $\frac{5x-1}{(x+1)(x-2)} = \frac{2}{x+1} + \frac{3}{x-2}$
Partial sumalso Sₙ: The sum $S_n$ of the first $n$ terms of a series. The sum of an infinite series is the value the partial sums approach as $n$ increases, if there is one.
Introduced in 1.8 Infinite geometric series
Particular solutionHL only: The one solution of a differential equation that also satisfies a given condition, found by using the condition to fix the arbitrary constant in the general solution.
Introduced in 5.18 First-order differential equations
Pascal's triangle: A triangular array of numbers with 1 at the ends of each row, in which every other entry is the sum of the two entries directly above it. Row $n$ (counting from row 0) holds the binomial coefficients $\binom{n}{0}, \ldots, \binom{n}{n}$
Pearson's correlation coefficientalso r, PMCC, Pearson's product-moment correlation coefficient: A number $r$ , with $-1 \le r \le 1$ , measuring the strength and direction of the linear correlation between two variables. Values near $\pm 1$ show strong linear correlation; values near $0$ show little or none.
Introduced in
Percentile: The value below which a given percentage of the ordered data lie; the $p$ th percentile has $p\%$ of the data below it.
Introduced in 4.2 Presenting data
Periodic functionalso period: A function whose values repeat at regular intervals: $f(x + p) = f(x)$ for all $x$ in its domain. The smallest such positive $p$ is the period.
Introduced in 3.7 Circular functions
PermutationHL only · also nPr, arrangement: An ordered arrangement of objects. The number of permutations of $r$ objects chosen from $n$ different objects is ${}^nP_r = \frac{n!}{(n-r)!}$
Perpendicularalso perpendicular lines: Meeting at a right angle. Two lines with gradients $m_1$ and $m_2$ are perpendicular when $m_1 \times m_2 = -1$
Perpendicular bisector: The line through the midpoint of a line segment at right angles to it. Every point on it is the same distance from the two ends of the segment.
Introduced in 2.1 Equations of straight lines
Piecewise functionHL only · also piecewise-defined function, hybrid function: A function defined by different rules on different parts of its domain, for example $f(x) = x^2$ for $x < 1$ and $f(x) = 2x - 1$
PlaneHL only · also Cartesian equation of a plane: A flat surface extending without limit in every direction. In three dimensions a plane has a Cartesian equation of the form $ax + by + cz = d$ .
Introduced in 3.17 Vector equations of planes
Point of inflexionalso inflection point: A point on a curve where the concavity changes, from concave up to concave down or the reverse, so $f''(x)$ changes sign there. The gradient at the point may be zero or non-zero.
Introduced in 5.8 Stationary points, optimisation and inflexion
Point of tangencyalso point of contact: The point at which a tangent touches a curve. It lies on both the curve and the tangent, and the gradient of the tangent equals the derivative there.
Introduced in 5.4 Tangents and normals
Point symmetryHL only · also rotational symmetry of order 2, half-turn symmetry, centre of symmetry: A graph has point symmetry about a point $M$ if a rotation of $180^\circ$ about $M$ maps the graph onto itself; $M$ is the centre of symmetry.
Introduced in 3.11 Symmetry of trigonometric graphs
Polar formHL only · also modulus–argument form, cis form: The way of writing a non-zero complex number by its modulus $r$ and argument $\theta$ : $z = r(\cos\theta + \mathrm{i}\sin\theta) = r\operatorname{cis}\theta$
PolynomialHL only · also degree, leading coefficient: An expression of the form $a_n x^n + a_{n-1}x^{n-1} + \dots + a_1 x + a_0$
Polynomial divisionHL only · also long division, quotient: Dividing a polynomial $P(x)$ by a polynomial $D(x)$ to write $P(x) = D(x)Q(x) + R(x)$
Population: The complete set of individuals or items about which information is wanted in a statistical investigation.
Introduced in 4.1 Populations, samples and sampling
Position vectorHL only: The vector from the origin $O$ to a point $A$ , written $\overrightarrow{OA} = \boldsymbol{a}$
Posterior probabilityHL only · also posterior: The updated probability of an event after new evidence is taken into account, found with Bayes' theorem, such as $P(\text{disease} \mid \text{positive test})$ .
Introduced in 4.13 Bayes’ theorem
Power rule: The rule for differentiating a power of $x$ : if $f(x) = ax^n$ , then $f'(x) = anx^{n-1}$
Present valuealso PV, principal: The value of an amount of money now: the amount invested or borrowed at the start, written $PV$ .
Introduced in 1.4 Financial applications of geometric sequences
Prime numberHL only · also prime: A positive integer greater than 1 whose only positive factors are 1 and itself, such as 2, 3, 5, 7 and 11.
Introduced in 1.15 Proof by induction, contradiction and counterexample
Principal axisalso midline: The horizontal line midway between the maximum and minimum values of a sinusoidal graph; for $y = a\sin(b(x + c)) + d$ it is $y = d$ .
Introduced in 3.7 Circular functions
Principal valueHL only · also principal range: The one angle an inverse trigonometric function returns: in $[-\frac{\pi}{2}, \frac{\pi}{2}]$ for $\arcsin$
Prior probabilityHL only · also prior, base rate: The probability of an event before new evidence is taken into account, such as the proportion of a population that has a disease.
Introduced in 4.13 Bayes’ theorem
Prismalso cross-section: A solid with two identical, parallel end faces joined by flat sides, so every slice parallel to the ends is the same shape, its cross-section. Volume = cross-sectional area × length.
Introduced in 3.1 Distance, midpoint, volume and surface area
Probabilityalso P(A), chance: A number from $0$ to $1$ that measures how likely an event is: $0$ for an impossible event, $1$ for a certain one.
Introduced in 4.5 Concepts of probability
Probability density functionHL only · also pdf: A function $f$ describing a continuous random variable $X$ , with $f(x) \ge 0$ for all $x$ and $\int_{-\infty}^{\infty} f(x)\,dx = 1$
Probability distribution: A list, table, graph or formula giving every possible value $x$ of a discrete random variable $X$ with its probability $P(X = x)$ . The probabilities are all between $0$ and $1$
Product principleHL only · also multiplication principle, fundamental counting principle: If one choice can be made in $m$ ways and, after it, a second choice can be made in $n$ ways, then the two choices together can be made in $m \times n$ ways.
Introduced in 1.10 Counting principles and the extended binomial theorem
Product rule: The rule for differentiating a product of two functions of $x$ : if $y = uv$ , then $\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$
Proofalso deductive proof: A chain of logical steps that starts from definitions, known facts or assumptions and shows that a statement must be true in every case it covers. Checking examples is not a proof.
Introduced in 1.6 Simple deductive proof
Proof by contradictionHL only · also reductio ad absurdum, indirect proof: A method of proof that assumes the statement is false and shows, by valid steps, that this assumption leads to something impossible, so the statement must be true.
Introduced in 1.15 Proof by induction, contradiction and counterexample
Proof by inductionHL only · also mathematical induction, principle of mathematical induction: A method of proving a statement $P(n)$ for every integer $n$ from a starting value: show that $P(n)$ is true for the first value, and that whenever $P(k)$ is true, $P(k+1)$
Proper algebraic fractionHL only · also proper fraction: An algebraic fraction whose numerator has a lower degree than its denominator, such as $\frac{3x + 1}{x^2 - 4}$ .
Introduced in 1.11 Partial fractions
Purely imaginary numberHL only · also imaginary number, pure imaginary: A complex number whose real part is zero, $z = b\mathrm{i}$ with $b \in \mathbb{R}$ , $b \neq 0$
Pythagoras's theoremalso Pythagoras: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: $c^2 = a^2 + b^2$ .
Introduced in 3.2 Trigonometry in triangles
Pythagorean identity: The identity $\cos^2\theta + \sin^2\theta = 1$ , true for every angle $\theta$ . It follows from Pythagoras's theorem applied to a point on the unit circle.
Introduced in 3.6 Trigonometric identities