MATSEC AM Applied Mathematics key terms

The vector giving the straight-line distance and direction of a particle's final position from its starting point. It differs from distance travelled, which is a scalar measuring total path length.

The rate of change of displacement with respect to time, a vector quantity. Average velocity divides total displacement by total time; instantaneous velocity is the time derivative of displacement.

The scalar magnitude of velocity, measuring how fast a particle moves regardless of direction. Average speed is total distance travelled divided by total time taken.

The rate of change of velocity with respect to time, a vector quantity. Constant acceleration allows use of the standard uniform-acceleration formulae linking velocity, displacement and time.

The set of equations relating initial velocity, final velocity, acceleration, displacement and time when acceleration is constant, commonly written as v = u + at, s = ut + ½at² and v² = u² + 2as.

Motion of a particle under gravity alone after projection, analysed by resolving initial velocity into horizontal and vertical components. Horizontal acceleration is zero; vertical acceleration is g downwards.

The resultant force on a particle equals the rate of change of its momentum, or mass times acceleration when mass is constant. It links dynamics to kinematics through F = ma.

The single force that has the same effect as all forces acting on a particle combined. Finding it requires vector addition, often by resolving forces into perpendicular components.

Splitting a force into two perpendicular components, usually horizontal and vertical or parallel and perpendicular to an incline, so that equilibrium or motion can be analysed component by component.

The state in which the resultant force and resultant moment on a body are both zero, so it remains at rest or moves with constant velocity.

The turning effect of a force about a point, equal to force multiplied by the perpendicular distance from the point to the force's line of action. Measured in newton-metres.

For a body in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that same point.

A pair of equal and opposite forces whose lines of action do not coincide. A couple produces a pure turning effect with moment equal to one force times the perpendicular separation.

The point at which the whole mass of a body or system may be considered concentrated for analysis of translational motion and weight. For a uniform lamina it coincides with the centroid.

The force opposing relative motion or tendency of motion between surfaces in contact, acting along the contact surface. Its maximum value is limited by the normal reaction and the coefficient of friction.

The maximum frictional force possible between two surfaces before sliding begins, equal to the coefficient of friction multiplied by the normal reaction. At this point the body is on the point of moving.

The perpendicular contact force exerted by a surface on a body resting on or pressing against it. It adjusts to prevent penetration and is not always equal to the weight.

The energy transferred by a force acting through a displacement, calculated as the component of force along the displacement multiplied by the displacement. Measured in joules.

The energy a particle possesses due to its motion, equal to one half of its mass times the square of its speed. It is a scalar quantity measured in joules.

Energy stored in a body because of its position in a conservative force field, most commonly gravitational potential energy equal to mass times g times height above a chosen datum.

The principle that total mechanical energy remains constant when only conservative forces do work, so loss in potential energy equals gain in kinetic energy, or is balanced by work done against resistance.

The rate at which work is done or energy is transferred, measured in watts. For a constant driving force it equals force multiplied by velocity.

The product of a particle's mass and velocity, a vector quantity measured in kilogram metres per second. Total momentum is conserved in collisions when no external resultant force acts.

The change in momentum produced by a force acting over a time interval, equal to force multiplied by time for a constant force. Measured in newton-seconds, equivalent to kilogram metres per second.

The principle that total momentum of a system remains constant during a collision or explosion when no external resultant force acts on the system.

The set of all possible outcomes of a probability experiment. Events are subsets of the sample space, and probabilities of outcomes in it sum to one.

Two events that cannot occur together, so the probability of both occurring is zero and the probability of either occurring is the sum of their individual probabilities.

Two events where the occurrence of one does not change the probability of the other, so the probability of both equals the product of their individual probabilities.

The probability that event A occurs given that event B has occurred, written P(A|B) and equal to the probability of both events divided by the probability of B.

The distribution of the number of successes in a fixed number of independent trials, each with the same probability of success. Defined by parameters n and p.

A continuous symmetric bell-shaped probability distribution defined by its mean and variance. Many sample means are approximately normally distributed by the central limit theorem.

A measure of central tendency found by summing all values and dividing by the number of values. For a frequency distribution it uses class midpoints weighted by frequency.

A measure of spread equal to the square root of the variance, expressing typical distance of values from the mean in the original units.

A measure between minus one and one of the strength and direction of linear association between two variables. A value near zero indicates weak linear relationship.

The straight line fitted to bivariate data that minimises the sum of squared vertical deviations. Used to predict one variable from another within the observed range.

The default assumption tested in a significance test, usually stating no effect or no difference. It is rejected only when sample evidence is sufficiently unlikely under it.

The threshold probability, often five or one per cent, below which the observed result is judged too unlikely under the null hypothesis and the null hypothesis is rejected.

The probability of obtaining a test statistic at least as extreme as that observed, assuming the null hypothesis is true. Small values suggest evidence against the null hypothesis.

The result that the sampling distribution of the sample mean approaches normality as sample size increases, regardless of the population distribution, with mean equal to the population mean.

The standard deviation of a sample statistic's sampling distribution, for a sample mean equal to the population standard deviation divided by the square root of the sample size.

Deliberate choices in building a mathematical model, such as treating a body as a particle or ignoring air resistance, which make a problem tractable but limit how far the model reflects reality.

A simplified mathematical description of a real situation, built from variables, assumptions and relationships, then used to make predictions whose validity is judged against observed data.