UAE TLS Mathematics Test flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Divisibility rule for 3

An integer is divisible by 3 exactly when the sum of its decimal digits is divisible by 3; for example, 738 gives 7+3+8=18.

LCM and GCD relation

For positive integers a and b, the product a times b equals the least common multiple of a and b multiplied by their greatest common divisor.

Percentage increase formula

Percentage increase equals the difference between the new value and the original value, divided by the original value, then multiplied by 100.

Rational versus irrational numbers

A rational number can be written as a fraction of two integers with nonzero denominator; an irrational number cannot be expressed that way and has a nonrepeating decimal expansion.

Quadratic formula

For ax squared plus bx plus c equals zero with a nonzero, solutions are x equals negative b plus or minus the square root of b squared minus four ac, all divided by two a.

Discriminant interpretation

For a quadratic with real coefficients, the discriminant b squared minus four ac is positive for two real roots, zero for one repeated real root, and negative for no real roots.

Function composition order

The composition f of g, written f(g(x)), applies g first and then f; generally f(g(x)) does not equal g(f(x)) unless the functions have special symmetry.

Logarithm product rule

For positive arguments and a positive base not equal to one, the logarithm of a product equals the sum of the logarithms of the factors.

Pythagorean theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs; thus c squared equals a squared plus b squared.

Circle area and circumference

A circle with radius r has circumference two pi r and area pi r squared; diameter equals two r, so circumference also equals pi times diameter.

Similar figures scale factor

If two similar figures have scale factor k, corresponding lengths multiply by k, areas multiply by k squared, and volumes multiply by k cubed.

Midpoint formula

For points with coordinates x one, y one and x two, y two, the midpoint coordinates are the averages of the x-coordinates and of the y-coordinates.

Sine, cosine, tangent ratios

In a right triangle, sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent for a given acute angle.

Law of cosines

For a triangle with sides a, b, and c and angle C opposite side c, c squared equals a squared plus b squared minus two ab cosine C.

Radians to degrees

To convert radians to degrees, multiply the radian measure by 180 divided by pi; to convert degrees to radians, multiply by pi divided by 180.

Pythagorean identity

For every angle where the functions are defined, sine squared theta plus cosine squared theta equals one; this identity follows from the unit circle definition.

Probability complement rule

For any event A, the probability that A does not occur equals one minus the probability that A occurs; probabilities always lie from zero to one.

Independent events multiplication

Events A and B are independent exactly when the probability of both equals the product of their individual probabilities, P(A) times P(B).

Mean, median, mode

The mean is the arithmetic average, the median is the middle value after ordering data, and the mode is the value occurring most frequently.

Normal empirical rule

For a normal distribution, approximately 68 percent of values lie within one standard deviation of the mean, about 95 percent within two, and about 99.7 percent within three.

Derivative definition limit

The derivative of f at x is the limit as h approaches zero of f of x plus h minus f of x, all divided by h, when that limit exists.

Power rule derivative

For a real exponent n, the derivative of x raised to n is n times x raised to n minus one, valid where the expression is differentiable.

Fundamental theorem of calculus

If F is an antiderivative of continuous f on an interval, the definite integral of f from a to b equals F of b minus F of a.

Critical point test

A critical point occurs where the derivative is zero or undefined; sign changes in the derivative can indicate local maxima or minima, while concavity gives additional confirmation.

Work rate formula

When tasks are combined, add rates expressed as work per unit time; if one worker completes a job in t hours, that worker's rate is one over t jobs per hour.

Counterexample method

To disprove a universal statement, exhibit one valid case in which the statement's hypothesis is true but its conclusion is false; this single case is sufficient.

Necessary versus sufficient

A condition is necessary if the conclusion cannot hold without it; it is sufficient if satisfying it guarantees the conclusion; the two ideas are not interchangeable.

Proportional reasoning setup

When two quantities vary proportionally, set up equal ratios and solve by cross multiplication, checking that units in corresponding positions match.

Formative assessment cycle

Teachers gather evidence during instruction, interpret student thinking, and adjust subsequent tasks or explanations so that learning gaps are addressed before summative evaluation.

Concrete to abstract sequence

Introduce mathematical ideas with physical or visual models, then connect representations to symbolic notation, and finally require fluent symbolic reasoning with decreasing scaffolding.

Productive mathematical discourse

Classroom discourse supports learning when students explain strategies, compare representations, justify claims, and respond to peers using precise mathematical language rather than only giving answers.

Common fraction misconception

A frequent misconception is adding numerators and denominators separately, such as one half plus one third equals two fifths; instruction should confront why common denominators are required.