GCE O/L Mathematics flashcards

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

Order of operations

The agreed sequence for evaluating expressions: brackets first, then indices, then multiplication and division left to right, then addition and subtraction left to right.

Highest common factor

The largest integer dividing exactly into two or more given numbers, found by multiplying the prime factors common to all of them, each to its lowest shared power.

Standard form

A way of writing numbers as a × 10ⁿ where a is at least 1 and less than 10 and n is an integer, convenient for very large or very small values.

Rationalising a denominator

Rewriting a fraction so no surd remains in the denominator, for example multiplying numerator and denominator of 1/√3 by √3 to obtain √3/3.

Upper and lower bounds

The range of values consistent with a rounded figure; a length given as 7 cm to the nearest centimetre lies between 6.5 cm and 7.5 cm.

Expanding double brackets

Multiplying each term in the first bracket by each term in the second, then collecting like terms, as in (x+3)(x+5) = x² + 8x + 15.

Quadratic formula

For ax² + bx + c = 0, the solutions are x = [−b ± √(b² − 4ac)]/(2a); the discriminant b² − 4ac shows how many real roots exist.

Gradient of a line

The steepness of a straight line, calculated as the change in y divided by the change in x between two points, written m in y = mx + c.

Perpendicular gradients

Two straight lines are perpendicular exactly when the product of their gradients equals −1, so a line perpendicular to gradient 3 has gradient −1/3.

Solving by elimination

Adding or subtracting two simultaneous equations, or multiples of them, so one variable cancels, leaving a single equation to solve.

Index laws

Rules for powers: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1 and a⁻ⁿ = 1/aⁿ.

Interior angle of polygon

For a polygon with n sides the interior angles total (n − 2) × 180°; in a regular polygon each interior angle equals that total divided by n.

Area of a sector

The portion of a circle's area enclosed by two radii and an arc, calculated as (θ/360) × πr² where θ is the central angle in degrees.

Volume of a cone

One third of the base area multiplied by the perpendicular height, written V = (1/3)πr²h for a cone of base radius r and height h.

Pythagoras' theorem

In a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides, written a² + b² = c².

Similar shape scale factors

When corresponding lengths of similar shapes are in ratio k, areas are in ratio k² and volumes in ratio k³.

Three-figure bearings

A direction measured clockwise from north, always written with three digits such as 072°, with a reverse bearing differing by 180°.

Congruence tests

Two triangles are congruent if SSS, SAS, ASA/AAS or RHS conditions are satisfied; matching angles alone proves similarity only.

Calculating the mean

Add all the data values together and divide by how many values there are; for grouped data use class midpoints as approximations of the values.

Interquartile range

The difference between the upper quartile and the lower quartile, describing the spread of the middle half of a data set and ignoring extreme values.

Frequency density

Frequency divided by class width, plotted on the vertical axis of a histogram so that the area of each bar represents the frequency of that class.

Reading a cumulative frequency graph

Plot cumulative totals against upper class boundaries; the median is read at half the total frequency and quartiles at one quarter and three quarters.

Line of best fit

A straight line drawn through the centre of a scatter graph's points to show the trend, used to estimate values and describe correlation.

Complementary probability

The probability that an event does not happen equals one minus the probability that it does, since the two outcomes together are certain.

Mutually exclusive events

Events that cannot occur at the same time; for such events the probability of either happening is the sum of their separate probabilities.

Independent events

Events where one outcome does not affect the other; the probability of both occurring is found by multiplying their individual probabilities together.

Relative frequency

The number of times an event actually occurs divided by the total number of trials, used as an experimental estimate of probability.

Tree diagram rules

Multiply probabilities along a branch to find combined outcomes, then add the results of separate branches that produce the same overall event.

Direct proportion

A relationship where one quantity is a constant multiple of another, y = kx, so doubling one value doubles the other and the graph passes through the origin.

Inverse proportion

A relationship where one quantity increases as the other decreases so their product stays constant, y = k/x, meaning doubling one halves the other.

Compound interest formula

The total after n years is P × (1 + r/100)ⁿ, where P is the starting amount and r the annual percentage rate, with interest added each year.

Using SOHCAHTOA

In a right-angled triangle, sin = opposite/hypotenuse, cos = adjacent/hypotenuse and tan = opposite/adjacent, used to find missing sides or angles.