BCS Written Math & Mental Ability key terms

The value a digit carries because of its position in a numeral; in 4,725 the 7 means seven hundreds, so shifting a digit one place left multiplies its value by ten.

The digit itself, ignoring where it sits in the numeral; the face value of 7 in 4,725 is simply seven, while its place value is seven hundred.

The set of rules and symbols used to write numbers, such as the decimal system with ten digits, or the binary system with only 0 and 1, each using positional weights.

A quick test that decides whether one whole number divides another exactly; for example, a number is divisible by 3 when the sum of its digits is a multiple of 3.

A whole number that divides another exactly, leaving no remainder; the factors of 12 are 1, 2, 3, 4, 6 and 12, since each divides 12 cleanly.

The result of multiplying a given whole number by any counting number; the multiples of 6 begin 6, 12, 18, 24 and continue without end.

Highest common factor: the largest whole number dividing each number in a group exactly; for 18 and 24 the common factors are 1, 2, 3 and 6, so the HCF is 6.

Lowest common multiple: the smallest counting number that every number in a group divides exactly; for 4 and 6 the multiples meet first at 12.

A whole number greater than 1 whose only exact divisors are 1 and itself; 2, 3, 5, 7 and 11 are prime, while 9 is not because 3 divides it.

A fraction whose numerator is smaller than its denominator, so its value lies between zero and one; three-quarters and five-eighths are proper fractions.

A fraction whose numerator is equal to or larger than its denominator, so its value is one or more; seven-quarters and nine-ninths are improper fractions.

Different fractions naming the same quantity, obtained by multiplying or dividing numerator and denominator by the same number; one-half equals two-quarters and five-tenths.

The version of a fraction whose numerator and denominator share no common factor except 1; twelve-eighteenths reduces to two-thirds by dividing both parts by 6.

A position after the decimal point, each worth one-tenth of the position to its left; in 0.376 the 7 sits in the second decimal place, meaning seven hundredths.

A decimal in which a digit or block of digits repeats forever, such as 0.333... for one-third; it can always be rewritten as an exact fraction.

A fraction expressed out of one hundred, written with the percent sign; 45% means 45 parts in every 100, which is the fraction forty-five hundredths or 0.45.

The size of an increase or decrease stated as a share of the original amount; a rise from 40 to 50 is a change of 10 on a base of 40, hence 25%.

The original quantity against which a percentage is calculated; if a price rises from 200, the 200 is the base, and a 15% rise adds 30 to it.

The amount a trader pays to obtain an article, including any buying expenses; profit or loss is always measured against this figure.

The amount finally received when an article is sold to a buyer; comparing it with the cost price reveals whether the deal produced profit or loss.

The gain when selling price exceeds cost price; buying at 400 and selling at 460 gives a profit of 60, which is 15% of the cost price.

The printed or labelled price of an article before any reduction; a shop may mark an item at 500 and then allow 10% off that figure.

The reduction allowed on the marked price, usually quoted as a percentage of it; 20% off a marked price of 750 lowers the amount payable by 150.

Two or more discounts applied one after another, each on the reduced amount rather than the original; 10% then 20% off 500 gives 360, not 350.

A comparison of two quantities of the same kind by division, written as 3:5 or three-fifths; it states how many times one amount contains the other.

An equality between two ratios; 3:4 and 9:12 are in proportion because the cross products, 3 times 12 and 4 times 9, are both 36.

A link in which one quantity grows exactly as the other grows; if 4 pens cost 60, then 10 pens cost 150, since the price per pen stays fixed.

A link in which one quantity rises while the other falls by the same factor; if 6 workers finish a job in 10 days, 12 workers of equal speed finish it in 5.

A business arrangement where partners share profit in the ratio of the capital each has invested multiplied by the time it stayed invested.

The share of a whole job completed in one unit of time; a worker finishing a task in 12 days has a rate of one-twelfth of the task per day.

Problems that combine individual work rates to find how long a group needs, or how much of a job is finished when people labour together or separately.

A tank-filling variant of work problems: inlet pipes add to the tank at a stated rate while outlet pipes remove water, and their rates are combined algebraically.

The distance covered in one unit of time, found by dividing distance by time; a car covering 180 km in 3 hours travels at 60 km per hour.

The rate at which the gap between two moving objects changes; bodies moving in opposite directions add their speeds, while those moving the same way subtract them.

A standard problem type where a train clears a pole using its own length as the distance, or clears a platform using train length plus platform length.

The sum of a set of quantities divided by how many there are; the average of 12, 18 and 24 is 54 divided by 3, which equals 18.

Total distance travelled divided by total time taken, not the simple mean of the separate speeds; equal distances at 40 and 60 km per hour average 48, not 50.

A method using the differences between ingredient values and the desired mixture value to fix the ratio in which the ingredients must be combined.

Interest computed only on the original principal for the whole period, found as principal times rate times time divided by one hundred when the rate is a yearly percentage.

Interest charged on principal plus previously earned interest, so each period's interest is added to the amount that earns interest next period.

The sum originally lent or deposited, on which interest is calculated; a deposit of 5,000 earning 8% simple interest gives 400 each year.

An equation in which every variable appears only to the first power, so its graph is a straight line; solving it usually means isolating the unknown.

A statement comparing two expressions with a sign such as less than, greater than, or at least; solving it gives a range of values rather than one answer.

A list of numbers in which each term after the first is obtained by adding a fixed constant, called the common difference, to the term before it.

The constant added to each term of an arithmetic sequence to reach the next one; in 7, 11, 15, 19 the common difference is 4.

The total length of the boundary of a closed plane figure; for a rectangle it equals twice the sum of its length and breadth.

The amount of flat surface enclosed by a figure, measured in square units; a rectangle's area is length multiplied by breadth.

The space occupied by a solid, measured in cubic units; a cuboid's volume is length times breadth times height.

The distance around a circle, equal to twice pi times the radius; with radius 7 and pi as twenty-two sevenths it measures 44 units.

A sequence of numbers following a hidden rule, such as adding a constant, multiplying, or combining squares; the task is to supply the missing or next term.

A reasoning task in which words or letters are converted into a code by a fixed rule, and the candidate must apply that rule to new material.

A pair-based reasoning item stating that two things relate in a certain way, then asking for a partner that relates to a third thing in the same way.

A reasoning item listing several items where all but one share a common property, and the candidate must identify the item that does not fit.