AFM Enlistment (Maths) flashcards

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

Order of operations

Evaluate brackets first, then powers and roots, then multiplication and division from left to right, and finally addition and subtraction from left to right.

Prime number

A whole number greater than 1 whose only positive factors are 1 and itself. 2 is the only even prime; 1 is not prime.

Highest common factor

The largest number that divides exactly into two or more given numbers. It equals the product of their shared prime factors at the lowest powers.

Lowest common multiple

The smallest number that is a multiple of two or more given numbers. It uses every prime factor at its highest power.

Dividing signed numbers

Dividing numbers with the same sign gives a positive answer; dividing numbers with opposite signs gives a negative answer. The same rule applies to multiplication.

Divisibility test for 3

A number is divisible by 3 exactly when the sum of its digits is divisible by 3. The same digit-sum test works for divisibility by 9.

Equivalent fractions

Fractions with the same value, produced by multiplying or dividing both numerator and denominator by the same non-zero number, for example 2/3 = 8/12.

Adding fractions

Rewrite the fractions over a common denominator, usually the lowest common multiple, then add or subtract the numerators only and simplify the result.

Dividing by a fraction

Multiply by the reciprocal of the second fraction, turning the divisor upside down. For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2.

Mixed number to improper fraction

Multiply the whole number by the denominator, add the numerator, and place the total over the original denominator. For 2 3/5 the result is 13/5.

Comparing fractions by cross-multiplication

To compare a/b with c/d, multiply a by d and c by b. The larger product sits under the larger fraction, avoiding decimal conversion.

Fraction of a quantity

To find a/b of an amount, divide the amount by b and multiply the result by a. The word 'of' between fractions means multiply.

Percentage change formula

Subtract the original value from the new value, divide by the original value, then multiply by 100. A negative answer indicates a decrease.

Percentage multiplier

A rise of p% multiplies by 1 + p/100; a fall of p% multiplies by 1 − p/100. Successive changes multiply their multipliers together.

Finding the original amount

After a percentage change, divide the final value by the multiplier to recover the starting value. If 120 follows a 20% rise, divide by 1.2.

Sharing in a ratio

Add the ratio parts to get the total number of shares, divide the amount by that total, then multiply by each part to find each share.

Direct and inverse proportion

Direct proportion keeps the ratio of two quantities constant; inverse proportion keeps their product constant, so one falls as the other rises.

Expanding double brackets

Multiply every term in the first bracket by every term in the second: (x + p)(x + q) = x² + (p + q)x + pq, then collect like terms.

Solving linear equations

Apply the same operation to both sides until the variable stands alone. Undo addition or subtraction first, then multiplication or division, and check by substitution.

Changing the subject

Rearrange a formula by applying inverse operations to both sides in reverse order until the required variable appears alone on one side.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality symbol, turning < into >.

Collecting like terms

Add or subtract the coefficients of terms with identical variable parts. 3x and 5x combine to 8x, but 3x and 5x² cannot be combined.

Substitution into formulas

Replace each letter with its given value, placing negative values in brackets, then evaluate following the order of operations.

Angle sum of a triangle

The three interior angles of any triangle add to 180 degrees. An exterior angle equals the sum of the two opposite interior angles.

Angles on a straight line

Angles forming a straight line add to 180 degrees, and angles around a full point add to 360 degrees. Vertically opposite angles are equal.

Pythagoras' theorem

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

Area of a trapezium

Half the sum of the parallel sides multiplied by the perpendicular height between them: A = ½(a + b)h.

Interior angles of a polygon

For a polygon with n sides the interior angles total (n − 2) × 180 degrees. In a regular polygon each angle is this total divided by n.

Similar shape scale factors

Corresponding angles are equal and sides are in proportion. If the length scale factor is k, areas scale by k² and volumes by k³.

Mean, median, mode, range

Mean is the total divided by the count; median is the middle of the ordered values; mode is the most frequent; range is highest minus lowest.

Speed, distance, time

Speed equals distance divided by time. Rearranged, distance equals speed multiplied by time, and time equals distance divided by speed.

Average speed of a journey

Total distance travelled divided by total time taken. It is not the mean of the separate speeds unless the times at each speed are equal.

Metric unit conversions

1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g and 1 litre = 1000 ml. Convert by multiplying or dividing by these factors.