BGCSE Scientific Mathematics 1237 flashcards

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

Place value of a digit

The value a digit has because of its position in a number. Each position is ten times the one to its right, so in 352 the 3 means 300 and the 5 means 50.

Order of operations

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

Highest common factor

The largest number that divides exactly into two or more given numbers. It is found by taking the lowest power of each shared prime factor.

Standard form notation

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

Percentage change formula

Change divided by the original value, multiplied by 100. It expresses an increase or decrease as a proportion of the starting amount.

Expanding double brackets

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

Difference of two squares

The identity a² − b² = (a + b)(a − b). It factorises expressions such as x² − 49 into (x + 7)(x − 7).

Quadratic formula

For ax² + bx + c = 0, the solutions are x = (−b ± √(b² − 4ac)) ÷ 2a, provided a is not zero.

Discriminant of a quadratic

The expression b² − 4ac. If positive there are two real roots, if zero one repeated root, and if negative no real roots.

Simultaneous equations by elimination

A method where one variable's coefficients are made equal in both equations, then the equations are added or subtracted to remove that variable.

Laws of indices

Rules for powers: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1 and a^(−n) = 1 ÷ a^n.

Inequality sign reversal

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign must be reversed to keep it true.

Interior angle sum of polygon

For a polygon with n sides, the interior angles add up to (n − 2) × 180°. A pentagon therefore has an interior angle sum of 540°.

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.

Angle in a semicircle

A circle theorem stating that the angle subtended by a diameter at any point on the circumference is a right angle, that is 90°.

Similar figures

Shapes with equal corresponding angles and proportional corresponding sides. Their areas are in the ratio of the squares of the scale factor.

Volume of a cylinder

The space inside a cylinder, calculated as πr²h, where r is the base radius and h is the perpendicular height between the circular ends.

Exterior angle of a polygon

The angle between one side of a polygon and the extension of the adjacent side. For any convex polygon the exterior angles sum to 360°.

Converting km/h to m/s

Multiply by 1000 to change kilometres to metres, then divide by 3600 to change hours to seconds. So 36 km/h equals 10 m/s.

Speed, distance, time relation

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

Arc length of a sector

The curved part of a sector's boundary, found by multiplying the full circumference 2πr by the fraction θ ÷ 360, where θ is the central angle.

Area of a trapezium

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

Surface area of a sphere

The total area of a sphere's curved surface, given by 4πr², where r is the radius. It is four times the area of a great circle.

Density formula

Density equals mass divided by volume. Rearranged, mass equals density multiplied by volume and volume equals mass divided by density.

Median of a data set

The middle value when data are arranged in order. With an even number of values, it is the mean of the two central values.

Interquartile range

The difference between the upper quartile and the lower quartile. It describes the spread of the middle half of the data and ignores extreme values.

Mutually exclusive events

Events that cannot happen at the same time. For such events, the probability of either occurring is the sum of their individual probabilities.

Independent events rule

Events whose outcomes do not affect each other. For independent events, the probability that both occur is the product of their separate probabilities.

Frequency density in histograms

Frequency divided by class width. It is used as the height of bars when class intervals are unequal, so that bar area represents frequency.

Vertical line test

A graph represents a function only if no vertical line crosses it more than once, meaning each input value has exactly one output.

Gradient of a straight line

The change in y divided by the change in x between two points. It measures steepness; parallel lines share the same gradient.

Perpendicular line gradients

Two lines are perpendicular when the product of their gradients equals −1. If one gradient is m, the other is −1 ÷ m.

Composite function fg(x)

A function formed by applying g first and then f to the result. The order matters because fg(x) is usually not equal to gf(x).