## Glossary

Use the alphabetical list below to find words beginning with each letter.

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

### A

**Asymptote** - A line which a graph approaches, while never actually meeting it. An example would be the graph of y = 1/x, which has both the x and y-axes as asymptotes.

### B

**Bar chart** - A means of displaying frequency data using bars of varying heights to represent the frequency of occurrence in different categories of data.

### C

**Coordinates** - The values relative to horizontal and vertical axes which enable us to fix the position of a point on a graph.

### D

**Denominator** - The number or expression on the bottom of a fraction; for example, the denominator of 3/5 is 5; the denominator of x/(x + 6) is x + 6.

**Dependent** - variable In an expression such as y = 3x2 – 2x + 1, y is known as the dependent variable because its value depends on the value we give to x. The dependent variable is generally plotted on the vertical axis of a graph.

**Derivative** - The result of performing a differentiation. The derivative of x4 with respect to x is 4x3.

**Difference** - The result of subtracting one number from another. For example, the difference of 7 and 5 is 2; the difference of 5 and 7 is –2.

**Discrete data** - Data which can take only certain specified values. An example would be the number of broken eggs in a box, which must be 0, 1, 2, …

**Dividend** - The number being divided in a division calculation. For example, the dividend in the calculation 5 ÷ 2 is 5.

**Divisor** - The number by which we are dividing in a division calculation. For example, the divisor in the calculation 5 ÷ 2 is 2.

### E

**Exponent** - The power in an expression such as x3; here the exponent of x is 3.

### F

**Frequency** - In statistics, the number of times a particular value or range of values occurs in a set of data. For example, in the set of data 1, 1, 2, 2, 2, 3, 3, 4, the frequency of 2 would be 3.

**Frequency** - distribution A table showing the frequency of each value or range of values within a dataset. Also called a frequency table. If ranges are used, we refer to a grouped frequency distribution.

**Function** - A relationship between a dependent variable and one or more independent variables; often represented by an equation. For example, the general linear function of a single independent variable can be written as y = ax + b.

### G

**Gradient** - The slope of a graph. If the graph is plotted on (x, y)-axes then the slope is the increase in y per unit increase in x. A positive slope means that the graph runs uphill from left to right; a negative slope (i.e. y decreasing as x increases) means the graph runs downhill from left to right.

### H

**Histogram** - A way of displaying a grouped frequency distribution by means of blocks, whose width is proportional to the width of the classes in the distribution, and whose area corresponds to the frequency of the class.

**Hyperbola** - The shape of graph which results from plotting a function containing a term of the form 1/x, l/x2, etc. For an example see page 69.

### I

**Inequality** - An algebraic or arithmetical expression representing the relationship between the sizes of two quantities. The signs <, >, =, = are used to represent ‘less than’, ‘greater than’, ‘less than or equal to’, and ‘greater than or equal to’. So 2 < 6, etc.

**Integer** - Whole number, such as 11, 362 or –50.

**Intercept** - The value of y in a linear equation when x = 0. Also the point where the graph of the equation crosses the y-axis, assuming the x-scale starts at 0.

### L

**Linear** - equation An equation in which no variable is raised to any power other than 1 or multiplied by any other variable. A linear equation in a single variable can always be put into the form ax + b = 0.

**Linear** - function A function in which the dependent variables only occur raised to the power 1. Can be expressed in the form y = a0 + a1x1 + a2x2 + …

**Local maximum** - The function y = f(x) has a local maximum when x = x0 if dy/dx = 0 when x = x0 and dy/dx is positive to the left of x0 and negative to the right of it; or equivalently, if d2y/dx2 is negative at x = x0. This means that f(x0) is greater than the value of f(x) anywhere else in the immediate neighbourhood of x0.

**Local minimum** - The function y = f(x) has a local minimum when x = x0 if dy/dx = 0 when x = x0, and dy/dx is negative to the left of x0 and positive to the right of it; or equivalently, if d2y/dx2 is positive at x = x0.. This means that f(x0) is smaller than the value of f(x) anywhere else in the immediate neighbourhood of x0.

**Lowest common denominator** - The smallest number into which the denominators of a group of fractions will all divide. For example, the lowest common denominator for the fractions 1/4, 1/3 and 1/6 is 12, because this is the smallest number into which 4, 3 and 6 will all divide. Used in addition and subtraction of fractions.

### M

**Mean** - The arithmetical mean, which is usually contracted to ‘mean’, is what is colloquially called the ‘average’; so the mean of 3, 4 and 5 is (3 + 4 + 5)/3 = 4, and so on.

**Median** - The central value in an ordered set of numbers (or the mean of the two central values if there is an even number of values). For example, the median in the set 21, 33, 47, 68, 74, 91 is (47 + 68)/2 = 57.5.

**Mode** - The most common value in a group of numbers. The mode in the group 1, 1, 2, 2, 2, 3, 3, 4 is 2.

### N

**Numerator** - The number or expression on the top of a fraction. For example, the numerator of 11/12 is 11; the numerator of (x + 2)/(x — 3) is x + 2.

### O

**Ogive** - A graph plotted from a cumulative frequency table.

**Origin** - The point (0, 0) on a graph, which is often, but not invariably, the point where the coordinate axes meet.

### P

**Parabola** - The shape of graph which results from plotting a quadratic function. For examples, see pages 66–8.

**Percentage** - A fraction expressed on a denominator of 100; the denominator is not explicitly written. Thus 25% means 25/100, etc.

**Pie chart** - A means of displaying frequency data using sectors of a circle to represent subgroups of the data.

**Point** - of inflexion A point on a graph where dy/dx = 0, but dy/dx does not change sign.

**Power** - An expression such as xn is called the nth power of x. More loosely, we sometimes refer to n as the power of x in this expression.

**Product** - The result of multiplying two or more numbers or expressions. So the product of 2x and x2 is 2x3.

### Q

**Quadrant** - One of the four parts into which the coordinate axes divide the Cartesian plane.

**Quadratic** - A quadratic expression in x is one where the highest power of x occurring is a square. A quadratic equation is one involving only quadratic expressions; a quadratic equation in one variable can always be put into the form ax2 + bx + c = 0.

**Quartile** - A number which divides an ordered set of figures into quarters. The smallest quartile is the lower quartile, the middle one is the median (see above) and the biggest is the upper quartile.

**Quotient** - The result of dividing two numbers or expressions. The quotient of 12 and 3 is 4; the quotient of 3 and 12 is 0.25.

### R

**Range** - The difference between the largest and smallest values in a set of data.

**Rate** - of change If y is a function of x, the rate of change of y with x is the increase in y per unit increase in x. A negative rate of change means y decreases as x increases.

**Root of an equation** - x = a is a root of an equation in x if substituting x = a into the equation makes the two sides equal. For example, x = 2 is a root of 2x + 8 = 10 + x because when x = 2, both sides of the equation are equal to 12. A root is said to satisfy the equation in question.

### S

**Significant figures** - The number of digits which actually carry information, as distinct from those which simply indicate place-value. Thus in 30,270, there are four significantfigures: the 3, 2, 7 and the zero between the 3 and the 2. The last zero is, however, not significant, since it only indicates the overall place-value.

**Slope** - The rate of change of the dependent variable in a graph per unit increase in the independent variable.

**Solution** - The solution of an equation is the value or set of values of the unknown(s) which make the two sides of the equation equal.

**Standard deviation** - A measure of the spread of a set of data, found by taking the square root of the mean of the squared deviations of the data values from their mean.

**Sum** - The result of adding two or more numbers or expressions. The sum of 11, 2 and 3x is 13 + 3x.

**Summation sign (S) ** - Sx means ‘add up all the values of x’.

### T

**Tangent** - A line which meets a curve only at a single point.

**Turning point** - A general term for a local maximum or minimum (see above).